[math-fun] Fwd: [n.wildberger@unsw.edu.au: Video of Jim and Norman's debate on infinity]
An interesting debate (I think Norm won too). Brent ----- Forwarded message from Norman Wildberger <n.wildberger@unsw.edu.au> ----- Date: Fri, 26 Sep 2014 02:20:26 +0000 From: Norman Wildberger Subject: Video of Jim and Norman's debate on infinity Hi everyone, Earlier in the week Jim Franklin and I had a robust discussion on the topic `Infinity: does it exist??' in the Pure Maths seminar. Thanks to all who came and showed an interest in our opinions, and thanks for the many questions and comments afterwards. The video is now at the School YouTube site, at https://www.youtube.com/watch?v=5CiiGdaYEPU Unfortunately our microphone could not pick up audience questions and comments very well, and in fact our battery died near the end anyway. So apologies for those who asked interesting questions and comments, and we invite you to post them directly on the comments section of the video, where we can try to answer them! Best Regards, Norman Wildberger ----- End forwarded message -----
I had a hard time listening to what I consider abject nonsense. I could no longer stomach listening after hearing the first speaker insist that positive integers admit prime factorizations only up to some finite point and not beyond. He excludes not only infinite sets but also unbounded phenomena. He made no distinction between a) what a computer can do and b) what is the case in mathematics. He used the limited capabilities of computers, and descriptive (but not reasoned) quotations from Weyl, Gauss, and other mathematicians of the past, as arguments against the existence of infinite sets. Not my cup of tea at all. --Dan On Sep 25, 2014, at 11:27 PM, meekerdb <meekerdb@verizon.net> wrote:
An interesting debate (I think Norm won too).
Brent
----- Forwarded message from Norman Wildberger <n.wildberger@unsw.edu.au> -----
Date: Fri, 26 Sep 2014 02:20:26 +0000 From: Norman Wildberger Subject: Video of Jim and Norman's debate on infinity
Hi everyone,
Earlier in the week Jim Franklin and I had a robust discussion on the topic `Infinity: does it exist??' in the Pure Maths seminar. Thanks to all who came and showed an interest in our opinions, and thanks for the many questions and comments afterwards. The video is now at the School YouTube site, at
https://www.youtube.com/watch?v=5CiiGdaYEPU
Unfortunately our microphone could not pick up audience questions and comments very well, and in fact our battery died near the end anyway. So apologies for those who asked interesting questions and comments, and we invite you to post them directly on the comments section of the video, where we can try to answer them!
Best Regards,
Norman Wildberger
----- End forwarded message -----
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I'd be interested to see ultrafinitists' opinion on the following system of mathematics: 1. We operate in the first-order Peano arithmetic with the usual axioms and rules of inference. 2. We also include the following additional axiom: "For every natural number n, we can find a sequence of n simple graphs where every vertex has degree <= 3, such that the kth graph has at most k + 3 vertices, and if i < j, then the ith graph is not a minor of the jth graph." (This axiom can be encoded in terms of natural numbers, since we're only reasoning about finite objects. This can be done in a routine way, by translating the statement into the non-haltingness of a particular Turing machine, which can in turn be translated into a statement about the insolubility of a particular Diophantine equation.) Now, this system is inconsistent, in that there exists a finite proof of false. But no such proof can fit in the observable universe, so someone living in our universe with this system of mathematics would never notice anything amiss. So would ultrafinitist model theorists consider this to be a consistent theory? More importantly, why do all ultrafinitists seem to have surnames of the form ".*berger" (c.f. Doron Zeilberger)? Sincerely, Adam P. Goucher
Sent: Friday, September 26, 2014 at 4:26 PM From: "Dan Asimov" <dasimov@earthlink.net> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] Fwd: [n.wildberger@unsw.edu.au: Video of Jim and Norman's debate on infinity]
I had a hard time listening to what I consider abject nonsense.
I could no longer stomach listening after hearing the first speaker insist that positive integers admit prime factorizations only up to some finite point and not beyond. He excludes not only infinite sets but also unbounded phenomena.
He made no distinction between a) what a computer can do and b) what is the case in mathematics. He used the limited capabilities of computers, and descriptive (but not reasoned) quotations from Weyl, Gauss, and other mathematicians of the past, as arguments against the existence of infinite sets.
Not my cup of tea at all.
--Dan
On Sep 25, 2014, at 11:27 PM, meekerdb <meekerdb@verizon.net> wrote:
An interesting debate (I think Norm won too).
Brent
----- Forwarded message from Norman Wildberger <n.wildberger@unsw.edu.au> -----
Date: Fri, 26 Sep 2014 02:20:26 +0000 From: Norman Wildberger Subject: Video of Jim and Norman's debate on infinity
Hi everyone,
Earlier in the week Jim Franklin and I had a robust discussion on the topic `Infinity: does it exist??' in the Pure Maths seminar. Thanks to all who came and showed an interest in our opinions, and thanks for the many questions and comments afterwards. The video is now at the School YouTube site, at
https://www.youtube.com/watch?v=5CiiGdaYEPU
Unfortunately our microphone could not pick up audience questions and comments very well, and in fact our battery died near the end anyway. So apologies for those who asked interesting questions and comments, and we invite you to post them directly on the comments section of the video, where we can try to answer them!
Best Regards,
Norman Wildberger
----- End forwarded message -----
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On 9/26/14, Adam P. Goucher <apgoucher@gmx.com> wrote:
I'd be interested to see ultrafinitists' opinion on the following system of mathematics: [snip] Now, this system is inconsistent, in that there exists a finite proof of false. But no such proof can fit in the observable universe, so someone living in our universe with this system of mathematics would never notice anything amiss. So would ultrafinitist model theorists consider this to be a consistent theory?
I watched the first half or so of this video. Both participants labour under what I consider untowardly naive concepts of "existence", particularly where that notion concerns mathematical concepts. In particular, yer man apparently proposes to base elementary mathematics on contemporary estimates of the size, age and potential computational granularity of the universe, all of which are themselves the culmination of extended chains of mathematical reasoning as well as multiple delicate experiments, and are in any case necessarily provisional!
More importantly, why do all ultrafinitists seem to have surnames of the form ".*berger" (c.f. Doron Zeilberger)?
The "Follies Berger" ? WFL
On Sep 25, 2014, at 11:27 PM, meekerdb <meekerdb@verizon.net> wrote:
An interesting debate (I think Norm won too).
Brent
----- Forwarded message from Norman Wildberger <n.wildberger@unsw.edu.au> -----
Date: Fri, 26 Sep 2014 02:20:26 +0000 From: Norman Wildberger Subject: Video of Jim and Norman's debate on infinity
Hi everyone,
Earlier in the week Jim Franklin and I had a robust discussion on the topic `Infinity: does it exist??' in the Pure Maths seminar. Thanks to all who came and showed an interest in our opinions, and thanks for the many questions and comments afterwards. The video is now at the School YouTube site, at
https://www.youtube.com/watch?v=5CiiGdaYEPU
Unfortunately our microphone could not pick up audience questions and comments very well, and in fact our battery died near the end anyway. So apologies for those who asked interesting questions and comments, and we invite you to post them directly on the comments section of the video, where we can try to answer them!
Best Regards,
Norman Wildberger
----- End forwarded message -----
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On Fri, Sep 26, 2014 at 5:36 PM, Adam P. Goucher <apgoucher@gmx.com> wrote:
I'd be interested to see ultrafinitists' opinion on the following system of mathematics:
1. We operate in the first-order Peano arithmetic with the usual axioms and rules of inference. 2. We also include the following additional axiom:
"For every natural number n, we can find a sequence of n simple graphs where every vertex has degree <= 3, such that the kth graph has at most k + 3 vertices, and if i < j, then the ith graph is not a minor of the jth graph."
(This axiom can be encoded in terms of natural numbers, since we're only reasoning about finite objects. This can be done in a routine way, by translating the statement into the non-haltingness of a particular Turing machine, which can in turn be translated into a statement about the insolubility of a particular Diophantine equation.)
Now, this system is inconsistent, in that there exists a finite proof of false. But no such proof can fit in the observable universe, so someone living in our universe with this system of mathematics would never notice anything amiss. So would ultrafinitist model theorists consider this to be a consistent theory?
Presumably the first N for which this is impossible is huge. But I'm confused by your statement that no proof of it fits in the observable universe. Presumably the reason you think this is true is that you've seen an (informal) proof of it that fit comfortably in the observable universe. Why does that proof expand by such a large amount when formalized? Is it that this theorem has a short proof in ZF, but only a very long proof from the Peano axioms? Andy
Sent: Friday, September 26, 2014 at 4:26 PM From: "Dan Asimov" <dasimov@earthlink.net> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] Fwd: [n.wildberger@unsw.edu.au: Video of Jim and Norman's debate on infinity]
I had a hard time listening to what I consider abject nonsense.
I could no longer stomach listening after hearing the first speaker insist that positive integers admit prime factorizations only up to some finite point and not beyond. He excludes not only infinite sets but also unbounded phenomena.
He made no distinction between a) what a computer can do and b) what is the case in mathematics. He used the limited capabilities of computers, and descriptive (but not reasoned) quotations from Weyl, Gauss, and other mathematicians of the past, as arguments against the existence of infinite sets.
Not my cup of tea at all.
--Dan
On Sep 25, 2014, at 11:27 PM, meekerdb <meekerdb@verizon.net> wrote:
An interesting debate (I think Norm won too).
Brent
----- Forwarded message from Norman Wildberger <n.wildberger@unsw.edu.au> -----
Date: Fri, 26 Sep 2014 02:20:26 +0000 From: Norman Wildberger Subject: Video of Jim and Norman's debate on infinity
Hi everyone,
Earlier in the week Jim Franklin and I had a robust discussion on the topic `Infinity: does it exist??' in the Pure Maths seminar. Thanks to all who came and showed an interest in our opinions, and thanks for the many questions and comments afterwards. The video is now at the School YouTube site, at
https://www.youtube.com/watch?v=5CiiGdaYEPU
Unfortunately our microphone could not pick up audience questions and comments very well, and in fact our battery died near the end anyway. So apologies for those who asked interesting questions and comments, and we invite you to post them directly on the comments section of the video, where we can try to answer them!
Best Regards,
Norman Wildberger
----- End forwarded message -----
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-- Andy.Latto@pobox.com
participants (5)
-
Adam P. Goucher -
Andy Latto -
Dan Asimov -
Fred Lunnon -
meekerdb