I will try to read your essay in the near future. This issue with the Euler formula hinges around the unit circle in the complex plane with

e^{iﾎｸ} = cosﾎｸ + isinﾎｸ,

where this is a way of thinking about trigonometry. the multiplicity of these functions for angles ﾎｸ 竊' ﾎｸ + 2ﾏ\ is a part of the reason ln(-x) = ln(x) + iﾏ\, but also the entire set {..., -3iﾏ\, -iﾏ\, iﾏ\, 3iﾏ\, ...}. This leads to the concept of Riemann sheets, where the complex plane has multiple copies.

Cheers LC

Lawrence,

Hope you have time to check mine out before the deadline: https://fqxi.org/community/forum/topic/3396

Jim Hoover.

Dear Peter,

I believe we are kindred spirits on the topic of spin. I regard it as one of the fundamentals of physics along with charge. As you already know I have derived my theories from scratch, from the basic particles of the Universe to a computational TOE, and a working theory of time. I have given small glimpses of what I have found in some of the many posts I have made but I would certainly value your opinions and insights on a deeper level. It seems that my math and philosophy and even physics are sorely lacking when compared to others, but I have achieved something they haven't.

Regards

Lockie

The quantum numbers such as spin I think are independent. An elementary particle is I think an entanglement of states for each of these quantum numbers. In solid state physics these are called quasi-particles, such as phonons, plasmons, spinons etc. Experiments done recently have shown that an electron can be placed in a state where the spin is in one location and the charge at another. I actually think elementary particles are these entanglements of quantum states corresponding to these quantum numbers.

LC

Dear Lawrence,

Very good and informative essay, with interesting insights and connections, thank you! I liked how you connected different structures and techniques in quantum mechanics to build an argument about the relation with undecidability. Particularly, I am interested in the topological obstructions, but for independent reasons. Thanks again, and I wish you success with the essay!

Cheers,

Cristi

    Thanks for the boost. Try to read Szangolies' essay on a related development, and Palmer's on the fractal geometry.

    Your paper works with the connection between Gödel theorem or self-reference and consciousness. I have thought that consciousness is a sort of epiphenomenology that is an illusion having an illusion of itself. I have not read it in its entirty, and I do see you connect with what look like fractals.

    I have been slow. I have had Covid-19. It hit me at the 3rd week of March and lasted about 10 days. It relapsed in April and the fatigue part of this was serious. I still sleep more than I used to, but the most pernicious aspect of this has been dogging me. It is as if my brain has been rewired, or maybe hormone setpoint levels changed. I am not quite the same person I was; I feel as if I am an abruptly changed person. The worst part of this change is that I am more depressed and irritable than I was. It has been hard for me to participate much in this contest.

    Cheers :LC

    Dear Lawrence,

    Here's what I replied to your comment on my page:

    Thanks for the visit. I am very sad that you got Covid-19, I hope it is the easiest form and you'll be well as soon as possible. Don't worry about my essay until you get well, but please get well, because I would love to hear some feedback from you, if possible about the longer version, even if it will be long after the contest ends.

    > Your paper works with the connection between Gödel theorem or self-reference and consciousness. I have thought that consciousness is a sort of epiphenomenology that is an illusion having an illusion of itself. I have not read it in its entirty, and I do see you connect with what look like fractals.

    I didn't appeal to self-reference or fractals, although I'd agree with you that they play a role. But it has strong relation with no-go theorems. As for consciousness, I am interested in the hypothesis that there is something irreducible about it (this irreducible I called "sentience"), and I try to see if this makes testable predictions. My claim is that it does. Indeed, for many who think consciousness is irreducible, the epiphenomenal position seems a good refuge, since it makes the hypothesis unfalsifiable. But I think we should be brave and don't avoid the fact that it does make predictions. So we can test it. We risk, those who deny it risk to see the predictions confirmed, but they can still continue to deny it, since the test of a prediction is not necessarily a proof of what led to the prediction. A rejection of the prediction is a rejection of what led to the prediction, so it is more risky for those who endorse the position that consciousness is not fully reducible. If we want to bring the hard problem into science, we have to take this risk.

    I wish you to get back in shape soon!

    Cristi

    Dear Lawrence,

    Glad to read your work again.

    I greatly appreciated your work and discussion. I am very glad that you are not thinking in abstract patterns.

    While the discussion lasted, I wrote an article: "Practical guidance on calculating resonant frequencies at four levels of diagnosis and inactivation of COVID-19 coronavirus", due to the high relevance of this topic. The work is based on the practical solution of problems in quantum mechanics, presented in the essay FQXi 2019-2020 "Universal quantum laws of the universe to solve the problems of unsolvability, computability and unpredictability".

    I hope that my modest results of work will provide you with information for thought.

    Warm Regards, `

    Vladimir

      Dear Lawrence,

      I beg for the best and a full recovering from COVID19. Here in Germany, everybody try to enforce the goverment to open the restaurants, we have demonstrations agains the lock-down. I hate it. your case show it that it is wrong and we have to be careful to not getting the virus.

      But now back to your very thoughtful essay. I'm a fan of the magic Tits square and now I use very much discrete groups, fractals (or the higher-dimensional generalizations like wild embeddings),...

      I gave your essay the highest vote,

      Good luck for you

      Cheers

      Torsten

        Hi Torsten,

        I somehow missed that you had an essay in lot here. I will queue that up to read. I just looked and today is the deadline! Somehow I thought it was in June. I will surely pull you essay up and make a quick judgment about it. I remember your previous work was interesting.

        The Covid=19 was not that bad at first. Last years beginning 2019 I had influenza that made me a whole lot more sick, threateningly so. I had a mild fever, a dry and not compulsive cough, lost my sense of smell, etc, but the next to worst part is that I have been very fatigued, and that has persisted.. However, the most disturbing part is that I feel as if this has rewired my brain. Seriously, I feel slightly different or that I am a different person now.

        I think Europe is better set than the US, where the hybrid between Godzilla and an orange baboon, Don-the-Con t'Rump, who runs this country is leading us into complete ruin. It can be worse, a friend of mine in Brazil has given me the fill on Bolsanoro, who is a complete moron.

        Gotta get to some essays.

        Cheers LC

        I brought your essay up and I find that today is the deadline. I thought it was a bit later. I have a several of these to read.

        LC