[PD-ot] Real numbers (WAS: [PD] CVs) (fwd)

Mathieu Bouchard matju at artengine.ca
Sat May 21 22:06:27 CEST 2011


I wasn't on pd-ot...

---------- Forwarded message ----------
Date: Sat, 21 May 2011 15:53:19 -0400 (EDT)
From: Mathieu Bouchard <matju at artengine.ca>
To: Bryan Jurish <jurish at uni-potsdam.de>
Cc: pd-ot at iem.at
Subject: Re: Real numbers (WAS: [PD] CVs)

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.

  _______________________________________________________________________
| Mathieu Bouchard ---- tél: +1.514.383.3801 ---- Villeray, Montréal, QC


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