So the circles vicious as opposed to innocuous? — Manuel

That's the world that MU lives in. :roll:

Grow older. At my current age it seems five minutes passes in a minute.

I'm missing your point also. What's your gripe about the innocuous Riemann sphere? :chin: — jgill

To make infinite numbers into a circle is to make a vicious circle. It is to say that the beginning is the same as the end. — Metaphysician Undercover

How can one argue about this? It is so silly. :lol:

Most rigorous students of mathematics will require some form of proof. But I argue that proof is not so separate from what we consider as computation. — kudos

For most mathematicians proof is separate from computation. But one can go down the rabbit hole of computerized proofs if one is so inclined. For me, I use programs I have written to gain insights into problems I pose for myself. For example, if a number of computer examples imply a certain idea is not true, I will adjust my thinking, and move in another direction.

I think your ideas of proofs and computation are suspect.

This dilemma creates a neurological state of fear vibrating in the chest caverns of all persons affected, — Sha'aniah

I know what you mean. Stay put and let the world come to you. I admire your convoluted reasoning.

Oh wait. Those coming to you will drive or walk, so staying put is not the answer. What is? :chin:

Perhaps mathematical Platonism will give way to a recognition of maths as another language in which we should look not to meaning but to use. — Banno

Mathematics earns meaning through use.

To compute is to enact, which aims ultimately to destroy the concept as its opposite. — kudos

Au contraire, over many years I have found that computation enriches and supports concepts. :roll:

jgill was referring to the Riemann sphere, a way of viewing the complex numbers as a sphere . . .— fishfry

I beg to differ — Metaphysician Undercover

I'm missing your point also. What's your gripe about the innocuous Riemann sphere? :chin:

That could be true if the first marriage is to a high school flame. Sometimes, no matter where one goes in life that emotional fire still quietly smolders.

Otherwise, the answer is possibly, but not necessarily. Not for me in any event.

Quick answers to a complicated scenario.

Capitalism is the reason for climate change. — Xtrix

That certainly lets the USSR and the CCP off the hook. Marxists thank you! :smile:

Certainly a balanced account of history is desirable. But is that possible these days in the USA?

This is the best analogy for forcing. — fishfry

Thank you. That's very clear. I appreciate your commentary.

She puts the "pop" in pop science — fishfry

She popped Cohen's Filter pretty good. :smile:

I'm not a set theorist, but I have some thoughts. — TonesInDeepFreeze

And good ones they are! Thank you for your commentary.

It seems hard to separate conformation bias from appreciation of interesting ideas.

How could you do that? Or is this a non-issue?

That said, can you say what "this" refers to? Cohen's invention of forcing in general? — fishfry

That would be good. I had heard the expression but had no idea what it was. The article came as a revelation to me. And here I thought the reals consisted of rationals and irrationals. :chin:

You and Tones are far more set theorists than me!

multidimensional (differentiable) manifold in which every point is a matrix of real or, hell why not, complex numbers. — Pfhorrest

Good move! :cool:

I found the comments about Cohen's Filter in the article I linked fascinating. Like most math people I knew of his breakthrough results, but was unfamiliar with the actual math. I'd be interested to hear opinions from the set theorists on the forum about this. :cool:

Here is an interesting article about cardinality. Seems appropriate for the ongoing discussion.

Continuum Hypothesis?

There's a problem with the implementation of the new system, which is that you no longer get the total post count — fishfry

I agree. I would prefer to see the total post count and then, possibly, only the "likes" for that specific post, not cumulative - which seems meaningless. Unless the forum is a kind of popularity contest.

This leads me to make a troubling discovery, and that discovery is the overuse of ideals such as, ‘You’re too young to understand,’ — Bradaction

Occasionally, this is a matter of psychology and not parental avoidance. Years ago I read that generally it is inappropriate to expect a child under fifteen to understand a subject like calculus. Of course, there are exceptions for precocious children, but if a child twelve years old says, "I want to learn calculus" (probability of this happening=.0001), and then fails to understand it, the parent should not be surprised. :smile:

In complex analysis one speaks of all lines in the complex plane extending from the origin (0+0i) to "the point at infinity" - which makes little sense other than when one looks at the one-to-one correspondence between points in the plane and points on the Riemann sphere. The north pole "corresponds" to the hypothetical "point at infinity", which seems to exist in all directions, barely out of grasp.

There are probably modern complex variables people who have more sophisticated ideas about complex infinity. Directed infinity is one such notion, in which the line has a particular slope (or the point at infinity has an argument). And then there are the various geometries and ideal points, manifolds, etc.

So, there's quite a bit more about infinities or infinite than what is found in set theory. As I have mentioned, when I play with dynamical systems, infinite means unbounded in whatever context it appears and I rarely speak of the point at infinity :cool:

Infinite is a quality, not a quantity. — Possibility

Tell that to a mathematician. — Banno

Depends on the mathematician. For me, usually infinity is unboundedness, hence a quality of sorts.

Denying someone's identity is tantamount to genocide — K Turner

Are you comparing someone who fails to call a non-binary person "they" to a guard at Auschwitz locking a Jew in a gas chamber in the 1940s?

As with the thread on climate change, staying calm and sticking to facts is more convincing than excessive hyperbole.

Just my opinion.

The information escaped a bookbinder's assistant. She was a bit drunk. When I asked out of curiosity, she was fired, ergo ... — gikehef947

The plot thickens . . .

same thing could be said about poetry

which is the opposite of math — MikeListeral

Curious. How is poetry the opposite of math? I'm not saying it isn't. But there is poetry in math, usually comprehensible only to those who study the subject.

I don't think one can go much further on this topic. But, as usual, I could be wrong. — jgill

How wrong I was, and how deep the posts that followed . . .

Can you have a shape with a finite area and yet an infinite perimeter? — Banno

nothing is created or destroyed only changed — MikeListeral

As my best friend, Paul A. Spenser said it, "My parents now think I should be lucky to amount to nothing." — god must be atheist

I gave you a boost, gmba. You deserve it for this gem.

deleted — TonesInDeepFreeze

1+2+3+ ...

$\sum\limits_{1}^{\infty }{n}=-\frac{1}{12}$

:scream:

There is nothing I ever did that "embodied" math for me like taking surveying in college. — T Clark

I took a class in surveying at Ga Tech in the 1950s, roaming all over campus with classmates and equipment. Then, the next summer, working for the US Forest Service, I led a three man (student) team through two miles of forest, laying a timber sales line. We started at one end and worked toward the midpoint, then began at the other end working towards that hypothetical point. Coming in the second time we found nothing where there should have been our markers. Not even familiar surroundings. It took four hours of determined scouting to find the initial midpoint. We never told authorities about their smooth continuous survey line being instead pretty jagged in the middle.

My enjoyment of math did not stem from that experience.

I agree. — Kenosha Kid

Me too

And contrariwise in other articles. I'm sure you wouldn't want to cherry pick just gainsaying quotes — TonesInDeepFreeze

I skimmed the first article and this caught my eye. I only know renormalization from afar.

Thanks for the links. Here's a short excerpt from the first that is germane:

In terms of recursion theory, Bridgman’s claim can be re-interpreted such that no diverging algorithm should be allowed as legal input of any other (terminating) algorithm.One may go even further than Bridgman and assume that, since infinite entities are not operational, infinities have to be abandoned altogether.

Thanks for chiming in. Thought-provoking comments! :cool:

For this reason, in conjunction with the rapid ascent of automated theorem proving and functional programming that are based on type theory, the awkward, misleading and practically false language of real analysis can only die fast. — sime

Well, I'm glad I won't be around to see that.

Has an actual, real live physicist posted on this thread? There have been a lot of assumptions about physics, interesting opinions, but I wonder what people in the profession have to say about the number systems they employ. fishfry provided a link to a novel paper on constructivism in physics that shows there is some degree of interest in the subject in the physics community. Kenosha Kid is a quantum researcher. :chin:

Whether people should be allowed to have opinions is a different issue. — TheMadFool

What agency would allow or disallow opinions and enforce their ruling?

It took me a moment to understand your comment. Then it dawned on me you are returning to the OP! Thanks. :cool:

so bare with me — TiredThinker

I think not! Some nerve. :gasp:

No butterfly effect. Just the opposite. I wouldn't say the ocean is infinite. It just seems that way.

I don't think one can go much further on this topic. But, as usual, I could be wrong.

Some people who claim a near death experience (or actual death experience that was impermanent) say they experienced something more real than real. Is that possible to experience? — TiredThinker

It may certainly seem that way. But I suspect it's a trick of the mind and not comparable to physical reality. Who knows?

But I do make it a point to go into discussion threads about business and economics and make my boredom with the subject well known. — TonesInDeepFreeze

Among the two or three participants? I would think it might provide viewer relief. But to each his own. :roll:

jgill posted a while back about the tiny percentage of overall math papers that are devoted to set theory. Few working mathematicians give any of these matters the slightest thought. — fishfry

Just thought I'd supply recent information regarding.

Donato Carrisi. "The Whisperer", 2012

ArXiv.Org : 161 math papers on Wednesday. 4 in Logic (foundations).

No one I knew in my corner of the mathematical community had anything much to say about set theory or foundations, other than, perhaps, something along the lines of "Oh yeah, neat how Peano Axioms do that."

In my Intro to Grad Math course in 1962 when we got into the second half of Halmos Naive Set Theory most of us lost interest. I remember thinking, "chains, towers, etc.- sounds medieval".