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.

Let's say I fit the neurodivergent stereotype, and this sentence especially fits most of my attempted careers down to a T - "I ended up concluding that I didn't have the communication skills needed to do X".

At times (I feel like) I am a great communicator, the other times I can see people thinking I'm damn slow, and most of the time it's bimodal like that.

I am almost 36 as well, never finished a damn thing in my adult life.

This could be me as well - I’ve had a few careers and similar neurodivergencies, along with a nice smattering of trauma. This wasn’t asked for so take with a grain of salt, but as someone who had “rapid cycling bipolar II” as my closest dx which never felt entirely correct, I found looking into dissociation and dissociative disorders to actually fit the bill for me after decades of muddling around with “almost but not quite right” models. I only say so because it would have saved me a lot of time if someone had even mentioned the possibility to me.

How tf do you come back from being "homeless in the woods" to "working towards a mathematics PhD"?

Also, as what did you reinvent yourself in the end?

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 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.

(Joke) Yes, usually the path is reverse.

Wow, GEB came immediately to mind.

Well I got a lot from it, but human nature? I may have missed it.

Dune and Dune Messiah in 22 hours.

that's the novel movies are based on right?

Yes.

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.

>if there was anyplace that could diagnosis autism savant syndrome

Wouldn't most qualified psychiatrists working with autism (or adult autism) do? All it takes is diagnosis autism (what they do anyway) and being able to identify savant abilities (which is even easier).

If you have a moment, how do you deal with boredom when you are really really really smart? How do you deal with stress? How do you stay motivated?

I had a look at your writings, and was wondering if you saw any worthwhile ideas on here: https://www.timecube.space/

Which writings? Calling someone schizophrenic is pretty rude. I don't see anything confused about their site, but I'm not a mathematician.

No worthwhile ideas. Why, what worthwhile ideas do you see that reminds you of my writings?

See 'Entropy bagels' and other complex structures emerge from simple rules at https://news.ycombinator.com/item?id=39529374 for a related post.

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."

Thanks for contacting him! I'll do some diving into his work, that's super cool =)

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.

order=10;

H[0]=0;

H[1]=f'[0]^t ;

Do[H[max]=First[r[t]/.RSolve[{r[0]==0,r[t]==Sum[Derivative[k][f][0]BellY[max,k,Table[H[j]/.t->t-1,{j,max}]],{k,2,max}]+ f'[0] r[t-1]},r[t],t]],{max,2,order}];

Schroeder=f'[0]^t z+Sum[1/k! H[k]z^k,{k,2,order}]

Abel=Limit[Schroeder,{f'[0]->1}]

Are there applications?

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.

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.

Flow[f_, t_, x_, L_, order_ : 3] := Module[{s}, H[0] = L; H[1] = f'[L]^t ; Do[H[max] = First[r[t] /. RSolve[{r[0] == 0, r[t] == Sum[Derivative[k][f][L] BellY[max, k,Table[H[j] /. t -> t - 1, {j, max}]], {k, 2, max}] + f'[L] r[t - 1]}, r[t], t]],{max, 2, order}]; s = Sum[1/k! H[k] (x - L)^k, {k, 0, order}] ];

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.

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.

I won't pretend to fully understand this, although I do understand the basic theory of higher-order hyperoperators. I'm curious, though -- where/what are the applications for this?

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.

That explanation was surprisingly accessible, thank you! It also blew my mind. I'd never thought of the building blocks of the universe as forming a hierarchy before, although in retrospect, it feels obvious.

Were you being literal when you gave the examples of chemistry as hexation and biology as heptation? If so, why are they those levels specifically? Or were you just using those as examples because they're roughly one "step" apart on the hierarchy (i.e., molecules -> cells)? Sorry if this is a dumb question.

I strongly believe that quantum field theory is at the level of tetration or pentation. The others were possible examples. Thanks for the question.