Mathematical structure: I don't know what this means, and I don't think Wikipedia's definition is the relevant one. Can we give minimal examples of mathematical structures? What's simpler than the empty set? Is a single axiom a mathematical structure? (What if that axiom is ridiculously (infinitely?) long---how short does something have to be to be an axiom? Where are we getting the language we use to write out the axiom, and where did it get its axioms? ("Memetic evolution?! That's not even a... what is this i dont even"))

Research on numerica... (read more)

(Warning: I be hittin' the comment button without reviewing this carefully, views expressed may be inaccurately expressed and shit, ya dig? Aight yo.)

Thanks for the pointers. I wish there were a place for me to just bring up things I've been thinking about, and quickly get pointers or even conversation. Is Less Wrong IRC the best place for that? I've never used it.

I tend to think that in order to tackle this issue it might be necessary to understand how to implement a program that can 'understand' and generate new mathematics at least as generally as a h

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Why no uniform weightings for ensemble universes?

by Will_Newsome 1 min read31st Jul 201135 comments

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Every now and then I see a claim that if there were a uniform weighting of mathematical structures in a Tegmark-like 'verse---whatever that would mean even if we ignore the decision theoretic aspects which really can't be ignored but whatever---that would imply we should expect to find ourselves as Boltzmann mind-computations, or in other words thingies with just enough consciousness to be conscious of nonsensical chaos for a brief instant before dissolving back into nothingness. We don't seem to be experiencing nonsensical chaos, therefore the argument concludes that a uniform weighting is inadequate and an Occamian weighting over structures is necessary, leading to something like UDASSA or eventually giving up and sweeping the remaining confusion into a decision theoretic framework like UDT. (Bringing the dreaded "anthropics" into it is probably a red herring like always; we can just talk directly about patterns and groups of structures or correlated structures given some weighting, and presume human minds are structures or groups of structures much like other structures or groups of structures given that weighting.) 

I've seen people who seem very certain of the Boltzmann-inducing properties of uniform weightings for various reasons that I am skeptical of, and others who seemed uncertain of this for reason that sound at least superficially reasonable. Has anyone thought about this enough to give slightly more than just an intuitive appeal? I wouldn't be surprised if everyone has left such 'probabilistic' cosmological reasoning for the richer soils of decision theoretically inspired speculation, and if everyone else never ventured into the realms of such madness in the first place.

 

(Bringing in something, anything, from the foundations of set theory, e.g. the set theoretic multiverse, might be one way to start, but e.g. "most natural numbers look pretty random and we can use something like Goedel numbering for arbitrary mathematical structures" doesn't seem to say much to me by itself, considering that all of those numbers have rich local context that in their region is very predictable and non-random, if you get my metaphor. Or to stretch the metaphor even further, even if 62534772 doesn't "causally" follow 31256 they might still be correlated in the style of Dust Theory, and what meta-level tools are we going to use to talk about the randomness or "size" of those correlations, especially given that 294682462125 could refer to a mathematical structure of some underspecified "size" (e.g. a mathematically "simple" entire multiverse and not a "complex" human brain computation)? In general I don't see how such metaphors can't just be twisted into meaninglessness or assumptions that I don't follow, and I've never seen clear arguments that don't rely on either such metaphors or just flat out intuition.)

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