You are mistaken both about the Mathematics and about my perceptions. The ration of the diameter to the circumference is pi only on the Euclidean plane. On a sphere, the ratio depends ont only on the curvature but also on the size of the circle, and is always less than pi. Nor do I think that the flatlanders are mistaken about the radius.
It's certainly a mistake "to dismiss their curved surface as an illusion, and to assume our uncurved space is the only reality.", but It's not a mistake that I have or ever would make, nor would anybody familiar with Gauss's Theorema Egregium make such a mistake. Don't they tech Spherical Geometry in High School any more? -- Shmuel (Seymour J.) Metz http://mason.gmu.edu/~smetz3 ________________________________________ From: IBM Mainframe Discussion List [IBM-MAIN@LISTSERV.UA.EDU] on behalf of Bob Bridges [robhbrid...@gmail.com] Sent: Friday, June 18, 2021 1:29 PM To: IBM-MAIN@LISTSERV.UA.EDU Subject: Re: Coding for the future Aha, my evil troll worked! BWA-HA-HA! Shmuel, I'm happy to take this off-line if you prefer, but I take the definition of pi to be the ratio of the diameter of a circle to its radius. In an uncurved space that ratio is constant; on the surface of a sphere, it varies. If you insist on thinking in three dimensions -- three uncurved dimensions -- then it will seem to you that the Flatlanders on that sphere are simply mistaken about the radius about their circle. But I submit that it's a mistake to dismiss their curved surface as an illusion, and to assume our uncurved space is the only reality. I'm assuming you understand what I'm saying, and just disagree with me. But if you don't follow what I'm saying about the radius of a circle drawn on the surface of a sphere, I'll bore you with further description. --- Bob Bridges, robhbrid...@gmail.com, cell 336 382-7313 /* No single raindrop considers itself responsible for the flood. */ -----Original Message----- From: IBM Mainframe Discussion List <IBM-MAIN@LISTSERV.UA.EDU> On Behalf Of Seymour J Metz Sent: Friday, June 18, 2021 12:48 Sturgeon's Law. There is a lot of bad Mathematics and Bad Physics in Science Fiction. pi is a true constant, not a physical variable, and curvature is another animal entirely, whose definition doesn't even include a factor of pi; it's defined entirely in terms of derivatives of the metric tensor, at least in the cases relevant to current Physics. Bafflegab is always easier than a correct explanation. If you're a flatlander living on a sphere pi doesn't change, but formulae for, e.g., area, become more complicated. ________________________________________ From: IBM Mainframe Discussion List [IBM-MAIN@LISTSERV.UA.EDU] on behalf of Bob Bridges [robhbrid...@gmail.com] Sent: Friday, June 18, 2021 12:34 PM Completely OT, I'm reminded of Greg Bear's _Eon_, in which someone carried around a device for measuring the local value of pi. It's a way of detecting curvature in space, you see. You may think pi is 3.141519 everywhere, but if you're a Flatlander living on the surface of a sphere you'll have to get used to the fact that it can be anywhere between...let's see...between 0 and 4, I think. -----Original Message----- From: IBM Mainframe Discussion List <IBM-MAIN@LISTSERV.UA.EDU> On Behalf Of Seymour J Metz Sent: Thursday, June 17, 2021 14:01 It may be tongue in cheek, but while the value of pi will never change, the precision that you need may change, and changing a single precision 3.14159 to a more precise extended precision value is a lot easier if it's only in one place. Besides, while mathematical constants don't change, some physical constants, e.g., g, represent local conditions rather than laws of Physics. Take the length of the day - please! ________________________________________ From: Mark Jacobs [00000224d287a4b1-dmarc-requ...@listserv.ua.edu] Sent: Thursday, June 17, 2021 11:49 AM The primary purpose of the DATA statement is to give names to constants; instead of referring to pi as 3.141592653589793 at every appearance, the variable PI can be given that value with a DATA statement and used instead of the longer form of the constant. This also simplifies modifying the program, should the value of pi change. ― FORTRAN manual for Xerox Computers ---------------------------------------------------------------------- For IBM-MAIN subscribe / signoff / archive access instructions, send email to lists...@listserv.ua.edu with the message: INFO IBM-MAIN ---------------------------------------------------------------------- For IBM-MAIN subscribe / signoff / archive access instructions, send email to lists...@listserv.ua.edu with the message: INFO IBM-MAIN ---------------------------------------------------------------------- For IBM-MAIN subscribe / signoff / archive access instructions, send email to lists...@listserv.ua.edu with the message: INFO IBM-MAIN ---------------------------------------------------------------------- For IBM-MAIN subscribe / signoff / archive access instructions, send email to lists...@listserv.ua.edu with the message: INFO IBM-MAIN
