jgill

Actual measurements fail beyond Planck's constants. These paradoxes are all hypothetical involving motions of dimensionless points along rational numb...

Heuristics may not be precise, but its value can be substantial in an introductory course. I've never come across this sort of philosophical detail in...

Rubbish. :roll:

And what's the alternative? Are you implying that owning a home is a bad thing? Or renting?

Even mathematics is a little sloppy in this regard. A vector field is not a mathematical field. The reason I prefer the expression vector space. And i...

Field as a mathematical term or field as an area of land devoted to growing crops? Or field as an encompassing environment of some sort, a philosophic...

Trump Derangement Syndrome

From math to woo. A little like the aether.

As for understanding space/time, my Corgi still cannot comprehend simple high school algebra. We have to learn our limitations.

Are you recommending adding this to a classical education?

I would be surprised if there were a proof to the contrary. Isn't all of non-analytic philosophy speculation?

I think he has a PhD in biophysics. This thread seems to be in a rut of sorts. He might add something original to the discussion. My own ideas, shallo...

It's useful in physics for wave functions that might otherwise be cluttered with sines and cosines. It crops up from time to time in things that inter...

Euler's Formula: 1740 Considering the complex plane a vector space helps to see the connections. e^{i x} = \cos x + i \sin x,

Neither space nor time come equipped with intrinsic measurements. Relativity sees to that. Without objects in play there is nothing. There is no indep...

Guess where I was walking? In the bedroom towards the closed door - which I walked through, like moving through a panel of smoke. I was fully consciou...

In the sort of lucid dream I described, one realizes exactly what is happening. I remember testing the state by knocking on a table while strolling by...

The closer one gets to lucid dreaming the more pronounced this effect. I've commented before on Castaneda's Art of Dreaming, and how the process leads...

Sure they do. A simple graph describes the aging of the glass, then, abruptly, there is a discontinuity when the glass breaks. Draw your own picture. ...

There is a continuity of existence that is mechanically measurable. A car sitting by the curb ages a bit over twenty four hours in a an approximation ...

I agree with everything you say. Latin used to be a high school course available to those students having aspirations in the medical areas, especially...

A breathe of fresh air. A history over time exists whether it is recorded through human perception or not. Paleontologists discover this truth frequen...

This is news to me. Hillsdale is a conservative college frequently cited in the more conservative news shows, and I have no problem with that. However...

I think nothing of TREE(3). From my background in classical complex analysis it is merely notation without any connection to my area of interests. Jus...

Now I see why you seem infatuated with Graham's Number. I looked it up and found that it's the largest number associated with an actual mathematical p...

I see from your location on your info page you have followed Yogi's advice and have taken the fork in the road. Sorry to see the only moderator who is...

https://en.wikipedia.org/wiki/Experimental_testing_of_time_dilation

I see nothing of substance in this philosophical discussion of time. But, if something can be physically manipulated and scientifically measured, I wa...

Interesting comment. I've wondered about our health care system, and this past year I have discovered how well it functions for senior citizens during...

More the dimensionality of thought than geometry. You might illustrate by describing an educational curriculum in elementary physics embodying your co...

:up:

A misuse of the word "size".

This has come up before. There are categories in my own subject of complex analysis, but in order to work with them you need a solid background of com...

I like this. However, category theory - which includes categories of sets - an outgrowth of algebraic topology and what ever else of similar abstracti...

Classical mathematics doesn't need "infinity" as a sort of number with associated features. The limit concept works well. However, modern math defines...

From the OP article: I'm not sure how to interpret this statement. If math is an exercise in pure logic and pure logic is a human construct, then so i...

Thanks for your reply. Very informative.

I checked with Copilot and AI agrees with you. (Well, it used to be - it hasn't provided much guidance in recent years, unless one means scientists wh...

Only those relative few who have an interest in Foundations. :roll:

You apply Banach-Tarski to one apple, turning it into two the same size, then eat all three. But only if you have faith in the Axiom of Choice. If you...

"Years and Years" (2019) A British limited series that explores what might have arisen during and after Trump's first term. Excellent cast and intrigu...

So, the world has transfinite ordinal numbers. Or does it?

:clap: This happens in mathematics as well. Long involved arguments get turned over to grad students and end up disappearing. Make it short and concis...

So, numbers are fictions that don't exist as fictions. Does The Maltese Falcon exist as fiction? Word games

Assuming you mean the ordered pairs of real numbers that identify points on the circumference have at least one member, x or y, irrational, what are t...

Hmmm . . . never thought of it that way. Mazur's article on category theory introduces one to modern mathematics. Not necessarily mathematics as pract...

Sounds like a typical PhD program in mathematics. Occasionally a student flies off in an interesting exploration of their own. Usually knowledge advan...

This gives pause for thought. When I think of progress in math compared to progress in physics, say, the initial step of A to B requires speculation a...

I agree. We are all amateurs in this regard. Mathematicians rarely spend their time discussing or arguing the issue. It has so little to do with tradi...

Of course not. Science works pretty damn well. If you were an astronaut would you distrust the science that got you to the moon and back? The proof is...