## February 04, 2005

So say we all

February is LGBT History Month in the UK. Good thing? Bad thing? Discuss.

Did you know that next week is "Random Acts of Kindness Week"?

LGBT History Month?

My first reaction is: Hey, that's a good thing.

My next reaction is: We have Black History Month in the States, and you know what? We don't hear too much about black heroes, geniuses, leaders, etc, the rest of the year. It's like we put 'em in a little box, haul 'em out once a year for a pat on the back and some easy self-righteousness, and don't think about 'em again. Until next year.

And then I think about Tom Lehrer's song, 'National Brotherhood Week,' which ends with the line:

'It only lasts for one short week so have no fear,
Be thankful that it doesn't last all year!"

So, I'm not really sure LGBT History Month is a good idea. There's a fine line between consciousness raising, which is what these Special Edition History Months are all about, and putting people in precisely the kind of box they're fighting to get out of.

Anybody well-read in philosophy know a paper by someone (maybe named Gold) about a paradox involving hard determinism - given sufficient computing power and the initial state condition of the universe, one could produce a book describing what you'll have for breakfast tomorrow, and so you eat something else - from at least 15 years back? The info would be useful in a poem.

CaseyL,

I love Tom Lehrer.

"Once the rockets are up,
Who cares where zey come down.
It's not my department,
Says Wernher von Braun."

cf. Alberto Gonzales.

Seriously, it is interesting how well his songs speak to modern issues, given that they are 30-40 years old.

I love Tom Lehrer.

"Once the rockets are up,
Who cares where zey come down.
It's not my department,
Says Wernher von Braun."

I'm also fond of Mort Sahl's addition to the title of von Braun's autobiography, I Aim For The Stars, "but sometimes I hit London."

Re Tom Lehrer, I've often been reminded of lines from Send the Marines! during the whole Iraq war thing:

When someone makes a move
Of which we don't approve,
Who is it that always intervenes?
U.N. and O.A.S.,
They have their place, I guess,
But first -- send the Marines!

...

For might makes right,
And till they've seen the light,
They've got to be protected,
All their rights respected,
Till somebody we like can get elected...

KenB,

Great excerpt.

Gary,

"...the widows and orphans of old London Town,
Who owe their large pensions to Wernher von Braun."

I'm a Mort Sahl fan too. (Showing my age, I guess).

"What's the difference between a Russian pessimist and a Russian optimist?

A Russian pessimist says, 'Oy, it's terrible. Things can't get any worse in Russia.'

A Russian optimist says, 'Oh yes they can.' "

I hate Francisco Goya. But think Elisabeth Vigee Le Brun was a babe.

Hey, it is an open thread, and is what has been on my mind for 24 hours.

The best Tom Lehrer song ever is definitely "We Will All Go Together When We Go"...

rilkefan: I am away from my office just now, so don't actually know. But I think it's Alvin Goldman. He is, however, wrong. Consider any case in which you can decide what to do and then act on your decision. (There may be some things you wouldn't do even if you decided to, like hovering 10' in the air unaided, but assume there are at least two values of X such that if you decide to do X, you will do it.) Now suppose that you will learn what the computer will tell you to do. It is possible that this knowledge will not affect your decision. In this case, the computer can predict what you will decide to do, but ex hypothesi it makes no difference. Alternately, suppose that learning what the computer tells you you will do does affect your decision, either because you will do what it says you'll do or because you will do anything but that. In this case, in order for the computer to predict what you will do, it must first figure out what it will predict that you will do: that is, it must figure out what its prediction is in order to know what to predict. Can't happen.

The computer could, of course, decide that in such cases it would decide what to tell you on some other grounds. (All it has to do to arrive at a prediction is to tell you something, so it decides to tell you whatever will get you to do what it wants, say.) In this case, what it tells you is not a prediction based on its (supposedly) perfect knowledge etc., and you have no reason to accept it as one.

So the only way in which there could be a justified prediction of what you'll do next is if what is predicted doesn't affect what you do, either because (a) it's not up to you in any case (e.g., if I have fallen off a cliff, the computer can predict my trajectory), or (b) I will make up my mind independently whatever it predicts.

watching a little anti-Cylon propoganda

I don't know whether to thank or curse you folks for recommending the new Battlestar Galactica. Being unwilling to spend $40+ a month on cable, I rented the miniseries on DVD. Now I'm hooked, but I can't watch the series. Well, actually, I'm a hard determinist, and as best I recall the argument was against that viewpoint. So if I understand, there are two good practical arguments - first off, the output of the computer calculation is not, "You will eat a Denver omelet for breakfast", but "At time t0.32....73...etc particle x0 will be at position foo with velocity bar, particle x1 will be ...", which can't be translated into anything human-readable; and second, the program would have to run on a computer bigger than the universe and would take an unfathomable amount of time. However, from my viewpoint that there is no such thing as a decision and no such thing as a person, it's not clear to me (setting aside the above practical objections) why a universe with known physical laws/starting conditions can't be simulated by a computer running in that universe, with the effect of the computer included in the evolution of the universe. rilkefan: the problem doesn't depend on whether or not the computer is trying to predict your actions in, um, shall we say: human or physicist terms ;) Nor odes it depend on whether there are or are not decisions in any sense but the ordinary one (i.e., I think, shall I do this or that? I opt for that, and do it.) In either case, if you are going to find out about the prediction, and if what you do depends on what the computer predicts, the computer must know what it predicts in order to know what you will do. This is true regardless of the idiom in which it couches its predictions. Just ask xanax, who has apparently been reading all about it. Hmm, I don't know where "you are going to find out" fits in my reductionist view of what's happening. The computer's particles bounce around in some way determined by physics, and so do mine, and at some point the bounces in the latter depend strongly on interactions between the two sets, but that interaction is captured in the program/data. Imagine I had a computer running two programs - one based on some data, and the other encapsulating the other in some way I haven't thought through yet so let me do that first. rilkefan: it's basically a self-reference problem . The result the program is trying to come up with has to figure as one of the inputs to the program. (Since either (a) what the computer tells you does not affect your conduct, in which case it can just plug in any old thing and not affect the result, or else (b) it will, in which case it must have the answer in order to arrive at it. I don't see how one program embedded in another will help with this, but I could be missing something. Consider this, though (not exactly the same problem, but a related one): suppose a computer were trying to predict its own future, and could do it faster than real time. Then given some very long calculation, it would be able to predict what result it would come to faster than simply calculating it. Well: this prediction is itself a caluclative problem of some sort, presumably, so it could predict the result of this problem faster than it could calculate it. Iterate until the time needed to solve any problem is infinitely small, for reasons that have nothing to do with Moore's law. Doesn't it seem to you that something must be wrong with this picture? rilkfan,I'm not sure if this is relevant, but according to quantum theary certain events are simply not completely predictable, as a result given our current understanding of physics hard determinism is impossible. Though again this is probably totally irrelevant to the discussion about how such a hypothetical thing would affect our perceptions. I'll have to think about this some more, but I don't see the problem when you take all the intelligence and interpretation out of the problem. There's no "If he plays this I'll play that so" involved - from the point of view of physics, there's no prediction going on. I.e., I don't see how there's any difference between my set of particles seeing the book and my set of particles feeling the particular gravitational pull of the book. I agree that there's a practical problem of complexity - I suspect the computer has to be significantly more complex than the universe, hence it can't be in the universe, hence it can't address the envelope containing the book. Anyway, maybe this won't work in my poem, or any poem... "but according to quantum theary certain events are simply not completely predictable" Not what I was taught in grad school (when I was listening) - (of course people argue about this and I represent a minority view among physicists who care) - in particular there's a Feynman representation where you take the initial state, evolve it with the Hamiltonian or whatever, and voila, final state. (Shuffling a lot of stuff under the rug with "state", probably.) Also heard a seminar (which I should try to trace) from a guy at Harvard who had a plain deterministic version of ordinary QM. The evolution via the Hamiltonian only gets you to a state that is a probability density, the final step that takes you from that probability density to an observable is the one that cannot be predicted. Yeah, I'm probably happy saying the real thing is the probability density and the rest of the standard collapse-of-the-wave-function interpretation is mysticism. According to whoever I failed to cite above, even that isn't necessary. A "compare and contrast" of Europe and the US from the NY Review of Books. Makes for interesting reading. "An open thread for the weekend. Use it wisely. Use it well." Is this a genuine Elvish thread? By your command. second, the program would have to run on a computer bigger than the universe and would take an unfathomable amount of time. I think a related problem is it would take more energy than is available in the universe. You would essentially have to remake the universe in a less efficient analog. More Tom Lehrer, please! Who needs a hobby, like tennis or philately? I have a hobby: re-reading Lady Chatterley! Gettin' ecstatic Sort of dramatic Doing the Vatic- an rag. You would essentially have to remake the universe in a less efficient analog. There is another theory which says this has already happened. 1. My favorite Lehrer line: "As the judge remarked the day that he acquitted my aunt Hortense To be smut it must ut-terly without redeeming social importance." First runner up: the Werner von Braun one above. Second runner up: "Now it's fiesta time in Akron Ohio but it's back to Guadalajara I'm longing to go Far away from the strikes of the AF of L and CIO..." 2. On the "do House Republicans have any redeeming qualities front," here's a doozy of a proposal: SEC. 102. WAIVER OF LAWS NECESSARY FOR IMPROVEMENT OF BARRIERS AT BORDERS. Section 102(c) of the Illegal Immigration Reform and Immigrant Responsibility Act of 1996 (8 U.S.C. 1103 note) is amended to read as follows: (c) Waiver- (1) IN GENERAL- Notwithstanding any other provision of law, the Secretary of Homeland Security shall have the authority to waive, and shall waive, all laws such Secretary, in such Secretary's sole discretion, determines necessary to ensure expeditious construction of the barriers and roads under this section. (2) NO JUDICIAL REVIEW- Notwithstanding any other provision of law (statutory or nonstatutory), no court shall have jurisdiction-- (A) to hear any cause or claim arising from any action undertaken, or any decision made, by the Secretary of Homeland Security pursuant to paragraph (1); or `(B) to order compensatory, declaratory, injunctive, equitable, or any other relief for damage alleged to arise from any such action or decision.'. (via this kos diary.) Here's another doozy from the same bill, from section 103(a): (i) IN GENERAL- Any alien who... (IV) is a representative (as defined in clause (v)) of- (aa) a terrorist organization; or (bb) a political, social, or other group that endorses or espouses terrorist activity... is inadmissible. (the ellipses are of other classes of inadmissible immigrants. I promise I'm not Dowdifying). "Social or other group that endorses or espouses terrorist activity"? Like what? Hypothetically, would it include, say, "Muslims"? I'm not sure that's what it means but neither am I sure that it doesn't mean that. Things that vague make my hair stand on end, because the courts usually defer to agencies in interpreting terms that vague. And as the Supreme Court understands it, there's nothing in the Constitution that prevents Congress from banning Muslim immigration. Oh, and by the way, according to Section 104(a)(1)(B), "Any alien who would be considered inadmissible pursuant to subparagraph (B) or (F) of section 212(a)(3) is deportable.'" Here's a link to the THOMAS search engine. The Bill # is H.R. 418. I have no idea if it has a chance in the world of passing or if President Bush would sign it. I would think and hope not--in the House yes, but not the Senate and or the President's signature. But I have no real idea. avast, scurvy blockquoting. Okay, I looked up the statue it's amending. The current statute says that an alien can be excluded if he "(IV) is a representative (as defined in clause (v)) of....(bb) a political, social or other similar group whose public endorsement of acts of terrorist activity the Secretary of State has determined undermines United States efforts to reduce or eliminate terrorist activities." and defines "represenative" as follows: the term "representative" includes an officer, official, or spokesman of an organization, and any person who directs, counsels, commands, or induces an organization or its members to engage in terrorist activity. This implies they're talking about a political group like the PLO, and "social group" is in there so a group can't claim it's really just a charity or a benevolent society or whatever. I am used to the very different, much broader use of "social group" in asylum and refugee law, where it could include a really, really broad category of people who don't have to be formally organized in any sense. So I don't think it's as bad as I first thought, and the ACLU seems more worried about other stuff in the bill. But it bears watching. Also, the stuff about waiving all laws applies to laws that stand in the way of this, from a 1996 law: "(b) Construction of fencing and road improvements in the border area near San Diego, California. (1) In general. In carrying out subsection (a), the Attorney General shall provide for the construction along the 14 miles of the international land border of the United States, starting at the Pacific Ocean and extending eastward, of second and third fences, in addition to the existing reinforced fence, and for roads between the fences." But it does not appear that there is a geographic restriction on the legal obstacles to the fence that the secretary can waive. The 1996 law already allowed the INS to override the Endangered Species Act and the National Environmental Policy Act for the purpose of building these fences. I don't know what other laws are standing in the way. Yeah, I'm probably happy saying the real thing is the probability density and the rest of the standard collapse-of-the-wave-function interpretation is mysticism. If it makes you happier, you can think of "state" as short for "vector in Hilbert Space" and "measurement" as "projection onto the orthonormal basis of the measurement operator". It is, unfortunately, still a probabilistic projection so I'm not sure if this gains you anything. [Fun fact that is occasionally used in quantum computing: you can transform the state |0> into the (orthogonal) state |1> with probability 1-\epsilon using nothing but repeated measurements; no unitary transformations or nuttin'.] As for the various paradoxes of hard determinism*, hilzoy's point is, essentially, the same as the proof of the non-solvability of the Halting Problem: given an oracle of sufficient power, a program can be written that, using the oracle, defeats the oracle. I'm tempted to say that, in fact, a "hard deterministic oracle" is, in fact, a corollary of the Halting Problem but I suspect that I'd have to wave my hands so hard at the Church-Turing thesis that I'd actually attain liftoff. [The most interesting variant I've seen on this dilemma is Philip K Dick's "The Minority Report" -- the short story, not the movie -- wherein this kind of causal/acausal loop is explored in depth.] * By which I really mean hard determinism coupled with free will. There's a variant of hard determinism I sometimes use when fanwanking various SF shows that asserts, in its most simplistic form, that the act of accurately predicting the future involves a partial collapse of the wavefunction of the universe -- for those of you familiar with such terminology, think of it as an approximate tracing out of the event being predicted -- which in turn makes such prophecies self-fulfilling. What a frighteningly-smart thread. My head is still hurting from reading Hilzoy's and Rilkefan's exchange. gromit: Being unwilling to spend$40+ a month on cable, I rented the miniseries on DVD. Now I'm hooked, but I can't watch the series.

There are other possibilities.

here you find the guides and here BSG

A question completely unrelated to what's come before it: can anyone point me towards a source, preferably online, for naming conventions in the ancestor tongues of Arabic? [I'll take more than just the naming conventions but that's the bare minimum I'm looking for.] I'm not exactly sure which Semitic languages qualify as "ancestor tongues" here -- Aramaic, perhaps? -- but I'm trying to get a feel for "proto-Arabic" and having a devil of a time doing so.

Ok, this is all getting a lot clearer to me. I think I'm happy saying that any system simulating another has to be more complex, and thus a system that simulates itself has to be more complex than itself (esp.? for systems which conserve information, which I believe is the case for the universe). This is in fact a Goedelian argument a la the Halting problem (btw, Anarch, I asked you that exact question in email a month or so ago and never heard back, tsk tsk.) The point of the two-program argument I started was to demonstrate to myself that this isn't a question about the viability of determinism, since the same problem arises with obviously-deterministic programs that simulate other o-d programs.

This seems to me a fine disproof of a physical G*d, not that anyone needed one.

And maybe I can in fact work this into my poem, which argues in part that there is no thought, just algorithms which don't a priori even finish running.

Also for the poem - any (practical) math people out there want to recommend any special functions they find elegant or useful?

Btw, thanks for the identification, hilzoy, and where does one find whatever xanax is reading?

On the subject of smartness, a friend of mine ran into Ed Witten, the leading theoretical physicist of the day, and found him an actual person. My friend had mentioned Witten to another theoretical physicist, who works in a field devoting to calculating something of horrible complexity; and it turns out that Witten had spent two months working in the field and completely revolutionized it. My friend asked this other guy if he felt bad about not having come up with Witten's ideas, and he said, No, I would never have thought of that. (I've heard similar stuff from a pure math prof at a snooty institution.) So my friend is of the opinion that Witten is not just smarter than everybody else, but he's a _lot_ smarter.

Anyway, it's interesting to wonder what the distribution is like at the far end, even for those of us in the bulk. (Subject of another poem - trying to write about stuff it's impossible to actually describe lately, stupidly.)

rilkefan: no problem. Just look me up on Amazon.com.

For the record, about this: "I don't see the problem when you take all the intelligence and interpretation out of the problem. There's no "If he plays this I'll play that so" involved - from the point of view of physics, there's no prediction going on." -- Suppose we're not dealing with a problem involving prediction, just one that's insoluble, like: given that x=x, solve for x (without further info.) My assumption was: if it's genuinely insoluble, then there is no such thing as 'the computer predicting each step it goes through when it solves it, by running its program that takes as input the complete state of the universe at T and the laws of nature'. SInce, of course, it won't solve it.

What I was trying to argue was just: in the same way that you can't, without more info than "x=x", solve for x, since you'd need to know what x was in order to do so, a computer can't solve for 'what rilkefan will eat for breakfast tomorrow', assuming that it is going to tell you. (Which implies that it is in the universe it is supposed to be modelling.) It's an insoluble problem not, I think, because I'm imagining the computer actually thinking and getting into trouble with the propositional content of its thoughts; it's because, like "x=x", you need the solution as an input in order to solve the problem.

If so, then there is no such thing as 'the computer predicting its own states as it solves the problem.'

As for what xanax is reading: he just mentioned on another thread that he's reading this. As I said there, I think that's sort of heroic of him.

rilkefan: I think I'm happy saying that any system simulating another has to be more complex, and thus a system that simulates itself has to be more complex than itself (esp.? for systems which conserve information, which I believe is the case for the universe).

Insofar as I'm comfortable talking outside my area of expertise, I think that's Chaitin's variation/expansion on the Halting problem. [It's sort of the computability-theoretic analogue of Godel's Second Incompleteness Theorem: in order to prove the consistency of a given system of axioms, we have to assume a stronger set of axioms.] I'm not sure whether you can argue that you'll need something more powerful than the universe to simulate the universe, since it seems that the universe itself is doing a pretty good job of it, but you can certainly argue that you can't simulate it with anything less powerful than the universe itself. In Chaitin's terminology this is the same as saying that the universe is "random", which isn't a completely unrealistic assumption given what we know of the Big Bang and the nature of quantum-mechanical collapse.

[At the very least, you could claim that any simulation of the universe, being of size N particles, would require O(N) particles to simulate, and a) most people would believe you, b) that gives you the effective result you're looking for.]

As for Conservation of Information, there's some really really cool stuff coming out of Quantum Computation in the vein of "Information is a physical resource". Turns out that you can explain scads of statistical theorems on entropy (including, most coolly of all, the way a black hole's event horizon interacts with the rest of the universe?!) as consequences of Shannon's coding theorems applied to qubits instead of classical bits. I don't understand a damn thing of it, but there might be some vaguely comprehensible lay renditions out there.

(btw, Anarch, I asked you that exact question in email a month or so ago and never heard back, tsk tsk.)

Whaaaa? I never got any email from you; stupid Hotmail gremlins were probably playing silly buggers with my account again. Feel free to re-send, though.

Also for the poem - any (practical) math people out there want to recommend any special functions they find elegant or useful?

hooooooboy. Took a class on special functions with Richard Askey, a veritable god in the field; alas, I've forgotten most of them in the interim :)

That said, I was just mucking around with the Hahn polynomials; I like the Legendre polynomials; one of my former hall-mates was working on asymptotic expansions of the Airy functions; and "hypergeometric series" is just plain fun to say. Oh, and the Bernoulli numbers/polynomials are right cool too. Barry Mazur spoke at UW last semester and he's convinced that the Bernoulli numbers connect something like five or six completely disparate branches of mathematics*, so you can probably count those too.

That said, special functions aren't even peripherally related to my field so you might want to grab some of the engineers -- Slarti, I'm looking at you! -- and get them to rattle off a few.

* The part I best remember is that the denominator of the p'th Bernoulli number in lowest form relates to the multiplicity of the zero (I think; maybe the multiplicity of the singularity?) of a particular p-adic modular form which in turn determines the number of non-diffeomorphic manifold structures that can be put on the p-sphere. Yes, it really was that cool, and that incomprehensible, in person.

Finally:

So my friend is of the opinion that Witten is not just smarter than everybody else, but he's a _lot_ smarter.

The distinction used about Feynmann -- maybe by him? -- was that there are lots of "geniuses", but very few "magicians": people who are so awesomely smarter than everyone else that watching them is literally like experiencing magic, you have no idea how they're doing what they do. The ones I know of working today include Grothendieck (if he's still out there), John H Conway (a prick, but an awesomely talented one) and Saharon Shelah (currently the most-published mathematician in the world, IIRC, maybe the most-published in history after Euler). I'm sure there are others out there -- I can only talk about fields I know enough of to distinguish between magicians and mere geniuses -- but those are the only three that absolutely leap to mind.

It's an insoluble problem not, I think, because I'm imagining the computer actually thinking and getting into trouble with the propositional content of its thoughts; it's because, like "x=x", you need the solution as an input in order to solve the problem.

Depending on the precise way in which this problem is encoded, it need not be insoluble. This is the whole point of the Godel Diagonalization Lemma in elementary logic: you can produce predicates which "talk about themselves", i.e. somehow act as both their own input and output. This in turn is what gives the Incompleteness Theorems and the unsolvability of the Halting Problem: since this kind of self-referentiality (my solution is my input, that sort of thing) is representable, the existence of certain kinds of predicates (in arithmetic, truth; in the real world, perfect predictions of the future) is ruled logically inconsistent.

I agree with you that this is dangerous territory -- for example, I think that's what's at the core of Liar Paradox -- but like I said it crucially depends on what, precisely, you're encoding and how, precisely, you're encoding it.

Added in proof: there is another alternative, of course. It's entirely possible that a) you can perfectly simulate the universe at a small enough reduction factor (say log*(N) qubits), b) such a simulation can be run to predict the future faster than than the actual evolution of the system (and, necessarily, the prediction of the future system incorporates the evolution of the simulation itself), and c) this simulation is perfectly accurate, which more or less translates to being perfectly deterministic. If that's the case then, well, all we've accomplished is to prove the falsity of free will :)

"and, necessarily, the prediction of the future system incorporates the evolution of the simulation itself"

Here's where I think the complexity blow-up occurs.

I had thought about Airy functions, but that seems a little too easy and poetical. Like "Saharon Shelah".

hilzoy, I think it's the case that for given values of t and delta-t and point of interaction there could in fact be solutions to the problem - e.g., "I won't have breakfast because I'll be dead" (reading which I'll keel over.) Whatever that means.

I suspect that there is in fact only one possible universe, which adds another layer of difficulty to the whole conversation...

A question completely unrelated to what's come before it: can anyone point me towards a source, preferably online, for naming conventions in the ancestor tongues of Arabic?

After going to preview and re-reading your request Anarch, I realise you might be asking for naming conventions of languages rather than people. A quick recommendation is http://www.ethnologue.com, which has the generally agreed linguistic family relationships. But if you were asking about how people named themselves...

I think that's a real tall order because those naming conventions interacted with Roman naming conventions (and Christian naming conventions when Constantine converted) and then with Islamic naming conventions. Also, given that Jews did not generally have public last names until the Napoleonic era, which suggests that other naming conventions were similar, and thus were supplanted. Here's a link about the difference between Sephardic and Ashkenazi Jewish names which also suggests that it is only with moving outside of the middle east that Jews took additional names (which makes sense, as the need for multiple names arises with either citizenship or taxation or if groups are prostyletized, and Sephardic Jews are those who were accorded some rights within the Iberian penisular and then were kicked out) (This is all from googling, so any with more detailed info are welcome to correct me)

Some other interesting links dug up while Googling
here is a page about researching Sephardic ancestors

This is an basic link on naming conventions around the world.

This is some hard core linguistic stuff, but the suggestion here is that

In her highly influential book on Linguistic Diversity in Space and Time, Johanna Nichols (1992) has provided a new way of juggling genetic and areal linguistic history. She distinguishes between spread and residual zones; in her terminology the ancient Near East was a spread zone. Clearly, the area we are interested in has been affected by a number of Semitic spreads. In historical times we must reckon with three, if not, more such spreads: the early one that gave birth to the languages attested in the ED III documents, Amorite, and the controversial Aramaic spread.

If this is right (I really like Nichols explanation for why we have extreme linguistic diversity in some places, but not in others, and her thesis, if applied to the Middle East, makes it a 'spread zone', where indigenous languages have been supplanted/absorbed) it would be very difficult to discern previous naming traditions.

Perhaps we can link up the mathematicians and the Lehrer-philes with a rousing chorus of "Lobachevsky."

LJ: I was interested in how people named themselves, yes. Those links look interesting, although a bit slanted towards the Hebraic; I'll check them out tomorrow and see if they have what I'm looking for. Thanks muchly.

[I'm also looking for a usable online Akkadian dictionary in case anyone has one handy. I've found several but they tend not to be the most, um, user-friendly of pages.]

Bernard: Perhaps we can link up the mathematicians and the Lehrer-philes with a rousing chorus of "Lobachevsky."

I knew I was a real mathematician the day I understood the title of Lehrer's supposed paper.

Anarch,

That is legitimate? I knew Lehrer was a mathematician, but always wondered whether that title was gibberish.

And what's the story on the plagiarism?

That is legitimate? I knew Lehrer was a mathematician, but always wondered whether that title was gibberish.

Well, it's borderline gibberish AFAICT -- not even close to my field of specialty -- but it's close enough to meaningful that it makes sense to me. F'rex, I think Smale's results on the non-diffeomorphic structures of the 7-spheres would count. Unless I'm horribly, horribly wrong :)

The full title, btw, is Analytic and Algebraic Topology of Locally Euclidean Metrization[s] of Infinitely Differentiable Riemannian Manifold[s]. I'm not really sure what he means by "analytic topology" -- I can venture a few guesses but that's about it -- but yeah, the rest of it makes a certain amount of sense. The one problem I have with it (let the ubergeekery commence!) is that a Riemannian manifold is usually assumed to have a metrization structure in the definition, especially if you're going to talk about differentiable ones (let alone infinitely differentiable ones). I have a feeling that he basically threw in a bunch of redundacies of a similar vein in order to make it sound, well, longer. That said, you'd need to talk to a specialist in either differential geometry or general relativity to be sure.

And what's the story on the plagiarism?

Which? "Plagiarize, let no-one else's work evade your eyes?" Or Lobachevsky's supposed plagiarism? If the latter, it's bunk AFAIK; Lobachevsky never done anyone wrong like that.

Which? "Plagiarize, let no-one else's work evade your eyes?" Or Lobachevsky's supposed plagiarism? If the latter, it's bunk AFAIK; Lobachevsky never done anyone wrong like that.

The latter. I always assumed that Lobachevsky had been involved in some sort of plagiarism scandal, though I never actually read about it anywhere. You're saying that's not so, to your knowledge?

You're saying that's not so, to your knowledge?

Nope. So far as I know that's entirely Lehrer's invention, and I think he says as much on the record jacket.

well, i feel undereducated.

we could talk instead about the problems with designating critical habitat under the federal endangered species act.

or i could just go play with my trains.

thanks for a most impressive if utterly unilluminating thread.

Francis

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