No, it’s not. This is an idea that’s gone a bit viral and I’ve been getting messages from people who are scared of the eclipse this August. It’s totally normal. We get an eclipse of the sun every year or two. Many of them are total.

Often those who contact me are particularly scared because the eclipse track spans midday and they connect this with some bible passage about darkness at noon. So, it is very common for the eclipse to span midday at some point along its track too.

An eclipse of the sun is just the small shadow of our Moon moving over the surface of Earth. Sometimes the shadow cone doesn’t quite touch Earth and we get an annular eclipse. And sometimes it does touch it and we get a total eclipse. But it will only go dark for at most a minute or two, and you have to be inside the shadow when it passes by to see the total eclipse.

It’s a small shadow 70 miles across and travels across the US at supersonic speeds, over Mach 3 at times. It is just a shadow and can’t harm you, but is a spectacular natural event. “Eclipse chasers” will travel hundreds of miles to see one.

Meanwhile half the Earth is plunged into shadow for half a day on average, once a day, we call it night. It causes us no harm at all, so I hope you can understand that you can’t be harmed by experiencing two minutes and 40 seconds of darkness in the middle of the day.

If you watch the eclipse - be sure to get eclipse glasses. Only cost of the order of dollars. You may also be able to get them on the cover of astronomy magazines. You don’t sense any pain even when the back of your eye is burning - or more likely - getting bleached by UV light. You can lose your eyesight in the center of your vision temporarily, and in rare cases, permanently, by staring at the sun without protection.

For more on this: Is it safe to observe a partial solar eclipse?

The only time it’s safe to stare at the sun without eye protection is when the sun is completely blocked by the Moon and you see the corona (see below).

Though they are common, because the shadow is small, then it’s rare to see an eclipse anywhere particularly. You have to be standing within the blue eclipse track shown on the map here: this shows the eclipses from 2001 to 2020 including the US one.

The last total eclipses in the US were back in the 1960s and 1970s so young people will not have seen one. Even older people won’t have seen it unless you traveled to the eclipse track. Here is the map for those US eclipses. All the blue lines here are total eclipses. The red ones are annular, meaning that the sun is not totally blocked out.

This is NASA’s eclipse page, with lots of maps like that in the map section. Solar Eclipse Page

Because they always happen at new moon, you won’t see the moon until it starts to take a bite out of the sun. It’s lit up from behind. In the same way if you stand in the shadow of anything, you will see the darker side of it, not the sunlit side. There’s no scattered light in space, apart from a bit of light from the Earth, so the shaded side of the Moon is pitch black. It is, quite literally, behind the blue sky, so you don’t see anything of it until it passes between you and the sun.

Some people worry because there will be a total eclipse around midday - because of some Bible passage about darkness at noon. Well eclipses that span midday are very common.

First example: Solar eclipse of August 11, 1999

This eclipse was maximum at 11 am in Romania but was still total over India around midday. This was the last total eclipse in the UK

Photograph of the 1999 solar eclipse by Luc Viatour

That photograph shows the corona - white rays radiating out from the Sun which you only see at times of total eclipse. If you are lucky enough to have a clear sky, you may see this awesome sight. The sky goes dark and you will even see the brightest stars in good viewing conditions.

It's rather spectacular if you get to see a total eclipse - "eclipse chasers" travel around the world to see eclipses. There are several stages to it, first partial eclipse. Then as the moon covers the sun, you get "Bailey's beads" when light shines between gaps in the mountains around the Moon often ending with a single "diamond ring" when just a tiny patch of sun is left. Then it goes dark and the sun's corona shows and you may see the brightest stars.

And yes, if you stand in just the right place, it turns dark in the middle of the day but only for a minute or so and you have to be exactly on the eclipse track to see this too.

Second example: Solar eclipse of June 21, 2001

This one had greatest eclipse at 12:04:46 so as close to noon as makes no difference - that’s when the eclipse lasted the longest for this one.

Wikipedia has lists of eclipses, so you can follow through to find any other eclipses that you are interested in: Lists of solar eclipses

This is what an eclipse looks like from space - the dark patch here includes some of the area of partial eclipse - it’s only seen as total from the very center and darkest part of the shadow.

You have to be on the narrow path of the Moon's shadow - the Moon is small and the Sun is huge, and the Moon's shadow is shaped like a cone and only just touches the Earth which is why it is so tiny. You have to be positioned within that tiny shadow to see an eclipse.

This example Solar eclipse of August 21, 2017

The maximum possible eclipse is 2 minutes 40 seconds for this one.

It’s tricky to find a place that experiences the eclipse at midday. Grand Island, Nebraska, USA Nebraska has an eclipse that starts at 12:58 and finishes at 13:01. Further east you get eclipses that start and end before midday.

But because of the transition from mountain daylight time to central daylight time, I don’t think there is anywhere that experiences a total eclipse at noon in their local time as they measure it.

If you count midday as the time of day when the sun is highest in the sky, irrespective of your time zone, then there will be a place that experiences the eclipse at that time of day though the clock may not say midday, or 1 pm or any exact time like that because of the large regions spanned by the time zones.

Here is an animated eclipse map. Notice how tiny the shadow is

And map of entire eclipse across the US

There the dark strip is the strip of totality. More detailed maps for states along the track here Total Solar Eclipse 2017 including an interactive map you can zoom into

Details here Total Solar Eclipse of 2017 Aug 21 - they warn: “The eclipse predictions presented here DO NOT include the effects of mountains and valleys along the edge of the Moon. Such corrections for the lunar limb profile may shift the limits of the eclipse path north or south by ~1-3 kilometers, and change the eclipse duration by ~1-3 seconds.”

So, yes, if you stand in just the right place, it turns dark in the middle of the day in this astronomical sense but only for a minute or two, and you have to be exactly on the eclipse track to see this, and your local clocks probably won’t say midday or an exact hour of the day either.

You have to travel to the eclipse track to see a total eclipse (unless you are already on it). Most people in the US will only see the sun partly covered - a partial eclipse. But if you are on the eclipse track, you will see a total eclipse.

DOES IT GET COLD?

Perhaps rather surprisingly, it can get a fair bit cooler, a bit like night falling, but only for a short while. Here is an example from Zambia, the temperature dropped by 15 F or about 8 C. Similar to the change from day to night. That’s the air temperature not the ground temperature.

Temperature Change During Totality

HOW BIG IS THE SHADOW AND HOW FAST DOES IT MOVE?

The central shadow is about 70 miles wide (see Total Solar Eclipse 2017 ) and crosses the USA at the speed of Concorde, at varying speed.

This is one of the best interactive online calculators - you can click on your location to find extra details such as the path width where you are, and the speed the shadow is moving. USA - 2017 August 21 Total Solar Eclipse - Interactive Google Map - Xavier Jubier

So for instance, its speed is 2410 mph or Mach 3.14 in Western Oregon and 1402 mph or Mach 1.83 near Charleston SC. (from How fast is the shadow moving across the US during the eclipse? )

NASA will send some jets to observe the eclipse, because it’s a chance for scientists to study the solar corona for faint details that are otherwise hard to spot. NASA has a brilliant plan to make the total solar eclipse last nearly 3 times as long

However to see the eclipse for as long as possible you need a supersonic aircraft. In 1973 eight lucky astronomers were able to observe totality for 74 minutes in a supersonic Concorde aircraft in 1973 When Astronomers Chased a Total Eclipse in a Concorde

The French prototype Concorde 001 - which at that point was an experimental aircraft doing test flights, taking off for its 1973 eclipse mission. It flew at Mach 2.05, more than twice the speed of sound. This is Concorde 001 on its last flight on June 30th before it was retired on October 19th to the Air and Space Museum at Le Bourget Airport, Paris.

It was the first Concorde to fly (on March 2nd 1969) and did 249 supersonic flights in total and had 245 hours 49 minutes of supersonic flight hours in total. See Heritage Concorde. The British prototype was 002.

Photo: Jim Lesurf

One of the specially-designed instruments for observing the composition of the sun's corona. Photo: Pierre Léna

Pierre Léna wrote a book about the mission, Racing the Moon's Shadow with Concorde 001 (Astronomers' Universe)

The Concorde prototype they used with its modifed portholes is on display at the as a permanent exhibit at Le Bourget Air and Space Museum

Interviewed by motherboard vice, Léna says: "There's no aircraft flying today that would let us do what we did, nothing that can fly that fast for that long. There are military jets that can fly faster, but not with the endurance of Concorde—and of course they couldn't carry the instruments. Our record is safe for the foreseeable future."

Here is a video about their experience

So, yes, if you stand in just the right place, it turns dark in the middle of the day in this astronomical sense but only for a minute or two, and you have to be exactly on the eclipse track to see this, and your local clocks probably won’t say midday or an exact hour of the day either.

You have to travel to the eclipse track to see a total eclipse (unless you are already on it). Most people in the US will only see the sun partly covered - a partial eclipse. But if you are on the eclipse track, you will see a total eclipse.

GOING TO SEE THE ECLIPSE

It's well worth going to see if it is reasonably close to you, many people say it is a sight of a lifetime. Unless it is clouded over. In that case it just gets dark for a minute or two and you don't see anything much else.

If you do see it, then the sun gets blocked out by the moon and then you see white rays emanating from the shadow. That's the solar corona. So not totally black, you see the corona and you may see the brightest stars. If you are lucky enough to have a clear sky that is.

This can help you find the best place to see it. You need to be inside the shadow. You also need to have clear skies. So best if you can go to a place that has clear skies more often.

This is a copy of my Why the eclipse this August is a wonder of nature and not something to be scared of

See also List of the articles in my Debunking Doomsday blog to date

No, it is nonsense and BS. David Meade in his book just repeats many of the misconceptions floating around on the internet. He makes no attempt to check if they are true or not.

He thinks that the gravitational pull of the Earth is so great that an approaching entire solar system will be diverted into a loop around Earth, and he thinks that a planet approaching from the South would only be visible in a plane flying high above South America (for some reason) and lots of other nonsense things.

There is nothing here to be scared about.

Somewhat more detailed debunking here: Debunked: Nibiru will hit or fly past Earth in September (or October or November) 2017 - David Meade’s “prophecy”

Well it’s not even an astronomical theory. The thing is that it doesn’t make sense as astronomy. The whole thing is nonsense, total BS. Promulgated by youtube uploaders and bloggers who don’t have the slightest clue about the basics of astronomy. To try to disprove it is to give the idea more dignity than it deserves.

It's like someone who claims to be an expert on sport, who in the next sentence says that Usain Bolt is a top seeded tennis player and won Wimbledon. If you know the basics of astronomy, the things they say are as absurd as that. They give away their complete ignorance of astronomy within a couple of sentences.

"INVISIBLE" BROWN DWARFS

By way of example, they read in genuine astronomy articles that brown dwarfs can be spotted in the infrared when far from any star even in pitch darkness. They conclude from this that they are invisible in ordinary light - that's like concluding that you are invisible because you are warm. Since when did warming something up make it invisible?

Humans are easily visible at night with infrared goggles. We can’t however be seen in pitch darkness if you see with what we call “visible light”, because we don’t fluoresce and aren’t in any other way luminous. A glow worm can be seen at night. Does this prove that we are invisible in daylight, because we can’t be seen at night?

Similarly brown dwarfs are invisible in pitch darkness far from any star but stars are visible because they shine by their own light. Brown dwarfs can be seen in infrared even in pitch darkness, just as we can be, for a similar reason.

That’s the level of reasoning that you get from these people. They don’t even look clearly at their assumptions.

CAN'T SEE ANY DIFFERENCE BETWEEN A PLANET THAT NEVER COMES CLOSER THAN SIX TIMES THE DISTANCE TO NEPTUNE AND A PLANET THAT FLIES PAST EARTH

They read that astronomers think that there is a chance we may have a planet that's in an orbit that takes it at its closest to 200 au from the Sun and at its furthest, 1200 au from the sun - and if it exists, it must currently be at its furthest point or we'd have spotted it already easily. Neptune is 30 au from the Sun - so at its closest this "Planet 9" if it exists reaches more than six times the distance to Neptune - but to be not spotted yet, it has to be five or six times further away than that right now.

They conclude that this proves that they have been right all along that there is a planet in an orbit that goes from way beyond Neptune all the way to Earth's orbit and back again every 3600 years and is currently very close to us, "hiding behind the Sun" and just about to hit us or fly past us. Do you see a difference between these two scenarios? They can't seem to see any difference.

Bill Nye shows the scale of our solar system. If "Planet 9" exists then the closest it comes to Earth is six times the distance to Neptune. It must be several times further away than that at present or we'd see it already. Do you see a difference between this and the idea of a planet that comes as close to the Sun as Earth? They can't see the difference which shows the level of their understanding of astronomy.

IMPOSSIBLE PLANET

Their orbit is impossible because it would cross the orbits of all four gas giants. It can't keep missing them time after time because they have different orbital periods and it would hit one of them or be deflected out of its orbit or mess up our solar system within a million years. If our solar system ever had such a planet, it is long gone ,more than four billion years ago.

Even a 1 km comet would be easy to spot two years before it gets to Earth or Mars as we know from experience too, e.g. Siding Spring found nearly two years before its flyby of Mars and it was between 400 and 700 meters in diameter.

TWO SUNS

Then they go on to pile on the most absurd things. They say that we have two suns. I frequently get people asking me if it is true that we have a second sun and that we are in danger of it flying past Earth! Honestly. Don't they believe their own eyes? This is very easy to check. Don't stare at the Sun. Hold a finger in front of the Sun and then look to left and to right. Hold your finger at anothre angle and look above and below. Do you see a second Sun?

You have just disproved their theory that we have a second Sun.

BALDERDASH AND BULLSHIT

They say so many absurd things. They dress them up in videos with stirring sound tracks and authoritative sounding voice overs. And somehow people who know nothing about astronomy come to believe these things. Who knows if they are just unable to reason logically, or if they are hoaxing everyone else, or don't understand astronomy or what it is. Some are certainly just doing it as hoaxes for the ad revenue. And the ones who are selling Doomsday bunkers obviously have a commercial reason for running these stories. There are dozens of books on it also. It's like a minor industry, all based around balderdash and bullshit.

The common sense way to respond, when you find that someone spouts bullshit, is just to treat them as an unreliable source.

ASTRONOMY NIBIRU BULLSHIT TESTER - WOULD YOU READ A SPORTS COLUMN THAT STARTS "WHEN USAIN BOLT WON WIMBLEDON IN 2008..."?

I suggest you try out my Nibiru Bullshit Tester - and - well you don’t even need to do that. If a website or a news site or a TV channel or blog talks about a planet called Nibiru in all seriousness and they are not debunking it, then - just cross them off your list of people who know anything about astronomy.

To continue to read after that is like reading in all seriousness an alleged sports blog that starts "When Usain Bolt won Wimbledon in 2008 ...". It's even more absurd than that. Usain Bolt is a human being and could in principle win a tennis tournament, it is just not his sport. But their ideas don't even make logical sense in astronomy. They are bullshit through and through.

It’s best to just cross them off your list of people you go to when you want to know about something in astronomy. They will fill your head up with strange ideas that make no sense, and confuse you. You may waste a lot of time trying to make sense of the BS. And you may need to do a lot of unlearning of this nonsense before you begin to get some understanding of how astronomy really works.

See also

• Debunked: Nibiru will hit Earth on [Insert Date here]
• Debunked: Nemesis is Nibiru - updated
• Nibiru Bullshit Tester.

This is based on my: Is Nibiru a Hoax?

No, not with naked eye. Some people have had their eyes damaged after staring at it for minutes, perhaps particularly susceptible for some reason. Though, according to the sources, some people have stared at the sun for minutes, and in one medical experiment, several people (who were just about to have their eyes removed to prevent spread of cancer ) stared at the sun for an hour, with no harm to the retina. So, you just don’t know which you are. That’s why staring at the sun at any time is not recommended at all and you get these warnings.

Also, that’s in full sunlight not an eclipse. We seem to be particularly susceptible to eye damage during solar eclipses - perhaps because the eye opens wide in the darker conditions, an unusual situation with darkened surroundings, staring at a small bright spot in the sky. Doctors often have to deal with cases of people who have damaged their eyes by staring at the sun, during eclipses - so don’t let it happen to you.

It’s actually the UV light, short wavelength light that seems to be what cause the most harm here.

As for looking through a telescope or binoculars at the sun - that can harm you very quickly through infrared - heat. It’s like focusing light from the sun onto something with a lens to set it on fire.

The thing is we have no pain receptors in the retina. So the first you know of it, that anything is wrong, is when you notice that your vision has been affected - that you have a spot in the center of your vision where you can’t see anything.

SUN PROJECTION AND CRESCENT SHAPED DAPPLES

There are many ways to enjoy the eclipse. First the projection method. This actually happens naturally, if you are lucky enough to see it. The dapples beneath trees are actually each little images of the sun in a pinhole camera type effect from chinks in the leaves. So during a solar eclipse you see all the dapples turn to crescents like this, in ideal conditions:

Photo from here: File:IMG 1650 zonsverduistering Malta.JPG

So you can look out for those Making eclipse magic

You can also make your own simple pinhole camera to look at the sun projected onto a sheet of paper (say). Though it’s likely to be a bit faint and dim.

Or you can set up a telescope to look at the sun and then project the image onto a sheet of paper. You need to be careful you don’t damage the telescope optics. So you need some kind of a heat shield, to reduce the aperture of your telescope. Instructions here from Sky at Night.

How to make a solar projection screen

This is what it is like - you’ll see sunspots too:

ECLIPSE GLASSES AND SAFE AND UNSAFE FILTERS

What most people do is to get eclipse glasses. They make the sky very dark. You just see blackness apart from the sun.They normally tint the sun yellow-orange. It’s not really that colour at all, it’s white. But people expect it to look yellow, and so the manufacturers of these glasses tint them accordingly.

These are very low cost, just a few dollars, so it’s worth ordering a few in advance for yourself and for anyone else who might watch it with you. Or you may get them for free with an astronomy magazine. Be sure not to use them though if they have been damaged and have holes in them, even tiny chinks, and get from a reputable seller.

It is not safe to use dark plastic wrappers and the like to block out the sun. They may or may not block out the necessary frequencies and as they are not designed for that, there is no way to know.

You can use welder’s goggles but you need to be sure to get the right grade of goggle. It must be at least welder grade 14. Also stacking lower grade welder glass is not safe.

Things like sunglasses and mylar balloons, food wrappers etc are definitely not safe.

It’s far easier and safer just to use the proper eclipse glasses.

SOLAR OBSERVING TELESCOPES

You can also get a dedicated solar observing telescope or add a filter to use a normal telescope for solar observing.

Telescope owners can use a filter that goes over the the front of your telescope which blocks out 99.99% of the incoming light. However, don’t try a filter at the eyepiece end.. A filter over the eyepiece can be burnt. Don’t try looking through a telescope or binoculars with eclipse glasses. They aren’t designed for that.

Some telescopes used to come with eyepiece solar filters. They are not safe, throw them out..

VIDEO BY AN ASTRONOMER ON HOW TO OBSERVE THE SUN SAFELY - AND WHAT’S UNSAFE

Here is a video on safe and unsafe ways to do it.

The only time it’s safe to look directly at the sun during an eclipse is when the rest of the sky goes dark and the sun’s corona shows. Before that you get the diamond ring effect - even though it’s just a chink of sun, it’s still not okay to stare with naked eye vision. Your pupils are wide open and your eyes are vulnerable.

You might wonder, what about all the people who stare at the sun at sunrise and sunset?

Well the sunlight gets to you almost horizontally through the thickest part of the atmosphere, and there are often clouds in the way. Even so, people don’t tend to stare at the sun for long. They look at the clouds and many other things. And unlike a total eclipse, it’s still quite light so your pupils are contracted too.

When you watch a solar eclipse, even a partial one, your attention is all on the sun, and if it is a total eclipse or close to, then your pupils will open wide.

SUNGAZING AS A RELIGIOUS OR HEALTH PRACTICE AT SUNRISE AND SUNSET

It’s not a good idea to stare at the sun even at sunrise and sunset either - yes the light is somewhat more filtered but it’s not like looking at the sun through a safe solar filter.

You might be one of the few whose eyes are particularly susceptible to this. Some people stare at the sun as a religious observance of sungazing especially at sunrise and sunset or for their alleged health benefits. It’s an alternative healing method.

But the sun isn’t guaranteed safe at sunrise or sunset. Compare what you see at those times with what you see with eclipse glasses.

And maybe many of them do it just fine - this chap seems to have managed okay - but you might be one of the unlucky ones, as doctors occasionally see patients with eyes damaged through these religious observances.

Here is an example, of five patients treated for serious eye problems after attending a gathering of 10,000 catholics staring at the sun hoping to see a miracle. The Catholic Church warned them against attending according to this article but many did anyway and a few went blind: It's no miracle, I could see but now I am blind -

There again that’s 10,000 people and presumably they didn’t all go blind, but five, at least, did. Temporarliy anyway, and some of those might have lost some of their sight, in the area used for detailed vision and reading, permanently. If you are unlucky, you could lose the ability to read through this practice, as Isaac Newton did, temporarily, or permanently.

COULD YOU SUBSIST ON SUNLIGHT ALONE THROUGH SUNGAZING?

Some practitioners from India think it is possible to live only on sunlight, without eating, and some of these engage in sungazing.

This doesn’t make scientific sense, so if they are able to do this, it’s basically a miracle, something science can’t explain. The cells at the back of our eyes may actually get a tiny amount of energy from sunlight. There are some microbes, the haloarchaea that obtain all their energy from sunlight not by photosynthesis, but by a process very similar to the way that we see. They use bacteriorhodopsin, and our eyes use rhodopsin. It’s much the same.

Lake Hillier in Western Australia, a "pink lake". It's pink partly because of the purple haloarchaea, and partly because of red carotene accumulating in a green algae dunaliella salina.

The green algae use chlorophyll. But the haloarchaea use rhodopsin and don’t fix carbon dioxide or generate oxygen but convert light directly into energy via a “proton pump” in much the way that our eyes use to see sunlight.

But that’s just one tiny bacteria subsisting off sunlight, which indeed they can do, just fine. Perhaps the cells at the back of your eye could subsist off sunlight, but not your whole body, at least not according to scientific understanding.

There’s no way, scientifically, that your entire body could subsist from photosynthesis through your eyes. See also Sungazing - RationalWiki

Also it’s not safe to stare at it through light cloud or to stare at its reflection in a mirror or in a bowl of water.

Most of the dangerous rays of light are invisible to your eyes, and for instance a cloud that blocks out the sunlight in visible light might let the dangerous UV light through.

MEDICAL EXPERIMENT STARING AT THE SUN FOR ONE HOUR

From: Galileo, solar observing, and eye safety

“Tso and Piana asked three middle-aged people, each with an eye that was to be surgically removed to prevent the spread of malignant melanoma, to stare directly at the Sun for one hour, a day or two before the operation. To quote from their summary:

“Two of the patients sungazed with an undilated pupil, and, 24 hours later, recovered their preexposure visual acuity with no detectable scotoma. One of the patients looked at the sun with a partially dilated pupil, and 24 hours later her visual acuity dropped from 20/20 to 20/25.

“But even in that eye, whose pupil was dilated to 4 mm, acuity was back to 20/20 after another day, though the scotoma remained.

“After surgery, the eyes were examined under the microscope. Although damage to the retinal pigment epithelium was seen in every case, the photoreceptors appeared perfectly normal. The ages of the patients were 49, 55, and 57 years.

“On the other hand, there are also cases of people who stared at the Sun for only a few minutes, when it was much lower in the sky, and suffered long-lasting scotomas:”

NEWTON’S TEMPORARY BLINDNESS - UNABLE TO READ

Newton reports that he damaged his eyes to the extent that he couldn’t read, by staring at the sun, which he did repeatedly over a period of some hours, after which he stayed in total darkness for three days to try to recover. He eventually did but for some months later he still saw effects from his eye damage in dark conditions. You can read the details here: Eye problems of other early solar observers

You might well be okay like Newton eventually - but there again you might not.

DON’T EVEN GLANCE AT THE SUN THROUGH A TELESCOPE UNLESS SET UP FOR SOLAR OBSERVING WITH THE PROPER FILTERS OVER THE OBJECTIVE - BURNING LENS EXPERIMENTS

It’s especially important not to look through any kind of telescope or binoculars. In that case, it’s the infrared more than the UV, it can literally burn your retina.

This is why you must not look at the sun through a telescope unless it has a properly installed solar filter:

SUMMARY

So for most of us, the advice is to use the proper eclipse glasses to look at the sun, and only take them off for the solar corona. Or of course to look around at the crescent dapples etc. And be ready to put them back on as soon as the diamond ring effect appears again. As for projection, looking through a telescope etc - maybe you can some nearby astronomers with telescopes to show it to you through their scopes?

But you don’t need to be like David Mitchell

It’s okay to glance at the sun as happens normally in daylight.. It’s staring for it for long periods that’s the issue and this is something we don’t normally do except during a solar eclipse. Normally you can just rely on what comes natural to you, it’s so bright you just look away again naturally, unless you deliberately stare at the sun, and your eyes are kept safe.

The safety tips for observing the sun are due to accidents that happen to only a few people out of thousands, (at least 5 out of 10,000 for that Catholic sun gazing miracle seeking crowd). But they do happen, which is why doctors warn us not to stare at the sun. They want us to be safe and not be one of the people in that statistic which leads to them having to treat patients with sometimes irreversible eye damage.

And - just never look through binoculars or a telescope even for a fraction of a second, except during the solar corona. When you see the corona it is safe to look even through a wide aperture high power telescope. But you need to keep an eye on the time and be sure to look away in good time, e.g. 30 seconds before totality is due to end or some such.

See also When is it "safe" to view a solar eclipse with the naked eye? Or is it best just to utilize a telescope?

We can work this out pretty much from first principles most of the way, but need to look up a couple of figures at the end. So, one way to look at it - the sun seems to rise in the east, that means that the Earth's surface is moving towards the east as it rotates. The moon like just about all the larger moons in our solar system except Triton, orbits our planet in the same direction it rotates. So the moon also is moving more slowly towards the east, through the night sky.

From that, from basic astronomy and what we know from our experience you can then work out things like this. For instance the moon is a bit further east every time the sun rises, so that means the moon rises and sets a bit later every day.

So for the solar eclipse, well as seen from Earth yes the sun moves very slowly against the fixed stars, but does that only once a year, The moon moves through them once a month, from west to east. So its shadow at solar eclipse has to move from west to east.

But the Earth's surface is moving from West to east too. So it's a question of which does this faster. Although the Earth rotates once a day, and the Moon orbits only once a month, 28 times more slowly, the Moon is also much further away. Earth's radius is 6,371 km. The distance to the Moon is 384,400 km which is about 60 times further away.

This means the Moon has to complete a circle of radius 60 times Earth's radius in a time that is only 28 times Earth's rotation speed.

So the Moon is moving much faster through space than the Earth's surface is, about twice as fast. So the Moon crosses the sun faster than Earth's surface moves so the shadow beats Earth, at quite a lick. It actually reaches over Mach 3 at times, in its travel from West to East, traveling at a speed of 2410 mph or Mach 3.14 in Western Oregon

This is one of the best interactive online calculators - you can click on your location to find extra details such as the path width where you are, and the speed the shadow is moving.

USA - 2017 August 21 Total Solar Eclipse - Interactive Google Map - Xavier Jubier

The shadow is only 70 miles across and is moving faster than Concorde at its fastest. That’s why it’s so short, maximum time of totality for this one is 2 minutes and 40 seconds.

At that speed, A military jet can match its speed but can’t keep it up for long.

Nevertheless, NASA will send some jets to observe the eclipse, because it’s a chance for scientists to study the solar corona for faint details that are otherwise hard to spot. NASA has a brilliant plan to make the total solar eclipse last nearly 3 times as long

However to see the eclipse for as long as possible you need a supersonic aircraft capable of long haul flight at supersonic speeds. In 1973 eight lucky astronomers were able to observe totality for 74 minutes in a supersonic Concorde aircraft in 1973 When Astronomers Chased a Total Eclipse in a Concorde

The French prototype Concorde 001 - which at that point was an experimental aircraft doing test flights, taking off for its 1973 eclipse mission. It flew at Mach 2.05, more than twice the speed of sound. This is Concorde 001 on its last flight on June 30th before it was retired on October 19th to the Air and Space Museum at Le Bourget Airport, Paris.

It was the first Concorde to fly (on March 2nd 1969) and did 249 supersonic flights in total and had 245 hours 49 minutes of supersonic flight hours in total. See Heritage Concorde. The British prototype was 002.

Photo: Jim Lesurf

One of the specially-designed instruments for observing the composition of the sun's corona. Photo: Pierre Léna

Pierre Léna wrote a book about the mission, Racing the Moon's Shadow with Concorde 001 (Astronomers' Universe)

The Concorde prototype they used with its modifed portholes is on display at the as a permanent exhibit at Le Bourget Air and Space Museum

Interviewed by motherboard vice, Léna says: "There's no aircraft flying today that would let us do what we did, nothing that can fly that fast for that long. There are military jets that can fly faster, but not with the endurance of Concorde—and of course they couldn't carry the instruments. Our record is safe for the foreseeable future."

Here is a video about their experience

More about the eclipse here

Why the eclipse this August is a wonder of nature and not something to be scared of by Robert Walker on Debunking Doomsday

Note the question I originally answered was about emojis, or the graphical symbols specially designed to convey emotions,designed by artists.

Emoticons like :-) of course can be used here as with any site that permits text editing.

But I see most of the answers here are about emojis and that’s probably what is intended. So, you can embed them as images.

http://unicode.org/emoji/charts/...

Perhaps that might be useful on occasion? For instance Facebook permits emojis, but not mixed in with the text. The unicode emojis are just black and white symbols anyway and rather small and hard to read.

Here on Quora, they have to be only one to a line because quora puts images in new lines and doesn’t let you mix images with text freeform.

I agree that it seems that it doesn’t let you include them as characters.

There are many Buddhist schools of philosophy in the Tibetan Buddhist traditions. But they approach it differently from Western philosophy.

We’d call them schools of philosophy that is, as it is the closest we have. But it’s not really quite the same idea.

For instance they may analyse things into conceptual atoms and moments of consciousness, or an approach rather similar to Idealist philosophy, that everything is not different in substance from mind.

I forget them now. But unlike Western philosophy, they aren’t an attempt at a final answer, a “theory of everything” in philosophy at least not in the sense of developing a theory. The aim isn’t to understand a theory intellectually, but to wake up and realize something.

Rather, they are a form of meditation. It’s a bit like the sand mandala.

Buddhist monks will often set up an elaborate Mandala. They may spend days building up an elaborate mandala. Then they just wash all the coloured sand away. This is a shortened version with just a few clips. The whole thing probably took anything from many hours to days.

In the same way, you build up an elaborate philosophy - everything as atoms, or everything as mind, or something more subtle than those ideas. And meditate on it.

But then at the end you see through it and all that intellectual support dissolves away.

It’s rather refreshing after Western philosophy or I found it so.

And the thing is, that we all have a kind of philosophy in this sense already. Indeed that’s where the confusions come from, that we build up a kind of elaborate philosophy of how things work and what we are and how we relate to everything else and it seems so natural we don’t see it as such. Our world changes as a result. Sometimes that’s obvious, for instance when you are terrified or angry, then the whole world seems scary orthreatening. Things loom up and magnify. You can jump in alarm on sight of a shadow. In a way your actual perception changes as a result of the way you are intellectualizing and reacting. Your perception of the world itself, others, and yourself.

The Buddhist path is to do with seeing through this confusion, to see a truth that’s been there all along.

One particular meditation practice of this sort is the practice of “progressive stages of meditation on emptiness”. For some schools of Tibetan Buddhism it’s four stages and for others, it’s five. The emptiness there isn’t nihilism but rather, seeing through the projections and crazy things we overlay, like the way things loom up and seem sharp edged and dangerous when you are angry.

I just did a bit of meditation like that. Most of my meditation has been just the simple breath meditation which happened to be more suited to me, the same meditation beginners do. I used to go to Quaker meetings before when I was Christian and the way they sit in silence is very similar to this basic meditation I’m taking about, though they have different ways of conceptualizing it.

In Therevadhan schools it’s a bit different. They don’t build up these elaborate philosophies in the same way as the Tibetan Buddhists do.

But they too have this idea of the truth, the goal of the path, which just “is” and was true all along but you never saw it.

And for the Tibetan Buddhist traditions - well all of this is just a meditation technique. It’s not an attempt to find a philosophical “theory of everything” in the sense of Western academic philosophy.

That’s not the aim in Buddhism. If that was Buddha’s path, to develop an elaborate intellectual theory, it would be something you could forget. You get Alzheimers, or you get old or a bit tired and you forget how the intellectual theory works. It would be something impermanent and dependent on conditions and part of Samsara, conditioned existence.

Nor is it nihilist, or existentialist. It’s not the idea that the ideas dissolve away because everything is valueless or that there is no point in doing anything. That’s just another build up of complex ideas and a tangle of ideas too.

Though they build up elaborate detailed theories and complex meditation instructions, the aim all along is to help the practitioner along the path in a practical sense.

Instead you may get a glimpse of the path of true wisdom and true compassion perhaps when the elaborate intellectual ideas dissolve away like a sand mandala.

We are not at all vulnerable to a dinosaur killer asteroid. They have already found all the asteroids of 10 km and larger and none are headed our way at least until 2200.

We can’t map out all the comets in the same way, but comets at present are very rare. As of 3rd August 2017, we know of 106 comets that do regular flybys of Earth out of 16,468 total so one in 155 is a comet (these numbers change frequently, as they find new asteroids, for instance, they have found five new asteroids since 1st August). The chance of an impact by a 10 km asteroid per century is about 1 in a million. So that makes it a tiny negligible chance of 1 in 155 million that Earth is hit by a comet as big as 10 km in the next century. We’d spot a comet that large many years in advance also, for instance, the much smaller Siding Spring 400 - 700 meter comet that did a close flyby of Mars was spotted on 3 January 2013, a year and nine months before its flyby on 19 October 2014.

Siding Spring seemed to have a tiny chance of hitting Mars when first discovered, but as they refined its orbit, they found it would miss. Since Mars is a very small target, that’s what you’d expect. It’s the same for Earth. If we found a small comet headed our way, we’d know of this many years in advance, and to start with we might not know if it would hit, but as astronomers refined the calculation, the most likely thing always is that we find that it misses.

Asteroids as large as a hundred kilometers can’t hit us at all. The craters on the Moon are from well over 3 billion years ago and those big asteroids have all been cleared out of Earth’s orbit long ago. The only ones left of that size are in the asteroid belt, asteroids like Ceres, Vesta, Pallas etc. We are protected from ones beyond Jupiter by Jupiter itself. For details, see Debunked: Earth could be struck by a huge asteroid hundreds of kilometers across

Yes there are people monitoring them. What’s more, they publish all their observations as they make them. Everything is done in public. It involves teams of professional astronomers from many countries world wide and then many amateurs. The asteroids are found by big telescopes like Pan STARRS. The amateurs are mainly involved in tracking them, as there are so many asteroids to track, that professionals can’t keep up with the task with the big telescopes.

CURRENT IMPACT RISKS

It is easy to keep up to date with the latest news by visiting this page:

Current Impact Risks. Then click “Use unconstrained settings”.

This is the first place to go if you see one of those stories. It is automatically updated with all the new observations.

It is ordered with the entry of most risk first. So you just need to look to see if the first entry in the table is orange or red. As of writing (August 2017), this has never yet happened.

DETAILS OF HOW THIS WORKS

If any of them go red, a collision is certain, but how much of a threat depends on the number.

If the number is 8, it is either localized on the land and large enough to form a small crater, or if it falls in the sea, it could cause a tsunami. Sooner or later we are bound to see a level 8 red alert, as these are expected to happen about every fifty years.

Often these are not even noticed, because the impacts are in remote parts of the world. Much of the world is still desert or sparsely inhabited. But with our population growing, there's more and more of a chance that one of these impacts will come close to a populated area. If one of these were to hit a city, it would be devastating.

It's a bit like being able to predict a normal terrestrial hurricane, volcanic eruption, earthquake or tsunami - with the extra twist that if we can get enough data, we can actually predict it decades in advance. It’s also the one disaster we can not only predict, but prevent as well. With our space technology, we may be able to deflect the asteroid and prevent the disaster altogether if we can predict it long in advance. If not, at least we have plenty of time to evacuate the impact zone and we would know the exact date and time of the impact to the minute.

If the entry is red, and the number is 9 or a 10, then it's a much more serious threat, either regional, threatening an entire country, or global. These are rare. The chances are that we probably won't see one of these in this century.

If the number is orange, then there is a significant possibility of a major impact, but it is not yet confirmed. Again, the severity depends on the number.

If any entry is yellow, then it merits attention by astronomers, but there is at least a 99% chance that it will miss (for levels 3 and 4) and it may be far less likely than that to hit (for level 2). It may be of significance to the public if the potential impact is less than a decade away. However, since it is so improbable, the chances are that it will soon be reassigned to level 0. For instance if there is a 99% chance it will miss, then there is a 99% chance that it will soon be reassigned to level 0.

The Near-Earth Asteroid 2004 MN4 briefly reached level 4 in 2004, so it went right up to the highest level in the yellow section, setting a record. But it was soon reassigned first to level 1 and then by 2006, to level 0. See 99942 Apophis (on wikipedia) for the details (2004 MN4 was a provisional name, and it was renamed to 99942 Apophis).

This should be no great surprise as, after all, there was a 99% chance of it missing Earth even when the news first broke.

If (as is usual) all the entries are coloured blue (very small objects), or white or green then there is no confirmed impact threat for the next 100 years.

It's quite common for an asteroid to reach level 1, green briefly. This means that it will do a close flyby of Earth, with a collision extremely unlikely.

Another thing to look out for. Sometimes astronomers make an announcement saying that an asteroid is definitely going to miss Earth, but that it could miss by anything between a few thousand kilometers and a few million kilometers. How can astronomers be so uncertain of the flyby distance, and yet know it will miss?

Well that’s because the largest uncertainty is usually about its exact speed along its orbital track - and so, about where Earth will be when it crosses close by to Earth’s orbit.

An analogy I use - it’s like driving along a road that crosses a railway track on a bridge. If you cross that bridge every day at the same time, and a train also goes under it every day at that same time, say 6 pm, then from time to time you will cross the bridge exactly at the same time the train goes under the bridge.

But it just needs the train to be delayed by a minute, or you to be delayed by a minute, and the train, even traveling at a modest speed of say 60 km per hour will be a kilometer away when you cross the track.

In none of those encounters will you ever be hit by the train because you are on a bridge and the train track is below the bridge. It’s like that.

For more about all these levels, see Torino Scale.

For more on this see my Giant Asteroid Headed Your Way? - How We Can Detect And Deflect Them

No, there is nothing at all to worry about. Nothing astronomical of any significance at all happens on that date. The only thing that happens is actually an absence of anything interesting - the visible planets are all briefly so close to the sun that they can’t be seen easily.

Short summary - planetary alignments can be a pretty sight in the night sky. But they are of no astronomical significance and can’t harm us in any way at all. This particular alignment is an alignment with the sun as well, which means that there is not even anything to see. It’s rather an absence of anything interesting for astronomers who like to observe planets.

The book of Revelation is meant a a message of hope, not despair. It’s so enigmatic though, that you can fit almost any message to it and claim that’s what it is saying. The Bible is not noted for its astronomy, and they didn’t even know that meteorites came from space, thought comets were like high clouds, and they didn’t know that Earth orbited the Sun so didn’t know it was a planet. It doesn’t even have eclipse predictions in it, although a few astronomers at the time could do them (though not nearly as accurately as us). It’s just not a work of astronomy at all. It has much to say in other ways that many people find of great value, but to look to the Bible for a guide to astronomy is to look in the wrong place I think.

DETAILS

There is a very rough alignment with the planets and the Moon spread out over the sky from Leo to Libra. However, there will be nothing to see in the sky because the sun is right in the middle. It's a non event visually, most interesting as one of the few times when you won't see any of the planets or the Moon.

Amateur astronomers like alignments though they have no astronomical significance, just because they look interesting and they can get nice pictures of them. This is the most uninteresting sky you could possibly have if you are interested in visual alignments.

As for the idea of it being a “sign” - this is just a work of imagination and numerology. His page is here: Signs of the End. It spins a story out of the book of Revelations, which is notorious for having so many enigmatic statements in it that you can interpret to mean almost anything.

There are many different ideas on what it actually meant - was a late addition to the Bible. Views about it include:

• Perhaps it describes events that happened already in the first century AD.
• Perhaps it is about how to lead our lives and the events described have no location in time or space.
• Perhaps it does describe future events.

If you aren’t a Christian then you don’t need to interpret it at all. After all, it was written specifically for Christians.

It is generally agreed it is meant as a message of hope, so if you find it scary, something has gone wrong. The Eastern Orthodox church has gone so far as to exclude it from its lectionary - passages that can be read from the pulpit, because it is so easily misunderstood.

There’s nothing of any astronomical significance on that date. Yes, all the brighter planets are hidden in the bright area around the sun in the sky, so won’t be visible. That’s all. Here is a screenshot

Charts of the Night Sky - shows how all the main visible planets will be hidden in the bright area of the sky around the Sun briefly on 23rd September 2017.

It has no meaning at all. Unless you think you can read signs in the sky like reading signs in tea leaves. It’s not even a pretty sight to look out for in the night sky. It’s rather an absence of anything of interest as you won’t be able to see it because the sun blots it out.

They have just made up a story around the stars and the planets. The constellations themselves are just patterns of stars as seen from Earth. The stars are constantly moving. They are at different distances from us.

This shows how the big dipper is changing:

And this is Orion

More examples here: The fault in our stars: Why the Big Dipper could become the Big Duck

Most of the constellations are not made up of stars that are close together in space either. Look at the constellation from a slightly different angle, if we could travel away from the Sun and it would look different again.

“A scientific visualization of the Orion constellation as viewed from a three dimensional perspective. The true space distribution of the constellation is revealed by circling around the stars.

“The camera begins with a pan across the sky to Orion. The lines of the stick figure constellation are drawn in, which unfortunately gives the viewer an impression of a 2D drawing. As the camera slowly begins to circle around the centroid of the stars, the stick figure quickly breaks into a long extended 3D structure. The camera backs up to keep the entire figure onscreen for the complete circle. At the end of the circle, the camera pushes forward to finish back at the location of the Earth/Sun.

“Note that the stars are rendered with 3D distance dimming relative to the camera position. Stars get brighter or fainter as they are closer or farther from the camera viewpoint. Also, to avoid an obvious distraction, the Sun is not included in the visualization.”

The planets are much closer to us than any of the stars. To say that Jupiter is “in Virgo” is like pointing at a distant mountain and saying your finger is in the mountain. It just means that your finger is between your eyes and the mountain.

It’s like looking at a cloudy sky and seeing clouds that look like fortresses or houses, or boats or animals - and then making up a story about it. Google’s “Deep Dream” generator can turn clouds into images of various creatures:

Inceptionism: Going Deeper into Neural Networks

That could be a fun thing to do but the clouds are not affected by your story in any way. In the same way making up stories about the stars and planets makes no difference to the stars or planets and doesn’t mean that they endanger us in any way at all.

Planetary alignments are very common. For instance there was one early this year with all five visible planets Five planets align: how to see this spectacular celestial show. They are of no astronomical significance but amateur astronomers enjoy watching them.

This is about Muslim views on the Bible Books of Revelation - for them the “Book of Revelation” is not one of their “Books of Revelation”. Islamic view of the Christian Bible. And it’s obviously not a Jewish sacred text. And for any other religion, well they don’t accept the Bible as a sacred text at all, not for themselves, just for Christians, so why should they pay any attention to it?

The book of Revelation, it's a notoriously enigmatic book and you can fit almost any "prediction" you like to it, and many Christians don't think it was meant to predict the future, and others think it was meant as a warning of events that happened already in the first century BC. Whatever the truth of that, at any rate there’s a huge problem of false prophets in modern Christianity, with the Bible itself warning about them, and numerous false prophecies for the last 2000 years of the end of the world. The Eastern Orthodox church has gone so far as to exclude Revelations from its "lectionary" - passages of the Bible that can be read from the pulpit

If you are Christian, then Revelations should be a message of hope, not fear and despair. If you aren't Christian, there is no need to try to interpret it at all as it is written for Christians. Not even Jews or Muslims accept Revelations as a sacred book.

And the Bible is not noted for its astronomical predictions. Remember that back then, they didn’t know that meteorites came from deep space but thought they came from volcanoes or stones picked up by strong winds. They thought that comets were atmospheric phenomena like high clouds. They didn’t know that Earth orbited the Sun, so they didn’t know it was a planet.

The Bible doesn’t even have predictions of eclipses in it, or anything astronomical at all, as far as I know. It’s just not an astronomical prediction book. There are ancient texts that do, not nearly as good as modern predictions but good for their time. But this is simply not the Bible’s strong point.

See also Debunked - The world will end because the Bible (or some other sacred book) says so - which goes into more details about Revelations.

This is a copy of my Debunked - an alignment of the visible planets behind the sun on 23rd September 2017 is a sign of the end of the world

You could do. But a much easier approach is to write your details as a comment on the question. Then link to that comment as your question source.

You can find the link to the comment from the date or time just below your name after you post the comment.

I’ve done that in my question here.

“Which Tank will Will Fill up First? (example with 12 tanks, A to L, see question source for image)

It’s a question that makes no sense at all without the image. But rather than link to an image on an external site, where it might be lost through link rot, I just put the image into a comment on the question and then linked to that comment.

Anyway you can do that with anything that you’d previously have as a question detail. Far better than putting it on an external non quora site.

I describe this and other solutions in more detail in my answer to Why were question details removed from Quora on August 3, 2017?

Yes it can be. Depends on the situation. For instance a natural response to this question is to say “What particularly do you have in mind as an example?”

Do put in more details.

I know Quora has removed the option to add question details, but you can put in details in a comment and then link to the comment as the “question source”. To get a link to the comment, look for the date or time below your name after you post it.

I can think of a number of other ways it could happen.

E.g.: “What should I say in such and such a situation?” - the best answer might be “Ask a question such as …”

Or, if it is a question in algebra, say, someone might ask a question back so as to encourage them to think about the problem rather than just learn a solution parrot fashion.

Other answers might give the full solution, but the ones with questions can be interesting to read, help you understand the problem more deeply.

Probably lots of other ways.

This is a recent meme that’s getting shared on facebook and elsewhere. Repeating the image from the question source:

This is a question that has gone viral recently. Most people answer “G”.

But look closely, as the question says. Many of the pipes are blocked - the line that blocks off D from C is not a mistake.

To find the real answer (this is assuming a low flow rate, as after all it is shown as a drip in the diagram):

From A to B to C is straightforward. None of them can fill before the next one.

J is a bit more complex. But as you fill J, as soon as the water rises to the outlet to L it overflows to L. So it can never get any higher. Yes, its level also rises in the outlet tube leading to I, but it can never get high enough to overflow to I.

So it flows to L, which in turn fills F.

So which fills first, L or F?

By the time F is full, L will only be partly full (with the water at the same level for both).

So your F is the answer.

This video shows the idea, an animation by Nick Rossi using a physics engine, Algodoo

It doesn't quite flow like a real fluid, as he says, but it's enough to get the answer and show how it works.

Here is another animation Which will fill first? from THE FLOW... by CorneliaXaos

Which will fill first? by CorneliaXaos

That answers the question, since it shows a dripping tap at a slow flow rate. But let’s go off on a tangent.

WHAT HAPPENS IF THE WATER IS POURED INTO A AT A FASTER FLOW RATE

If the flow is very fast then obviously A will fill first. However, could any of the others fill up first before F and before A?

It’s’ governed by the Hagen–Poiseuille equation so long as

• the flow is due to a pressure difference.
• the fluid is incompressible and Newtonian (water is, approximately).
• the flow is laminar (not turbulent) - it is with water if it flows slowly through a narrow pipe.
• through a pipe of constant circular cross-section
• that is substantially longer than its diameter,
• and there is no acceleration of fluid in the pipe.

All those conditions seem to apply. The pipes are substantially longer than their diameter which is one of the most important requirements. And they are narrow, and the fluid is water.

Under those conditions

• If the outlet is above water, the flow rate is proportional to the height of the head of water above the inlet to the pipe.
  
  If the outlet is below water, it’s proportional to the difference in height between the water above the inlet and the water above the outlet.
  
  The difference in height of the water here is often called the “head” of water.
• It is inversely proportional to the length of the pipe.

Or in short, the flow rate for laminar flow, in a pipe significantly longer than its diameter, is proportional to the pressure difference, and so to the head of water, but it is also inversely proportional to the length of the pipe.

(it also depends on the radius of the pipe and the viscosity of the water but those are the same for all our pipes).

Techy details. The equation is:

There L is the length of the pipe and R is its radius.

Q is the flow rate (what we are looking for).

ΔP is the difference in pressure between the two ends of the pipe, which for water is proportional to the difference in height of the inlet and the outlet.

Finally μ is the dynamic viscosity

All of those are constant (the pipes are all the same radius, and the viscosity is constant) except for L, the length of the pipe, Q which we are interested in and ΔP.

So our equation simplifies to Q = c ΔP / L, where c is a constant which is the same for all the pipes in our example because they are all the same radius.

Double the length of the pipe and you halve the flow rate. Double the head and you double the flow rate.

So now for instance, can L fill at any flow rate?

Its outlet is a very long pipe. Even if L is nearly full of water ,the head of water in F will mean the difference in heads between L and F is quite small even if F is nearly full and L is likewise.

Its inlet is a much shorter pipe. Whether L can fill will depend on whether we can get J to have a high head to increase the flow rate of L's inlet pipe to more than that of its outlet pipe. But, at least at first sight, it would seem that such a high flow rate could mean that one of the other tanks earlier in the chain could fill first

So - it’s quite a finely balanced question, and hard to answer.

A obviously can fill first with a very fast flow rate, just fill it faster than it can empty.

Well we can actually try this out with a real world experiment :).

Well we can actually try this out with a real world experiment :).

Prozix has made a 3D printed version of the puzzle. If you have a 3D printer you can download it here and print it out and test it yourself: Answer to the question Which one fill First / water equilibrium system by prozix

I don’t have a 3D printer but he has uploaded some videos.

First this is what happens with a slow flow rate

Note that at 22 seconds in, J nearly fills briefly.

If you look closely, you see that a bubble forms in the outlet from J to L, which makes sense, it’s a downward pipe and air is buoyant. The bubble then gets pushed out into L and then bursts.

This shows the bubble just before it bursts (you can show the video at 1080p from the Settings)

So - if the pipes are very thin - or the flow is just right - that might lead to J filling right there, if you can arrange it to fill before the bubble disperses.

So even at a slow rate we have something anomalous already, though its because of a bubble.

But what happens at faster flow rates? I asked in a comment to the video, and Prozix was interested and answered with a new video

At 28 seconds in, at one of the flow rates, then L and F fill at the same time.

Here, it all makes sense up to J. J can’t fill (apart from that possibility due to the bubble) at this stage because the pipe from C to J has only a tiny head above its inlet. It’s outlet is about twice as long as its inlet, perhaps more.

Aside: If C was nearly full, J would start to fill, and if we could have the level of water stay below the outlet into L while J fills, then C with its shorter pipe could continue to fill J even when it is nearly full. But as it is now, there is no chance of J filling.

So that makes sense. But how can F fill at the same time as L? That's more mysterious.

The pipe from L to F is three times the length of the pipe from J to L. Meanwhile, in the situation shown here, the head from J to L is about double the head from L to F.

So by the Hagen Pousseville equation again, the flow rate from L to F should be about two thirds of the flow rate from J to L in this situation where J is half full and both L and F are almost full.

So you expect L to fill faster than F.

So, I don’t think they can get into this situation at all, with a steady flow into L. There must be something going on that doesn’t fit our assumptions of laminar flow, or something else such as a bubble forming.

Let’s look at what lead up to this. If you look at the video, L fills faster than F to start with, keeping nearly the same head from L to F as from J to L.

L is clearly filling faster than F and is on track to beat it. There is no sign of any bubbles in the inlet to L.

But then a little while later you get this (25 seconds in)

Now F is filling faster than J. Something has happened to reduce the flow rate into L, which then permits the two levels between L and F to equalize.

But the head going into L hasn’t changed. Also the input pipe to L is full and there are no bubbles. I think the only possible answer is turbulence.

You can see waves forming in J so maybe that means there’s a bit of turbulence impeding the flow from J to L, especially since the water level for J is exactly at the level for the outlet to L. What are your thoughts?

This is what happened with a moderately fast flow rate:

Here is the video starting at that point.

All of A, B, C, J, L and F are just about full. B, L and F started to overflow first and I think L just about beat the other two though it was almost simultaneous. In this frame you can see L just about to overflow and the other two though they have the water raised above the level of the top, haven’t yet actually started to flow down the side.

So how do we understand that as a possible state in terms of the flow rates? Back to our diagram again

With A, B, C, J, L and F all filled, then A to B to C to J all have the same length of pipe and same head (height difference of the water in the tanks above inlet and outlet) so have the same flow rate. J to L has around 2.5 times the head of C to J, and the pipe is around 2.5 times the length, so the flow out of J is about the same as the flow into it, and the difference in head between the top of J and the outlet to I is small. From L to F, the difference in head is about the same as for C to J (which we already know is about the same as the flow from J to L) but the pipe is far longer, so L shouldn’t be able to empty as fast as it fills, and the water flows out of J faster than it flows out of L, so L should fill before J.

From L to F, the difference in head is about the same as for C to J but the pipe is far longer, so L shouldn’t be able to empty as fast as it fills, so it should fill long before J fills,

So if the flow rate is high enough for J to fill like this, L should fill before J and F doesn’t get a look in.

So how could it happen? Well it could be the bubble from J to L, slows down the flow out of J so that J fills first before L.

As for F filling, how did that happen? Let’s look at it again:

The head from J to L is far higher than from L to F and the pipe is shorter, so the flow into L should be a lot more than the flow out of L to F. So it seems impossible for F to fill like this. It's not the bubble - the two tanks fill up reasonably steadily at the same rate. You can watch the video at quarter speed to check. Click the Settings icon in the lower-right corner, then click the Speed selector.

Perhaps at this flow rate, its the double kink in the pipe from J to L causing more turbulence and so slowing down the input to L? What do you think? That could also help explain why J fills at this flow rate, if the pipe from J to L, has a slower flow rate than you’d expect from its length and head. What do you think? Do say in the comments.

Even K can fill, though it is pretty hard to do. This is with a very strong flow into A, and several of the others have been overflowing for some time. They have turned off the inlet pipe at this point.

Amusingly, in the real world, E ends up half full too after some time of running it at a high flow rate with the water overflowing from A.

Here is the complete video

So far the only confirmed alternatives to F are A (obviously) and L (pretty sure it wins at the moderate flow rate).

That’s just a start. There are many other things to try

• Varying flow rate. Can you get, J, say, to fill first or even K by turning the flow rate up and down at critical points during the filling process? This could cause bubbles to form, as well as adjust the heads of the various tanks.
• What happens if you scale the whole model up, or scale it down to a very small size? Scaling it down could make the flow rates out of some of the pipes very slow. It could also mean that bubbles like the one from J to L take a long time to disperse too. Scaling up could lead to more possibility of turbulent flow through the pipes.
• Try adding sugar for viscosity
• What if it is really hot, and you use a slow flow rate so that the water evaporates quickly?
• What if it is really cold so that the water freezes? That would seem to be a way to fill even B first, if the water freezes by the time it gets to B to C but remains unfrozen as far as the flow from A to B.

NOTE

If you see anything in this to correct, however small or important it is, please either suggest an edit for my answer or say in a comment. Thanks!

Just to say - for old questions, the details get moved to a comment automatically. It seems to take a while for that to happen, so you may see no comments, and a day later the old details appear as a question comment.

Some questions make no sense without the details. E.g. questions such as: “What is this animal?” with a photograph uploaded by the questioner.

There is no way to fix that by editing the question, no matter what the limit as you can’t put a photograph into a question.

SOLUTION 1: QUESTION DETAILS AS COMMENT, LINK TO COMMENT AS QUESTION SOURCE

The best solution I’ve seen so far is to put the question details in as a comment on the question. Then link to that comment in the source.

You can find the link to the comment by right clicking on the date or time shown below the name of the author of the comment.

You can see how it works with this question - which had a couple of images. Author wanted to know if the animal was a possum.

What is this animal? Is it a possum?

It obviously needed that photo (and their other one) just to make sense of the question.

I rewrote the title to say (see question source) and updated the question source to link to a comment into which I inserted the two photographs which I found from the log (by appending /log to the url)

This is how you find the link to the comment:

This was the result:

What is this animal? Is it a possum? (see question source for photos)

It’s a specially good very simple example of a situation where the question is a natural one that someone will want to ask: “What is this” with some photographs they took of it. All such questions will make no sense without the details. Well this is a way to fix past questions like that and to ask new ones.

Sadly it doesn’t embed the photographs into the question itself, but it’s better than nothing.

For an example involving text, which I have just fixed in the same way, see Are the tenses and punctuation in this English paragraph correct? (See question source)

There are many budding authors and the answers to such questions are important, and you learn by seeing how it is done in specific examples like that.

A general question of the type “how do you punctuate paragraphs” would be too vague to answer.

This ingenious solution goes back to a suggestion by Joachim Pense - in a comment -

SOLUTION 2 (NOT RECOMMENDED): ADDING THE DETAILS IN AN ANSWER AND LINKING TO THE ANSWER AS THE QUESTION SOURCE

Of course its awkward to have the photograph on a separate page. I expect those who answer questions like this will start putting copies of the photograph at the head of their answers, resulting in lots of answers with duplicate photos in them.

I did a new question of this type myself, it’s another type of question that just makes no sense at all without an image. You simply can’t ask the question without the image and the image is best put on Quora rather than some external site.

“Which Tank will Will Fill up First? (example with 12 tanks, A to L, see question source for image)

As you’ll see I duplicated the tank image in my answer to the question.

To help deal with that issue, you could add the image in an answer instead of a comment and link to the answer - it’s slightly abusing the question format. But you could phrase it as an answer as in “This is the photograph from the question. My answer is that it might be a possum, what do you think?”

I think though that they might complain if you have an answer as a question source, I don’t know, but that’s why I’ve said “not recommended”.

Alternatively, just do an answer to your own question with the image or details, to get it started. Even if you don’t know the answer, you can include the image and say you don’t know and that’s why you are asking the question. It will help get it off to a good start.

There are many other questions like that such as “How do I punctuate this paragraph” or “Where am I going wrong in this complex maths reasoning” or “should I buy this product - I’ve been told by friends that it has these flaws (bulleted list) - are they right?”

Indeed many scientific, technical and mathematical questions, questions on medicine, art, poetry, literature, architecture, music etc etc.

I think they should encourage question details of the right sort myself. To find a way to encourage details that are necessary to questions and discourage unnecessary details, though I’m not sure how that’s best achieved.

SOLUTION 3 QUORA BLOG POST

Another solution is to write a blog post. Everyone on quora can start new blogs. Have a question details blog post and put your details there and link to it as the question source. Then it can be as long as you like. It’s like an answer with formatting tools ready to hand (not easily accessible for comments except using copy and paste) but there’s no risk of quora having an issue with it by linking to an answer as a question source - though I don’t know if they will have problems with that as I haven’t tried.

You can combine that with a tentative answer that includes the image, but not linked to as the question source, for questions where that is appropriate.

SOLUTION 4 (NOT RECOMMENDED!) MISUSE OF THE ANSWER WIKI

I’ve also seen some questions where they misuse the answer wiki to embed an image or text so you can see it on the question page. Put the question details at the head of the answer wiki.

It seems likely to me that Quora won’t permit this once they get around to reviewing such questions. It’s a neat solution otherwise as it basically replicates the question details as they were before. Thought I should mention it for completeness.

WHATEVER WORK AROUND YOU DO, BEST DONE ON QUORA AS A COMMENT, (ANSWER?)OR BLOG POST

I think this solution of using a comment on the question as a question source is far far better than trying to create a copy of the question details off site and then linking to that.

RECOMMENDATION - MAKE USE OF EXTENDED 250 CHARACTER LIMIT FOR QUESTIONS

For instance for the possum question:

What is this small grey animal with a pointed nose and arched legs which I spotted outside my home in Northern California? Is it a possum? (see question source for photos)

(rephrasing of the question suggested by Tim Bushell)

THIS NEW CHANGE MAKES QUORA VULNERABLE TO LINK ROT AND SPAMMING

I don’t understand the reason for implementing it in quite the way they did. It’s encouraging people who ask questions which need details to create the details off quora on some other platform, e.g. their private blog, or facebook or whatever and link to that as the question source.

The great thing about quora is the way it copies images into answers and questions if you link to an image off site. There’s such a problem of link rot on the web, why encourage people to post links to off wiki sites instead of just putting the image or text into the question details themselves?

It also seems likely to be abused too as you don’t normally have to click through to a link to a site off of quora. It’s very rare that I’ve had to do that to answer a question, even if it’s a youtube video then it is embedded in quora. You could end up on a site that asks you to pay to see the content, or spams you, or a site with pornography, or it could just be that it’s on a social site like facebook and you find you have to join to see the photograph.

After this change, any question that has details, even if it is just a photograph or a paragraph of text or a youtube video will require you to click on a link. The link could go anywhere (unless you look at it carefully to check it is a quora url or a youtube link) just to see what the details are.

It also could take the reader to another Q/A site that permits you to enter the details, like Yahoo Answers or stackexchange etc, so you end up on a different Q/A site and end up reading the answer there instead of on Quora so it could lead to Quora losing customers if that becomes prevalent - and how can they complain if someone does that?

IT’S DETRIMENTAL TO INTERESTING CAREFULLY THOUGHT OUT QUESTIONS

Also as someone who has written many answers - often the most interesting questions to answer are the ones that have details - the author of the question cared enough about their question to go into some more detail about what the question was - or it’s an interesting and complex question that needs details.

For instance a detailed question about some topic in science that is more in depth and doesn’t just ask the obvious newbie questions on the subject. Not just a question you could answer by typing your question into google, but a detailed question that you have to ask an expert in person.

This change favours the sort of question where a decent answer will often be “just search in google”, with less of the detailed questions that can only be asked on places like quora.

So - at any rate this fix to do the details as a comment, and then set the question source as a link to that comment does keep the details on quora and avoids issues of link rot. Why didn’t they do it like this automatically? Could they still, or is it too late?

It’s also a way to ask questions like this in future on Quora.

The best solution I’ve seen so far is to put the question details in as a comment on the question. Then link to that comment in the source.

You can find the link to the comment by right clicking on the date or time shown below the name of the author of the comment.

You can see how it works with this question - which had a couple of images. Author wanted to know if the animal was a possum.

What is this animal? Is it a possum?

It obviously needed that photo (and another one).

I rewrote the title to say (see question source) and updated the question source to link to a comment into which I inserted the two photographs which I found from the log (by appending /log to the url)

What is this small grey animal with a pointed nose and arched legs which I spotted outside my home in Northern California? Is it a possum? (see question source for photos)

Then at the end of the comment I added

“For the answers, see What is this animal? Is it a possum?”

That’s necessary for newbies who don’t know how quora works, go to the question source and then don’t know where to go next for the answers.

It’s a specially good very simple example of a situation where the question is a natural one that someone will want to ask: “What is this” with some photographs they took of it. All such questions will make no sense without the details. Well this is a way to fix past questions like that and to ask new ones.

Sadly it doesn’t embed the photographs into the question itself, but it’s better than nothing.

I describe this and other solutions in more detail in my answer to Why were question details removed from Quora on August 3, 2017?

Yes of course, unless they are already liberated or Buddha. This is why it’s often not a good idea to just give everything away when you learn about Buddhism. It’s easy to give away your possessions but not so easy to give away your attachment which probably pops up as regret at what you did.

Meanwhile if you can give up your attachment, there’s no need to give away the possessions or the things you are attached to :).

Losing your attachment in this sense actually means greater love and compassion and more happiness and pleasure and enjoyment too. It’s not at all a Vulcan like repression of emotions and feelings. That again is something one might well do when one learns about Buddhism - try to push feelings and thoughts and emotions away thinking you mustn’t be attached to those. So then you get very attached to the idea of being free of emotions and being calm and peaceful - and that then means you are in a worse state than if you didn’t do that, because it is really hard to spot that kind of an attachment.

It’s not really what we in the West think of as attachment, but it’s a hard word to translate. When we laugh a bit at ourselves and all the antics our minds get up to to try to prove that it is making progress in understanding what it is, and doing something about it, then there might be a chance for some chink of understanding to come in :).

Meanwhile there are many other things one can do along the path :). Generosity is good. But if you think you can get rid of attachment by giving everything away - that doesn’t work.

It can help you to find a simpler way of life with fewer complications which is why Buddhist monks and nuns renounce possessions when they take their vows. But there are many other Buddhist paths and that’s just one of them, and if you think that by giving away everything and becoming a monk or a nun you will instantly be rid of all attachment you are in for a big disappointment. It’s not as easy as that.

Yes. I can understand their reasons, that it permits lots of slightly different questions with inessential differences in the details, that are hard to merge. But people sometimes do have questions that have to be spelt out in detail and can only be summarized in the title, for instance in science and maths areas, or if it is something to do with their own personal situation and experiences. Or it might involve images or links, not just one but several.

There may be no single link that summarizes it. They may have to resort to writing out the details on another social platform, say, as a post on their personal blog, and then referring to it here which is clumsy.

Sometimes the answer you give, if they leave out the details, just won’t answer their original question.

Here is a mathematical example, the author drew a diagram and uploaded it to show what it was they were confused about in a simple question about quadratic equations. It's now a comment of course. Unless you look at the drawing in the comment, you can’t really understand fully what they were confused about.

If there is an equation 0 = ax^2+bx+c, why can't we conclude that the equation must not have real roots, even though it says that y = 0?

SUGGESTED SOLUTION

Why not just move the question details into the comment section, as they are doing already. But do it as a special new type of comment actually labeled as “question details”.

So you can add the details but they are done in the comment section so hidden away. Make them communally editable also, as before. And the questioner can still say “(see details)” if they are essential to the question.

That would discourage use of details for unnecessary trivial distinctions, which would help with their stated aims - but without getting rid of them altogether for those who do need them?

(I put this idea forward before in Robert Walker's answer to Do you think Quora removing the question details feature was a good idea? )

It’s going to be a bit clumsy for maths and science questions - which sometimes require you to set out the problem in some detail, and can't just present the problem in its entirety in the title. It doesn’t make them impossible. But they will have to say "(see comment)" I suppose instead of "(see details)".

Here is a mathematical example, the author drew a diagram and uploaded it to show what it was they were confused about in a simple question about quadratic equations. It's now a comment of course.

If there is an equation 0 = ax^2+bx+c, why can't we conclude that the equation must not have real roots, even though it says that y = 0?

The main problem there would be that sometimes the question gets many comments so how will you know which of the comments the question refers to?

Also it’s going to be an issue for all those questions where the author wants help with some particular detailed scenario they are in. E.g. in my case, scared of fake doomsday news which they want debunked. They may put valuable details into the question. What exactly is it that scares them about the story? Though sometimes it’s obvious ,sometimes it isn’t so much.

SUGGESTED SOLUTION

Why not just move the question details into the comment section, as they are doing already. But do it as a special new type of comment actually labeled as “question details”.

So you can add the details but they are done in the comment section so hidden away. Make them communally editable also, as before. And the questioner can still say “(see details)” if they are essential to the question.

That would discourage use of details for unnecessary trivial distinctions, which would help with their stated aims - but without getting rid of them altogether for those who do need them?

Interesting suggestion by Joachim Pense - in a comment - you could add a comment and then just link to the comment as your source for the question. So that would be a way to add details just as before :).

I describe this and other solutions in more detail in my answer to Why were question details removed from Quora on August 3, 2017?

The main risk is from ash. The further you are from the center, the less ash you get. This map from a computer simulation gives an idea of one possible outcome:

You’d get 1–3 millimeters thickness of ash right out to New York, which is enough to “reduce traction on roads and runways, short out electrical transformers and cause respiratory problems”. There would be centimeters of thickness over much of the mid west, enough to disrupt crops and livestock, especially if it happened at critical time in the growing season. and a meter of thickness out to quite a distance. The worst affected in their list of cites is Billings, population 109,000, which their model predicted would get an estimated 1.03 to 1.8 meters thickness of ash.

So, you want to avoid the dust. After that, the main risk is from crop damage then - and longer term it can cause a reduction in global temperatures by up to 10 C for a decade, which is a lot. Also jets would be grounded, for some time, until the dust settles.

But it’s far more likely to be an ordinary eruption. There have been 80 non explosive eruptions in the 640,000 years since the last supervolcano eruption. So that’s the most likely eruption by far. The last 20 of those were mainly lava flows. An eruption like that would disrupt activities in the Yellowstone national park itself, but it’s likely to lead to few deaths and would not be catastrophic.

It’s also possible that it’s ended its supervolcano phase. It has three known supervolcano eruptions, 2.1 million years ago, 1.2 million years ago and 640,000 years ago. It’s possible that the last one was its last one ever.

Also if it does go supervolcano they expect to have from weeks to months of warning of it. It must be one of the most closely monitored volcanic sites in the world. In the weeks leading up to the eruption I’m sure there would be lots of advice about what to do and probably they would clear the national park too.

See also my What really happens if Yellowstone erupts as a supervolcano, or if some other supervolcano erupts?

It’s just fake news. People click on these stories and share them and chatter about them and so you get talk about them. But unlike the 2012 fake news stories, there isn’t that much talk about this. You must have clicked on many such links, or avidly follow fake news sites like “Before It’s News” or the conspiracy reddits etc to see it at all. Or perhaps you read the sensationalist UK red top tabloids or watch US tv programs that favour such stories like “Coast to Coast FM”

People are just gullible and can easily be lead to believe fake news, especially if they don’t know much about the subject. It seems absurd to us now, but back in 1957 there was no internet, much less travel than today, and many people were convinced, on April fools day, that spaghetti grows on trees as a result of watching this video.

For more on this with modern examples, see my Debunked: How can the videos and photos be hoaxes when so many people believe them?

Also, I think I should debunk your two points and explain why they are neither of them anything to be scared about.

First on the eclipse. We get an eclipse of the sun every year or two. Many of them are total. It is very common for the eclipse to span midday at some point along its track too. ~An eclipse of the sun is just the small shadow of our Moon moving over the surface of Earth. Sometimes the shadow cone doesn’t quite touch Earth and we get an annular eclipse. And sometimes it does touch it and we get a total eclipse. But it will only go dark for at most a minute or two, and you have to be inside the shadow when it passes by to see the total eclipse. It is just a shadow and can’t harm you, but is a spectacular natural event. “Eclipse chasers” will travel hundreds of miles to see one.

If you watch the eclipse - be sure to get eclipse glasses. Only cost of the order of dollars. You may also be able to get them on the cover of astronomy magazines. You don’t sense any pain even when the back of your eye is burning - or more likely - getting bleached by UV light. You can lose your eyesight in the center of your vision temporarily, and in rare cases, permanently, by staring at the sun without protection.

The only time it’s safe to stare at the sun without eye protection is when the sun is completely blocked by the Moon and you see the corona (see below).

Though they are common, because the shadow is small, then it’s rare to see an eclipse anywhere particularly. You have to be standing within the blue eclipse track shown on the map here: this shows the eclipses from 2001 to 2020 including the US one.

The last total eclipses in the US were back in the 1960s and 1970s so young people will not have seen one. Even older people won’t have seen it unless you traveled to the eclipse track. Here is the map for those US eclipses. All the blue lines here are total eclipses. The red ones are annular, meaning that the sun is not totally blocked out.

This is NASA’s eclipse page, with lots of maps like that in the map section. Solar Eclipse Page

Because they always happen at new moon, you won’t see the moon until it starts to take a bite out of the sun. It’s lit up from behind. In the same way if you stand in the shadow of anything, you will see the darker side of it, not the sunlit side. There’s no scattered light in space, apart from a bit of light from the Earth, so the shaded side of the Moon is pitch black. It is, quite literally, behind the blue sky, so you don’t see anything of it until it passes between you and the sun.

Some people worry because there will be a total eclipse around midday - because of some Bible passage about darkness at noon. Well eclipses that span midday are very common.

Solar eclipse of August 11, 1999

This eclipse was maximum at 11 am in Romania but was still total over India around midday. This was the last total eclipse in the UK

Photograph of the 1999 solar eclipse by Luc Viatour

That photograph shows the corona - white rays radiating out from the Sun which you only see at times of total eclipse. If you are lucky enough to have a clear sky, you may see this awesome sight. The sky goes dark and you will even see the brightest stars in good viewing conditions.

It's rather spectacular if you get to see a total eclipse - "eclipse chasers" travel around the world to see eclipses. There are several stages to it, first partial eclipse. Then as the moon covers the sun, you get "Bailey's beads" when light shines between gaps in the mountains around the Moon often ending with a single "diamond ring" when just a tiny patch of sun is left. Then it goes dark and the sun's corona shows and you may see the brightest stars. And yes it turns dark in the middle of the day but only for a minute or so and you have to be exactly on the eclipse track to see this.

Solar eclipse of June 21, 2001

This one had greatest eclipse at 12:04:46 so as close to noon as makes no difference - that’s when the eclipse lasted the longest for this one.

Wikipedia has lists of eclipses, so you can follow through to find any other eclipses that you are interested in: Lists of solar eclipses

This is what an eclipse looks like from space - the dark patch here includes some of the area of partial eclipse - it’s only seen as total from the very center and darkest part of the shadow.

You have to be on the narrow path of the Moon's shadow - the Moon is small and the Sun is huge, and the Moon's shadow is shaped like a cone and only just touches the Earth which is why it is so tiny. You have to be positioned within that tiny shadow to see an eclipse.

You have to travel to the eclipse track to see a total eclipse (unless you are already on it). Most people in the US will only see the sun partly covered - a partial eclipse. But if you are on the eclipse track, you will see a total eclipse.

It's well worth going to see if it is reasonably close to you, many people say it is a sight of a lifetime. Unless it is clouded over. In that case it just gets dark for a minute or two and you don't see anything much else.

If you do see it, then the sun gets blocked out by the moon and then you see white rays emanating from the shadow. That's the solar corona. So not totally black, you see the corona and you may see the brightest stars. If you are lucky enough to have a clear sky that is.

This can help you find the best place to see it. You need to be inside the shadow. You also need to have clear skies. So best if you can go to a place that has clear skies more often.

As for David Meade, his book is just complete BS, he believes every conspiracy theory that is going around, and presents it without any fact checking at all. E.g. he trots out the conspiracy theory that the catholic church built a gigantic telescope to watch Nibiru. Actually it is a small telescope that happens to be on the same mountain as one of the very largest telescopes in our world, and the Catholic church has a long term interest in astronomy, has been running small observatories for centuries, so there is no surprise there at all.

Modern telescopes tend to be built, if you have the choice, in a few favoured sites that have exceptionally good seeing so it’s also not much of a coincidence that they built their telescope on the same mountain as a much larger one. The big telescope has no connection at all with the Catholic church and is run by an international consortium of astronomers.

For more on this, as it would make this answer very long to go into it all here:

• Debunked - an alignment of the visible planets behind the sun on 23rd September 2017 is a sign of the end of the world.
• Debunked: Nibiru will hit or fly past Earth in September (or October or November) 2017 - David Meade’s “prophecy”

This answer uses my article: Why the eclipse this August is a wonder of nature and not something to be scared of

See also List of the articles in my Debunking Doomsday blog to date

Note, original question details are here:

Oh, for sure, it can have real roots. You can express it as $ax^2 = -c -bx$

So, you are looking for an intersection of a quadratic with a straight line. It’s often going to have solutions.

By the Quadratic formula, the requirement for it to have real roots is $b^2 >= 4ac$. So for instance, if a and c are 1, then $x^2 + bx + 1 = 0$ has real solutions for $b >= 2$

The solution for $x^2 + 2x + 1 = 0$ is x = -1. But if you put b less than 2, it’s got no solution. This graph using the Desmos Graphing Calculator may help you see how it works, for that case, re-arranged as $x^2 = -2x - 1$

Notice that the graphs meet at x = -1.

And here it is for the equation $x^2 = -x - 1$, a rearrangement of the equation $x^2 + x + 1 = 0$which has no real solution.

I can’t find a genuine news story of this nature. There’s a lot of fake news out there about Nibiru. They are just totally made up stories and sometimes they can look convincingly like a real news website.

The whole thing is just BS and the only “news” about Nibiru is in fake news websites, the “red top tabloids”, sites like “Before It’s News”, Coast to Coast FM and similar dubious news sources. Another source is from youtube videos by uploaders who some of them earn thousands of dollars a month from the ad revenue. Others know nothing of astronomy but have told that any unexplained bright light in the sky is “Nibiru”.

Of course, if you have never paid much attention to the sky and then start to look at it you will see many things that surprise you. I even get contacted by people who get scared because they see the Moon in daytime (it’s been in the daytime sky for most of their entire life, except at times close to new moon and full moon, and they never noticed). Similarly if you have never tried to photograph the sun before you will spot lens flares and offset lens reflections for the first time. If you have been primed by these hoaxers to assume that everything you see that’s bright and unexplained is “Nibiru” then you end up getting more and more scared, maybe eventually scared even to leave your house, or you may end up holed up in some kind of bunker in the countryside. You may also notice that the sun rises at a slightly different position each day and get convinced that the Earth’s poles are shifting. Again this is perfectly normal and part of how the seasons work, why we have summer and winter. It’s been doing this for their entire life and they never noticed before. It’s so sad that anyone gets scared by this utter codswallop.

No astronomer gives this the time of day. It’s total nonsense and BS. See for instance my

• Who else says Nibiru is nonsense?
• Nibiru Bullshit Tester - How to check if they know anything about astronomy
• Is Nibiru a Hoax?
• Debunked: Nibiru will hit Earth on [Insert Date here]

It’s the nearest small number rational approximation. You can use the method of continued fractions to get a series of best approximations

3/1, 22/7, 333/106, 355/113, 103993/33102, 104348/33215 etc.

These are the best approximations in the sense that for instance 355/113 is closer to PI than any fraction with a lower denominator than 113.

If you want to memorize a reasonably exact value of PI then it’s easier to memorize its expansion as 3.14159

That’s more accurate than 22/7 = 3.1428 and 333/106 = 3.141509.

What is easier to remember, 22/7 or 3.14? Admittedly, 22/7 is a smidgen closer to PI than 3.14 (difference of 0.00126 for 22/7 and 0.00159 for 3.14)

The approximation 355/113 = 3.14159292035 gives you one extra decimal place

compare PI = 3.14159265358979

You could say that 355/113 has a slight advantage over 3.141592 as it has one less character (including the division sign), and it’s a lot closer to PI than 3.14159. On the other hand, PI to six decimal places is actually 3.141593 (rounding up).

Anyway - I think it is more practical to remember PI as 3.14159265 than as 355/113. It’s shorter than a typical telephone number, and is as many places as you need except in very specialist calculations. But the ratios are fun :).

That the historical Buddha was born perhaps as early as Thales of Miletus, at the time of the birth of Greek philosophy, and at any rate, before Plato. His traditional Therevadan birth date is 624 BC, though he may have been born as late as 500 BC or even later. The birth date for Thales is the same year, 624 BC. Plato was born 428 BC or a few years later. For discussion of the different attempts at a chronology to work out when he was born, see Notes on the Dates of the Buddha Shåkyamuni

Lumbini, birthplace of Buddha Shakyamuni - rediscovered by Nepali archaeologists at the end of the nineteenth century when they unearthed a pillar that King Ashoka placed here.

• Lumbini - Wikipedia
• Lumbini, the Birthplace of the Lord Buddha
• Lumbini the Birthplace of Buddhism, Spiritual places in Nepal

The earliest date matches the birth of Thales of Miletus 624BC - this is the birth of Greek philosophy - before Pythagoras, never mind Plato and Aristotle. The range of dates spans pretty much the entire range of early Greek philosophy. At any date Buddha’s birth, and quite probably his paranirvana or death, predates Plato who was born in the late fifth century BC, 428 BC or maybe a year or two later, up to 423 BC.

I find that rather striking, and surprising.

Interestingly we know far more about Buddha Shakyamuni’s teachings than we do about Thales, although Northern India didn’t have writing at the time of Buddha, while Greece did have writing of course. India has a long tradition of memorizing texts accurately, from before it had writing. Writing was introduced to Northern India a century or two after Buddha, as it had it by the time of King Ashoka, a couple of centuries or so BC.

Note, later Buddhists sutras do mention writing. But the earliest ones, the ones that may have been memorized since the time of the Buddha himself, they don’t according to the Pali scholars who have studied this (the Pali canon is vast like an encyclopedia, it also includes some texts that all scholars recognize as later but most of the texts are very early). For more detail, see Robert Walker's answer to Was Buddha literate?

Anyway let’s have a look at a few of the things we know about Thales, who just possibly might have been a contemporary of Shakyamuni Buddha in Greece..

Thales was a geometer as well as a philosopher, and Thales' theorem is attributed to him - that the angle at B in this diagram is always a right angle where AC is a diameter.

He may also be responsible for the Intercept theorem.

He is reported as having measured the height of the pyramids by measuring their shadows (somehow, there are various ways he could have done it). He might have done it empirically or semi empirically by noticing that at certain times of day the length of an object’s shadow is equal to its height, or he may have used more elaborate reasoning based on similar triangles.

He was also keen on astronomy. If Herodotus’ account is valid, he is also the first person in recorded history to successfully predict a solar eclipse. Eclipse of Thales - Wikipedia on May 28, 585 BC (probably it involved a measure of luck if the story is true).

Not much is known about his philosophy, because his work hasn’t survived, so what we know is based on what other philosophers like Aristotle wrote about him. But he probably thought that everything is made up of water as a fundamental substance and that our Earth is flat.

That may have been revolutionary at his time. Sambursky wrote.

“It was Thales who first conceived the principle of explaining the multitude of phenomena by a small number of hypotheses for all the various manifestations of matter.”

Later Greek philosophers were to run with this idea, which went through many stages eventually leading to early ideas of the atomic nature of matater. Plato recorded as an anecdote about him, that he fell into a well while gazing at the stars, see The Astrologer who Fell into a Well

For more about him:

• Thales of Miletus - Wikipedia
• Thales biography

If this is on Earth: water but frothed up with air, or perhaps - carbon dioxide?

If I can somehow arrange to have lots of air mixed in the top layers, and then less and less the further down I go, it should decelerate me slowly and break some of the impact. I don’t know if it could be made enough to survive a fall from height. Then you want the frothing localized or somehow to stop as soon as you fall in, or you’ll sink to the bottom of the frothy water and getting water in your lungs is dangerous so it would be hard to breathe -or better - you are equipped with a robust aqualung or similar with plenty of air to breathe when you jump, to get you to safety afterwards.

You could also have fluids of decreasing density one above the other. But you don’t get liquids that much lower density than water, not enough to make a difference. Apart from liquid helium, density about an eighth of that of water. That’s in another answer already, and is very sci. fi. Also, that would freeze the water, you could have ethane then methane, gases / liquids of decreasing density and freezing point poured at the last minute - and how do you then survive when you return to the surface of the water after your dive, now floating beneath layers of ethane, methane and liquid helium? So I can’t really see where to go with that except by frothing up the liquids again. But you want water you can float on ideally so that takes us back to water. If you are permitted to modify the atmosphere as well, you could arrange to have denser gases to fall through with lower terminal velocity which might help (and again closed system breathing)..

However, if you allow me to pick a location, as you didn’t say where this is, and I can choose anywhere in our solar system, well it’s easy. There’s one obvious place.

Let me pick Titan with an insulated suit (because it is incredibly cold there), and air to breathe (there’s no oxygen in its atmosphere) - but you don’t need a pressure suit because the pressure is the same inside and out. Just heat insulation and air to breathe.

In that case the gravity is only 1.352 m/s² and the atmosphere is higher pressure than Earth’s, 45% higher

It’s oceans are somewhat lower density than water, with a mix of methane and ethane. But you’d survive anyway. Terminal velocity would be very low. A tenth of your terminal velocity on Earth. Calculated here as 6.9 meters per second (about 15 miles per hour): At what g is terminal velocity not terminal? (see answer by Mark Beadles). That’s the same speed you are traveling on Earth if you jump down to the ground from a height of 70 centimeters.

So, I’d choose to fall 2,000 feet into its ethane / methane seas. They would provide a bit more cushioning for the impact. But you don’t really need it and it might be inconvenient to end up under the surface in your spacesuit (you would surely sink). So maybe just try to target a puddle instead, for the purposes of fulfilling the conditions of the question of landing in a liquid :).

See also

• Let's Colonize Titan
• Atmosphere of Titan - Wikipedia
• Interplanetary Cessna
• Liquids and Densities
• What is the termial velocity of a falling human on other planets? • r/askscience

Interesting question. The sun never goes dark, not for trillions of years. But it does have an interesting future

• Gets brighter gradually for maybe 5.4 billion years. All this time it is burning hydrogen into helium in its core
• Its core now is saturated with helium, but not hot enough for helium burning. So it starts to collapse. This brings more hydrogen into the hot center so then it burns hydrogen in a layer around the center. It’s now a “subgiant”. This causes the sun to expand and cool down but because it’s so big (a couple of hundred times larger than today) it’s also much brighter overall (2000 times brighter).
• It’s now a red-giant like Arcturus. In this phase it keeps throwing off lots of matter, and after a billion years it’s lost a third of its mass.
• Next it ends up with so much helium in its core that it’s almost all helium with no hydrogen left to burn. At that point it is degenerate matter, in the core, so no proper atoms. Too compressed for that. When it runs out of hydrogen there, it suddenly burns around 6% of its core from helium into carbon (by nuclear fusion as usual). Its core by now is 40% of the sun’s mass - so that’s equivalent of 2.4% of our sun’s mass in the form of helium, all burnt away in minutes in a quick helium flash. All that converts the core into carbon - which can’t burn any more because the star isn’t hot enough.
• It now shrinks to around 10 times the current size of the Sun, 50 times its luminosity, so though much smaller and not so bright as the red giant, it’s still a very bright star. It’s now in the the red clump or horizontal branch (a bit above the main sequence stars in the Hertzsprung–Russell diagram) and it stays there for about 100 million years until the helium is exhausted.
• When it’s exhausted, the sun starts burning hydrogen in a shell over the helium, alternating with times when it burns a shell of helium, in the asymptotic-giant-branch phase, for about 20 million years.
• After that it gets unstable and throws off lots of matter and with lots of heat pulses, Towards the end it ends up 5,000 times brighter than our Sun, and it grows so large it fills Earth’s orbit. Earth is probably already gone by now, unless of course you have technological beings changing its orbit and protecting it in that future. This is when it creates a “Planetary nebula” after the last of its thermal pulses. Our sun is predicted to have four of them before it throws off its outer envelope. The whole process takes a very short 500,000 years.
• Now, it’s just the exposed core, with half of its mass already thrown into space as the planetary nebula. This can’t fuse any more as it’s just degenerate matter. It never got so dense as to fuse higher elements like carbon. So it just sits there as a “naked core” or a white dwarf. Temperature of 100,000 K. It then just stays there for trillions of years, eventually fading to a black dwarf (no star in our universe is old enough to be a black dwarf though white dwarfs are commonplace).

There I’m summarizing the Wikipedia on this in the Sun life phases - but in my experience it is very accurate on things like this as a result of checking many of their articles - astronomers seem to be very active in keeping it accurate - so though I haven’t checked those figures, for something that has had as many astronomers eyeballing it as this, I’d have thought it would be correct. (There are other topics where in my experience wikipedia is very unreliable).

This diagram summarizes the future evolution of our Sun based on the Hertzsprung–Russell diagram - a rather simple idea - you chart stars according to their luminosity, and their temperature. You can read the temperature easily from their colour spectrum. So those are things you can measure very easily with simple measurements, for any star, so you can just observe a star and pop it on the HR diagram. It turns out that all stars start off on the “Main sequence at the bottom of this diagram and stay close to it for billions of years, so typical diagrams like this, say for a galaxy, or a star cluster, have lots of stars near the main sequence line, and this is how astronomers began to figure out the basics of stellar evolution.

File:Evolution of a Sun-like star.svg - Wikipedia

This shows the position of many well known stars on the HR diagram.

File:Hertzsprung-Russel StarData.png

So - it’s very unlikely that anything could remain habitable all the way through to the white dwarf phase especially during those thermal pulses and the end when it throws off half its mass in a planetary nebula. But life could survive maybe by jumping from one place to another - and if there are technological beings here by then, who knows what they could do with billions of years old megatechnology.

But - surprisingly, there are planets sometimes found orbiting white dwarf stars. This is the first to be discovered. Astronomers find the first planet known to orbit a white dwarf

The big question is whether they were there all along and somehow got brought inwards at some point or they formed from scratch.

Either way - might they have life? Well - they seem unlikely candidates, but they are worth searching because - they would be amongst the easiest for us to observe. It’s like that story of looking for your keys beneath a street light if you lost them in the street. We can look there more easily than many other places, and just possibly might find life, or conditions where life could evolve again from scratch. See Does Life Exist on Planets Orbiting White Dwarfs?

So anyway back to Europa. I don’t think there’s any chance of life surviving there right the way through. It’s mainly ice and - it turns out that after the Helium flash - Europa is too close to the Sun to be in its habitable zone. But it would be possible for life to flourish there right through to the sub giant and red giant phase when the habitable zone ranges from 2-9 AU. Jupiter is 5.2 au from the sun. At that point it would no longer need tidal heating, and the surface ice would melt. Figure for habitable zone here See Can Life develop in the expanded habitable zones around Red Giant Stars?

Now - could it retain its water at that point? Well if exposed to a vacuum it would lose it quickly. I did a calculation here for Ganymede, which is a bit larger than Europa. Robert Walker's answer to Do water planets exist? - I worked out that it would vanish completely in only 67 years if directly exposed to vacuum without any atmosphere.

However it would quickly form a water vapour atmosphere. I figured out that it could last for several million years in that case. All that assumed fresh water, would be slightly different for salty water but I didn’t try to estimate that. Then finally it could develop a layer of scum on the top, especially if it had photosynthetic life. If so that could reduce the rate of water loss, depending on the nature of the scum. But if it stops the water evaporating (rather than encouraging it) then maybe it could survive for tens of millions of years or more.

So - maybe in natural course of events Ganymede becomes habitable. Europa being smaller and warmer loses its water a bit more quickly but some gets to Ganymede. Maybe if somehow it develops a surface layer of scummy organics that’s very good at retaining the water it can last all the way through the billion years of the red giant phase. For instance, suppose it has photosynthetic life - but there’s not much protection from UV, so the life is killed on the surface but survives just below the surface - the dead life maybe is very good at protecting the water from evaporation.

Once it goes through the helium flash though, Europa is toast, it would just boil away as it would be inside of the habitable zone, and same also for all of Jupiter’s icy moons. The habitable zone now extends from 7 to 22 au. So now it’s the turn of Saturn (9.6 au) and Uranus (19.2 au), from Can Life develop in the expanded habitable zones around Red Giant Stars?,

Saturn has Enceladus which may well have life. It also has Titan which has methane and ethane oceans which may have exotic forms of life, but they won’t be able to survive once it gets that warm, they depend on very cold conditions. If they can migrate (if they exist) they would now be looking for niches in the very distant parts of the outer solar system way beyond Neptune and Pluto to survive). However it probably also has a subsurface ocean may have life there too.

I can’t imagine Enceladus lasting long as it is so small unless it has very evaporation preventing scum. But Titan could last a long time as an ocean world with scum + water vapour atmosphere.

Then we have the thermal pulses and the planetary nebulae. That’s only 500,000 years. Short enough so that even if the life survives in dormant form it could revive after that time. So - need some way for the life from Saturn and Uranus to find its way into the newly forming planets around the white dwarf - or else those are planets that migrate inwards in which case - maybe there’s lots of inward motion of matter to bombard them with life giving asteroids or comets from impacts into Titan?

So you could imagine life managing all the way through to the white dwarf phase I think. But in a series of stepping stones. Not in one location all the way through.

BTW in the near future starting perhaps half a billion years into the future (may seem close but that’s long enough for humans to evolve all the way from the smallest microscopic creatures a second time) - as the sun warms up, Mars, and then maybe Ceres and Vesta and perhaps other large asteroids also could be useful oases for life when Earth is no longer habitable, and before Europa, Ganymede and Callisto get their turn.

All of this is not taking account at all of technological intelligent creatures which could do many things to ensure habitability. E.g. if they can move Europa - well within the capability of megatechnology - and cover its surface with ionic fluids, or even, give it an artificial atmosphere and put an artificial covering over that atmosphere to hold it in - or whatever - they could keep it habitable all the way through perhaps. Or do many things. Perhaps by then they live in the Oort cloud using fusion reactions for mini suns and are so far from our Sun that what it does hardly bothers them and they just enjoy watching the planetary nebula from a safe distance. There’s no way to predict once you have megatechnology + intelligence, just depends what they decide to do in that distance future, which would depend on their motivations which we can’t hope to predict really.

If you spot any mistakes in this, however small or major, please don’t hesitate to say, for instance in the comments below.

Oh, I think it’s almost the opposite. If there is life already there, we probably can’t live there. First a bit of context about what exactly they hope to find.

WHAT TO ASTRONOMERS HOPE TO FIND IN THE NEAR FUTURE E.G. WITH THE JAMES WEBB TELESCOPE

Astronomers when they are looking for habitable planets mean any kind of life including microbes. Our Earth only had microbes for much of its history - so maybe nearly all planets have microbial life. Hard to say with only one example, but it’s our only starting point for now.

But would we detect a planet with only microbial life, even if it is a very habitable ocean world like ours? There’s doubt about that, because, life on Earth was probably undetectable from a distance with the tools we have available until terrestrial life evolved - because everything happened in the sea and the atmosphere was more or less in equilibrium. Sometimes oxygen excess, earlier on perhaps methane excess, but never both together in any quantities until recently. The problem there is that you can get either an oxygen or a methane excess easily by natural processes. What is hard to get without life is both of those together (or two other gases that react with each other quickly) though even that is also possible to some extent without life.

The main ways we have for detecting life at a distance is through changes in the atmosphere - or - unusual colours and spectra from the land. Not much we can do about detecting life that’s in an ocean directly (apart from really huge planet scale algae blooms or some such). And not much we can do to detect it indirectly either - changes in the ocean chemistry won’t be anything like as easy to detect from a distance as changes in atmosphere chemistry. Life in the oceans does affect the atmosphere, but in our Earth’s history anyway - it did it in a way that could be mimicked by natural processes.

So if we detect life unambiguously around a distant Earth like planet, it’s probably going to have spread to the land anyway and quite probably multicellular - just to go by what happened on Earth at the stage when life here got (fairly) easy to detect from afar. They would also try other things to search for including the “red edge” of chlorophyll vegetation - or the unusual colours of vegetation of all sorts, or fluorescence etc. All that again likely to work best if it has spread to land. Another possibility is to detect industrial pollutants in the atmosphere, or of course a signal from ET or megarchitecture, in which case it’s got intelligent life like ourselves.

Apart from that it’s a rather strange situation - where they would search maybe a thousand planets, but can’t say of any particular one that it has life. But statistically some of them probably do because of excesses of oxygen or methane that just seem on average to be more than you’d expect from natural processes, to have so many with such large excesses.

So, maybe they detect terrestrial life at a similar stage to Earth or later. Or else if that’s very rare, maybe they find lots of planets with microbial life but they’d need a large sample of those to have a decent chance of concluding that some of them are inhabited (without knowing which). But they could find anything of course, Earth might or might not be a good example of what to expect. Or they may even find intelligent life like ourselves that’s also got technology (intelligent life without technology wouldn’t be detectable, and you could have intelligent sea creatures just as hard to detect as the almost undetectable microbes in the sea).

More on this at the end, anyway back to the question.

IF THERE IS ADVANCED MULTICELLULAR LIFE THERE

First, if there is advanced life there, plants, animals etc, probably we can’t eat much except for sugar and alcohol.

Unless, that is, we are both results of seeding by the extraordinarily advanced Star Trek Ancient humanoids :).

Some of this food could easily be toxic to humans, or vice versa, even if we are all biologically closely related. In the Star Trek universe then they have an underlying hypothesis that all the planets with the various humanoids on them were seeded by the Ancient humanoids, so it's reasonable that they all use the same amino acids as Earth life. That could also be the situation if the ETs and us have a common shared microbial ancestor, e.g. all our planets seeded by life around earlier stars that pass through the forming nebulae.

In Star Trek they go one step further (rather improbably) that the humanoids are so closely related they can actually interbreed (again a result of the amazing mastery of the processes of evolution of the ancient hominids, able to seed the worlds with just the right organisms to ensure that hominids would co-evolve on all these worlds pretty much simultaneously several billion years later), which would suggest that they can eat just about anything we can. Still, even then, they need to take some care.

Humans vary a fair bit in their tolerance to foods and in allergic reactions that can be deadly. A Thanksgiving Look At Great Meals In Star Trek History

IF THEY ARE INDEPENDENTLY EVOLVED - WHY THEIR PROTEINS MAY NOT BE NUTIRITOUS FOR HUMANS

Humans need amino acids to stay healthy. When we digest food, any proteins are broken down first into polypeptides, then peptides, then into their component amino acids. Protein Digestion and Absorption Process - Video&Lesson Transcript | Study.com

So, it seems that what matters are what the amino acids are in the food. There are nine essential amino acids that humans need in their food. Essential amino acid

There are an estimated around 4,000 possible biologically reasonable amino acids in one computer search. Alien Life Could Use Endless Array of Building Blocks. And many of them occur in nature. Out of those, life uses 20 (or 21 or 23 depending how you count them) (Amino acid). Of course many of those won't occur in nature - but Earth life also uses some amino acids that don't occur naturally either. Also other searches might change or refine those numbers.

It's clear that there are many more amino acids than those used by life. For instance, 52 amino acids have been identified in the Murchison meteorite. Amino acids in meteorites.

So, the food is likely to be missing essential amino acids. It's also likely to include extra amino acids that our body is not used to.

And then, the amino acids are asymmetrical, and any of those amino acids can be in either its left or right form to build the proteins. We can only use it in its "left hand" form.

OTHER ESSENTIAL NUTRIENTS

Humans also have many other essential nutrients e.g. vitamins, that have to be in our food or eventually we'll die. Essential nutrient

Their equivalent of our vitamins, for instance, instead of being health giving, may be Antimetabolites for us - drugs that interfere with the normal functioning of the cell.

And vice versa, our vitamins might interfere with their metabolism equally.

And the trace elements we need might some of them be deadly to them and vice versa.

IF IT IS NOT RELATED TO EARTH LIFE

So, unless related to us, it's not going to be able to give us all the amino acids and vitamins and other essential nutrients we need to survive, bar an extraordinary coincidence.

Barring an extraordinary coincidence, it wouldn't have toxins that are targeted at humans or animals specifically. But there are many things that are poisonous for us, so it doesn't need to specifically target vulnerabilities in humans to do that.

For instance, maybe your ET just loves to eat hydrogen cyanide, or arsenic, or perchlorates. These are delicacies for them, but deadly to us.

COULD BE TASTY HOWEVER

Apart from that - well it could be tasty even if not actually nutritious. And it could have carbohydrates to give you energy.

SWEETENERS

Sugars seem quite possible.

Glucose, the form of sugar you have in fruit juice,

Seems reasonably possible they'd have something like that, simple carbohydrates that we may be able to eat. So you'd be able to use ET food as a source of energy at least.

At least you could hope to eat the icing of their cakes.

As other possibilities, maybe it naturally produces an artificial sweetener, e.g. Aspartame which is a combination of two amino acids.

Or Saccharin

Or lead acetate, which of course would give you lead poisoning if you used it a lot.

See Sugar substitute

ALCOHOL

Ethanol is simple enough, so good chance you can at least share a drink with ETs. That is, if they happen to also like alcohol, which of course depends on their metabolism.

Romulan Ale

TASTY POISONS

But tasting nice is no guarantee that it is good for you, or indeed not poisonous. E.g. antifreeze, as simple as ethanol chemically, just ethanol with an extra hydroxyl grouping, Ethylene glycol, tastes sweet.

And is so simple you can easily imagine an ET food including it.

But it is moderately toxic, and because it is sweet, sometimes children for instance drink it in large quantities, which can lead to Ethylene glycol poisoning and death.

OTHER CONDIMENTS

Of course also salt is tasty - sprinkling ET originated salt (maybe with trace elements) on your food might well be fine unless it contains mercury, arsenic or some such.

So there might well also be tasty condiments from ET planets.

Salt on Mars. But this isn't table salt, these are sulfates. Salts on Mars are always highly oxidized, so not much chlorides. Sulfates, chlorates, or perchlorates dominate them.

But you'd need to be careful, for instance, salt deposits on Mars consist of sulfates, chlorates and perchlorates with almost no chlorides. The perchlorates, particularly, are poisonous to humans.

So, if an ET host offers you salt, you need to ask "what kind of salt?". In case they have a taste for perchlorates, for instance, as a condiment.

COULD CAUSE ALZHEIMERS OR OTHER TANGLE DISEASES

It could also contain chemicals that are similar enough to ones our body uses that it takes it up as food - but they are not quite identical.

Example:

L-serine, resembles

BMAA which is created by green algae.

It’s been suggested that BMAA can be misincorporated to cause tangle diseases like Alzheimers.

So - if it is similar enough so that you find it tasty - might be that your predilection for ET food gives you Alzheimers in your later life.

BE SURE TO STERILIZE YOUR FOOD AND NOT SIT IN THE SAME ROOM AS YOUR ET HOST - BEST - USE TELEROBITIC AVATARS

As well as that, you'd need to be sure to sterilize the food because the biggest danger I think would be from ET microbes. Which you might also get from the ETs themselves.

You might think that ET microbes would have no effect on a human, but the thing is - that though they wouldn't be adapted to us, our immune system also wouldn't be adapted to them. Just as you can have e.g. artificial implants that your body doesn't reject because it doesn't trigger your immune system, so also ET life could quite possibly invade your body and your immune system doesn't even notice it because it doesn't produce the chemicals characteristic of life. This has been suggested as a motivation for developing synthetic life in the laboratory - that you could create implants that the body wouldn't recognize as life and so wouldn't reject. See Xenobiology: A new form of life as the ultimate biosafety tool

Joshua Lederberg who took a special interest in this said about Mars life, which might not produce the same peptides and carbohydrates as Earth life:

"On the one hand, how could microbes from Mars be pathogenic for hosts on Earth when so many subtle adaptations are needed for any new organisms to come into a host and cause disease? On the other hand, microorganisms make little besides proteins and carbohydrates, and the human or other mammalian immune systems typically respond to peptides or carbohydrates produced by invading pathogens. Thus, although the hypothetical parasite from Mars is not adapted to live in a host from Earth, our immune systems are not equipped to cope with totally alien parasites: a conceptual impasse"

Then these microbes themselves, once they are able to make a home on and in your body, may make various chemicals that are toxic to you. Or interfere with your body functions. And the other way around, your microbes may make chemicals toxic to them.

Or another thought - just to think about - might they even just slowly eat you? What if you are edible to some of the microbes, general purpose feeders - and your cells don't realize what's going on? They will respond to the trauma but their reaction may have no effect on the ET microbes that just gobble up everything your cells create.

Bowl of yoghurt, photo by Schwäbin

If your host offers you live yoghurt, be sure to sterilize it first. Unless you have proved that our microbes and theirs are compatible first.

But as well as that - after visiting an ET and sharing a meal with them, your lungs, sinuses, eyes, stomach, the surface of your skin, and every accessible part of your body may be inhabited by trillions of ET microbes that your body has no idea needs to be eliminated. Microbes that are used to living on the skin and inside the stomach etc of an ET host that has a different biology from you.

And of course would be the same likewise for them, they'd surely find that at least a few of the hundred trillion microbes in ten thousand species that make human bodies their home have jumped over to them and are inhabiting their body as well.

They may be well behaved bacteria, perfect symbionts for the ET. But are they going to be as well behaved for you with the different biochemistry of your body, which may not recognize them as life?

This is from my What Food Can You Share With An ET?

IF WE CAN’T LIVE THERE RIGHT AWAY, COULD WE GROW FOOD THERE THAT WE CAN EAT?

Now, that doesn’t really address the question completely. Maybe Earth life can be compatible with other forms of life. Or maybe some biochemistries are compatible and play nicely with us and others don’t. We can’t eat their food, except things like alcohol, salt, sugar etc, but perhaps if we are lucky we can plant our own crops there and they grow fine and we eat those. And perhaps we can breathe the air and there is nothing in it that’s poisonous to us, and no microbes that eat our alien (to them) biology.

Or it might be that they are so incompatible that our crops just can’t grow there at all - the microbes in the soil just don’t play nicely with them. Or they have pests that just gobble up our crops and the crops have no defenses and maybe they gobble us up too with our bodies mounting no defenses. Any of that seems possible.

Even if there is only microbial life there - would it be compatible with Earth life to the extent we can have a mix of Earth and ET life? Or is the only way to grow food on another world to somehow sterilize their entire planet first?

Perhaps it depends on the planet. Some have compatible life that plays reasonably nicely with Earth life and some just don’t?

That might be an issue even with Mars. We don’t know enough about it yet to know if there is life there now, or was in the past. It may well have had life in the past though we don’t know, and if it did, there’s a decent chance it is still there. So would it play nicely with Earth life, or not? There’s no way to know. Can we have both forms of life on Mars at once, or must it be only the one or only the other? Again nobody knows yet. Though we’ve sent many missions to Mars we haven’t searched for life there since Viking in the 1970s. All the other ones since then have been mainly geology missions, and nothing we’ve sent since Viking would be able to detect life in, say, the driest part of the Atacama desert. Also we haven’t sent anything to the places that scientists now think are the most likely to have habitats on present day Mars (it’s difficult sterilizing our robots well enough to visit such places).

Luckily there are plenty of other places we can live even in our solar system. To start with, the Moon, ice at the poles. Also materials from the asteroid belt and later on from comets. It’s far easier to live on Earth of course, and always will be surely, as we evolved here. It’s the place we are adapted to. Anywhere else has to be forced into Earth’s mold, “terraformed” in some way. But we could live comfortably perhaps in large habitats, kilometer scale, if those can be made low maintenance, with closed system ecology inside. I’m skeptical about whether we will ever live on other planets except inside habitats like that myself. Terraforming seems easy on paper - but I think the challenges would be formidable, trying to speed up what took hundreds of millions of years on Earth, and with no guarantees that it will get to where you want, it could go in many surprising directions.

ABOUT WHY LIFE ON A PLANET LIKE EARTH WOULD PROBABLY BE HARD TO DETECT THROUGH MOST OF ITS HISTORY UNTIL IT DEVELOPED TERRESTRIAL LIFE

The problem is that for much of Earth's history, before the land was colonized, a lot of the biological activity happened in the ocean and the ocean sediments.This would have been largely decoupled from the atmosphere.

Sometimes there was an excess of oxygen in the atmosphere, but the amount of oxygen present is hard to estimate. It should have been easily detectable for the last 500 million years, and also there may have been an oxygen "overshoot" from about 2.2 billion years ago to 2 billion years ago. Apart from that, howeer, although there was oxygen in the oceans, the amounts in the atmosphere could have been too low to spot remotely.

At other times, there was an excess of methane in our atmosphere (from about 3.8 billion years go to 2.5 billion years ago). However it is difficult to have large seasonal variations in methane without a terrestrial biosphere, so it wouldn't be a clear cut case that it was the result of life, as seen from a distance.. It's also hard to have both methane and oxygen in the atmosphere together in detectable quantities, for an ocean planet without a terrestrial biosphere.. Ozone might be easier to detect.

Their general conclusion is that it's hard to detect atmospheric biosignatures in an ocean world like Earth, even though this would count as one of the most habitable types of planet. It may only become easy to detect life on a world like ours once it develops a terrestrial biosphere. Of course we only have our one example to judge this by, but our Earth only developed one at a very late date. Another civilization looking at our Sun from a distant star probably would not have managed a definite detection of any life here for most of Earth's history, at least, not using the methods we are likely to have available to us in the near future.

Quoting from a paper by Christopher Reinhard et al, published in April 2017, "False Negatives for Remote Life Detection on Ocean-Bearing Planets: Lessons from the Early Earth" (emphasis mine)

As a proof on concept, we briefly summarize the remote detectability of O2/O3, CH4, and the O2-CH4 disequilibrium throughout Earth's history. Our analysis suggests that the O2 - CH4disequilibrium approach would have failed for most of Earth's history, particularly for observations at low to moderately high spectral resolving power (R≤10,000). In addition, it is possible that O2 /O3 may only have been applicable as a potential biosignature during the last ~10% of Earth's lifetime. As a result, most of our planet's history may have been characterized by either high abundances of a single biogenic gas that can also have significant abiotic sources (e.g., CH4 ) or by a cryptic biosphere that was widespread and active at the surface but remained ultimately unrepresented in the detectable composition of Earth's atmosphere. Finally, we argue that cryptic biospheres may be a particularly acute problem on ocean-bearing planets, with the implication that many of the most favorable planetary hosts for surface biospheres will also have high potential for attenuation of atmospheric biosignatures.

and from the final Discussions and Conclusions section:

"Our analysis suggests that a planet with a biosphere largely (or entirely) confined to the marine realm will in many cases remain invisible to remote detection as a result of biosignature filtering by ocean biogeochemistry—a difficulty that may apply to both presence/absence and thermodynamic techniques. Our analysis suggests that the possible detection of oceans at a planet's surface (Robinson et al., 2010; but see Cowan et al., 2012) is a critical piece of contextual information for validating potential atmospheric biosignatures, and that planets with terrestrial biospheres (e.g., partially or entirely subaerial in scope) may be the most readily detected and characterized because of their more direct geochemical exchange with the overlying atmosphere. Ironically, in some cases planets that are very conducive to the development and maintenance of a pervasive biosphere, with large inventories of H2O and extensive oceans, may at times be the most difficult to characterize via conventional biosignature techniques."

In this earlier paper from 2014, "The future of spectroscopic life detection on exoplanets" by Sara Seager, she makes a similar point, that even with present day Earth then the methane signal is far weaker than the oxygen signal and that in the past, when one of these signals is strong, usually other is very weak. She recommends that to have a decent chance of detecting life on a planet like Earth, we need a large pool of planets to observe. She also suggests that we also search for a single active gas well out of equilibrium, by much more than you'd expect from the dissociation effects of the sunlight, and that this might give results at an earlier stage, but would lead to false positives, so the result would just be a probability that one of the planets being studied has life..

"The Lederberg–Lovelock approach could be useful at the time when hundreds or thousands of rocky exoplanets have observed atmospheres—to increase the chance that two spectroscopically active gases that are redox opposites might simultaneously exist in the lifetime evolution of a planet. In the shorter term, a different approach is needed to optimize our chances to detect biosignature gases, if they exist, around a handful of accessible potentially habitable worlds. (Note that subsurface life is problematic for astronomical techniques because remote sensing may not be able to detect weak signs of life by biosignature gases coming from the interior.)"

"An idealized atmospheric biosignature gas approach is to detect a single spectroscopically active gas completely out of chemical equilibrium with the atmosphere that is many orders of magnitude higher than expected from atmospheric photochemical equilibrium. False positives will, in many cases, be a problem, and in the end, we will have to develop a framework for assigning a probability to a given planet to have signs of life."

In her conclusion she suggests that we have a sample of at least 1,000 Sun like stars, in order to have decent statistical evidence of the presence of life on some of them, though because of the problem of false positives, one might not be able to say of any of them definitively that it has life.

This last bit is from the section

• Lovelock's method wouldn't even have detected life on Earth for most of its history!

in my OK to Touch Mars? Europa? Enceladus? Or a Tale of Missteps?

No, it’s nonsense, total BS. Promulgated by youtube uploaders and bloggers who don’t have the slightest clue about the basics of astronomy.

It's like someone who claims to be an expert on sport, who in the next sentence says that Usain Bolt is a top seeded tennis player and won Wimbledon. If you know the basics of astronomy, the things they say are as absurd as that. They give away their complete ignorance of astronomy within a couple of sentences.

"INVISIBLE" BROWN DWARFS

By way of example, they read in genuine astronomy articles that brown dwarfs can be spotted in the infrared when far from any star even in pitch darkness. They conclude from this that they are invisible in ordinary light - that's like concluding that you are invisible because you are warm. Since when did warming something up make it invisible?

CAN'T SEE ANY DIFFERENCE BETWEEN A PLANET THAT NEVER COMES CLOSER THAN SIX TIMES THE DISTANCE TO NEPTUNE AND A PLANET THAT FLIES PAST EARTH

They read that astronomers think that there is a chance we may have a planet that's in an orbit that takes it at its closest to 200 au from the Sun and at its furthest, 1200 au from the sun - and if it exists, it must currently be at its furthest point or we'd have spotted it already easily. Neptune is 30 au from the Sun - so at its closest this "Planet 9" if it exists reaches more than six times the distance to Neptune - but to be not spotted yet, it has to be five or six times further away than that right now.

They conclude that this proves that they have been right all along that there is a planet in an orbit that goes from way beyond Neptune all the way to Earth's orbit and back again every 3600 years and is currently very close to us, "hiding behind the Sun" and just about to hit us or fly past us. Do you see a difference between these two scenarios? They can't seem to see any difference.

Bill Nye shows the scale of our solar system. If "Planet 9" exists then the closest it comes to Earth is six times the distance to Neptune. It must be several times further away than that at present or we'd see it already. Do you see a difference between this and the idea of a planet that comes as close to the Sun as Earth? They can't see the difference which shows the level of their understanding of astronomy.

IMPOSSIBLE PLANET

Their orbit is impossible because it would cross the orbits of all four gas giants. It can't keep missing them time after time because they have different orbital periods and it would hit one of them or be deflected out of its orbit or mess up our solar system within a million years. If our solar system ever had such a planet, it is long gone ,more than four billion years ago.

Even a 1 km comet would be easy to spot two years before it gets to Earth or Mars as we know from experience too, e.g. Siding Spring found nearly two years before its flyby of Mars and it was between 400 and 700 meters in diameter.

TWO SUNS

Then they go on to pile on the most absurd things. They say that we have two suns. I frequently get people asking me if it is true that we have a second sun and that we are in danger of it flying past Earth! Honestly. Don't they believe their own eyes? This is very easy to check. Don't stare at the Sun. Hold a finger in front of the Sun and then look to left and to right. Hold your finger at anothre angle and look above and below. Do you see a second Sun?

You have just disproved their theory that we have a second Sun.

BALDERDASH AND BULLSHIT

They say so many absurd things. They dress them up in videos with stirring sound tracks and authoritative sounding voice overs. And somehow people who know nothing about astronomy come to believe these things. Who knows if they are just unable to reason logically, or if they are hoaxing everyone else, or don't understand astronomy or what it is. Some are certainly just doing it as hoaxes for the ad revenue. And the ones who are selling Doomsday bunkers obviously have a commercial reason for running these stories. There are dozens of books on it also. It's like a minor industry, all based around balderdash and bullshit.

ASTRONOMY NIBIRU BULLSHIT TESTER - WOULD YOU READ A SPORTS COLUMN THAT STARTS "WHEN USAIN BOLT WON WIMBLEDON IN 2008..."?

I suggest you try out my Nibiru Bullshit Tester - and - well you don’t even need to do that. If a website or a news site or a TV channel or blog talks about a planet called Nibiru in all seriousness and they are not debunking it, then - just cross them off your list of people who know anything about astronomy.

To continue to read after that is like reading in all seriousness an alleged sports blog that starts "When Usain Bolt won Wimbledon in 2008 ...". It's even more absurd than that. Usain Bolt is a human being and could in principle win a tennis tournament, it is just not his sport. But their ideas don't even make logical sense in astronomy. They are bullshit through and through.

See also

• Debunked: Nibiru will hit Earth on [Insert Date here]
• Debunked: Nemesis is Nibiru - updated
• Nibiru Bullshit Tester.

More details

Here is an example video that might scare you. It’s a clip from a longer BBC documentary - not a news program.

I’ve added a comment to the youtube video clip here

Here are the most recent major extinction events

Middle Miocene disruption - 14.5 Million years ago - climate change due to change of ocean circulation patterns and perhaps related to the Milankovitch cycles?

Eocene–Oligocene extinction event - 33.9 Million years ago - Popigai impactor?

Cretaceous–Paleogene extinction event - 66 million years ago, Chicxulub impactor or Deccan Traps?

The really big extinction was 66 million years ago - so you’d expect the last two to have happened 66, 39 and 12 million years ago and the next one to happen 15 million years into the future.

They have gone back 250 million years and found what seems to be a statistically significant correlation with a period of 27 million years, but obviously it’s not an exact periodicity, and obviously also very variable, sometimes big spikes in extinctions, and sometimes nothing much happens. It's always been a controversial theory.

It’s obviously very approximate with the timing varying by millions of years, and sometimes there’s almost no effect - also the one 15 million years ago doesn’t seem to be due to comets, so if the theory was true, perhaps that one was just skipped.

At present only 1 in 155 near earth objects are comets. So we are certainly not in the middle of an increase in comets coming into the inner solar system at present. If the theory is correct, we’d expect this to happen around 15 million years into the future, give or take a few million years, with the event anywhere between a complete non event and something as big as the dinosaur extinctions.

But the theory has been ruled out pretty much by the WISE infrared survey which proved that we have no companion star, and we can’t have a companion brown dwarf either unless it is unusually cold, which would be very unlikely. For more details, see Debunked: Nemesis is Nibiru - updated by Robert Walker on Debunking Doomsday

This is based on my: Is Nibiru a Hoax?

Short answer: No, not if you mean “all life”, nowhere near. There is nothing that can do that in the current solar system for millions of years into the future. It will of course kill some life. It would have major local effects over a region up to several hundred kilometers from the point of impact, if it landed on land. If landing in the sea, it may or may not cause a tsunami. It would have no global effects.

IN DETAIL

No. It’s too small even to cause a tsunami, probably. If it hit the land, it would have major effects but only locally. Chances are it hits a desert or remote region that’s uninhabited or hardly inhabited - and you might get a few casualties, but probably not many. Chance of hitting a highly populated region is low. If it does, you’d get thousands, or even millions of deaths. But it is not big enough to have global effects.

With tsunami - then that’s not very well understood. But it’s different from a tsunami resulting from an earthquake. With an earthquake the entire floor of the ocean over a large area shifts up or down. But with a meteorite impact, the impact creates a temporary hole in the ocean which quickly fills up again. This means that you have a big wave goes outwards, but then it gets pulled back in again almost immediately. It’s hard to calculate the effects of this, but probably it has most effect if the asteroid hits in shallow seas close to the land. So the 800 meter asteroid - maybe it is just large enough for a tsunami if it is close to land and hits a shallow sea. The experts would probably argue back and forth on that.

You can use this calculator from Imperial College London to get a first idea of the effects of an asteroid impact. Putting in 800 meters, it would have major effects locally. At a distance of 100 km, wall bearing multistory buildings are blown down, most trees get blown down, windows shattered, and you will get a fine dusting of ejecta with occasional larger fragments, clothing, newspaper, trees etc all ignite. Calculated Results. It will make a crater over 17 km in diameter so you don’t have any chance of survival if you are within the region of that crater. Even out to 200 km clothing, newspaper etc ignites, but at 300 km you are safe from that. Glass windows would shatter. Calculated Results

That’s just one model of what happens, so to take it with a pinch of salt, but it gives a good first order idea of the results.

An asteroid 1 km or larger starts to have global effects, and from 10 km upwards, then it has major impacts on our climate for many years. But none of those would destroy all life on Earth. For that, you need an asteroid of several hundred kilometers in diameter. An asteroid as large as that would melt the crust globally and cause oceans to evaporate and the Earth would be sterile to some depth - but even then, you’d have some life still survive kilometers below the surface, probably.

However we haven’t had impacts large enough to do that since the early solar system. They stopped some time after the formation of the Moon. All the big craters and the lunar Mare on the Moon happened in a short time period of a few hundred million years - some think they may have happened over an even shorter timescale of just millions of years. The Apollo and other lunar missions in the 1960s through to the 1970s didn’t return enough by way of samples and data from the Moon to answer that question to that level of detail, because they only sampled a relatively small part of the Moon’s surface, so the question remains open.

However whether they ended 3.9 billion years ago, or just under 4.5 billion years ago, it hardly makes much difference. The main thing is we just don’t get impactors that big any more. This is clear from the cratering record of Mars, the Moon, Mercury and what we have of the geological histories of Venus and Earth. There are plenty of objects large enough to do that, but they are either in orbits that are stable at least for millions of years, in the asteroid belt, or they are beyond Jupiter. Jupiter protects us from the largest asteroids and comets by breaking them up, or they hit Jupiter or the Sun or are ejected from the solar system long before they can hit Earth. It doesn’t do such a good job of protecting us from asteroids up to a bit over 10 km in diameter.

Those can’t make all life extinct. At least a few percent of species will survive. And humans are great survivors. With just minimal technology, clothes, fire, boats, we can survive almost anywhere on Earth - many of us may have forgotten how to do so, but at the least, some of us would survive on shellfish, insects, fruit, seeds etc, and it just needs a few things like that to survive the impact, as they would ,and humans can cultivate them, travel to find them. We wouldn’t go extinct.

But we don’t need to worry about this happening at present anyway. The recent all sky surveys have been very successful in searches for the largest asteroids and we know the orbits of all the asteroids of 10 km or larger that could hit Earth. None are going to hit us in the next several centuries. We’ve found more than 90% of the 1 km ones and none of those will either. This is as expected because such impacts are very rare (not been any in all of human history) but we know for a certainty now about the 10 km ones and will find 99% of the 1 km ones by the late 2020s.

As for comets, at present only 1 in 147 is a comet, of the ones that pass Earth. That reduces the chance of a large comet 10 km in diameter or larger hitting us this century to a really tiny 1 in 100 million. We’d see a comet coming years in advance anyway, especially one that big, many years before. And Earth is such a tiny target, that it’s almost bound to miss us like the comet Siding Spring that had a tiny chance of hitting Mars but missed. But that 1 in 100 million is such a tiny figure we can ignore it. Smaller comets could hit us with a higher probability, but they are not the top priority of the searches at present because they also are very rare too compared with ordinary asteroids..

See also my Giant Asteroid Headed Your Way? - How We Can Detect And Deflect Them

With difficulty. 2 + 2 = 4 is a simple theorem which you can deduce from the definition of addition. There are ways to make 2 + 2 = 5, however, you can expect them to be rather bizarre.

First, it’s easy to prove that 2 + 2 =4. You just need the rule x + Sy = S(x + y) where Sx means the successor of x, or x + 1. With some more steps, with simple natural axioms, you can also derive a contradiction from 2 + 2 = 5. Proof indented so it’s easy to skip.

Define 2 = SS0, 4 = SSSS0, and 5 = SSSSS0, then 2 + 2 = (SS0 + SS0) = S(SS0 + S0) = SSSS0 = 4.

So, if you add 2 + 2 = 5 (or SS0 + SS0 = SSSSS0) as an axiom to your axiomatization of arithmetic, then you deduce immediately that 2 + 2 = 4 = 5.

So then, so long as you have the rules that

• Sx = Sy -> x = y, and that
• 0 is not the successor of any number

you end up, after a few more steps, proving that S0 = 0, contradiction.

Here I'm using the rules of Robinson arithmetic - leaving out the rules about multiplication - rules 1 to 5 here. See Robinson arithmetic You don't need the rule 3 that every number has a predecessor to derive a contradiction from 2 + 2 = 5.

So, basically it’s just Robinson’s first three axioms, the fifth one, and the definition of 2, and 5, and the contradiction drops out. This is one of the simplest axiomatizations of arithmetic, and though you can add more powerful deduction rules, so long as you have addition at all, with any ordinary form of arithmetic, then this is going to drop out quickly as an easy result, that 2 + 2 = 4, and that this is inconsistent with 2 + 2 = 5.

So, you have to change something there, to make 2 + 2 = 5. Here are a few ideas:

1. change the definition of =. You could easily have 2 + 2 = 1 (mod 3) with modulo arithmetic, or “clock arithmetic”. E.g. on a clock, then 6 hours after 8 o’clock is 2 o’clock. So 8 + 6 = 2. That’s called modulo arithmetic, 8 + 6 = 2 mod 12, - means you treat numbers that are 12 apart as equal. You add a rule n + 12 = n, and drop the rule that 0 doesn’t have a successor.

So, you can do the same with modulo 3 arithmetic (say). Add the rule that n+3 = n. Drop the rule that no number has 0 as its successor. But that particular modulus of 3 won’t work because 5 = 2 mod 3.

It's not so easy to define an = with 2 + 2 = 5. You want to have 4 = 5 for that to work, but how can that be if the modulus is greater than 1?

I can only see one natural way to do this, and it's rather trivial. Modulo 1 arithmetic, where every number is equal to 0, and the successor of a number is itself, and bizarrely you decide to work with SS0 and SSSSS0 even though they are both equal to 0?

2, have non associative equality, that Sx = x for every x, and then 4 = 5, similarly 3 = 4, but you don't have 3 = 5 (otherwise it is just the same as modulo 1 arithmetic).

Or some other experiment along those lines, strange re-interpretations of =.

3. Redefine addition. That's the easiest way to do it, There are many binary operations and you can just make one up.

Define (+) so that x (+) y = x + y + 1. Easy peasy. Done!

4. Redefine 5 to be a symbol for 4. You now need a new symbol for 5, and might as well redefine 4 to be a symbol for 5.

5. Paraconsistent logic. Just add 2 + 2 = 5 as a new axiom, and accept that your system of axioms is inconsistent.

6. Strange deduction rules or conventions. E.g. use the convention that in any equation, you always add 1 to the right hand side, so that when you say 2 + 2 = 5, you mean the same as what ordinary folk mean when they write 2 + 2 = 4. Similarly you'd write 3 + 5 = 9 etc.where by 9, when it's on the right hand side of an equation, you mean 8. Then 3 + 5 + 7 = 8 + 7 (because 3 + 5 = 9) = 16.

7. Numbers that are time dependent, or for some other reason are fluid and changing, as you go through the equations. So, 2 (+) 2 = 5 because one of the objects you are counting split in two. For instance a number system to count clouds. Have a convention that when you say A = B then the = sign here represents the situation after a time step of ten minutes, say. Then 2 (+) 2 = 5 means that 2 clouds + 2 clouds, ten minutes later, became 5 clouds. It would be empirical without a deduction system, you are just noting down observations, not proving a result about numbers.

Blue Sky and White Clouds - if you had a system that’s based on counting clouds, and the convention that in an equation, time increases as you go to the right, then you could have numbers with bizarre seeming properties if you didn’t know the convention. This is a special case of redefining =.

Or maybe you have some rule about formation of new clouds, or whatever the objects are. E.g. that whenever you have at least 4 objects, a new one gets added, and more generally, you add as many new objects as there are multiples of 4 on the left hand side. E.g. 4 (+) 6 = 12 because 4 + 6 = 10, that’s two multiples of 4, so you get two new clouds (or whatever) so the right hand side needs 2 added to it. This is different from redefining addition because 12 doesn’t equal 4 + 6, rather, 10 = 6 + 6, because you have the convention that it’s a time series increasing from left to right. It’s more like a strange deduction rule combined with a reinterpretation of = than a way of redefining +. You’d also have 10 = 12 = 14 = 16 = 19 = …

Or perhaps the numbers just change randomly, so sometimes 2 clouds + 2 clouds = 4, sometimes they = 5, sometimes 1, sometimes 23 etc. If you were talking about clouds and understanding = with this time convention approach then that’s the most likely situation.

It’s fun to imagine what it might be like to be extra terrestrials who live in a constantly changing environment, where the numbers of objects are never the same, so you can’t count in the ordinary sense - not even themselves. Sometimes they may wake up and find they have split into a dozen individuals, sometimes a whole community becomes a single organism, and it’s constantly changing, even from one minute to another - you can’t complete a thought process without the numbers of everything in your environment changing, so much so that their maths has some rather weird version of topology perhaps as its fundamental idea, not arithmetic, and when they develop numbers, maybe they would come up with some strange notions of = and other operations on numbers. Maybe they live in the cloud decks of a gas giant - and can’t see anything around them except clouds and vortices, constantly changing, and are similar in nature themselves.

There may be other ways. I'd say that 3, redefine addition, is the easiest way to get lots of self consistent theories that have 2 + 2 = 5.

See also my answer to Is it possible that an alien civilization has completely different mathematics than ours?

It’s a while since I did much by way of proving of theorems. But I can speak from when I was doing maths research in the 1980s through to 1990s.

I think the main difference between maths theorem proving and most problem solving is the length of time it can take. If you are doing a chess problem or crossword or some such (I’m not actually good at either of those but just as a “for instance”), you expect to finish it in minutes or hours. You wouldn’t expect it to take weeks or months.

Sometimes you can see an answer in a flash, but often, you may spend weeks, even months, trying to find an angle on a way to prove a central difficult theorem. Not that you spend all that time just working on that theorem, well you might, you might spend years on one theorem, some mathematicians do. But more often - it’s like, you have a fair number of things you want to prove, but there’s one central result that’s your main pre-occupation. “If only I could prove that!” So you have it on your mind and you keep niggling away at it.

Sometimes when you make the breakthrough, it’s through dreams. I didn’t actually solve problems in dreams myself, as far as I know, but often when I went to bed with a difficult maths puzzle on my mind, as I woke up the next day, I’d see the solution. It would just fall together and it’s like “why didn’t I see that before?”.

I think myself that it’s actually the transition between sleep and waking, when everything is a bit kind of blurry and you are not sure if you are asleep or awake, that one’s mind is in a way particularly fluid. When that happens, you may find a new approach that somehow gets you out of the logjam or the fixed tracks you got stuck on.

So, how do you start? Well, you aren’t going to suddenly solve it, if you haven’t got it on your mind. You try the most straightforward way of proving it first. Sometimes it is just obvious how to tackle it, and then you just follow your nose as it were, and you get to the answer. But often it isn’t. You try to prove it, and you find a big gap in your proof. So you learn something from that. That way doesn’t work. What else can you try?

You break it up into smaller bits. You think “If I knew xxx was true the theorem would be easy to prove - so can I prove xxx?”. You start with the things you know already and just play around, looking for consequences.

If you are doing research level mathematics then you have probably read many proofs in the past. So you also have various ideas you can try from those proofs “So and so used such and such to solve a problem like this, I wonder if it will work here too?”.

A lot of the research consists of taking results that someone else has already proved - and tweaking their proofs, taking them in unexpected directions.

A lot of it does consist of breaking big problems down into smaller ones, which you then can solve one at a time.

You draw diagrams, you may also try concrete examples. I want to prove something for all numbers - well - how does it work for 2, or 3, or 55 or whatever? Surprisingly often mathematicians don’t bother trying to look at concrete examples of what they want to prove. But sometimes, just by working through it like that, you may spot something about the problem that you just didn’t notice until you tried getting your hands dirty as it were, a bit like working on a bicycle or a car engine. You can’t solve it just by looking at it, you need to maybe take it apart and really get involved in it.

So you do all that and more. But often the solution just comes “out of the blue” as you are waking up, or when you are walking somewhere, or just in the middle of something else, That’s one of the most satisfying things about proving theorems in maths, the way that it can come together like that, suddenly sometimes, it was so confusing and complicated and then, all of a sudden, you get it.

ADDENDUM

A few other thoughts. First, your supervisor makes a huge difference, if you are a post grad in maths. In my case, my supervisor was Robin Gandy (who in turn was a student of Alan Turing). He had been involved in research into the logic of maths (“mathematical logic”) for decades, completing his thesis in 1952, only . Not only that, he’d talked to all the logicians of his time, been to their seminars, and he understood just about everything on the topic - modern maths is so specialized that often even the professors will only have a thorough understanding of a small part of their field of interest. He had a good grasp of pretty much all the research ever done in mathematical logic. He also had an amazing memory for detail, could mention details from a talk someone had given years earlier.

So, when you were stuck, he’d say “have you seen the research by so and so, it might help” and off you’d go and find that yes, what they did was relevant to your problem.

Your colleagues also. My supervisor had two other students at the time, all working in the same general topic area, and we often would bounce ideas off each other. Also the weekly seminars - they weren’t so helpful in a direct way - unless the speaker was involved in a research interest very close to your own - as most of the time you couldn’t understand 90% or even 99% of what the visiting speaker was talking about (unless you were Robin Gandy) but it still helped just to be exposed all the time to these various ideas, to chat to other logicians and so on.

Oh, it does happen. One of the earliest examples is King Ashoka. He lived just a couple of centuries after the Buddha, and he was involved in quite bloody military campaigns, until he converted to Buddhism. After that, he went on tours preaching the dharma, he encouraged dharma teachers, he put up pillars with dharmic texts on them and he ended up emperor of much of India. In that way he helped the dharma to spread over much of India.

Here is a photo of one of his pillars.

Ashoka Pillar, Allahabad, 1870

Buddha himself wandered around Northern India as a monk, with his begging bowl, and he taught anyone who wanted to learn from him. He first taught his five companions who had been following the path of asceticism with him, before his sudden change of direction towards the “middle way” when he became enlightened. So those were the first five people to follow his path.

He ended up having thousands of followers, who were drawn towards the teachings. Some just heard the teachings through hearsay from someone who had heard Buddha teach, and repeated his words to them, and immediately “got it” the essential meaning of what he was teaching. They must have been very receptive to the teachings to do that.

So - it’s often like that - spreading of the ideas. People hear of them. Nowadays you may read books, watch videos. In my case it was through a friend who I met who became a Buddhist nun shortly after I met her, and we talked a lot about the Buddhist teachings and I decided I wanted to follow that path myself eventually - after a fair while of listening to many teachings.

So there are many ways that the Buddhist teachings spread. Nobody says “go out and convert everyone to Buddhism” as happens in the more evangelical Christian churches.

But there’s no reason why one shouldn’t try to spread the teachings, and debate them with others etc, if one is in a position to do so and you feel that it is helpful to do so. Or in other ways, publishing books, building retreat centers, supporting teachers. It’s just a matter of ones own individual decisions.

It’s a bit like, say, astronomy. If you are keen on astronomy, you will tell people about it, anyone who is interested to listen. You might write a book on it. You might run a planetarium, or show the night sky through your telescope. That’s all proselytizing in a way. But you don’t feel “I have to convert everyone to astronomy” :). Yet, if you think it is worthwhile, interesting, inspiring, you naturally want to share this with others. So, proselytizing in this general sense is a natural thing, and of course, Buddhists proselytize about their faith too.

If it is far enough from the sun, way way beyond Neptune, then it could be heavier than Jupiter but almost certainly not as heavy as a brown dwarf (not heavy enough to have had a phase of deuterium burning when it was born).

If it is closer to the Sun then the limits are much more stringent. It’s much easier to see something if it is closer. If you reduce the distance of an object by a half, it is four times easier to see because the light from the Sun is four times brighter. But it is also four times larger, as seen from the Sun, or from Earth which is also very close to the Sun. The combination of both those effects is that a very distant object which is illuminated by the Sun gets sixteen times brighter if you halve its distance from the Sun. If it is ten times further away, then it is ten thousand times fainter.

So - that’s why it’s impossible that there are extra planets inside of Neptune’s orbit that we have never spotted to date. We’d see them easily. But go to, say ten times the distance to Neptune, and we could miss rather large objects already. If it is over three thousand times the distance to Neptune, we could miss even an object as large as Jupiter out there, easily.

LIMITS FROM THE WISE SURVEY

The original paper for the WISE results implications for planets is here:

A SEARCH FOR A DISTANT COMPANION TO THE SUN WITH THE WIDE-FIELD INFRARED SURVEY EXPLORER

The survey is for gas giants, and stars rather than terrestrial planets shining only by reflected light. It was an automated computer search with any tricky borderline cases investigated by hand.

The scans overlapped at the ecliptic poles. Each spot of the sky was photographed twelve times in the ecliptic, but hundreds of times at the poles. So there is no way it can miss planets that are out of the ecliptic - it is more sensitive to those than planets in the ecliptic.

Artist's impression of the Wide Field Infrared Survey Explorer which has produced the tightest constraints to date on Planet X.

It gives strong constraints on a Jupiter or Saturn sized object. A Jupiter sized object must be at least 82,000 au from the sun, and a Saturn sized object at least 28, 000 au. But a brown dwarf can actually be similar in size to Jupiter and also very cold and as well as that, it can be much darker than Jupiter in appearance (though not invisible in reflected light, - our Moon is as dark as worn asphalt and of course, easy to see).

Anyway, apparently it would be possible for a small, dark and very cold five billion year old brown dwarf to be in our solar system at a distance of 26,000 au, even closer than the limit for Saturn. That's 650 times the distance to Pluto, or 0.41 light years away - so far away it would take light over 21 weeks to get from the brown dwarf to Earth.

The survey could spot the more usual 150 K brown dwarf (that’s a very cold brown dwarf, -123 C) out to ten light years away.

That's why the idea of an unseen star is getting increasingly unlikely. It couldn't have missed a red dwarf star, even the smallest. It couldn’t have missed any kind of a star at all. It just possibly could have missed a very dark very very cold brown dwarf in a rather distant orbit. But brown dwarfs are less common than they used to be thought to be. As a result of the WISE survey again, it's now thought that there are six normal stars for every brown dwarf.

Also it's not too surprising that our solar system turns out to have no companion star, not even a red dwarf - the majority (54%) of sun type stars are single. And a binary system is less likely to have stable planets, unless the companion is very distant, or very close to the sun. And what planets it has are more likely to be in very eccentric far from circular orbits, again unless the companion is very distant. So, given that we live on a planet with a stable near circular orbit - there's a selection bias in favour of non binary solar systems on top of that 54% result.

Constraints on dark matter in our solar system

By dark matter here the authors mean any form of matter not yet known including asteroids as well as the hypothetical "dark matter". So it's also relevant to things like "Nibiru".

See Constraints on Dark Matter in the Solar System

Any matter inside of Saturn would be easy to spot from its gravitational effects on Mars, Saturn and the Earth. The reason they chose those three planets is because we have had Cassini in orbit around Saturn for years, and many spacecraft sent to Mars, and of course with Earth also - it means we have very precise measurements of their position in their orbits going back many years now.

Then, taking account of the effects of all the known matter in the solar system, they concluded that there is at most 1.7 ×10^−10 M⊙ missing from the matter we know about inside of Saturn. That's unfamiliar units, for most of us, expressed in terms of the mass of the sun, which is 1.989 × 10^30 kg So this means we are missing at most 1.17 × 10^20 kg. By comparison, the mass of Ceres is 8.958 × 10^20 kg. So we are missing less than a seventh of the mass of Ceres.

To put it another way, if you had an asteroid with same density as Ceres, with this amount of mass, then its diameter would be 950*cube root(1.17/8.958) km or about 480 km in diameter.

So if all that matter was concentrated into a single object inside of Saturn's orbit, it can't be larger than about 480 km in diameter. Or if it was made of ice, it's diameter can't be larger than 950*cube root(2.161*1.17/8.958) km, or about 623 km in diameter

So there is no way that there are even any unknown large asteroids as large as Ceres inside of Saturn right now. If there were any, then we'd have spotted their effects on the orbits of Saturn, Mars and Earth through the sensitive position measurements we can do nowadays, no matter where they are.

When you get to the region inside of Jupiter, then as a result of the PAN-STARRS all sky survey for asteroids, we have a complete listing of all the asteroids of ten kilometers and larger. The only ones that could be not yet discovered are of order of one kilometer or so downwards. And we are discovering the one kilometer asteroids at one per month and have already found more than 90% of them.

There is another place where some largish objects could be hidden, and that’s close to the Sun, well inside Mercury’s orbit. They could be up to tens of kilometers in diameter, but there have been searches and nothing was found, not yet. These would be objects that permanently orbit the Sun very close to it, and are of no risk to us, not for thousands of years, probably millions of years anyway.

Note, none of the asteroids found by PAN-STARRS etc are headed our way either - though there are thousands of them, space is vast, and for them to hit us is harder than to hit a dust mote by throwing something even smaller in its direction in a large room. Whenever they find a new asteroid, they work out its orbit, and publish the latest calculations - it is all done in an open way and there is no possibility of hiding anything. They usually find out pretty quickly that it is not going to hit us in the next couple of centuries, up to 2200 which is usually as far as they go in the published information.

Godel’s incompleteness theorem was proved specifically for an axiom system that includes addition, multiplication, numbers, and more than that too, that those all have to have particular properties. And mathematicians generally believe them to be consistent, At any rate, there are many other complete, decidable and consistent axiom systems. Let’s unpack this in more detail.

Kurt Gödel who proved the remarkable incompleteness theorems. Turing and Church proved related theorems at around the same time.

There are many such systems of axioms but one of the easiest to state is the system of Peano axioms. It consists of some niggly axioms you have to add to define the operations of equality and adding 1. Then you also say that there’s a first number 0 (this is an axiom system for the non negative numbers only).

Then it has one very special axiom, the “induction axiom”. If a property is true of 0, and if you can prove that whenever it is true of a number n, it is also true of n+1, then this property must be true of all numbers.

This is the axiom that cause all the trouble. It lets you define addition, multiplication, and indeed what it means to take one number to the power of another one, e.g. 2^3, 5*7, etc etc. You can go on and prove many complicated theorems. For instance, you can prove that every number has a unique prime factorization. E.g. 30 = 2*3*5 where 2, 3 and 5 are all prime (are not divisible by any other prime numbers). And this is the only way you can express 30 as a product of primes. That’s the same for all numbers, they can only be expressed as a product of primes in one way.

Those were the main properties of numbers that Godel used to prove his theorem, together with frequent use of proof by induction. Once you have that much deductive power, then yes, you can’t prove that the resulting system is consistent.

So - that’s a big chunk of mathematics. We use numbers almost everywhere. But there are many areas of maths that don’t need numbers, or don’t need numbers with all that apparatus of deduction rules to prove things about them.

One excellent example here is geometry using rulers and compasses. Euclidean geometry. Euclid worked out the basic axiomatization, though he left out some things that seemed obvious to him, so obvious he didn’t realize they needed an axiom. One of the rules he left out is that if a line enters a three sided triangle, crossing one of its sides, it has to exit the triangle by crossing one of the other sides or the opposite vertex. It was so obvious that even with his careful logical mind, he didn’t realize he had it as an assumption.

Anyway - if you have a proper axiomatization of geometry - well there’s no mention of numbers there. And it turns out, not only that Godel’s theorem doesn’t apply, but if you are careful in how you set out your axioms, you can also prove that the resulting theory is consistent, decidable and complete. You can use Tarski’s axiomatization of geometry to prove this.

What’s more, even addition and multiplication are not enough for Godel’s theorem. They have to have very special properties, with quite a powerful deduction system. One nice system that you can prove to be consistent is the theory of real closed fields.

This is a theory with addition, multiplication, the numbers 1 and 0, fractions, so you can use it to express any ratio like 2/3, 4/5 etc. Also it’s “closed” meaning that given any sequence of numbers in it, then the limiting point of that sequence is also in it. In particular it’s going to include every infinite decimal, such as PI as the limiting point of 3, 3.1, 3.14, 3.141, 3.1415, …

It also has to have the <= relation which also has to work just as it does on the real numbers - given any pair of numbers, one is always smaller or equal to the other. But as well as that it has to have a total ordering. Given any pair of numbers, either they are identical or one of them is smaller than the other, and that if a<=b and b<=a then a = b, Also if a<=b and b<=c then a<=c. In short, it’s a total order.

Well - that may seem very similar to what you get with Peano’s axioms - after all we now have perfectly good numbers we can use for addition and multiplication. But - it turns out we just don’t have the same deductive power we have for Peano’s axioms. We couldn’t, for instance, use these rules to define exponentiation, primality, unique factorization etc because it doesn’t have an induction rule for the numbers. So we can’t prove Godel’s theorem for this theory either.

Well it turns out, if we add two more axioms, an axiom that it includes the square root of any number, and an axiom that it includes at least one solution of any polynomial equation of odd degree (linear, cubic, quintic etc) - then we can prove that the resulting theory is complete, consistent and decidable - that given any postulate you can state within the theory, then it is either true or false, and what’s more, there’s a procedure you can follow that is guaranteed to find the right answer.

Now - this process for finding the right answer to any question in the language is not very practical (nor is it practical for Tarski’s geometry either). The procedure is immensely complex and might take pretty much for ever on human timescales. Nevertheless, in the sense of Godel’s theorem, it’s decidable, consistent and complete.

So - now we’ve seen some rather powerful theories that are decidable, consistent and complete. So now let’s look at the opposite. Something that seems like a very weak theory, yet, it’s enough to prove Godel’s theorem, so it can’t be shown to be a consistent theory.

This is Robinson arithmetic

The axioms are, where “successor” here means the result of adding 1:

0 is a number and is not the successor of an number

If the successor of x equals the successor of y, then x = y.

Every number except 0 has a predecessor.

Adding 0 to a number has no effect: x+0 = x

Multiplying any number by 0 gives 0: x * 0 = 0.

Then, we have a couple of rules to define addition and multiplication. So, if S is the successor operation, then for every x and y:

x + Sy = S(x+y)

x . Sy = (x.y) + x

It hardly seems enough. Surely the resulting theory is logically weaker than the theory of real closed fields? Well, it turns out, the answer is no. There is enough deductive power here to deduce Godel’s theorem.

This theory therefore can’t be proven to be consistent except in a “stronger or equally strong theory”.

Now, this doesn’t mean that it is inconsistent. Indeed, it doesn’t actually rule out consistency proof. Indeed Gentzen did a consistency proof for Peano arithemtic, using a slightly different and in some ways simpler axiomatization of arithmetic called “primitive recursive arithmetic” plus something called “transfinite ordinals”. All of this is very techy, but mathematicians find this reassuring because Peano arithmetic with its induction axiom seems a bit uncomfortably like the powerful theory of Frege’s axiomatization of set theory, but this other axiomatization is in a way more straightforward. So it’s good evidence, perhaps, that we won’t get into any trouble by treating Peano Arithmetic as a consistent theory, even though we can’t prove this. Gentzen's consistency proof - Wikipedia

Rather, I think a better way of looking at it, by Godel's incompleteness theorem, any powerful enough system of axioms can never capture all the maths that is implied by those axioms.

If you've described it clearly enough so that it's totally clear how theorems are proved - then by Godel’s ingenious methods, that leaves it open to processes of adding new axioms to the system, which a mathematician can see must be true, but which are not included in your original list of axioms. It also leaves you open to the possibility of adding in the negations of those new axioms as well of course, if you want to explore systems that are omega inconsistent -if you are interested in these strange theories, where you can say “There is a number with property P” and yet can say “1 doesn’t have property P, nor does 2, nor 3, nor 4, nor 5, …” and every single statement of that sort is false. It seems inconsistent, but actually mathematically it isn’t possible to make a finite proof of an inconsistency. So it’s a bit weaker than normal inconsistency, and the techy word for this is “ω inconsistent” (there ω is a symbol used for the sequence of all the numbers 1 2 3 …. - it’s consistent unless you string together infinitely many statements which we can’t do in practice - so you can never prove it is inconsistent)

So anyway - you are not prevented from exploring those strange theories either in full knowledge of what you are doing. Indeed some mathematicians are also interested in “paraconsistent” theories - theories that have proofs of inconsistencies that are finite, but rather large, so you can work with them for a long time without hitting an inconsistency. These are not unlike ordinary logic that we use in everyday life. We are actually able to work perfectly well with inconsistent theories. E.g. - if you want to take something out of your house, you might think it is small enough to fit through the door upright, and actually try to take it out that way, only to find out it won’t fit. This means you had an inconsistent theory about that object. No problem. Modify your theory to say “oh I get it now, it has to be turned on its side” and now you can take it out of your door. In more complex situations you may work with beliefs or ideas you know to be inconsistent, but just avoid the situations where you have to face the inconsistencies. It might work just fine. In some areas, e.g. law, you may have to work with case decisions that are inconsistent with each other, and try to find a way through the situation. Basically we’d be hugely handicapped in our everyday life if we had to work only with consistent sets of ideas. So - sometimes it’s interesting to work with inconsistent sets of axioms in maths too.

So you can do all that. And you can also work with consistent theories of course. Or at least, theories that you have every reason to believe are consistent even though you can’t prove this.

Just use the axioms you can see to be true of numbers, based on Peano’s axioms, and then Godel’s sentence - see that it’s true - and so unprovable. Add it as an axiom. Just keep going. And you can then expand your axiom systems as needed in creative ways if you need to go beyond their limitations. Just on and on, as much as you like.

So - it means maths has to be creative, and never ending. And we can never know for sure that it is consistent once it reaches a certain level of complexity and power. But it doesn't have to be inconsistent.

Yes, there is a case of “once bitten twice shy” that when Frege published his life’s work, a foundation for all of set theory, then Russell found a mistake in it, he proved that it was inconsistent through Russell’s paradox. It could be fixed, but only in clumsy ways. This suggests that it’s not as easy to come up with a theory that you know for sure is consistent as one might think. Indeed Godel’s theorem shows we can’t prove that even the Peano axioms are consistent.

But I think most mathematicians would say that there is no real risk that the axioms are inconsistent in the sense of Frege’s set theory. We don’t need to worry that some ingenious fellow will pop up, like Russell did for Frege, and say “look, here is a proof of an inconsistency from the axioms of Peano arithmetic”. Most mathematicians would say we don’t need to worry about that possibility.

They are just impossible to encapsulate completely in an axiom system that captures all their properties. That’s why they aren’t decidable, are incomplete, and can’t be proven to be consistent.

Now, I should mention Gödel's completeness theorem because this confuses many people. It’s a different notion of completeness from the one used in Godel’s “incompleteness theorem”. It’s about the formal consequences of the axioms, not the informal consequences that you can see by reasoning about the theory in a meta mathematical way.

It says that if you enumerate all the proofs that you can make using the axioms of the theory - those are all the results you can deduce from the axioms and the only results you can deduce. There are no hidden extra axioms you need to add to “complete” the theory - it’s all there.

Put another way, then it says that if you interpret truth as “true in every possible model” then all such truths can be deduced from the axioms of your theory.

I should say - this is stuff I researched into back in the 1980s. I haven’t done any work on it at all since then, and if you asked me to go into details about some of these things, I’d have to “look it up and get back to you”. But hopefully it gives a reasonable idea of how it works.

It’s rather baffling, for sure. But I think the best way to look at it myself is that Godel proved that mathematics can’t stagnate and that there is need for endless creativity as it can’t be “cut and dried and diced” into a single overall theory that encompasses everything.

But some theories, notably geometry, can be made completely decidable, consistent and complete.

Also all the problems here are to do with infinity. If you are studying something finite, for instance a finite group, with a finite number of elements, so all questions can be answered by doing finite, if very complicated calculations - then that’s going to be a complete, consistent and decidable theory too. It’s just when you start having infinity come in in some way, that you may (but not always) hit this.

You might also be interested in my Russell's paradox