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Comment by dcow | Hacker News Reader

I find the idea of a universe with a discrete substrate/structure both natural and compelling. I wish we’d explore it more. If you really think about it, it’s hard to imagine nature would just happen into a system with irrational numbers as we naïvely (undergraduate level college and below) understand them. Things clearly look infinite on a macro level, but “what type of discrete systems give rise to the observed macro behavior” is a field that needs more exploration.

The maths analog is alternative number systems, which at least seem to be gaining interest and popularity.

The metaphor for programmers: is the universe just a beautifully seeded Conway’s game of life?

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The real numbers are irrational almost everywhere, they are uncomputable 'almost everywhere' also.

“what type of discrete systems give rise to the observed macro behavior” is what we have been doing forever through Laplacian determinism.

There are no alternative numbers systems that get around this.

That is the whole point of the problem of the cardinality of the continuum.

We know that Laplacian determinism fails, with quantum mechanics being the easiest counterexample but Cantor diagonalization is another.

The sofar unsuccessful efforts to produce string theory is an example of this effort, changing world lines into sheets.

With the discovery of strange non chaotic attractors and the discovery that our numerical systems are subject to the WadA property in time delayed and Hamilton systems it is possible that a unified model may not exist.

None of this is undergrad though, due to how we have chosen to teach it.

But it is very possible that existential quantifiers are what math limits is to building models of.

Couldn't agree more, though when I see this brought up, I've always seen "people who seem to know more than me" saying that it just leads to other problems, and they kind of hand-wave it away... but I still think there should be some more serious exploration of this. How could "real" numbers _truly_ exist, any more than "imaginary" ones?

I think anybody who thinks real numbers exist will also say that imaginary numbers exist. "real" and "imaginary" in the context of numbers are just arbitrary labels assigned for historical reasons, they're not meant to convey any philosophical judgements about existence.

I don't think so. You can have imaginary rationals, or even imaginary natural numbers (that is, a+bi, where both a and b are rational numbers or integers).

Although I will admit that a big part of the point of the reals was solutions to polynomials, and it takes complex numbers to be able to solve them all.

> I find the idea of a universe with a discrete substrate both natural and compelling.

I really like the idea of a finite, ever growing, and totally knowable universe. What Wolfram is searching for. The universe was a small finite graph at the beginning (which we can possibly know by looking at the sky), and it grows since that, according to some deterministic rules. This means that the universe is perfectly replayable, we can replay history, observe the thoughts of famous people, and such.

I believe there may be ways to introduce entropy into a system like that so it need not completely deterministic, but can’t quite remember the name for the topic…

Maybe someone has a survey paper? Two for discussion would be Loop Quantum Gravity and honorable mention for Wolfram's hypergraph.

> Maybe someone has a survey paper? Two for discussion would be Loop Quantum Gravity

What would you like to know about it?

> honorable mention for Wolfram's hypergraph.

I'd call it more of a dishonourable mention. If you're looking for niche theories in physics with discrete spacetime, I guess you'd want to look at https://en.wikipedia.org/wiki/Causal_sets

Why dishonorable?

His work is pretty interesting to me: graph taxonomy of all possible rules and rules spaces (what Wolfram calls the Ruliad) seems like a very natural extension of Computer science and Analysis.

Thanks.

Curious why the hypergraph diss? Regardless of their process, it sounds like they came up with a model which has some alignments with conventional theory.

Sounds like your describing complex systems thoery https://en.wikipedia.org/wiki/Complex_system

Not quite. I’m describing a system with discrete structure that gives rise to macro level complex system in the same way the game of life can implement arbitrary computation.

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