source file: mills2.txt Date: Fri, 3 Nov 1995 21:43:36 -0800 Subject: Transcendental Numbers From: Gary Morrison <71670.2576@compuserve.com> In beginning to read Brian's post about non-equal-tempered, non-just tunings, I promptly realized that I was missing one very basic piece of information that perhaps some others of you may also be wondering about: What the bloody hell is a transcendental number?! That sort of ignorance of course is difficult for a practicing engineer to admit, so please forgive the sarcastic tone of this message. It comes from having to swallow my mathematical pride even after taking twenty-some-odd heavily mathematical classes after Vector Calculus. Those included a mysterious class called Automatic Control Theory, the equations in whose textbook, I was once amused to notice, had more appeal as abstract visual artforms than as mathematical statements. Then again standards of amusement drop to all-time lows when you average (including weekends) four hours of sleep a night for an entire semester in a room located directly above the central water heater for the entire dormitory complex! Of course Brian makes a point - in belching out two printed pages of examples of transcendental and nontranscendal numbers (each of which approximately halves my estimate of my mathematical prowess) - to explain the concept ever so concisely by pointing out that "there appears to be NO general criterion for determining whether a number is transcendental". Gee thanks Brian, that just about sums it up for me! So having accepted the embarrassing truth that I'm a complete mathematical moron, I decided that maybe Grolier's CD-ROM encyclopedia might help out. "A transcendental number is an irrational number that is not a root of any polynomial equation with integer coefficients." Thank you, Grolier. Maybe some other blithering idiot like me was wondering... Fortunately, my mathematical ego having been deflated to about the size of a white pepper corn, I have the gratification of realizing the significance of a number being the root of a polynomial equation with integer coefficents. If on the other hand you don't, let me tell you a secret: playing the guitar is more fun! End of sarcastic tone. Sorry. Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 4 Nov 1995 08:33 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id WAA14620; Fri, 3 Nov 1995 22:33:17 -0800 Date: Fri, 3 Nov 1995 22:33:17 -0800 Message-Id: Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu