The numbers most physicists use are finitely specifiable. π, for instance, has an infinite and non-repeating representation and yet there exist algorithms to get whatever nth digit you desire. Numbers like π are said to be computable and so are expressible in a finite way. Physicists get to keep π. There are other numbers, like Chaitin's constant, which have no such algorithm. What is worse, there are so many more of these numbers that the numbers physicists use may as well not exist, they are so few. The paper goes on to speak of these non-computable numbers as being, in essence, what we mean by a random number. To my mind, this is akin to Peirce's statement that nearly everything is random. Gisin continues by pointing out that these numbers, as they would take an infinite amount of energy to store in a finite space, are decidedly non-physical. Chaitin points out that we cannot even really get to know them as there is nothing we can say about them. It seems, if Pierce excepted such a thing that he might too consider them to be non-meaningful.
So now, left with only those numbers which behave nicely in that they are finitely storable and can be computed, we are left with numbers that can be compared or related. Because everywhere the word number appeared above you can substitute some physical thing (energy-matter), we have a situation where we can speak about what is real through relations even though anything that can be considered real is vanishingly small wrt what is random. The last detail, which seems relevant is that some dynamics (really most dynamics) are notoriously badly behaved. That is, long term prediction in classical physics is notoriously sensitive to initial conditions. The fact that information in our model universe is finite, as understood above, those initial conditions will march towards randomness despite the fact that the dynamics are determined. I don't know Pierce's work outside of things you have told me, but it seems that there might be similarities worth persuing. -- Sent from: http://friam.471366.n2.nabble.com/ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/
