I just had a weird thought
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From: Aatu Koskensilta on 11 May 2010 11:32 Charlie-Boo <shymathguy(a)gmail.com> writes: > On May 11, 10:54�am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > >> A mathematician I know once went to a bar and had a beer. > > No he didn't. No, he did. He had several beers, in fact, and chatted with random acquaintances. The next day he gave a lecture. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Charlie-Boo on 11 May 2010 12:00 On May 11, 11:23 am, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > Aatu Koskensilta says... > > > > >Charlie-Boo <shymath...(a)gmail.com> writes: > > >> You see, mathematicians never actually DO anything - they only talk > >> about how they would do it if they did. > > >A mathematician I know once went to a bar and had a beer. > > That sounds like the start of a joke: > > A mathematician walks into a bar and orders a beer... Ok, how about: A Mathematician goes into a bar and orders a beer. The bartender tells him, Sorry, we dont serve beer to Mathematicians. The Mathematician asks for a justification. The bartender says, You guys keep talking about associative rules and cuntinuous functions. Were a nice place here. C-B > -- > Daryl McCullough > Ithaca, NY
From: Charlie-Boo on 11 May 2010 12:05 On May 11, 10:57 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Charlie-Boo <shymath...(a)gmail.com> writes: > > Then we compared solutions to the ant puzzle and I never got a chance > > to ask him for an example of a math thing that is not a model of the > > physical world. > > To pick a logical example, the constructible universe is hardly a model > of the physical world. BTW Godels results on the independence of the Axiom of Choice only apply to these sets and it is easy to define a non constructible set. A constructible set is really any recursively enumerable set when we represent the Nth constructible set (ordered by traversing the tree of sets formally defined to be in L) with the natural number N. (As Godel himself once said, it doesnt matter what the natural numbers represent.) Then simple diagonalization defines a non constructible set (parallel to showing that the set of Turing Machines that do not halt [yes] on themselves is not r.e.) and Godels results do not apply. Any questions concerning AOC or CH et. al. really should be in terms of sets in general. When we start limiting our sets in constructive ways, these questions become trivial consequences of our limiting definition. For example, Godels 1940 pamphlet is the equivalent of giving a universal Turing Machine in complete detail. We all know we can do it, so we really dont have to give it. Likewise Godels argument is reduced to a simple intuitive appeal the same appeal that does not require us to actually give the Turing Machines tuples (or Godels non recursive relation, # 45 I believe it is.) So Turing Machines model the constructible universe very easily. C-B > > I told them that math is physics without the units and they all > > laughed. > > Very droll. Ha-ha. > > -- > Aatu Koskensilta (aatu.koskensi...(a)uta.fi) > > "Wovon man nicht sprechan kann, darüber muss man schweigen" > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Aatu Koskensilta on 11 May 2010 12:13 Charlie-Boo <shymathguy(a)gmail.com> writes: > So Turing Machines model the constructible universe very easily. Your jokes do really rather fall flat. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: John Jones on 11 May 2010 14:50
taffer wrote: > I just had a weird thought. It actually left me confused about what is > mathematical, and what is physical. The statement was: > > "Every finite set can be generated by adding one element at a time, > starting from nothing". > > This seems to be true. But then (and this is what confused me) I > wondered, is that a mathematical statement? If so, would there not be > a formal mathematical theorem expressing the statement? Or if it's a > definition, a formal mathematical definition? Or maybe it's not a > mathematical statement after all? What mystifies me is how you, and other mathematicians, seem to think that adding one element at a time is one thing, and a new set is another thing AND that they are both the same thing. |