Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

The physicalization of metamathematics and the implications for its foundations

writings.stephenwolfram.com

Post reply on HN
Print view View original

101–106 of 106 posts

Re: The physicalization of metamathematics and the implications for its foundations

#101

Post by uoaei »

meroes wrote: post #90
uoaei wrote: post #76

Earlier quoted context omitted.

We could be a little more permissive here about what constitutes a "model". Models are not systems. Maps are not territories. Formal systems are models. They model the world. Depending on which formal system you use, one may model the world better than another. There is no "perfect" there is only "comprehensible", "insightful", and, when predicting the future, "accurate". All of these are measured in degrees, not kin…

To me this a problematic viewpoint. All these formalisms are not meant to be models of the world. I’d even argue for anything to be accepted as a formal system it must be far removed from taking stances on reality.

Not all formalisms are models of the world. Not all models are formalisms. But all formalisms are models.

Re: The physicalization of metamathematics and the implications for its foundations

#103

Post by mxkopy »

JackFr wrote: post #99
mxkopy wrote: post #95

Earlier quoted context omitted.

I think there is some sort of threshold analogous to Turing-completeness (it probably is just Turing-completeness) when it comes to intelligence, in that information is eventually accessible to any system that passes it. If there is a species that thinks in terms of things that humans never could understand, then I would argue that species isn't part of our physical reality. If their expression of concepts is at all…

> If there is a species that thinks in terms of things that humans never could understand, then I would argue that species isn't part of our physical reality. What if they think can think in our terms AND they can think thoughts we are physically unable to, thoughts that are literally inconceivable?

If the thoughts have any interaction at all between each other, we would be able to leverage that to understand those higher-level thoughts to the degree that they affect the ones on our level. As an analogy, we can project an N dimensional object onto N! planes and get a complete, but not intuitive, description of what it is.

Maybe they know the exact value of Chaitin's constant, but at least we know its properties.

Re: The physicalization of metamathematics and the implications for its foundations

#104

Post by [deleted] »

BreakfastB0b wrote: post #98
ganzuul wrote: post #59

Earlier quoted context omitted.

General Relativity does not conserve energy.

Underrated point. Conservation Laws emerge from symmetries via Noether's theorem. In particular, Conservation of Mass / Energy arises from Time Translation Symmetry. General Relativity doesn't have Time Translation Symmetry because the universe is expanding. Now the question is can we extract free energy from the expansion of spacetime and avoid the heat death of the universe?

[deleted]

Re: The physicalization of metamathematics and the implications for its foundations

#105

Post by [deleted] »

nyc111 wrote: post #46

> that we call the ruliad—and that our physical laws arise in an inexorable way from the particular samples we take of this structure. What is a physical law? To me a physical law is a proportionality, that is, an equality of ratios. When we find something that stays constant while something else is changing, we call this a law. But it is really a proportonality. So, mathematics and physics is tied by proportionality…

[deleted]

Re: The physicalization of metamathematics and the implications for its foundations

#106

Post by pierrebai »

boole1854 wrote: post #49
novaRom wrote: post #10

Wolfram is a famous crackpot. I wish a peer review before I start reading his essay. No doubt he is again advertising his Wolfram* products, New kind of science, etc. No?

It seems to me that 'crackpot' is a bit strong. Even if one thinks Wolfram's foundations of physics project will never bare useful fruit, it's undeniable that he has made progress in other fields that are of interest to many people. A simple case in point: the study of logic has been a interesting human endeavor for thousands of years, since at least the time of the Greek and Vedic schools. After thousands of years o…

The tricky bit is that "simplest" has no formal definition. Here Wolfram claims to simplicity is having the least number of axiom, even if that axiom is very complicated.

Unfortunately, that is a perversion of the idea of axiom. An axiom should be as simple as it can be and ideally self-evident. Being self-evident is a strong requirement because axioms are not proven but accepted as true.

Clearly, no-one would say that Wolfram's axiom is self-evident. As a matter of fact, even Wolfram does not find it self-evident: that it is equivalent and sufficient as a basis needed to be proven, via proving it can generate all other set of axioms.

Basically, once a field has matured enough and we found a simple set of axioms, one can come up with a new set. All set of axioms must encode the same information, so you can either have multiple simple one or a single complex one. The quantity of information that is encoded must be constant.

So having a single axiom is not simpler, except by the very naive measurement of count.

Post reply on HN