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Re: Re: Language vs. Library why it matters
*To*: mathgroup at smc.vnet.net
*Subject*: [mg61710] Re: [mg61692] Re: Language vs. Library why it matters
*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>
*Date*: Thu, 27 Oct 2005 05:01:35 -0400 (EDT)
*References*: <djk1c7$got$1@smc.vnet.net> <200510260501.BAA18798@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
On 26 Oct 2005, at 14:01, Richard Fateman wrote:
>
>
> Mathematica not only computes,
>
>
>> it also uses mathematical concepts. Some of these concepts are
>> "infinitistic".
>>
>>
>
> I don't know what this word means.
>
You can find the word is used quite often by logicians (if you
really don't understand it couldn't you just google for it?). I
suggest reading up a little logic. How about trying "On the
Philosophical Relevance of Gödel?s Incompleteness Theorems" by Panu
Raatikainen (a rather well known logician)? You will find the word
used a few times and will probably learn what it means.
> And
>
>
>> essentially anything infinitistic is subject to Godel's theorems.
>>
>>
>
>
>
>>
>>
>>
> Nope. First of all you need to have the prospect of explicitly
> generating
> an infinite sequence of objects. The integers will do. Saying
> Infinity or Infinitisticalafragislisticexpialadocious doesn't
> work.
>
I was referring to Godel's second theorem ("consistency") obviously
far more relevant to my original comment that generated this thread.
Example: I implemented a several algorithms to compute Matveev
complexity of a 4 manifold. However, since the concept of a 4
manifold is "infinitistic" (I refer to Raatikainen for the meaning of
the word) it is subject to Godel's second theorem. If the concept of
a 4 manifold involves some basic inconsistency, something that we
will never know, than my implementation may some day produce
inconsistent results. This is an example of the kind of inconsistency
that may come from mathematics to Mathematica. It does not have
anything to do with the halting problem. I can't still see why you
introduced it, since it has no relevance here at all.
>>
>>
>
> The point is, abstractly, one can describe this program on half a
> page or less.
> Starting at some initial configuration of a the computer process
>
> Since there are a finite number of states, this will eventually stop.
>
Eventually could mean after the universe is not longer here. However,
as I wrote above, the halting problem has nothing to do with what I
was writing about, you introduced it probably because you confused
the two theorems of Godel
>>
>>
> (In fact there are pretty
>
>
>> good reasons to believe that exposure to too much Lisp diminishes
>> ones ability to understand more complex mathematics, which is one
>> reason why I would object to teaching Lisp as a programming language
>> to math students.)
>>
>>
>
> Really?
> Can you state some of these reasons?
> big snip
>
>
Private communication ;-)
>>
>> I think I have now written more than I ever wanted to write on this
>> topic.
>>
>>
>
> No one is forcing you!
>
>
>
Indeed, I have too altruistic nature ;-)
Andrzej Kozlowski
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