4 hundred quadrillonth?

[Steven D'Aprano]

On Mon, 25 May 2009 16:21:19 +1200, Lawrence D'Oliveiro wrote:

> In message <mailman.674.1243192904.8015.python-list at python.org>, Dennis
> Lee Bieber wrote:
> 
>> On Sun, 24 May 2009 22:47:51 +1200, Lawrence D'Oliveiro
>> <ldo at geek-central.gen.new_zealand> declaimed the following in
>> gmane.comp.python.general:
>> 
>>> As for exactitude in physics, Gregory Chaitin among others has been
>>> trying to rework physics to get rid of real numbers altogether.
>> 
>> By decreeing that the value of PI is 3?
> 
> Interesting kind of mindset, that assumes that the opposite of "real"
> must be "integer" or a subset thereof...


(0) "Opposite" is not well-defined unless you have a dichotomy. In the 
case of number fields like the reals, you have more than two options, so 
"opposite of real" isn't defined.

(1/3) Why do you jump to the conclusion that "pi=3" implies that only 
integers are defined? One might have a mapping where every real number is 
transferred to the closest multiple of 1/3 (say), rather than the closest 
integer. That would still give "pi=3", without being limited to integers.

(1/2) If you "get rid of real numbers", then obviously you must have a 
smaller set of numbers, not a larger. Any superset of reals will include 
the reals, and therefore you haven't got rid of them at all, so we can 
eliminate supersets of the reals from consideration if your description 
of Chaitin's work is accurate.

(2/3) There is *no* point (2/3).

(1) I thought about numbering my points as consecutive increasing 
integers, but decided that was an awfully boring convention. A shiny 
banananana for the first person to recognise the sequence.




-- 
Steven