I got a job working one on one with an autistic teenager. The first month I lived in the woods, but I did have a car to drive to work. A year later I returned to college and lived off student loans for some years. Academia didn't work out, but I made a number of connections with significant mathematicians. A large portion of mathematicians have little coding ability, so I help some amazing people out, learn lots of mathematics and have lots of fun. I just don't make any money, but I'm retired now so it is no longer an issue. I'm now a gentleman of leisure.
I now have diagnoses of rapid cycling bipolar II and moderate autism, but in the early Nineties I realized I was dealing with ADHD. I was fortunate that one of my autistic abilities was being extremely good at mathematics and computer science. My important adjustment was becoming a computer consultant on projects that lasted several months. I can attack new projects with great intensity, but I fry out after a few months.
While I did great in the Nineties, I didn't leverage my work into a network of contacts. Giant mistake as the Dot Com crash destroyed me professionally. I went from making $65/hr to being homeless living in the woods.
I reinvented myself by going back to college working towards a Ph.D. in mathematics. I ended up concluding that I didn't have the communication skills needed to teach mathematics or the publications needed to be a researcher.
Ultimately I had to give up being a computer professional. I could no longer get intellectually and financially appropriate work. I have continued to work on a number of projects over the last twenty years, so I have preserved much of my programming skills. I have had a popular website for twenty years on http://tetration.org covering what exists beyond exponentiation.
I learned that something one must be ready to completely reinvent themselves to have a chance at happiness.
I've been wondering if there was anyplace that could diagnosis autism savant syndrome. It may be a useful label to communicate who I am to people. I have my early mathematical biography at https://tetration.org/index.php/Biography.
I contacted Dr. Tiozzo about the similarity of the two fractals and he replied,
From Giulio Tiozzo
"Of course, the similarity between the set of zeros of Littlewood polynomials and Thurston’s entropy bagel is striking.
In fact, I proved a few years ago that the two fractal sets the same inside the unit disk!
The difference is that Baez’s set is symmetric under circle inversion, while Thurston’s set is not: the parts outside of the unit disk are completely different."
Dynamics is basically fractionally iterated functions. So the equation should be applicable to all of physics. It also provides a new combinatorial view of dynamics.
I created http://tetration.org which explores what lies beyond exponentiation. My life's work has been to extend the Ackermann function to the complex numbers and matrices. I believe my website lead to a renaissance in tetration research.
The following Mathematica code replaces a thousand lines of earlier code. It computes the flows from maps. Combined with the historic three argument Ackermann function it allows the Ackermann function to the extended to the complex numbers.
What is the most significant one line of code that you have seen or written? Ideally something that takes the understanding of the system to a higher level.
I have written a flow function for extending iterated functions from discrete time to fractional or continuous time, known as a flow. One line of Mathematica code that does all the heavy lifting. This provides a foundation for extending tetration and the Ackermann function to the complex numbers.
I'm working for the Azimuth Project modeling the Coronavirus and deploying a new math web server for them.I'm learning Category Theory at https://categorytheory.zulipchat.com/. Both are projects supported by mathematician John Baez. The Azimuth Project is righteous as they supported the copying of climate data from the US government when Trump came into office.
The Universe is a hierarchy of orders; quarks and gluons, atoms, molecules, cells, multi-cellular and on. So hyperoperators form a natural hierarchy to model multilevel systems. Feynman's Path Integral with the integral removed is just tetration. So I believe the higher operators through self organization/renormalization are directly associated with specific levels of reality, but except for QFT I have no suspicion as to which hyperoperators might be associated with levels of physics. Here is how it might work. Hexation might model chemistry while heptation could model simple biological systems. Thanks for asking. This is fun stuff to work on.
Writing Mathematica software with Stephen Wolfram's support to extend the hyperoperators beyond exponentiation - tetration, pentation and so on, from the natural numbers to complex numbers and even matrices. I do this by extending the iteration of any smooth function to real and complex iterates. http://iteratedfunctions.com/ and http://tetration.org/.
Physics has two mathematical methods for it's representation, partial differential equations and iterated functions. My work is more general than physical systems or even the universe because I can consider both measure and non-measure preserving systems. I am looking at AI applications as a system that is tuned to solve for physically possible models.
The accepted message length is less than the limit for Twitter. Small is good. Microscopic, not so much. I figured I would just let my message find its own way back to Mozilla from here.
Let me add that the straw that broke the camels back was not my frustration with how Firefox itself ran, but Mozilla's appearance of a trying to radically limit customer input! As a software developer I know things can go wrong, but you always insure that the lines of communication are open. The attempt to limit communicate when things are not going well is tantamount to committing product suicide!
I have one of the main websites on tetration at http://tetration.org. Recently I worked on machine language comprehension of mathematics, https://fangornforest.org. I completed a four decade project working with Stephen Wolfram for Mathematica to support fractional iteration https://resources.wolframcloud.com/FunctionRepository/resour....
I now operate as a social activist helping people and non-profit organizations out.