[PD-ot] Real numbers (WAS: [PD] CVs)
Mathieu Bouchard
matju at artengine.ca
Sat May 21 21:53:19 CEST 2011
On Tue, 10 May 2011, Bryan Jurish wrote:
> Since they're patternless, they're incompressable (in the
> Kolmogorov/Chaitin sense), so they can only be realized by a
> non-terminating process (i.e. in an infinite number of discrete
> computation steps).
I don't understand that. Let's say a infinitely long programme just starts
spitting its own digits one after the other. Can't you say that each
digit is being spitted out in O(1) steps ? What are the Kolmogorov-Chaitin
assumptions of what a computer is ?
As far as I'm concerned, an infinite computer is impossible, so it doesn't
make much sense to me to postulate O(42) or O(log n) read-time for a digit
in nth position in the memory.
> I can dig the idea of a non-terminating process,
I can't. It makes me think about the bloody Crown of England.
> and I feel about the reals like some people of my acquaintance feel
> about deity: it's comforting to know that they're around, but I don't
> want to deal with them directly (at least not anytime soon) ;-)
But among themselves... would the Bible's God invite an unnamable,
unspecifiable number for dinner ?
>> It doesn't mean that those artifacts don't exist in the physical world,
>> it means that we had to invent those concepts by ourselves because we
>> can't perceive them from the physical world.
>
> Very Kantian of you, if I may say so. Historically, you're certainly
> right; but I'm more of a Platonist bent on this one:
I don't have enough of a philosophy background to associate myself with
one or the other. I never did read Kant and forgot much about Platon. I'm
pretty sure, though, that my main influence has been a lot of books about
Physics. They didn't talk about that topic, but imho a true scientist must
read between the lines about things like this.
> our (to be more precise Frege's) having come up with a logically
> consistent framework for talking about uncountably infinite sets --
> whatever its motivations --
Motivations for a lot of «pure math» topics tend to be « wow, it's amazing
that those sentences make sense at all and are truer than nearly all
things in life, even though we have no clue what they refer to ! ».
> External (physical) reality doesn't enter into it all.
Amen.
> Extra credit bonus question: does the empty set exist?
There exist ontologies for whichever conclusion you want to reach.
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| Mathieu Bouchard ---- tél: +1.514.383.3801 ---- Villeray, Montréal, QC
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