tag:blogger.com,1999:blog-20067416.post231170618586768556..comments2021-06-15T05:17:49.979-04:00Comments on Recursivity: Naming InfinityUnknownnoreply@blogger.comBlogger9125tag:blogger.com,1999:blog-20067416.post-53536175611842291482010-12-12T21:22:50.823-05:002010-12-12T21:22:50.823-05:00To end my posting spree on this blog, a personal o...To end my posting spree on this blog, a personal opinion on mathematics and its practitioners and a pointer to a good book.<br />The art of mathematics requires honest provable reasoning. Proof of correct reasoning does not require consensus (Galileo) or the misbegotten efforts of certain parties re: Poincare Conjecture. Regarding mathematical taxonomy in general reminds me of the tower of Babel and a few choice quotes from Paracelcus regarding the medical practicioners of his era .. as does a sojourn through the Sapir-Whorf hypothesis. As Einstein said, make it as simple as possible but no simpler. Mathematics may need another Dyson to synthesize equivalent statements from diverse forms of arbitrary expressions. Even canned software like Maple & Mathematica do the same things differently. At least in FORM you can roll your own.<br />To close, for those who have that special place on their desk to bang their head or who experience jaw-dropping stupidity on a semi-regular basis take a look at "Systemantics" by John Gall. The book may help your perspective on certain `goings-on`. I've had my 2nd edition copy since the early '90's.<br />Happy holidays everyone and may one of you out there win a Noble or a consolation ig Noble!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-20067416.post-70849118736000156382010-12-09T11:33:29.185-05:002010-12-09T11:33:29.185-05:00Mike from Ottawa:
Actually, I've published a ...Mike from Ottawa:<br /><br />Actually, I've published a paper in a history journal, so I think I have some idea what is done in academic history. But thanks for your advice.Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-44252998574006505232010-12-09T10:59:36.005-05:002010-12-09T10:59:36.005-05:00"It could have happened another way; but it d..."It could have happened another way; but it did not." But if this all they were saying, then so what?"<br /><br />Maybe someone from your U's history department can explain it to you, since the same could be said of most, if not all, history.<br /><br />Applies as well to large swathes of paleontology and geology as well, or any science where contingency is an element.Mike from Ottawanoreply@blogger.comtag:blogger.com,1999:blog-20067416.post-73285555291995039372010-12-09T06:56:45.949-05:002010-12-09T06:56:45.949-05:00@Takis,
I agree with what you're saying, hence...@Takis,<br />I agree with what you're saying, hence the scare quotes around the word "faith." In retrospect, I guess I should also have put scare quotes around the word "believe." Thanks for the clarification.Joel Reyes Nochehttp://joelnoche.multiply.com/noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-50441688405200647242010-12-09T02:05:30.776-05:002010-12-09T02:05:30.776-05:00Joel Reyes Noche said...
Excellent mathematicians...<em>Joel Reyes Noche said... <br />Excellent mathematicians regularly believe things without proof, in particular, axioms and definitions. I would say that this involves some "faith."</em><br /><br />Forget the adjective "excellent". It's unnecessary.<br /><br />I'm afraid you confuse the words "faith/believe" and "mathematics/science". If you had worked in the latter you would have quickly realized that neither axioms nor definitions are freebies in mathematics. A lot of serious work goes into them, and this is far from "faith" or "belief". <br /><br />However, to an untrained person it appears that proofs is the only thing mathematics is about. But it just ain't so.Takis Konstantopouloshttps://www.blogger.com/profile/14675216467783238403noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-22712897523722018652010-12-07T19:50:49.388-05:002010-12-07T19:50:49.388-05:00Excellent mathematicians regularly believe things ...Excellent mathematicians regularly believe things without proof, in particular, axioms and definitions. I would say that this involves some "faith."Joel Reyes Nochehttp://joelnoche.multiply.com/noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-16196506634905900032010-12-07T08:36:48.989-05:002010-12-07T08:36:48.989-05:00Vinayak:
People are very good at compartmentalizi...Vinayak:<br /><br />People are very good at compartmentalizing their beliefs, so it doesn't surprise me at all that excellent mathematicians can be theists. And it's a matter of record that they can. <br /><br />I know a good mathematician who believes in all sorts of silly "alternative" health practices.Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-89277813209433606702010-12-07T08:19:30.242-05:002010-12-07T08:19:30.242-05:00I don't understand how a good mathematician ca...I don't understand how a good mathematician can ever believe in God. For being a good mathematician you need to be excellent at logical reasoning; to be a believer in God, you need to be a mish-mash of logical fallacies. I can easily see a believer in God, when asked to prove something, first assumes it's true and then "proves" it. I guess if a person is both, then he probably is a believer in a very vague, pantheistic kind of way. And I am pretty sure that if it turns out that having such a belief really does have positive effects on your mathematical abilities, amphetamines have much better effects and they don't even screw up with your belief system.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-20067416.post-24012970385951341082010-12-06T13:28:22.343-05:002010-12-06T13:28:22.343-05:00Concerning Ramanujan: it is not entirely certain t...Concerning Ramanujan: it is not entirely certain that he really did believe that Namagiri whispered theorems to him in his dreams. G.H. Hardy, for example, gives a rather different account of Ramanujan's religious beliefs. See, for example, the account beginning at the bottom of p. 3 (Lecture I) of the collection "Ramanujan: twelve lectures on subjects suggested by his life and work".Naradnoreply@blogger.com