Study of Mathematics: Analog vs. Digital

I agree with what Prof. Benjamin is saying. It is not necessary for people to understand limits and functions, but it is necessary for people to understand probability and statistics.

It is necessary for scientist to understand that we live in an analog world. Our tools are functional. Thus they are digital and cannot describe nature.

The reason our Neural Networks work the way the they do is because our brain/culture are analog computers. The data they work with is analog. We use algorithms like Monte Carlo systems to convert analog information into digital data.

We know very little about analog systems. We know very little about converting analog information into digital systems. Yes, we can collect analog information on a digital CCD chip to create a picture. But we cannot reverse the process.

This is because of calculus. Sorry Newton. What is the probability an electron will change charge if the surrounding baryons forms a Copper atom? What is the probability an electron will change charge if the surrounding baryons forms a Carbon atom? These are analog questions.

To even setup an analog question, one needs 16 bits of information per baryon emission, minimum. To change a baryon, each affecting boson produces 4 bits of information. This is the many to one relationship. Thus the universe is analog not functional.