I wasn't on pd-ot...
---------- Forwarded message ---------- Date: Sat, 21 May 2011 15:53:19 -0400 (EDT) From: Mathieu Bouchard matju@artengine.ca To: Bryan Jurish jurish@uni-potsdam.de Cc: pd-ot@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.
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