Am I correctly summarizing this statement, for my own understanding?

“All values in the cosmos are integers. Decimals exist to help humans make comparisons between objects.”

No. They're talking about real numbers; even decimal numbers (rationals) are isomorphic to integers. The reals are different.

I mean, they seem to be saying the exact opposite of that based on the usual way people talk about the "reals".

You could put all the human knowledge in a single real number and still have infinite room left.

There exists an abstract mathematical mapping, sure. However, finding the spot in the real number where that's the case may require infinite storage (you need to store the pointer) or infinite time (you start searching through the number to find what you want). It also has a halting problem where you don't actually know how you'll know when you find that data.

> The universe is _literally_ a real number machine

I am wary of this. Just because you have a good predictive model based on math, and the math can be made rigorous using ZFC / Cauchy sequences / infinite decimals / etc., doesn't mean that any of those rigorous mathematical concepts are literally running the real universe.

I don't get what you say in the last paragraph. Isn't the mapping of zero and one to nothing and something kind of the easiest thing (e.g. one photon or no photon)?

For the first paragraph it is my understanding that the universe is discrete/quantizied and it is not running on 'real numbers'.

> I don't get what you say in the last paragraph. Isn't the mapping of zero and one to nothing and something kind of the easiest thing (e.g. one photon or no photon)?

You can map and mapping is useful, but the map lives in your head and isn't the territory.

> For the first paragraph it is my understanding that the universe is discrete/quantizied and it is not running on 'real numbers'.

This is a widely believed folk myth among software engineers, but it isn't supported by evidence. There are some speculative theories that try to solve some problems in physics by quantizing space, but right now they are no more empirically supported than other speculations.

Worth a read:

1. "Russell’s No Man’s Land" [0]

2. "The hollow universe of modern physics" [1]

[0] https://edwardfeser.blogspot.com/2020/08/russells-no-mans-la...

[1] https://edwardfeser.blogspot.com/2022/05/the-hollow-universe...

Mh, but I thought it was widely held that there are things such as the Planck constant which constitute bounds on divisibility. There rather seems to be no indication to believe conversely that the universe works on real numbers. Which makes at least intuitive sense that there isn't anything which contains infinite information.

There is such a thing as the Planck constant. It doesn't constitute a bound on the divisibility of space. It is a length scale below which we do not expect our current physical theories to make good predictions. See https://www.fnal.gov/pub/today/archive/archive_2013/today13-...

> Which makes at least intuitive sense that there isn't anything which contains infinite information.

There are no real numbers outside of human beings' minds. The information in a real number is a theoretical mathematical concept from human minds for which there is no evidence in nature.

There is no definitive evidence that nature confirms to either continuous or discrete math at the smallest scales, but for now, if you look at theoretical physics papers, you will see integrals and derivatives, not sums and differences.

>There is an easy counter model. The universe is _literally_ a real number machine, i.e. even a particular point is only describable to us in the approximate.

There is actually some debate about that, and for good reason. There are even a couple of practicing physicists looking at how predictions would differ assuming the universe has finite precision, and if I recall correctly the results from that investigation are non-trivial.