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

Mathieu Bouchard matju at artengine.ca
Sat May 28 20:06:00 CEST 2011


On Wed, 25 May 2011, Bryan Jurish wrote:

> apologies for moving to pd-ot without a direct reply... my bad.

You did send me a direct reply as well, but I couldn't reply to it on 
pd-ot until I was subscribed there.

> The pitfall of course being the `infinitely long program' part, since if 
> the program as such were infinitely long it wouldn't be a TM anymore, at 
> least not in Turing's sense...

At UdeM, there is/was a course called Informatique Théorique, for which 
I'm pretty sure I was told that it contained many infinite TM tapes, one 
for each infinite cardinal or something like that... several levels of 
uncountability. But I might be misremembering.

> but if you need an infinite description to generate the desired output 
> (number) anyways, then you might as well shove all the nasty patternless 
> data to the input part of the description pair, and then you can work 
> with a trivial program (cat) which just copies its input to its output: 
> then you've got a finite TM and incompressability, at the price of 
> "only" an infinite input sequence.

oh ok. I didn't study TM theory enough to know those distinctions. To me, 
the equivalence principle is good to know, but actual TM mechanics are 
somewhat like learning the Brainfuck language or anything similar : much 
more time-consuming than assembly language, for none of the benefits of 
assembly language !

>>> I can dig the idea of a non-terminating process,
>> I can't. It makes me think about the bloody Crown of England.
> :-D

It's still not terminated. Can I « force-quit » now ?

> Leibniz' too, if it could spare some attention from the umpteen 
> gazillion monads it has to keep track of.

Is that less than the number of virtual quarks ?

>> 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.
>
> I agree.  Sadly, most physicists I know tend not to do so to any great
> degree; the exception being a 70-year-old experimental molecular guy
> who's probably got a more solid background in philosophy than I do.

I'm not a physicist either. My last physics course was in grade 
thirteen... which was in 1996. But overall, I have more of a science 
background than a philosophy background, and I often read in physics 
manuals belonging to other family members... for fun.

>>> Extra credit bonus question: does the empty set exist?
>> There exist ontologies for whichever conclusion you want to reach.
> Best answer I've heard for that one yet!

Ever looked at ZFC and stuff ? (Zermelo Fried Chicken or whatever)

The saga of the questions of the family « what's the smallest number that 
is greater than the smallest infinity ? » and « is that the same as the 
number of different real numbers ? » led to all sorts of answers like 
« you need an extra axiom for that » which basically means that you can 
make up the answer that you want.

In some way, your question makes me think of that.

In the end, the conclusion you will want to reach will depend on what 
awaits beyond that conclusion. You will have to take into account what is 
going to be the purpose of the concept of existence, to see what are the 
requirements for the concept, the constraints on stuff you make up.

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


More information about the Pd-ot mailing list