Bruno Marchal wrote: Tegmark argues that reality is a mathematical structure and states that an open problem is finding a mathematical structure which is isomorphic to reality. This might or might not be clear: the mathematical structure with the property that all mathematical structures can be embedded within it is precisely the mathematical structure we are looking for.
The problem is in defining "embedded". I am not sure it makes set theoretical sense, unless you believe in Quine's New foundation (NF). I am neutral on the consistency of NF. With a large sense of "embedded" I may argue that the mathematical structure you are looking for is just the (mathematical) universal machine. In which case Robinson arithmetic (a tiny fragment of arithmetical truth, on which both platonist and non platonist (intuitionist) is enough. Indeed, I argue with comp that Robinson arithmetic, or any first order specification of a (Turing) universal theory is enough to derive the appearance of quanta and qualia. Actually, I'm using what's called NF with urelements (NFU) which according to what I've read is consistent. http://plato.stanford.edu/archives/sum2009/entries/quine-nf/ (section 7. Coda). Where would I go about finding out a survey of concepts including "universal machine"? Are they known to exist? How are they defined? It would be much easier if I didn't have to reinvent the wheel. The last sentence in the quote excites me: The leap from mathematics to things such as quanta and qualia is something I haven't really understood. Digital mechanism (the tiny arithmetic TOE) entails already a large part of Quantum Mechanics, and then group or category theoretic considerations (and knot theory) might explain the 'illusions' of time, space, particle, and (symmetrical) hamiltonians, and why indeed physical reality should appear as an indeterminate state of a physical vacuum. But the logic-math problems remaining are not easy to solve. That is normal in a such top down, mind-body problem driven, approach to physics (and psychology/theology/biology). Interesting! -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@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.
