[HN Gopher] How much math is knowable? [video]
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How much math is knowable? [video]
Author : diaphanous
Score : 86 points
Date : 2025-04-23 20:48 UTC (1 days ago)
(HTM) web link (www.youtube.com)
(TXT) w3m dump (www.youtube.com)
| munchler wrote:
| This is an excellent talk by Scott Aaronson, although it's not
| something that can be digested as quickly as the typical HN post.
| The summary slide at the end is perhaps a good introduction to
| the scope of the topic:
|
| * In math, we are finite beings trying to apprehend the infinite
|
| * The Busy Beaver function actually quantifies that (!)
|
| * Even the finite can exceed the scope of the cosmos. That's
| where we need physics and complexity theory
|
| * Quantum computers look like they're already _slightly_
| expanding the scope of what mathematical statements we can know
|
| * Can we know even more than that? Depends what the ultimate laws
| of physics are
| jerf wrote:
| "although it's not something that can be digested as quickly as
| the typical HN post"
|
| I really want a view of HN that is something like the upvotes
| divided by the number of comments (although, not necessarily
| linear). Those aren't necessarily the "best" by every metric,
| not saying this is the "best" view or anything, but it would be
| an _interesting_ one.
| gsf_emergency wrote:
| Pretty sure dang (or other mods) has that view as a sidebar
| or something, maybe you can request that as an exclusive
| feature for top karmies. It would, as a bonus, already cover
| the edge cases you haven't thought about..
| nh23423fefe wrote:
| true. lots of comments is an indicator of low quality
| calf wrote:
| What precisely is meant by simulating the laws of physics?
| There's a common understanding pitfall there, in that a lot of
| lay people quickly end up talking about "is the universe a
| computer" or "infinite Turing machines have nothing to do with
| the real world" sort of confusing arguments.
|
| I liked how this talk addressed the topic yet have questions
| about this talk's overarching argument. It's kind of an argument
| yet more like a philosophical position about CS--I know at least
| one paper that critiques the philosophical commitments made in
| something like the Church Turing thesis, etc., that paper called
| Aaronson the strong American style perspective or something, I
| forget, at any rate the issue is how transparent these
| philosophical premises are which those of us from computer
| science may take for granted.
|
| I also liked-disliked those one slide proofs. I couldn't follow
| them, I know they are right (and are great exercises for a
| student to go over offline) and that they are in service of
| showing that modern understanding can do the results in one slide
| and so forth, but yet there's an accepted style of academic
| presentation that kind of misleadingly "performs" in a way that
| is cognitively impossible for the audience to actually follow
| unless they already know it, technical talks are kind of a
| backwards lie in that way. There was a recent popular book by a
| French mathematician who said as much, that 99.9% of the time we
| can hardly understand mathematics talks and books and it's kind
| of an open secret how professionals deal with this phenomenon.
|
| Edit: I took undergrad CS theory but never "got" the
| exposure/fascination with Busy Beaver, but after this talk it
| became clearer to me that the reason for the Busy Beaver function
| is that it's a meta-function, it is a function _about_ Turing
| machines, which is how the BBF gets the special properties
| /results that it does. Which immediately reminds me of Chaitin's
| constant which also tries to encode/talk about the properties of
| Turing machines, e.g. Kolmogorov style complexity which was not
| explicitly mentioned in the talk.
| tromp wrote:
| > it is a function about Turing machines, which is how the BBF
| gets the special properties/results that it does.
|
| The properties of the Busy Beaver function carry over to any
| other computational model you could base it on. E.g. the lambda
| calculus based BBl[1] shares most of its properties.
|
| > Which immediately reminds me of Chaitin's constant which also
| tries to encode/talk about the properties of Turing machines,
|
| Chaitin's work on Algorithmic Information Theory (aka
| Kolmogorov Complexity) was actually focussed on custom Lisp
| languages of his own design rather than Turing Machines. One
| could be confused though by some of his articles on LISP
| program-size complexity like [2] where he calls his LISP
| interpreter a UTM (Universal Turing Machine).
|
| [1] https://oeis.org/A33347
|
| [2]
| https://www.jucs.org/jucs_2_5/the_limits_of_mathematics/Chai...
| meroes wrote:
| Hoping to watch the video soon. What's still a mystery to me is
| how Turing Machines (infinite, abstract, non-physical) are so
| useful for us finite beings. Similar could be said for
| mathematical infinity.
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