jgill

"The next reason that you might think you do not understand what I am telling you is, while I am describing to you how nature works, you won't underst...

Richard Feynman, one of the greatest physicists, I seem to recall stated that physics could never say why nature behaves as it does, only how.

I know very little about quantum physics, even as a mathematician. Philosophical speculation may easily drift into Quantum Mysticism. I prefer to leav...

Here's a PU in case you haven't seen one before: https://upload.wikimedia.org/wikipedia/commons/4/4e/Reproductive_universe.jpg :cool:

Getting your degree (a kind of union card) involves learning a little about various branches of mathematics as you begin to focus on a specific area o...

At 83 I'm still able to engage in math research (of a sorts), but the aspect of thinking that I have noticed the most change in is an increasing inabi...

With interest rates for savings where they are one might as well open an account with an imaginary rate. :worry:

As a retired mathematician I was going to say that has happened in math, but then I did a Google search and found out that amateurs - depending on how...

This is the most sophisticated OP I've seen in the eleven months I've been here. It will be interesting to read the philosophical comments in reply. I...

This is not meant as a pun. Under stipulations that will make the Kid's eyes roll, there is a fundamental form or principle underlying the math of bot...

When I study elementary dynamical systems in C, I sometimes employ functions that "reverse iterate", and those systems show the time symmetry. Time de...

There is no general answer. One can study a person over a long period of time and perhaps draw some sort of conclusion about that person, but there ca...

Certain mathematical formulae or processes in physics show a symmetry in the time variable. How this relates to "going back in time" is a reasonable q...

:smile: :up:

Is making a measurement in QM and getting a specific result time reversible? How much of "time reversibility" might be artifacts of the mathematics th...

Disceptatio succumbo :sad:

In how many different ways does the notion of "waves" appear in quantum theory?

I suspect I will not understand the truth about reality when you reveal it, but I'll give it a try. :up:

Go right ahead and spin your metaphysical web. Like the flock of sparrows now sitting on my fence, the peanut gallery awaits your penetrating views. :...

Although topologically the same. I have done quite a few investigations into linear fractional transformations, and one feature that makes them import...

As intriguing as complex representations in physics, for me, is how linear operators are so effective. One would think nature to be complicated and no...

And interests change.

This might trivialize C. Here's a quote from the web, from an educational perspective: "Question.Is C isomorphic to R2? Answer.As a what? A field?Ques...

It would help if this issue is clarified.

If a substantive thing, (massive object), is inclined toward temporal continuity (as inertia implies), yet "feels" a force which would impel that obje...

And thus you pave the road ahead - a passage fraught with loathe and dread. :groan:

Is quantum theory the "set theory" of physics? Weird at first but providing a foundation? :chin:

This idea appears to be connected to normal numbers, and I don't think pi has been proven to be such.

From the perspective of an 83 year-old this seems a bit naive. Especially the wisdom part. A lot depends on one's health, and if that remains fairly g...

From the perspective of an elderly mathematician jigsaws are like doing a problem in a textbook (I never liked that) - difficult, but uninspiring, the...

My best friend for over forty years was once a physics major, but he switched to math after taking an introductory course in quantum theory. He became...

Well done! :cool:

Ditto, although I use a simple contraction I like. My moniker was well known on a popular climbing forum before it vanished. My feeling is that we all...

Those were Dr. Patel's words, not mine. How amusing. Patel does have a way with words. I know so little of the subject; nevertheless, a particle havin...

Here's what Lalit Patel, PhD physics had to say in 2017 on Quora: "Planck time is an extremely small time duration, which current technologies are not...

And not merely be non-measurable? Very well. :sad:

A photon travels at the speed of light over a Planck length during this "time". Therefore, something happens as time progresses.

I don't think MU is a celebrated scientist. But I could be wrong. :wink:

Whoa, not so fast! Where is the link between complex numbers and the existence of man? Inquiring minds want to know. :chin:

A matter of notation and mathematical clarity. See definition 7.1 https://www.math.uchicago.edu/~may/VIGRE/VIGRE2011/REUPapers/Lian.pdf Not a big deal...

x=(a,b) and y=(c,d) are ordered pairs of integers, not integers themselves. So x and y belong to the Cartesian product of the integers. You're definin...

\left( c,d \right)\in Z'=N\times N

I'm curious about Neil Gorsuch in this regard. Is he really that bad?

Some time back on another thread I mentioned being curious about the process of going from the empty set to the fundamental theorem of calculus, step ...

True enough. What is not settled is whether it can be altered significantly. Especially with not all nations on board. Don't buy beachfront property i...

This is a very ambitious thread. But probably no more than the first 900 pages of Penrose's The Road to Reality. I may not live long enough to see its...

Look forward to this! Next, well-order an uncountable set of reals. :cool: :up:

I'm picking up tiny tidbits of math here that relate to topics I am familiar with, but it's all pretty fuzzy. For instance, SU(2)\subset GL(2,\mathbb{...

GL(2,C) is a Lie group corresponding to the group of linear fractional transformations (LFTs). When you matrix multiply two 2X2 such creatures it's th...

Better simply to eviscerate the "theory". :yikes: