Dear Stephen, A thing that I often ask myself concerning MMH is the question about what is mathematical and what is not?. The set of real numbers is a mathematical structure, but also the set of real numbers plus the point (1,1) in the plane is. The set of randomly chosen numbers { 1,4 3,4,.34, 3} is because it can be described with the same descriptive language of math. But the first of these structures have properties and the others do not. The first can be infinite but can be described with a single equation while the last must be described extensively. . At least some random universes (the finite ones) can be described extensively, with the tools of mathematics but they don´t count in the intuitive sense as mathematical.

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What is usually considered genuinely mathematical is any structure, that can be described briefly. Also it must have good properties , operations, symmetries or isomorphisms with other structures so the structure can be navigated and related with other structures and the knowledge can be reused. These structures have a low kolmogorov complexity, so they can be "navigated" with low computing resources. So the demand of computation in each living being forces to admit that universes too random or too simple, wiith no lineal or discontinuous macroscopic laws have no complex spatio-temporal volutes (that may be the aspect of life as looked from outside of our four-dimensional universe). The macroscopic laws are the macroscopic effects of the underlying mathematical structures with which our universe is isomorphic (or identical). And our very notion of what is intuitively considered mathematical: "something general simple and powerful enough" has the hallmark of scarcity of computation resources. (And absence of contradictions fits in the notion of simplicity, because exception to rules have to be memorized and dealt with extensively, one by one) Perhaps not only is that way but even may be that the absence of contradictions ( the main rule of simplicity) or -in computationa terms- the rule of low kolmogorov complexity _creates_ itself the mathematics. That is, for example, may be that the boolean logic for example, is what it is not because it is consistent simpleand it´s beatiful, but because it is the shortest logic in terms of the lenght of the description of its operations, and this is the reason because we perceive it as simple and beatiful and consistent. . > Dear Albert, > > One brief comment. In your Google paper you wrote, among other > interesting things, "But life and natural selection demands a > mathematical universe > <https://docs.google.com/Doc?docid=0AW-x2MmiuA32ZGQ1cm03cXFfMTk4YzR4cn...>somehow". > Could it be that this is just another implication of the MMH idea? If > the physical implementation of computation acts as a selective pressure > on the multiverse, then it makes sense that we would find ourselves in a > universe that is representable in terms of Boolean algebras with their > nice and well behaved laws of bivalence (a or not-A), etc. > > Very interesting ideas. > > Onward! > > Stephen -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.