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>In addition to this mathematical soul-searching regarding real numbers, some physicists are beginning to suspect that the physical universe is actually discrete [Smolin, 2000] and perhaps even a giant computer [Fredkin, 2004, Wolfram, 2002]. It will be interesting to see how far this so-called “digital philosophy,” “digital physics” viewpoint can be taken. Here is how far: Everything written in words about the physical universe is, by necessity, discrete. Thus all information that can be encoded in human languages is discrete. Any non-discrete behavior of the physical universe which causes a change in the discrete information available to us, must, by assumption, have a component which is orthogonal to all of the prior discrete information (otherwise it is fully discrete). Since this component is independent of all previously available information, it looks like randomness. In other words: from the viewpoint of a discrete (linguistic) observer, the behavior of a continuous universe looks identical to that of a discrete universe that contains random fluctuations. What is interesting, then, is that observationally, our discrete observable universe is full of random fluctuations. Speculation as to their true continuous underpinnings is, however, unfalsifiable, unless the randomness itself can be made to disappear. I usually turn the question around: is it inconceivable that there would be a continuous universe with inhabitants that used a discrete language? So: >According to these ideas the amount of information in any physical system is bounded "the amount of observable information in any physical system" -- any unobservable continuous information shows up as unpredictable changes in the observable information. |
Tegmark takes a similar, but rather extreme, MW approach in his book 'Our Mathematical Universe'.
Personally, I struggle with Tegmark's use of Measure Theory, and proponents of various Anthropic Principles, because they seem to have a completely broken frequentist view of probability and inference.