Wave is a computer language based on continuations. It comes out of my TTCA project. If more interest does not develop in the TTCA architecture, I might open source that as well.

As of this date, there is no proof that this is computationally hard. Over the past couple of decades, I've mounted a number of attacks on the problem, and have learned a great deal about its nature. I have a promising approach that I would like to spend some more time with.

In my master's thesis, I present a deterministic solution to a discrete optimization problem, that of designing optimum carry skip adders. In this case, I found a dynamic programming solution; however, I have a concept for a general solution for deterministic discrete optimization, and would like to work it out. This might also result in writing a book on number theory.

I'm curious to learn more about homotopy type theory, and I am intrigued by an old paper out of Rice University where the authors used Turing Machine objects to represent numbers. This method can represent rationals, certain irrational numbers such as Pi, and represent a concept such as infinity, with finite objects. I question if continuous functions even exist, as all descriptions of mathematics are based on language.

Consider a simple example of a parabola, y = x^2; this is a finite sequence of symbols, so in this sense it is a discrete function. Any analysis we might perform will be equivalent to putting these symbols on a Turing Machine tape and running a program, which is a discrete process. In this light, I would like to better understand Cauchy sequences and the taking of limits. A state machine that prints .99999... forever will never jump states to a 1.0 even though the two numbers are the same.

The basis of this work is already in my "Tom's Turing Complete Computing" book, but this goes in a different direction from that work.

I have a concept for moving beyond microwave communication, though at this point it is conjecture. I would like to set up some experiments in a physics or engineering lab.

I put up a paper on my Research Gate that provides some evidence that the mathematics of quantum physics is describing observations of a Bayesian fluid. I would like to know if the Schrödinger Equation can indeed be derived from the dynamics of a Bayesian fluid. It would be a purely mathematical exercise.

On my website, I used to have an animation showing that if all particles are expanding, but we rescale so that they appear to be constant size, what we observe is that particles are attracted to each other. More recently I have put up an explanation on my Research Gate. I would like to spend some more time to see where this observation might lead.