jgill

Is being = soul? The conversation has turned philosophical. :chin:

I keep learning things on this forum. I wonder if hyperreals will ever supplant the real number system. Infinitesimal calculus, touted as a more intui...

An infinitesimal is technically a "mathematical quantity", but not a real number. Real numbers have decimal expansions. Infinitesimals have an arithme...

The future of philosophy may be the past of philosophy, when the natural sciences and philosophy were closer and philosophy was able to keep up with t...

Amen to that. :up: "Garbage in = garbage out"

You and I, at 83, can barely remember FDR - who along with Washington and Lincoln top the list IMO. I'm not so certain Biden will be a huge improvemen...

Of course. :cool: The "Looking at one's hands" principle. :smile: OK. Forgive the intrusion. I was curious about first-hand knowledge of the topic bei...

From SEP:In the wide sense, let us say that a ‘mystical experience,’ is: A (purportedly) super sense-perceptual or sub sense-perceptual experience gra...

No. I'm old enough that I knew Leibniz, and am familiar only with his basic ideas about infinitesimals. Surreals by Conway are much more elaborate. On...

I'll pass that on to my colleagues. What a bitter disappointment. :sad:

In mathematics one learns the concept underlying a symbol, then develops a skill for manipulating it. I once read of a prominent mathematician saying ...

IMO wrong from the outset. The divine is not required. Forgive me for being blunt, but this conversation is like two guys throwing frisbees in a meado...

One way to make it kosher is to consider it a generalized function. I never worked with those either. https://en.wikipedia.org/wiki/Generalized_functi...

Picky, picky, picky! :smile: In over fifty years of complex analysis mathematics I don't think I ever really thought of these critters. The Dirac Delt...

Every real number is a complex number, but not vice-versa. There are certain types of surreal numbers that are complex: s = a+bi , where a and b are i...

The concept of infinitesimals goes back at least to Leibniz and Newton. Modern day non-standard analysis incorporates these ideas in a legitimate math...

Banach-Tarski is merely the result of bad grammar? :roll: Maybe by "grammar" you mean math here, and the AOC is "bad grammar"

B-T depends upon the Axiom of Choice. This shows how "dangerous" it is to simply add new axioms to ZF. One would think that AOC is obvious and of litt...

And then come the fractions . . .

I read that Søren Kierkegaard self-published his books. So don't discard this idea. :smile:

One of the weirdest is Banach-Tarski, and that one arises if one assumes the Axiom of Choice. Discard the AOC and it goes away. Another, the Diagonal ...

Possibly. But in the quantum world much of the physics is the math. For example, a virtual particle may simply be a mathematical entity, an yet amateu...

:cool:

Not quite the same as particle or interference wave. It's more a mathematical device for predicting certain quantum properties.

In mathematics it's easy to find examples of a passage of time with no change, as well as a change at an instant. Is that possible in the physical wor...

It makes doing mathematics like walking across a minefield! :fear:

From NOVA online: One of the missions of the Large Hadron Collider (LHC), the behemoth accelerator straddling the French-Swiss border, has been to tes...

A photo exists in a changeless environment and freezes time, but examining the photo involves time's passage. Do you really think that a changeless wo...

Our days runnith over with confirmation bias.

I agree there is the desire to know what may be lying beyond everyday reality, to experience something beyond the normal world. Teresa of Ávila had th...

Nice presentation. A little like the riddle, What is it that has quadrupedal movement, roams grasslands, prone to human domestication, gets hungry, et...

Create an algorithm to list all the penguins. Then take the complement in the Universal Set.

This crops up in the Wiki article Talk section: "Non random probabilistic flow of information in the Planckian order of magnitude" Whereas, in the art...

X={X} :roll: "...and among mathematicians only a small fraction are working in or at least interested in foundations." How true!

In the article in Wikipedia: In 1923, Ludwig Wittgenstein proposed to "dispose" of Russell's paradox as follows: The reason why a function cannot be i...

Goes to show that physics can be both speculative and poetic. :smile:

Obviously not, reading posts in this forum. :smirk:

{A} is a subset of X, not A. Ask fdrake or fishfry to explain this stuff to you. I'm done.

What does "useful" have to do with this example? In fact, the programs I write have a number of different input parameters that I alter frequently to ...

No, {a} is not "in" A,B,C,... IMO this stuff is not worth the effort.

None of them do. They have "a" as an element. D={{a},z} does. This stuff is deleterious to mental health. :scream:

x={x} Nonsense, however.

Set theory can drive a person nuts. :worry:

The formulae that involve a time variable seem to have this property. But keep in mind they merely describe phenomena and are not themselves phenomena...

When I write a dynamical systems program to obtain an image, I determine the image. When the program runs, it causes the image to appear. Sorry this i...

Sorry. I misread this as "dermatology". :meh:

Of course it can. I merely mentioned a kind of isometry between iteration and time. I deal with infinite sequences whenever I dabble with research, an...

More or less true in set theory, a particular branch of mathematics. My area was complex analysis and when I deal with the concept of infinity it is i...

Thanks for your comments. :smile: The discussion is as comprehensible and consequential as highly abstract and modern areas of mathematics appear to b...

Nice presentation. I hadn't thought about your #6 ( the second one) :cool: