Life Story of Mathematician & Philosopher of Infinity | The Human Podcast Ep 33 (Joel David Hamkins)

Joel David Hamkins is a Mathematician and Philosopher who researches infinity. He is the O'Hara Professor of Philosophy and Mathematics at the University of Notre Dame.
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TIMESTAMPS:
0:00 - Intro
0:48 - Humans Interest In Infinity
6:02 - Classic Paradoxes With Infinity
9:26 - Could You Really Always Keep Counting?
13:35 - Concrete & Abstract Objects
19:50 - What Is Infinity?
25:07 - What Exactly Is The Problem?
30:25 - Practical Implications of Understanding Infinity
33:13 - First Time You Thought About Infinity?
36:50 - Why Are You Fascinated By Infinity?
41:50 - Personal Life
43:58 - Artificial Intelligence & Understanding Infinity
49:21 - What Does It Mean To Live A Good Life?
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Hope You Enjoy 😄Timestamps: 0:00 - Intro 0:48 - Humans Interest In Infinity 6:02 - Classic Paradoxes With Infinity 9:26 - Could You Really Always Keep Counting? 13:35 - Concrete & Abstract Objects 19:50 - What Is Infinity? 25:07 - What Exactly Is The Problem? 30:25 - Practical Implications of Understanding Infinity 33:13 - First Time You Thought About Infinity? 36:50 - Why Are You Fascinated By Infinity? 41:50 - Personal Life 43:58 - Artificial Intelligence & Understanding Infinity 49:21 - What Does It Mean To Live A Good Life?

[@freddiealcock5439]

Love this, Joe!

[@TheHumanPodcast.]

Thanks Freddie, glad you’re enjoying the episode 😊

[@ALavin-en1kr]

Now the best telescopes cannot see the end and likely never will. Infinity is something we will never reach the border of, and look over the edge, otherwise it would not be infinity. Pascal when he first viewed the heavens through a telescope said: These infinite spaces terrify me. It is easier for the average person to think of it as extended space, rather than a mathematical problem. What is math other than the measurement of what is, and how do you measure infinity? Was it Cantor who went crazy when infinity could not be calculated. Talking of many infinities is a cop out. Chopping infinity up doesn’t cut it.

[@ddacaro]

in college I struggled with moving forward with infinity as a concept when I was forced to use in it equations. I became obsessed with this problem and began creating artwork which implied infinity conceptually and actually using for instance, circles (practically in 2 dimensions). later, somehow and without intent or belief of it being possible, i experienced infnity (there's many paradoxes there in using "I" simultaneously with infinity, but that's another conversation). This changed my life forever and everything I believe and resolved the personal struggle with it. I moved to the birthplace of buddhism for some time to explore the empirical, emergent phenomenon (or apparent phenomenon) which I described above. What I concern myself with now is how we cut up infinity into categories, and does doing so create false appearances of finitude, such that we idolize finitude which appears fundamental to us over infinity which for many as it did for me, appears paradoxical.

[@ivanalejandro-ct]

cool ! link your work somewhere here :)

[@Eris123451]

Well that made absolutely no sense whatsoever.

[@ddacaro]

@@Eris123451 Precisely. When someone (and there actually are many) claims to have an experience of infinity, I've found it pretty common that they will tell you that there is no way to describe it. It would be like saying, let me play the guitar to you so you can get a sense of the taste of pistachio nougat. They are different modes of experience all together, just as conceptualization is different from taste, from hearing music, to looking at visual art. I cannot tell you it was real because there is no evidence of first person subjective experience that can be externalized. But at least you heard here that some people very much are convinced some such experience appeared to have happened to them. That might open up the possibility for you since perpetual doubt can actively inhibit it, as I've found - not that faith conversely promotes it however.

[@ddacaro]

@@ivanalejandro-ct I don't have those original artworks or copies anymore, that was long ago. But if you are oriented towards infinity for whatever reason, I hope it is useful for you to hear that there are people like myself, and possibly you at some point, who regard an often rare and profound internal, subjective experience/state as appearing as boundless and infinite. It is life changing, but not something that one can control. One can however diminish the power of doubt of such experiences by understanding without proof for or against, neither insistence on it's actuality nor doubt are possible, leaving open it might be possible, a prerequisite (sort of) to it's emergence.

[@Eris123451]

It seems somewhat to come back to that old and seminal question is mathematics something that we discover or it something that we invent ?

[@countvlad8845]

I think infinity exists as long as we can count. If we couldn't count, then we could never understand infinity even rudimentarily. And because we wouldn't understand it, it doesn't exist; and when we do count and understand it, it exists. Which is quite unlike the natural world. So counting is the path to infinity and through infinity. By counting, you are walking through infinity. Maybe, more importantly, we are counting the same thing(s), but thinking of it as different things. We are on a thread mill in our heads thinking every number we count is different where it is the same number counted many times. We just imagine them as different. But math is not like the physical world or different physical objects. Counting is key. If we really understand counting, we would be further along. What does it mean to count is a more important and prior question? You have to understand counting before understanding infinity.

[@Jaggerbush]

Seriously question - as for Infinate sets - wouldn't the set of all real numbers be greater than the set of all prime numbers (assuming prime numbers to in fact be infinate)???

[@NineInchTyrone]

He’s. Some infinities are bigger than others. Or perhaps more dense

[@Eris123451]

Yes

[@Jaggerbush]

@@Eris123451 thank you

[@infinidimensionalinfinitie5021]

(t)he(y) could say; slam poet; along with mathematician and philosopher; infinite hats;

[@mariakatariina8751]

42:18 About intellectual activities and infinite games; you might be interested to try and learn some lavatanssit.

[@sonarbangla8711]

Philosophy of mathematics relates divine design with humans. Like what Ramanujan said about mathematics as reflecting god's mind.

[@Eris123451]

There is no, "divine ,"design not as far as anyone can tell.

[@sonarbangla8711]

@@Eris123451 You sure know more than god. Idiot.

[@esorse]

Wouldn't invoking qualitative context to explain Cantorean well ordered set * 'order type' ordinal numbers, { } := 0 . 1 := { { } } = { } and 1 . ω := {1, 2, 3, ...} = ω, the first countably infinite transfinite ordinal number, but 0 + 1 = 1 and 1 + ω = ω, for "." multiplication and ":=" assign, since adding an element to an infinite set doesn't change it's magnitude, implying a contradiction from zero and omega behaving like substitutes under multiplication, but complements under addition, undermine Cantor's infinity scheme mathematically, although maybe not mathemaligiously? * A well ordered set {X,

[@mariakatariina8751]

2:18 Axiom is not a proof....

[@pascalbercker7487]

Could one begin to argue that if someting is not finite then it's indefinite - and only indefinite - but it's another step to then say that it's infinite? Should we stop short of taking that further step which might not be warranted? Having an unlimited supply of something is not quite the same thing as having an infinite supply which strikes me as too much.

[@christopherrosado6053]

Infinity just "is".....a " thought" .... where we are in the big picture is always my thought , out in thr Universe...forward into space, backwards, up down, side ways., "Infinity" ... just an idea....or thought here... where's it all expandin, too ?? multi verse, cosmic inflation ?? Ideas?? in this realm known as " infinity

[@Eris123451]

15 minutes on, I gave up he hadn't told me a single thing that I didn't know already. Plus he's bit of a windbag.

[@robfrost1]

I could not disagree with professor Hamkins more, when he says that a proper superset is no bigger than the original set. I can of course see the paradox but this conclusion is the greater nonsense. Mathematicians in general need to wake up to the fact that proper superset trumps cardinality in the measure of "what is more?"

[@imperialfists]

Cannot disagree more with this view.

[@johnstarrett7754]

You might want to look at Benci's Euclidean numbers.

[@johnstarrett7754]

Better yet, look at fine asymptotic densities people.dm.unipi.it/dinasso/papers/24.pdf

[@imperialfists]

@@johnstarrett7754 thanks for the suggestion. Looks super interesting! : )

[@Woody-wz9vb]

its not a fact lol, 'bigger' is clearly imprecise. i think what you are talking about corresponds to 'rank' in set theory.