> 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.