----- Original Message ----- From: "Stephen Paul King" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Cc: <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]> Sent: Wednesday, January 21, 2004 5:39 PM Subject: Re: Is the universe computable
SPK wrote: > You are confussing the postential existence of a computation with its "meaningfulness". But in the last time you are getting close to my thesis. We should not take the a priori existence of, for example, answers to NP-Complete problems to have more "ontological weight" than those that enter into what it takes for "creatures like us" to "view" the answers. This is more the realm of theology than mathematics. ;-) > ..This is rather like an argument I like to put forward when I'm feeling outrageous, and one which I've eventually come to believe: That the real number line 'does not exist.' There are only countably many numbers you could give a finite description of, even with a universal computer (which the human mathematical community probably constitutes, assuming we don't die out), and in the end the rest of the real numbers result from randomly choosing binary digits to be zero or one (see eg. anything by G. Chaitin). So while the natural numbers and the integers have a rich internal structure (rich enough to contain the whole universe and more, according to most subscribers on this list, I suspect), the reals can be encoded in the single 'program' of tossing a coin. By this I mean that the only 'use' or 'meaning' you could extract from some part of the binary representation would be of the form 'is this list of 0s and 1s the same as some pre-chosen lis of 0s and 1s?', which just takes you back to the random number choosing program you used to create the reals in the first place. -- Chris Collins --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com). Version: 6.0.561 / Virus Database: 353 - Release Date: 1/13/04
