All of ThomasR's Comments + Replies

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.

Aguirre, Tegmark, Layzer "Cosmological interpretation of quantum mechanics"

Why do you think, the arxiv article is more precise than classical astronomy? Actually, it is about "vague" philosophical interpretations of QM, in this case leading it back to classical, newtonean concepts. Whereas the classical physics was free of such issues.

If you think I think that, then communication has failed. Let's try again. Could you explain your first comment in more detail?
Aguirre, Tegmark, Layzer "Cosmological interpretation of quantum mechanics"

Once upon a time, there was a prisoner in solitary confinement, a former public enemy number one of France, aside the wards alone in the prison and allowed only to read science books. When he came across an astronomy textbook by Lagrange, he suddenly had the same idea as you express.

Once I see the possibility that some idea may be expressed in crisp mathematics, I'm no longer interested in vague philosophical treatments of that idea.
Being your own censor

What do you think I would not undestand? Hinton's Cubes share since ages a bad reputation of disturbing the minds of his followers, fitting nicely to contemporary theories of learning and habit-development of the brain. Only two mathematicians seem to have profited from an exposition to them in their childhood. Ans the one who played around with constructing 3D/4D-analogues to Penrose/Escher 2D/3D-"impossible figure" doubted that such an endeavor woud threaten his health. The info on Talmud etc. came from a well known scholar. Both examples fit to the questions above.

Kasparov interview

I find it interesting that the cofounder of the Singularity Institute now expresses so sarcastic about attempted work on AI the past decades. Has there been any related discussion on this or similar sites?

Indeed, Gardner prints such a letter ['s%20cube&pg=PA171#v=onepage&q&f=false] in the midst of introducing those very cubes to a larger audience. I presume that the letter is the work of a joker or crank, as it appears to be. Citation needed.
I don't understand why this is being downvoted (at -3 when I saw it). Could someone explain please? "Hinton Cubes" sound fascinating. In ~1998 some friends and I sketched a plan to train people's brains to be good at 4D visual imagination (though, googling reveals Hinton's method and ours to be quite dissimilar). I was thinking that it could be done so that 3D shapes with complex internal workings might be more easily visualized all at once to boost mechanical design skills. The idea never went anywhere for lack of time, resources, or follow through but finding out that someone already tried something along these lines with negative side effects seems informative but not very dangerous. Saying that "systematic practice with X was reported to be harmful by those who tried it" can be informative and the listener can avoid the negative side effects by simply not "practicing X". I would think that logic would be obvious... though perhaps I'm missing something? And the Talmudic thing, if I understand correctly, just sounds like the fairly obvious generic claim that "smart people tricked into taking dumb pre-suppositions seriously can twist themselves in knots" combined with an accusation that this is what Talmudic study involves. Is the part of the post worth downvoting the bit where holy texts from a minority culture are implicitly bashed, or is there something else bad about it that is less obvious? I know relatively little about the referenced texts and enlightenment would be appreciated (if this is even the thing drawing the downvotes).
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.

Thanks. Try writing your posts more like this to begin with and they'll be less likely to get voted into the negative.
generalized n-categories?

Not quite so. The n-Lab contains a page on it: , but that is not that new. The usual deficiency of such constructs (and the many attempted definitions of n-categories) is their reliance on set theory. Grothendieck seems to have been the first to suggest to forget set theory as foundations, and Voevodsky's way to build a homotopy-theoretic foundation of mathematics on some sort of computer language (leading to entirely new approaches to artificial theorem proving/checking): (read more)

Do you visualize Omega?

What do yuo mean with "Omega"? E.g. Chaitin's Omega or large cardinals do not fit the remarks.

2[anonymous]12y [] A being with the ability to predict the future with 100% (or near) accuracy and with arbitrarily-large power. LessWrongian for 'God', to a first approximation.
The value of preserving reality

The talk you link to is below the level of 1960's and 1970's discussions of that issue. Exist no better contemporary discussions of such issues?

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"... (read more)

What do you read? What would "desk archeology" produce?

Just take "desk archeology" as metapher to be filled as one likes in that context.

I don't think I really understand what you're asking for, but here are my current reading habits and a vague idea of the state of my (home) office. I read mostly textbooks at the moment, but I made time for the library's copy of Siddhartha yesterday. In general I like to keep up with the New Yorker, because it's so well written and edited that everything in it seems to be interesting, regardless of the topic. (I'm currently in the middle of an article about carp.) But that's low priority and I've been busy lately, so for the first time since I acquired the habit I'm a couple of issues behind. The books on my media list are: 4-Hour Workweek (not planning to read it, but it came up in conversation and I wanted to glance through it), one of PJ Eby's, one of the vipassana books that was recommended by someone here, some fiction recommendations from friends (Beggars in Spain, Kraken), more recommendations from LW (Linguistic Pragmatics, Predictably Irrational, MoR, Refuse to Choose, Home Comforts), some philosophy (the Enchiridion), a couple from my anthropology teacher (Primate's Memoir and an article about tarsiers), and a couple classics I've been meaning to get around to (On the Road and Siddhartha, the latter of which I've now checked off). I miscounted, by the way. Four table surfaces. One with computers; one with printer, pattern pieces, and flashcards; one with sewing machine and fabric; and one with cutting mat, button-making apparatus and (at the moment) a bunch of sewing-related miscellany, because I dumped out a bag of it while looking for something in a hurry. The only other large groups of my stuff in this room are my fabric stash and mending pile, both of which are pretty sloppy but I don't have a better container handy for either.
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.

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.

DRAFT: Three Intellectual Temperaments: Birds, Frogs and Beavers

There is something which one could call the "Pirx paradigm", coming from Stanislav Lem:

The complexity of really nontrivial questions surpasses that of the formalized methods used by the conscious part of the scientist's mind. Only the whole mind's complexity meets the questions in view of complexity and flexibility. Therefore, a great mind/scientist works with his complete personality, which e.g. expresses in the observable unique and personal way big scientists write their work. What one perceives as "humbleness", puzzlement, irration... (read more)

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.

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.

Right, makes sense.
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.

Here I think you overestimate how common your breadth/versatility is. I've met very few people who have heard of all of the mathematical connections that you have. A point to bear in mind here is the fact that you've spent substantial time in very elite environments like MPI subjects you to a strong selection effect [] that may have subjected you to highly unrepresentative data concerning what most intellectually curious people know.
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...)

I upvoted your post and don't know what the people who downvoted it were thinking. One possible issue is an absence of background. I felt that the content was sufficiently strong so that it deserved to be upvoted, but few people in the audience have the relevant background knowledge, and so maybe they downvoted it because they didn't know what you were referring to when you mentioned QFT and homotopy theory. Another possible issue was the spelling/grammar/syntax/formatting. Concerning the spelling, "exiting" should be "exciting," "selfreported" should be "self-reported" and "Eifel" should be "Eiffel." Concerning the grammar, "analogue to localized categories" should be "analogous to localized categories," "here an example" should be "here is an example," "I wonder what else concepts" should be "I wonder what other concepts," "I myself take them only serious" should be "I myself only take them seriously." Concerning formatting, it looks like you attempted to format the links in the same way that one formats links in the comments on LW and this resulted in the words that you wanted to hyperlink not being hyperlinked. For top level posts one instead uses the html link button in the header.
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 acceptan... (read more)

I'll have to think about this. Certainly there are examples both of bird/beaver hybrids and frog/beaver hybrids. Thanks for the references which I had not seen before.
META: Who Have You Told About LW?

Those who can provide information. What is "OB"? Have you data on the level of knowledge in sciences and mathematics? "Libertarians" - is that not an other name for right-extremists? Then, "Singularity" is the 21st century libertarian's "Wunderwaffe"-myth?

I don't think anyone's in a position to conclusively confirm or deny your speculation on LW-participant demographics, although you might find useful the link to the survey results jimrandomh posted above. OB is Overcoming Bias [], formerly a blog on rationality with multiple contributors, including Eliezer Yudkowsky, now the personal blog of Robin Hanson. The only data on maths/science knowledge in the LW community I know to exist can be found in the aforementioned survey results. It is probably out of date. "Right-extremists" is probably not a helpful way to think of how the term "libertarian" is used here. It refers more to advocacy of individual liberty than a position on a classical 1-dimensional political spectrum. I wouldn't describe myself as a libertarian, though, and I'm certainly not an authority on them, so other people are probably better-placed to answer that question. "Singularity" is probably a bit too big to elaborate on in a couple of sentences, but it's conceptually distinct from libertarianism. I like to describe it as follows: there are technological achievements which we know to be theoretically possible, but which, if developed, would entirely rewrite the rules by which human beings exist. I don't believe this is comparable to the wunderwaffe concept.
META: Who Have You Told About LW?

A friend recommended it (and to look at the posts of some of his friends here). But I would like to know more about how the participants are, how many and what backgrounds. Many contributions look to me like from male teenagers with deficient education, but being hobby comuter users with interest in popular science. Correct guess?

It's a bit out of date, but there was a survey [] on Less Wrong's demographics.
Who exactly are you asking to appraise your guess?
HELP: Do I have a chance at becoming intelligent?

I find it hard to believe that there are no better solutions, esp. in London - do you really think London offers it's inhabitants so little? By far less than remote districts in Germany or the US?

Conc. books: A good way to orient is to define the field of one's interests and to look at the websites of seminars and workshops in good universities on those and related topics. This helps to formulate a few possible learning routes and with some luck you find the sources free online. But if you want to avoid to crash (because low altitude flights of learning... (read more)

HELP: Do I have a chance at becoming intelligent?

In mathematics, I would call "advanced" roughly what is above the average of "Springer Graduate Text" book series level. Of course, I do not say that one finds nothing, e.g. the Bourbaki seminar series is very good for autodidacts, or this site. It is a bit like the difference between a complex organism and the bunch of isolated cells.

HELP: Do I have a chance at becoming intelligent?

I never had a problem with free access as non-student to a university library (and usually to it's computing center). I would suggest to contact the people and to try it. And are there no good other libraries in London?

0Paul Crowley12y
£220/year []. I can get books on inter-library loan, but it's slow and time-consuming. Partly though it's that I'm still not convinced I need physical books enough to hurdle these barriers - what sort of books do you have in mind?
HELP: Do I have a chance at becoming intelligent?

University libraries are usually very good and have good long distance services. Have you looked for one? I would not buy books, as most of them one reads only once and science books are expensive. But one can suggest university libraries to buy them, I use those opportunities as the cheapest and fastest way to get them.

0Paul Crowley12y
I'm in London - how does one get access to a University library as a non-student? Surely they'd want money for that?
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

... (read more)
How advanced are you referring to? There are many resources at the advanced undergraduate or beginning graduate level (this is biased towards computer science and math, so maybe this is not true for the sciences): This is a link to a freely available 4-volume set on measure theory [] Here is a book on information-theoretic approaches to machine learning and inference [] Here is one on statistical learning theory [] Here is one on a "computational" approach to classical mechanics (Hamiltonians and Lagrangians abound) [] To get to the research level you certainly need journal access, which, as far as I know, is pricy for an individual, hence unrealistic. Hopefully more journals switch to open acccess.
3Paul Crowley12y
I haven't found my library particularly useful for the most part and I've bought very few books, but I've still largely managed to get up to speed.
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 p... (read more)

The internet is basically all you need. Anyone with that has access to a whole bunch of resources, including Wikipedia, OpenCourseWare [] and Khan Academy. Journal articles are often less available, but it is increasingly easy to gain access to journal articles through a combination of Google Scholar, the researchers' websites, and open access journals [].
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 bi... (read more)

HELP: Do I have a chance at becoming intelligent?

News on "intelligence" issues link: "But there are few more controversial areas of science than the study of intelligence and, in reality, there's not even agreement among researchers about what this word actually means. ... Now my team at the UK Medical Research Council's Cognition and Brain Sciences Unit in Cambridge has come up with the ultimate test of intelligence. ... Click here to test your own brain now:"

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.

HELP: Do I have a chance at becoming intelligent?

Did I write that you said that you are confused? The books I recommended were written for the general readership, and I do not see how your remarks should apply to them. Which books would you recommend?

HELP: Do I have a chance at becoming intelligent?

How is the educational level of the participants of this forum, by the way?

Just to continue your list of spectacular infos from math history: Newton probably suffered from microcephalia (as was speculated upon at Leibniz) by alcohol abuse of his mother during pregnancy.

If someone wants to walk in the footsteps of Ramanujan, here the textbook he used as teenager for autodidactism. Unfortunately I do not know if anyone tried that book with teenagers. Here someone's collection of basic math texts by which Gauß, Euler and other math geniusses learned to make their first steps.

HELP: Do I have a chance at becoming intelligent?

Dear jimr..., your confusion could be cured by "reading" and "thinking". Books and other texts should be taken with respect of their content, nor their age, cover design, typeset, or other features. However, if you want a more recent one, I'd recommend this, as a kind of emergency aid in cases of acute confusion.

My recommendations are entirely caused by the quality of the texts and by their fitting to the question above. That some were written between the beginning and the middle of the 20th century is not quite an accident: That was ... (read more)

This comes across as extremely condescending. I didn't say that I was confused, I said that old books in general tend to be confused. Particularly in philosophy, where clarity, accuracy and academic prestige don't seem to be well aligned.
HELP: Do I have a chance at becoming intelligent?

As you are already inclined to read texts you expect to broaden your mental scope, I would recommend to move to real literature, e.g. a few novels by Dostoyevsky. Or this excellent and beautifull to read history of civilization. This, a study-in-a-novel used like a textbook in french history seminars, on the mindsets and times when modern science was born, may be a bit complex, but recommendable. Russel's History of Western Philosophy is a very good and usefull book too. Among the smaller texts, I found some of Putnam's Essays good here. Plato's dialogues ... (read more)

For Plato, I would discourage most people from beginning with the Parmenides. It's something of a difficult work, and a lot of people will find it much easier to begin with one of the dialogues that's about something in particular - best if it's a topic they already are curious about.
I strongly disagree with those recommendations. Those are all old books. Old books are more prestigious, but they're significantly less educational and more confusing than new books on the same topics would be. Reading old books forces you to deal with the errors and confusions that later writers corrected, plus a culture gap and in some cases also a language gap.
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 ... (read more)

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.

Mathematicians are like everyone else, a human, susceptible to the common people tendencies, unless there is 'something' in mathematical thinking that would put them into a different category, more human (the definition of to be a human even if in the strict sense of mathematical rigor would fail, wouldn't it?) or less human ( (a thinking machine).
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").