jgill

Alas, were that so . . . :roll:

Good point, MU. :nerd:

You think Covid-19 is just a virus? Think again, Earthlings! :scream:

Who knows? I wonder if there is any truly empty space that is devoid of fields, like the electromagnetic field. :chin:

:smile: Thanks for your comments!

Sixty years ago I took a course entitled "Introduction the Graduate Mathematics" using Halmos' book on naive set theory plus handouts and lectures on ...

From my experience, this may be possible if you take a full complement of courses and don't get stuck with your research project. The PhD is a researc...

It's good someone has re-opened this ancient thread. Carbon's commentaries are particularly interesting, as I received my degree fifty years ago and r...

You and I don't really disagree, MU. I enjoy reading your posts, learning of philosophical perspectives I never considered the years I was a practicin...

Thanks. I should have looked it up. For those enraptured with set theory it must seem appropriate that it borders on the divine! :cool:

Then there is the sequence of continuously differentiable functions that converge uniformly on to that line segment, but whose arc lengths go to infin...

You are looking behind the symbols to the mathematics they represent. They are certainly equal in this regard. But if you look superficially at the co...

I'm speaking of the two symbols. 2+2 and 4 are not the same symbols. And I don't appreciate your snide remark. Of course they represent the same mathe...

Irrelevant. 4-ness is the ideal in discussion. :roll:

I can concede that "2+2" and "4" are equal but not the same. They do, however, represent the same Platonic ideal. Not being a philosopher, this is as ...

Things that may be true, but may not be provable: 1. There is a God 2. String theory

1. What is "absolute infinity"? 2. Give a rational explanation of how that implies anything. :chin:

Depends on the contexts of usage. My friend and I are equal (in the eyes of the law), but we are not the same (in the eyes of the law). This is distre...

A simpler example in a lower dimension is \int\limits_{1}^{\infty }{\frac{1}{{{x}^{2}}}}dx=1 This is the finite area between an infinite curve in the ...

This could be reduced to a simpler scenario: Might there be, anywhere in the universe outside our solar system, a Franklin Ace 100 personal computer (...

This is true only if "utility" includes fascination with exploring a subject, finding what's behind the next intellectual door, where an investigation...

The B-T paradox, as has been said several times in this forum, depends upon the Axiom of Choice. Not one of Euclid's. Sometimes the Axiom of Choice is...

Not "necessary". Useful as an alternative to normal calculus. Logical - in a sense, I suppose.

Not sure what you are saying. 1/1 + 1/2 + 1/3 + ... is the Harmonic series that is unbounded (adds to infinity, not 1). The addition of all fractions ...

A+ for original thinking, Greg! :cool:

It's somewhat beside the point, but many mathematicians seem to have musical talents as well.

"The question of whether situations and worlds can peaceably co-exist in the foundations of metaphysics is complicated by the fact that world theorist...

But he also says this (NYT): ''half-baked philosophy has sometimes gotten in the way of doing science." :smile:

Here is one direction modern metaphysics is moving. Even as an old mathematician, my eyes glaze over as I try to read it. Those of you more conversant...

Evergreen State College was designed as an experimental institution, opening in 1967. At one time I knew the Dean of Faculty, Willi Unsoeld, and Pete ...

Touché . . . Good point! :smile:

I was curious about what professional philosophers think of modern day metaphysics. In particular, is it possible to earn a PhD in the area of metaphy...

Math concerns theorems, which are logically provable. A "theory" in math might be something like Category Theory or Set Theory, areas of study which t...

Nice commentary, Kid. In 1954 I wrote a short paper on this for my physics class in high school. At the time I loved reading science fiction. Of cours...

There are no problems here. You have drawn a comparison with confederate monuments. I did not.

I grew up in the deep south before the civil rights era, and as I recall neither I nor any of my classmates paid any attention to the statues of confe...

Buddhas of Bamyan: The Taliban were good at cancel culture https://upload.wikimedia.org/wikipedia/commons/5/51/Taller_Buddha_of_Bamiyan_before_and_aft...

Some of that dust gets into my computer at times! Or, my computer gets into some of that dust at times! Very confusing . . . :worry:

This giant statue on top Gellért-hegy in Budapest was a Soviet icon representing the close alliance of Hungary and the USSR. After the Soviets abandon...

It would be good to hear from an actual physicist regarding these comments. We can all speculate. :chin:

It's not part of an argument. You asked a question and I answered it. It simply illustrates the support the military gave (gives) to scientific resear...

My mother was a "Southern Belle" and I can assure you she was anything but what you describe. In her later years she helped "women of color" as best s...

I was a meteorologist sixty years ago. A math prof 1971 - 2000. My interest stems from pure mathematics and I've written about extending the iterative...

Infinite compositions of linear fractional transformations. Pretty much pure mathematics. :cool:

:smile: Even one in the hard sciences would impress me. There are probably a few out there.

Roughly speaking, but needs elaboration. Not a definition of nonlinear in the strictly mathematical sense. And what is "small"?. For example: Linear: ...

Yes, that's what I was getting at. Thanks for your comments. :cool:

You make a good point about the humanities being pushed aside after Sputnik. I'm surprised this thread is languishing. :chin:

OK. I take it you are a physicist.

Is this exactly the case? I thought it was a bit more complicated than that, but I am not a physicist and could be mistaken. Kenosha Kid? :chin: It's ...