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Shut up and calculate: an extreme mathematical universe

arxiv.org

41–50 of 191 posts

Re: Shut up and calculate: an extreme mathematical universe

#41

Earlier quoted context omitted.

On the contrary, reality works because reality cannot contain contradictions. But the set of possible structures without contradiction is a superset of what is physically realizable. And mathematics is just discovering and cataloging the set of structures without contradiction. So reality works because math works.

Why wouldn't reality contain contradictions?

I mean in the logical sense. If reality could contain logical contradictions then that would mean reality isn't rule-based, which means unconstrained randomness, no information, no meaning, etc.

Re: Shut up and calculate: an extreme mathematical universe

#42
post #30
post #23

Alright, why not go one step further and make Universe computational instead? (i.e. state is important in von Neumann-style instead of meaningless in classical math-style; or algorithms vs formulas)

Tegmark's Mathematical Universe Hypothesis (MUH) is actually pretty much a computational theory of the universe. It basically makes the assumption that there exists somewhere the simplest process imaginable: One that counts through and runs all mathematical formulas which includes all programs, which, in turn, includes all (computable) universes. This assumption explains why our universe is oddly complex: If all univ…

>This assumption explains why our universe is oddly complex

That is, to me, a weird mixing of scales. The universe only seems complex to us because of the scale at which we experience it in terms of time and physical extent as well as the convoluted way our own systems of understanding developed and then were later mutated and stretched into different forms to be better suited, etc. By definition the universe itself can't really be more or less complex than anything. At least not anything we can experience.

The idea of a geometric computer is surprisingly close to things I've been considering recently, but 'position of objects can be determined with infinite precision' seems strange. It may be just that I don't understand what is fully meant when you say 'geometric computer' but I would expect 'position' would be mostly meaningless in that space except as an emergent/illusory 'property'... and I don't think arbitrary precision would necessarily be implied either.

Re: Shut up and calculate: an extreme mathematical universe

#43

An interesting article addressing this from Sabine Hossenfender: http://backreaction.blogspot.in/2007/10/mathematical-univers... Her more recent article (review of Max Tegmark's book) also comments on the same subject: http://backreaction.blogspot.in/2017/11/book-review-max-tegm...

This (the universe is 'made' of math) seems to me like the most egregious error in the general outlook of contemporary scientifically-minded people—and one I made myself for many years.

If you really consider the issue closely, you'll see it depends on not overlooking certain dark corners of it which you can sort of ignore and assume to not contain contradictions—but they're there! And once you see them, it's hard to unsee them: what in the world would it mean for a desk to 'made' of mathematics—it's nonsensical. I think programmers are especially susceptible to this mistake because they're used to using mathematical descriptions to generate things, but even there, the idea that the math is doing any generating is a bias of our perspective since we're focused on the math; what's actually going on is a physical process involving silicon and plastic and metals etc., which can also be described mathematically, but the leap to being math is an unfounded step which could probably be predicted by the fact that that's where our focus lies.

It also begins to look kind of silly when you consider how human math is: it's an outgrowth of an evolved mental faculty. Cognition is certainly impressive relative to the other things we and various animals are able to do—but it's probably still in the same category of our other faculties like the olfactory, visual, tactile etc.—and unlikely to be involved in the literal fabrication of the universe.

Re: Shut up and calculate: an extreme mathematical universe

#44
Two points:

- What he describes in the abstract is nothing new. Part of your work as an applied mathematician is to take mathematical models developed by others, e.g, in the form of systems of differential equations, and treat them as absolute truths (for the sake of computation; essentially you create "a mathematical bubble" for yourself and choose to live in it), study the consequences, and present the results. So his claim of "I advocate" is disgusting plagiarism/credit-snatching of a well-known technique.

- What he actually advocated is total bullshit as far as physics is concerned. You can live as long as you want in the bubble of your mathematical models. But if you have to connect your math to reality, you have to make your math subordinate to empirical data, and if the data disagrees, your shiny mathematical model is wrong, period. Also don't forget what George Box said "All models are wrong. But some are useful".

Re: Shut up and calculate: an extreme mathematical universe

#45

A purely mathematical universe immediately brings to mind a question: Since chaotic systems evolve in a way provably intractable to calculation, how could any system based solely upon calculation address, well, almost everything that exists?

That's an odd definition of chaotic systems you are using.

It's not so much that chaotic systems can not be calculated but instead that enough precision of starting conditions can't be obtained to ensure an accurate result (for example, highly non-linear systems). The double pendulum system is a perfect example where computation is simple yet the system is still chaotic.

Re: Shut up and calculate: an extreme mathematical universe

#46
post #34
post #18

Earlier quoted context omitted.

Not really. Berkeley's idealism contests the objectivity of reality, while here we are presented with another view of the foundation of the (objective) material world.

This is true, but: > When we derive the consequences of a theory, we introduce new concepts — protons, molecules, stars — because they are convenient Couldn't matter itself be just another "human", "convenient" concept? Indeed the author writes: > our external physical reality is assumed to be purely mathematical Why should a purely mathematical reality also be material? Doesn't this lead to the logical conclusion th…

1) But convenience is objective! (It is not convenient to sit in a chair that is hanging upside down.) Which is why matter, even if it is seen as a "convenient" mental construct, is still objective.

2) Materialism and "objectivism" are closely tied together. Mathematics consists of abstractions (or models), and those reside, in particular, in our mind; being "convenient", these abstractions are therefore reflections of what lies outside, and so - almost by definition - the objective world itself, matter, cannot possibly be built from math. (Besides our mind, "abstractions" can also reside in other, inanimate, objects; regardless, this still means that some part of matter merely reflects, to a degree, some other part).

Re: Shut up and calculate: an extreme mathematical universe

#47
It is remarkable how sufficiently advanced physics / cosmology sounds to the layperson like a conversation between two teenagers who smoked weed a little while ago.

(My favorite: https://en.wikipedia.org/wiki/One-electron_universe)

I do not say that to belittle physicists. Not at all, I have the utmost respect for what they do.

But as they dig deeper and deeper, what they come up with sounds like the universe is a pretty strange place to be. Personally, I am okay with that idea, because, if I look closely enough, I have been living all my life in a world that does not really make sense. But it is really strange, nevertheless.

Re: Shut up and calculate: an extreme mathematical universe

#48

Math works because reality works. Not the opposite. Reality is bigger than math. Math is just a tool that models reality.

On the contrary, reality works because reality cannot contain contradictions. But the set of possible structures without contradiction is a superset of what is physically realizable. And mathematics is just discovering and cataloging the set of structures without contradiction. So reality works because math works.

In _Road to Reality_, Roger Penrose has a diagram that illustrates the Platonic world of mathematics fully encompassing the physical world, and the physical world fully encompassing the mental world (since minds are physical), and the mental world fully encompassing the Platonic world of mathematics. Although each encompasses the other in its entirety, each depends only on a small part of its predecessor. Penrose says "...the Platonic world may be the most primitive of these three, since mathematics is a kind of necessity, virtually conjuring its very self into existence through logic alone."

Re: Shut up and calculate: an extreme mathematical universe

#49
It baffles me that people ignore the fact that they have subjectivity when making these claims. It makes a certain amount of sense since science itself aims to remove any taint of subjectivity in its practice, so folks who want to be thoroughly 'scientific' in other aspects of their lives (e.g. their personal philosophies of reality) carry over over this ideal.

But it's also a contradiction since science scientific methodology demands we check our results empirically: the fact that you have subjectivity (i.e. that qualia exist) and what it's like, is the most direct empirical fact we have access to and which needs reconciling in any discussion of the universe's constitution.

I think people sort of push this point aside either by saying that qualia/subjectivity could be generated by math (or a computational process), and that's what really matters. But we have no examples of abstract math generating anything; physical processes generate things and we use math to influence their behavior—but that's it! And furthermore, even if math generated subjectivity—it's still there in all of its un-mathematical obviousness at the end of the day.

I've yet to see an argument in favor of math having higher ontological status than this which wasn't every bit as unrestrainedly imaginative and unfounded as Plato's 'ideal forms'. I would expect a thoroughgoing adherent to scientific methodology to instead say something on the lines of, "this is outside the domain of science to judge one way or the other; the most we can say is the idea that reality is made of math is one untestable hypothesis among many whose probabilities of correctness each approach zero by dint of their many peers."

Re: Shut up and calculate: an extreme mathematical universe

#50
post #39

A purely mathematical universe immediately brings to mind a question: Since chaotic systems evolve in a way provably intractable to calculation, how could any system based solely upon calculation address, well, almost everything that exists?

Chaotic systems are only intractable if you measure the initial conditions with finite precision.

No, that is not true. Their intractability has absolutely nothing to do with the precision of measurement. Assume the initial condition with infinite precision and the further evolution of the system is still intractable. Ignoring the Heisenberg Uncertainty Principle for a moment and getting to the heart of chaos theory the problem is the production of information at a rate faster than any existant (and I believe, though I don't understand it well enough to give exact details) or fundamentally possible future system of mathematics can compensate for. Nonlinear systems (ie, essentially everything in existence) display chaos (extreme sensitivity to initial conditions, period-doubling, whatever you wish to call it) on every scale. Were the universe mathematics and mathematics alone, all things which are provably outside of the grasp of mathematics would also be non-existent. Such things, however, do exist.

While we may not be able to predict the location of a single molecule of air in a mere 10,000 years with a rough accuracy of a cubic femtometer, the universe does it. And our inability to predict it is not because we need a bigger computer. Our inability to predict it is because in order to predict it, we would have to simulate the entire universe and every single particle within it, and every interaction between all of them, to infinite (ehhh... maybe) precision. Which would have an information load exactly as big as the universe itself and increase entropy (which implies it takes as much time) as much as actual evolution of the entire universe over that course of time. To predict one molecule of air. And the universe does it for all the molecules of air. Along with all the other particles.

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