ThomasR

Karma: 3

ThomasR 27 Oct 2010 7:39 UTC
5 points
in reply to: [deleted]’s comment on: Learning the foundations of math
A very excellent recent book, with fascinating new ideas and superior readable intros into many themes, is the new edition of Manin’s “course in mathematical logic”. So I’d recommend that. But: Why “foundations”? Like “foundational themes” in th. physics, “foundations” are not an appropriate place to start, they are a bundle of very advanced research areas whose intuitions and ideas come from core fields of research. “Foundations” in the sense of “what is it, really?” can be exprerienced probably much better by studying a good piece of core math, like number theory. Cox’ “Primes of the form x^2 +n*y^2” or Khinchin’s “Three Pearls of Number Theory” is what I would suggest. If your mind prefers geometry, I’d suggest to browse a good library for some of the great projective geometry textbooks from the early 20th century.

ThomasR 28 Oct 2010 11:08 UTC
3 points
in reply to: nhamann’s comment on: HELP: Do I have a chance at becoming intelligent?
No, for several reasons (drawn from experiences in math, I am sure in physics and other sciences it is even worse):
1. Even if one includes hidden download-sites and special access by university subscriptions, only sources at the low or medium levels are available in a sufficient amount. The contents of an advanced level are only insufficient there, even some of the decades old and basic ones.
2. Suitable and really good existing texts on the web can be found only if one knows very precisely what one is looking for. But someone who wants to learn needs to find the better stuff, which is in part outside his/her mental frame. In contrast, good texts, even if found, still become hard to detect because of the noise by shallow pseudo-substitutes.
3. Browsing a real library makes your brain detect very quickly much more information and orientation, e.g. experiments (by friends who tutor at the local university) with beginning university students who were grouped and then asked to look for literature (in physics) by web/library only, for an hour, showed a very huge difference. An other experiment with students showed that students using a library have much better learning techniques that the other, but the later don’t notice. Maybe it is a special case of this. On the interesting ways of how subconscious learning and “active” memory gets connected by seemingly irrelevant sensory inputs may play a role then, a famous extreme case here.

ThomasR 27 Oct 2010 18:39 UTC
3 points
in reply to: Benquo’s comment on: HELP: Do I have a chance at becoming intelligent?
“novels/poems/etc. help you understand your own motivation and more easily put you in the shoes of others” That is only a very late and somewhat restricted idea. E.g. ancient greek science of history used novels etc. as epistomological tool, because the core of the things, that what really happened shows not in the surface of the facts, but has to be found and by poetic/artistic work (re)constructed. That was the reason, why their statues were colored like pop art, and why Thukydides’ history book contains poetic inventions as quotes . It is a bit as if in a documentary on e.g. the cold war, suddenly Thatcher, Reagan and Gorbatchev would sing an opera. In contemporary american literature you have this e.g. in Tim O’Brien’s The Things They Carried . Or in Reed’s “Naming of Parts.”. A friend (a great mathematician AND great intellectual ) allowed to illustrate that point by the poem there, scroll down.

ThomasR 14 Oct 2010 9:43 UTC
3 points
in reply to: John_Baez’s comment on: Vanity and Ambition in Mathematics
My experiences, as a kind of outsider who is just curious about some themes in math too and asks around for infos, explanations and preprints/slides, is that mathematicians are by far the easiest science community to communicate with. I conclude that status is of little relevance.

ThomasR 22 Feb 2011 16:16 UTC
2 points
in reply to: InquilineKea’s comment on: Age, fluid intelligence, and intelligent posts
That is hard to estimate, but I think I need the same or less time for studying them. But of course the issue is how one reads them and how much one spends into extracting the hidden ideas and translating them into one’s own mental structures (instead of turning one’s mind into an emulation of the author’s one) . One can study and understand very advanced papers fast and well without a productive “translation”, and the more one knows, the easier it is to restrict reading that way.

ThomasR 8 Nov 2010 23:24 UTC
2 points
in reply to: mindspillage’s comment on: What do you read? What would “desk archeology” produce?
Concerning “Guns, Germs, and Steel “: Murray Gell-Mann is involved in some interesting research on general patterns of civilization. But his and Diamond’s schemes are just about some general and indirect indicators, not about what the essence of “civilization” is. To get an idea of that, I am curious about instances where “civilization” went down quickly. This puts e.g. “Berlin Diary: The Journal of a Foreign Correspondent 1934-1941”, and “Human Smoke: The Beginnings of World War II, the End of Civilization” on my desk. A very remarkable case is told about in Simone Weil’s “L’agonie d’une civilisation”. I scanned two essay by Zbigniew Herbert on decivilization from this—someone curious to get them? “The Dream of Scipio” by Ian Pears sketches (in typical french history-through-novels manner) a thrilling pattern of several critical moments of the last 1500 years of European history.

ThomasR 2 Nov 2010 17:26 UTC
2 points
on: New Month’s Resolutions
A funny idea. My goal is to work further into these issues. Of course I have a precise idea what to do in which order, but as amateur-math reader my attitude is generic lazyness which only occasional deforms into real studying. Unfortunately some friends with whom I discuss those issues are away for more than a month, so there is not much of external motivation.

ThomasR 2 Nov 2010 17:04 UTC
2 points
in reply to: [deleted]’s comment on: I need to understand more about...
You may be curious about this information collecting project. Concerning “skeptical that we can do anything … through policy”: Just a few months before people teared down the Berlin wall, even the most respected researchers in sociology and economy estimated that East-Germany would last at least one hundret years more. Like cold war, which was generally extected to be solvable only by politics, but that this should be extremly complicated. Actually, it was easy. (And even more urgent than everyone had guessed, as an aquaintance had researched.

ThomasR 31 Oct 2010 23:45 UTC
2 points
on: Nils Nilsson’s AI History: The Quest for Artificial Intelligence
Thanks!

ThomasR 31 Oct 2010 23:42 UTC
2 points
in reply to: multifoliaterose’s comment on: Great Mathematicians on Math Competitions and “Genius”
Concerning “predict(ing) future success of high school students in research mathematicians by spending a few hours talking”: From my experience by private tutoring a wide variety of (university and other) students is that one develops an intuitive sensitivity for that. I wonder if others experience that too as quite unpleaseant: one has the feeling of an inappropriate intrusion into the personality of others, a violation of privacy, and because such intuitive guess comes very quickly, one feels to be very unjust. The obvious cause is that the human mind is less complex than usually estimated.

ThomasR 31 Oct 2010 17:05 UTC
2 points
in reply to: multifoliaterose’s comment on: DRAFT: Three Intellectual Temperaments: Birds, Frogs and Beavers
Felix Klein may be seen as a “bird/beaver” hybrid, in view of the calculational view on complex multiplication and class fields in the 19th century, leading to modular equations etc. Klein’s “icosahedron” and Weber’s 3 vol. “Algebra” (the best until v.d. Waerden’s book and E. Noether’s school). link A more modern example may be this, but I know only a part of the story.

ThomasR 31 Oct 2010 15:58 UTC
2 points
in reply to: multifoliaterose’s comment on: DRAFT: Three Intellectual Temperaments: Birds, Frogs and Beavers
Thanks for your answer. The html link button did not work when I posted it. As far as AI etc., the possible relevance of homotopy theory is a theme since the 1970′s, so it should be not too alien to anyone interested in pattern recogn. and related fields. It is similar unlikely that renormalization from QFT should be an entirely unknown theme, as that sort of dealing with generating series even in cases where they are seemingly ill-defined is a bit issue since long in e.g. combinatorics.

ThomasR 31 Oct 2010 6:21 UTC
2 points
on: DRAFT: Three Intellectual Temperaments: Birds, Frogs and Beavers
My previous post on QFT, Homotopy Theory and Ai etc. fits very good to this one, as it is about a special case related to computer science and AI (acc. to their selfdescriptions both a core part of “Singularity”-discussions and fitting to the forum member’s areas of specialization/interests), and at the same time part of research programs in which the mathem. mentioned above are active. So I wonder about the strange reactions? (Princeton IAS and Fance’s IHES surely are not below the intellectual level here, even if the selfreported IQ’s acc. to the survey are above those of Feynman or Grothendieck...)

ThomasR 30 Oct 2010 19:05 UTC
2 points
on: DRAFT: Three Intellectual Temperaments: Birds, Frogs and Beavers
The feedback by several of the mathematicians of “bird” type told me that this summary of some exchanges fits their mentality quite good. Actually, some of the remarks on poetry I made a few days ago in some other discussion here come directly from those feedbacks.

However, the distinction you draw between “birds” and procedure- or algorithm-mindedness is not so strict: You see this in the way they deal with QFT, leading to (among others) Kontsevich’s, Manin’s and Voevodsky’s previously posted thoughts comes directly from their acceptance that e.g. Feynman integrals are nice ideas, justifyed by their computational power, and that their deficient consistency a topic of minor importance (i.e. you don’t need a logical consistent th. physics, because your point of reference is the nature itself, whose consistency is not a reasonable issue; similar with the platonic world of mathematics). A close look to e.g. Manin’s and Kontsevich’s work shows that they are largely determined by computational issues.

Grothendieck is among those “giants of 20th century mathematics” a very special case, as one sees from the astounded admiration which one senses among those “giants” who met him personally. It is not surprising that Grothendieck thought of himself as “mutant” (after analysing his work and comparing it with that of others). And, as others around him with medical expertise observed, he was different, strangely similar to the novel figure Odd John. There is a very good talk by Yves Andre online and here an other great article by Herreman. A video of Scharlau’s talk (in english) at the IHES is here. It may be of interest that acc. to those who knew her, Grothendieck’s sister was a genius of comparable power.

And: Somehow my upvote of your post didn’t work, some of my links do not too in my QFT-AI post.

ThomasR 27 Oct 2010 19:55 UTC
2 points
in reply to: nhamann’s comment on: HELP: Do I have a chance at becoming intelligent?
A good collection of hints, fits to my experiences in autodidactism. But you need a very good library at hand for such browsing (I used as teenager what a mathematician had designed as “Bibliothekskontinuum” ). “Don’t … study … as if you had to pass a test on it” is IMO very good too. Skimming connects with the subconscious procedures of memory and learning and works much better that one usually expects. In a similar way, I would suggest to take interesting looking books at home, laying them aside your bed and browsing like you please each evening before sleeping. That helps very much in identifying fitting themes and texts. But then one should stick on one issue and dig deeper, learn and think about a specific topic. After that, the cycle starts again, but on a higher level. Making notices is simplified by having a small paper notebook all the time around.

And, of course, it helps not to be frightened by sensing how small one’s knowledge is. When I first entered the math library, I took a book by chance, and understood nothing, not even what the author told about. Then I tried an other one, with the same result. This continued until I came across a “Basic Number Theory” (by A. Weil) and could not believe that I even did not understand the first page. That was a bit too much for my taste—I stopped browsing then, sat down and worked systematically until I found out what to understand in which order for digesting that “Basic Number Theory”—a really tough job for me then. Some more than a few months later I happily finished it’s last page and asked some professor lurking in the library for “the 2nd volume”. He barely could supress laughter, as there was no “2nd volume”, I already was in some sense at the top of the mountain.

ThomasR 27 Oct 2010 15:21 UTC
2 points
in reply to: jimrandomh’s comment on: HELP: Do I have a chance at becoming intelligent?
No, that is wrong. E.g. Proust, Flaubert, Balzac, the Mann’s, etc. had a very strong focus on the cognitive content of their writings. Weil, Grothendieck, B. Mazur, Y. Manin and many other science writers (I am pretty sure that it fits to Dirac too, but lack precise infos) spend much thoughts on literature, language and poetics. The idea you express fit only to low level texts of both sorts (lit/sci). But the question was about good texts which help to improve the reader’s mind.

ThomasR 14 Oct 2010 9:08 UTC
2 points
on: Beauty in Mathematics
Thanks for the nice article! Cox’ book is really very beautifull on some of the most beautifull themes in mathematics! Here is the link to an old text on related issues. Conc. the comment below, I’d say that it does not relate to individual theorems or definitions, but to global ideas (which may allow several, different expressions, like Grothendieck’s “Dessins d’Enfant”).

The curse of giftedness:

ThomasR15 Nov 2010 13:32 UTC

1 point

2 comments1 min readLW link

generalized n-categories?

ThomasR8 Jan 2011 19:09 UTC

1 point

2 comments1 min readLW link

ThomasR 9 Jan 2011 11:43 UTC
1 point
in reply to: Risto_Saarelma’s comment on: Kasparov interview
I mean that substantial innovations came the past ca. 3 decades much rarer than one should have expected. Kasparov and Thiel say that in view of AI and communication technology, whereas my impression comes from science.

ThomasR

The curse of gift­ed­ness:

gen­er­al­ized n-cat­e­gories?

The curse of giftedness:

generalized n-categories?