1. Regarding reality as a set of numbers-
In physics numbers have units and I believe it is not possible to state what reality is without also stating what the units are. For example, he derived an equation that has the same form as the Schroedinger's equation. Since he thinks that only numbers exist, that equation has to be the one and only S... eq. However, in physics there are several different S... eqs depending on whether the wave functions are for photons or electrons or some other particle. The difference is in the units of the potential function V(x). Dick's potential function is a summation over data points. It is not at all clear how that is related to say the electric potential inside an atom.
2.On knowable vs. unknowable- This I believe is a misnomer. For example, what he should define is known and unknown data. If his data were truly unknowable, then it could never be used to determine V(x) which in the S... eq. is a known quantity.
3. Scale invariance- Fractals are scale invariant because no matter what resolution you look at them, they look the same. Turbulence is scale invariant- the eddies look the same at any size. The universe is not scale invariant- atoms, electrons, protons, etc. have certain sizes and when you look closely they look large, and when you look from a distance they look small. If they were scale invariant, they would look the same from any distance. Clusters of galaxies are thought to be scale invariant, probably because they had a tubulent birth. So Dick is plainly wrong here.
4. Reality must include senses as well as everything else. So I do not understand how he can exclude human sensations. In fact, this is where the idea of reality being just a set of numbers may be a good approximation. Somehow our brains combine hearing and sight and touch and taste into feelings or emotions, which may all have the same units; so it is safe to ignore the units when they are all the same. Dick's response about the models in the head seemingly supports this view.
I think that pretty well covers the issues you raised. Hope it is of some help.
I must confess that more often than not I do not understand your view of reality. I am not critical of it. I just do not get it. So when I fail to respond to your posts, it is because I fail to understand your view.
I do better with Dick's posts because they are grounded in math. Since doing a little research on what has been done previously on known and unknown data, I am getting a better handle on his work.
He essentially is solving the pollester problem. Pollesters have the problem of estimating the statistics of what a large group of people think based on a limited sample of what they think.
So the sample is the known data and the truth of what the whole group thinks is the summ of the known and the unknown data. Fisher solved this problem in 1925 coming up with what is now called the Fisher Information, that allows you to estimate your sampling error. Frieden wrote a book on it published in 1999 called Physics of the Fisher Information, or something like that (I have a very short memory). Hall took that body of work and extended it to derive Schroedinger's equation, and the uncertainty principle.