jgill

11,000 to 100,000 North Korean soldiers muddies the political waters. These special ops troops infiltrate and assassinate. Nevertheless, this madness ...

Depends on what "get with" means. After my first divorce one of my mature students showed up on the front row with an apple on her desk. Later that da...

Here is a brief note with images on the diagonal paradox, which some on this site argue is not really a paradox. Interestingly, a physicist on this si...

Perhaps that task has been relocated in psychology and psychiatry. Or where its been for eons, religion. Certainly in logic and foundations of mathema...

Where I taught we went through a gentler version of this, grading partly on grammar. But trying to teach both subjects simultaneously was counter prod...

We had a small anthropology/philosophy department where I taught. Actually, if I recall, one or two philosophers. In the larger universities, especial...

Give it time and it might explain these phenomena.

That's what I meant. To think of infinity itself as some sort of number. Trying to keep the discussion at an amateur level. I'm thankful for that. Why...

As disciplines go, it is by far the wordiest, in inverse proportion to its effectiveness perhaps. Some philosophers don't know when to stop. A millenn...

Refuting Gauss, who termed mathematics as that. Also in medieval terms, theology. What philosophical notions illuminating the mysteries of QM have bee...

Much of classical math existed before the introduction of set theory. So, no. Modern math is another thing.

You are correct. It's a mere mathematical simulation of cause and effect. The philosophical notions are out of my league. But it is a fascinating subj...

Why should this be the case? I drop an object from a certain height and predict when it will hit the ground. How does this eliminate causality? There ...

Thank you. I just learned a new word. :chin:

Sorry. Wrong @Hanover post.

Not sure how this fits in with the OP. I've used this approach from time to time, but never to the extent of assuming ~P is true and showing P follows...

I agree somewhat with the "required pace", but you and I know that in post-K12 math and related subjects it takes effort and time to accumulate a back...

"the Dismal Science"

The one trait I share with Feynman is understanding a concept through examples. You started with the imagery in 2D. Maybe more?

Forty to sixty percent of American PhD candidates do not complete their degrees. Many of these encounter a roadblock in the fundamental aspect of the ...

Waiting for someone to bring up quantum theory. :roll:

The "Lounge" is part of TPF.

At first I thought this is not true, but that is because I followed a learning curve that incorporated analytic geometry before calculus, and this all...

Albert Einstein: “If you can't explain it to a six year old, you don't understand it yourself.” If you can't illustrate a concept or process by applyi...

You've lost me. Guess it's time for me to quit. Overall, I think you have started down a path that is far too complicated for the desired result. Howe...

:up:

Just checking to see if you are AI.

Not necessarily true. I have known stupid people who admit they are stupid and don't try to compete intellectually. But it's not the definition of DKE...

Are you trying to demonstrate your argument? Just curious. Years ago, at a math conference in Marseille-Luminy, a prominent mathematician told me he c...

Mathematicians, specifically, are eager to present their research to the public. Publishing in journal reaches only very select readers. More mistakes...

I explore various properties of contours in the complex plane, defining a metric space whose "points" are contours. z(t)=u(t)+iv(t),\,\,\,0\le t\le 1....

It varies. Topics that are popular draw the attention of experts in those areas, who, in turn, make corrections that are discussed on talk pages. Very...

It's had 164 years. We'll see. :cool: (Wiki) OK. But it gets a bit anti-intuitive. Hard to imagine a curve is a vertex. But then, I treat curves in th...

A vertex represents an actual curve? In fact, I had never heard of the S-B tree before it was introduced on this forum. It is not true that every math...

Not all. The evolution of entropy in a closed system is deterministic (entropy always increases), but it is not time-symmetric because entropy decreas...

You could start with continuity described as a path in the Euclidean plane or complex plane taken by a moving particle. Or something similar. Careful....

Good luck with that. Probably of more interest to CS people. A sequence of rationals I assume. If you had two functions on Q then a suitable metric wo...

I assume you are speaking of "school" as in "university". It is taught at some elite institutions and some not so high on the scale as well. If you me...

I was speaking of ordinal numbers beyond the naturals. Our definitions of "actual" infinities differ. No big deal. Of course I have used R, but not a ...

Elementary calculus does not require "actual" infinities. It gets along quite well with unboundedness, or what you might call potential infinity. As I...

:up:

By "actual infinity" I suppose you mean a kind of number that can be manipulated by arithmetic processes. This is either very deep - or shallow gobbly...

So far I'm not seeing anything beyond a line segment between two points that converge to one. From a continuum to a point. Why should one care about t...

Reading the masters (Kant, etc) sometimes is confusing since they might not express themselves in the best ways. Read commentaries of them if you enco...

Unfortunately, I will be long gone when they sort this out. You may be around :cool:

Wiki: I'm not a physicist, merely an old mathematician who prefers this definition. So I don't see the magic.

Category theory is beyond my pay grade. It's quite popular (the Wiki page has over 600 views per day - people want to know what it's all about). So fa...

I see a mistake in your last figure, typo probably. And I assume -1/0 (meaningless) designates negative infinity, however you define that. I see nothi...

From Wiki: I have mentioned before that fundamentally the S. equation reduces to a simple calculus concept: the instantaneous change in a thing is pro...

Move on to 2.