>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.<p>Here is how far: Everything written <i>in words</i> 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.<p>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.<p>What is interesting, then, is that <i>observationally</i>, 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?<p>So:<p>>According to these ideas the amount of information in any physical system is bounded<p>"the amount of <i>observable</i> information in any physical system" -- any unobservable continuous information shows up as unpredictable changes in the observable information.