jgill

My comment about abstraction wasn't really in reference to foundations, just a general reflection on the profession. I mean no disrespect to construct...

In published mathematics research papers estimates of serious mistakes run from ten to thirty percent. (of course, my papers were error-free. :cool: )...

This stuff just gets more bewildering as time goes on. :worry: (One reason math has become so abstract is that classical areas of investigation have b...

This is a really good movie incorporating your idea: Prince of Darkness

"And of course, we know that LEM does not imply AC, since we know that ZF is consistent with ¬AC while LEM holds." (MathStackExchange) :chin:

Excellent commentary. Sitting in the bleachers awaiting MU's reply.

On the other hand, symmetry = invariance under transformations.

Don't feel badly. As a professor of math I rarely thought of sets that did not satisfy this definition. In passing I thought of Russell's paradox as q...

As a mathematician who has dabbled for years in complex analysis - a branch of math that involves the limit process, calculus, etc. in the complex pla...

True enough. I should have said random configuration of line segments or something like that. Are all acts founded on reason? Is there an axiom in set...

But as simple symbols, rather than meaningful symbols, they may have no IO or a different IO. If I make up three random symbols from finite lines, say...

I brought this up earlier, the notion that "ordering" and "order" were not the same, saying that order had to do with biological and other systems, ra...

It's unfortunate the word "block" is used in this regard. It immediately configures the mind in a certain way that might be hard to ignore when contem...

I like your new photo. Are you wearing your hair in a different fashion?

You are assuming the existence of an inherent order that lies beyond conscious recognition. Is there another aspect of mind that might register this p...

I suspect the image of a space/time "block" is just as misleading as the image of the Earth sinking into a kind of mesh representing how mass deforms ...

I went to lunch today with retired colleagues, one of whom was a professor of math education. I asked them about math trails or walks and neither was ...

It may be a matter of perspective or personality rather than philosophy. In my years as a math prof I don't recall any colleague particularly interest...

Beats me. I was a math prof for years and never had an interest in seeing math in everything. :chin:

Mathematical Universe This might be of interest. I'm doubtful, myself.

Introduction to Topology and Modern Analysis by George F. Simmons (1963)

As a math person, I view philosophy as rigorous speculation, which I do all the time (or so my wife tells me). Not much use for philosophers of Olde, ...

Well, I learned something. And "most physicists" might be an understatement: the Wikipedia page on relativistic mass almost never gets a view.

Whatever he might say we might not understand.

I wasn't aware of a conflict since I don't watch Youtube videos very much. What's the conflict?

I never thought of Native Americans having philosophies rather than simply beliefs, but, then, the word "philosophy" can be interpreted in more than t...

Reminds me that when I was at the U of Chicago 1958-59 each day I would walk past Stagg Stadium and peer into the fenced off area beneath it that hous...

Wow! That's pretty impressive. I didn't think the AOC ventured much beyond set theory. Some time back fishfry mentioned Zorn's lemma (or transfinite m...

Mass in Special Relativity Good point.

Probably the word "particles" can be misleading. They are not like tiny BBs. If light is a field a particle might mean a ripple in the field. From thi...

It's not a math history course. It's a sophisticated real analysis course, including calculus, based upon a rigorous concept of infinitesimals. I'm no...

In order for one hour of external observer's time to correspond to a half hour of traveler's time the ship needs to be moving at roughly 161,076 miles...

Inherent order is a wider concept, applying in particular to biological systems and natural phenomena. Ordering is more specific having to do with lis...

Not a "simple" "intuitive" with "beautiful reasoning" in my opinion. If it were you would see more of it in college curricula. The Leibniz notion is i...

Cauchy and Weierstrass did just that. Cauchy: "When the values successively attributed to the same variable approach indefinitely a fixed value, event...

Sorry, I haven't kept up. Are you speaking of inherent order or inherent ordering?

Yes, indeed. Even with a good instructor you can find yourself reading a paragraph over and over until its meaning sinks in. It's no picnic. You shoul...

If I Can't Can Kant?

I don't want to distract from this fascinating and delightfully lengthy discussion, but to return to the title of the thread: Physicists and infinity

Here's a math note I wrote a few years ago on the subject. Nothing of any real significance, just playing around. :cool:

Renegade, a French film about the American wild west, is one of my favorites. Some really neat hallucinated snakes.

One aspect of wisdom, particularly in the elderly, is to have learned from one's mistakes. Another is to know one's limitations. The latter expressed ...

Could be called, Salvation in a Block Universe. Kudos for the authors for conjuring up the unanticipated. Were it not so well written I might suspect ...

The OP essentially assumes the conclusion, then attempts to "prove" it. :roll:

It's a dynamical system in C that is observed in the computation of an analytic continued fraction when evaluated by backward recursion: {{F}_{n}}(z)=...

You probably can't. The question then becomes, Is it possible that time evolved in a way that conflicts with current analysis and provides a path back...

It may be possible that there was an initial moment and yet time extends infinitely into the past. Think time dilation and the Big Bang. Just ruminati...

The set of all primes between one and twenty-one has no order dependent upon its definition. However, when I begin to write down the elements of the s...

Thanks. Certainly in the study of combinatorics there are conjectures in which all possible cases are finite in number and a computer program can do t...