Joel David Hamkins answering Daniel Rubin’s questions is incredible. I just had to write this post. Both are great, Joel is friendly and explains extremely well, and Daniel is direct, honest, and engaging in a funny way. And they really talk with each other.
For example Daniel asks “How do you explain what it is that you do to a layperson” and Joel’s answer at 9:48 goes “… of course this is connected with set theory, and large cardinals, and forcing, and different universes of set theory …” then Daniel interrupts “you don’t use those terms right of the bat with the layperson” and Joel admits “probably not, no …”
When Joel talks about infinite chess and positions worth omega, or omega+omega, Daniel interrupts: “We have to go backwards a little bit, I think … I feel like I know what cardinality is, but I never really understood ordinals, what is going on there …” and Joel “… it is really quite easy … we gona set aside any ultrafinitist objections … this is how you count to omega^2 … I can define a linear order like that” and Daniel at 17:50 “I understand what you mean – at least – the way I’m thinking of it is subsets of the real line …”
Now I wondered: which ordinals can be represented by a subset of the real line? I understand where Daniel is coming from: Cantor invented ordinals during his analysis of the convergence of Fourier series, and here subsets of the real line somehow played an important role (but they occurred in a different role … where you also can ask which ordinals will be relevant).
(Zeb answered that those are exactly the countable ordinals. And this is true for both roles, because Cantor proved that every closed subset of the real line can be uniquely written as the disjoint union of a perfect set and a countable set.)
Daniel inquired about sets and classes and related paradoxes. At 1:10:36 Joel explains “And this is a picture how the set theoretic universe comes grows. And if you have that picture, then you shouldn’t believe in general comprehension. … But then, the collection of all x such that phi(x), so if those x’es had arrived unboundedly in the hierarchy, there was no stage where you have them all, and so you never got the set. That’s what a proper class is, that’s the picture.”
Other conversations of Daniel and Joel
Daniel Rubin has a Playlist with many other conversations. Another conversation I liked was Modularity of Elliptic Curves | Math PhDs Outside Academia (Jeff Breeding-Allison). At 1:46:00 Daniel starts to talk about his grievances, and at 1:50:00 he starts to really express his exasperation, engaging in a funny way.
Joel David Hamkins has his own playlists too. More importantly, he had a similar session as with Daniel before, answering Theodor Nenu’s questions. Also here, at 28:27 Joel explains “And if you have this picture how sets are forming into a cumulative universe, then there is no support for the general comprehension principle.” The version of this explanation for Daniel was a bit more detailed and delivered slightly better, but of course it remains the same explanation. Now I wonder: what is the picture for NFU (Quine’s new foundations with urelements)? Some of Joel’s explanations in this session are mode advanced compared to his conversation with Daniel. For example, at 1:03:20 he mentions Suslin lines, and then explains Suslin’s problem.
Not bad overall, but nowhere near as incredible or awesome as the conversation with Daniel. It was actually the first conversation in Theodor Nenu’s Philosophical Trials Podcast Playlist. He certainly has interesting guests. I quickly browed into the latest episode, and I got the impression that he got more relaxed and better.
Other awesome stuff with overlength
In his conversation with Jeff Breeding-Allison, Daniel at 17:13 says “lost again, kept alive by some muslims just copied greek texts and finally by the renaissance it made its way back to Europe and Pierre de Fermat has a copy of Diophantos”. I am currently reading “Pathfinders: The Golden Age of Arabic Science” by Jim Al-Khalili (or rather “Im Haus der Weisheit: Die arabischen Wissenschaften als Fundament unserer Kultur”), and he paints a very different picture from “some muslims just copied greek texts”. He wrote that book after producing the 3 part BBC series “Science and Islam” :
Science and Islam – Islamic Knowledge (part 1)
Science and Islam – Ibn al-Haytham & Optics (part 2)
Science and Islam – Medieval Islam Influences (part 3)
The ultimate overlength interviews on YouTube can be found at Web of Stories – Life Stories of Remarkable People – Playlists. I watched Edward Teller, Susan Blackmore, Hans Bethe, Freeman Dyson, and Murray Gell-Mann. But except for Susan Blackmore, I watched them before finding that global overview of the available playlists.
Looks like I watched a lot of physicists. For a bit more diversity, I regularly listen to
Sean Carrol – Mindscape Podcast
The are a wide variety of guests, and I try to respect that variety and listen to everybody, independent of background and subject.
A very special episode was Sean Carroll being interviewed by David Zierler of the American Institute of Physics’s Oral History project. Turns out that this oral history project has an impressive collection of interviews, for example:
N. David Mermin – interviewed by David Zierler
Werner Heisenberg – interviewed by Thomas S. Kuhn
Nicely produced “answer this nice question” sessions of a totally different kind are
Robert Lawrence Kuhn – Closer To Truth interviews
This post (or rather some of its links) existed since a long time. It also contained links to interviews from Joe Rogan of Sean Carroll, Jimmy Dore, Neil deGrasse Tyson, and maybe others. But most of those links were defunc, and I decided not to try to replace them. (I did try to recover them, but I have the impression that the material is no longer publicly available in its original form.)
Let me instead mention a logician and philosopher, who seems to consistently produce incredibly awesome overlength material: Walter Dean. I still need to read his latest paper on informal rigour. I really enjoyed his previous paper on consistency and existence in mathematics.