Additional Info (PDF of above — printable, zoom-able.) (Markdown version — for AI/search.)

FYIs

  • 2025: To be certain I was not inadvertently making any fundamental Math/Physics/CS mistakes, I asked AI to review this page for technical errors. It found none.
  • 2025-2026: I am now, when I have time, working with AI on several of these topics. The purpose is jointly to see if I can make actual progress, and to add “meat” to these ideas, to better interest luminaries in the various fields.

Related to "Mathematics and the desperate cries from Quantum Mechanics"

Historical context for the idea that mathematical structures could have their properties dependent on their history:

Long ago, at the Harvard Extension School where I am a math tutor, a student wrote on the blackboard something similar to the following: y = [stuff] / log(2) = [stuff] / .3010 = [stuff] - .3010. Now, this last step is clearly "", but it got me thinking... Their mistake included the belief that the past history of a number — how it came into being — affected its current properties. The more I thought about this, the more the fact that this was rarely if ever the case in the mathematical structures with which I was familiar, seemed both arbitrary and limiting.

Additional points:

i) I played around a bit with combinatorics, in terms of considering that it might "matter" how many ways a "5" say could have come into being — was it the result of 4 + 1, or 3 + 1 + 1, not to mention 7 - 2, etc. Unfortunately I did not get very far.

ii) It may be that it is only now, with the advent of computers, that we practically can, for every symbol, store its history — its origin story — along with the symbol itself.

(“Caveat+” re Special Relativity 2025-11-14: An AI just pointed out the existence of said note above, without corresponding content here. 🙂 I first posted this page long enough ago that I can't quite remember what I had been planning to include... If and when I do, will add.)

Related to "Consciousness — a possibly necessary condition for it"

A friend and colleague commented that one could bypass recursive levels of self-reflection and instead imagine a single subroutine — the "I've been asked who I am" subroutine, that simply increments a state variable regarding how many times it has been called, and responds commensurately. While technically I understand his point and agree that is possible, I do not find it a particularly convincing argument against my original supposition; I find his implementation simply too "shallow".

Related to "AI: The importance of a name."

See Affectionate Technology paper for additional context.

Related to "Information Theory."

Background — "Shannon Information":

From Scientific American article: "Shannon defined the quantity of information produced by a source--for example, the quantity in a message--by a formula similar to the equation that defines thermodynamic entropy in physics. In its most basic terms, Shannon's informational entropy is the number of binary digits required to encode a message."

Related to "A friend who kept me company during COVID lockdown."

Delightful squirrel photos and videos.