tea.mathoverflow.net - Discussion Feed (Should a mathematician be a robot?)

Todd Trimble comments on "Should a mathematician be a robot?" (17032)

2011-11-12T00:28:08-08:00

@akbarov: no, I can't enter a vote to close a meta discussion. At most I can propose or suggest to close a meta discussion, but there is no vote per se; it's up to the moderators alone whether a meta thread is officially closed. Anyway, I wasn't talking about this. I was talking about the closing of the original post over at MO (recall that I was one of the closers; one of your comments mentioned me by name).

That being said, I am fine with your suggestion of bringing this meta discussion to a close. I for one have nothing further I wish to add.

Sergei Akbarov comments on "Should a mathematician be a robot?" (17031)

2011-11-11T23:34:31-08:00

@Todd Trimble: perhaps it's me who did not understand something. "I entered a vote to close" - does it mean that you would like this discussion to be closed? If yes, I have no objections.

@quid: "how you can say that you agree with me that MO is better than Russia" -- I had in mind that in comparison with what happens in Russia, what happens here looks better. So I agreed with you when you wrote that "you can appeal, and the appeal was even successful".

@grp: I don't agree with what you write:

"Should mathematicians be robots? I don't know, but that has nothing to do with what is considered appropriate for MathOverflow."

But I agree that the further discussion will be a waste of time. I think everybody here made his point, and I do not believe that something essentially new can be added. However, if somebody wants to tell me something more, he is welcome -- I'll willingly answer by e-mail, or continue here, it's up to you.

Todd Trimble comments on "Should a mathematician be a robot?" (17029)

2011-11-11T16:14:17-08:00

@Todd Trimble:

"I entered a vote to close"

I agree.

I don't understand the point of this message. Yes, we agree that I entered a vote to close. And therefore?

quid comments on "Should a mathematician be a robot?" (17027)

2011-11-11T12:51:10-08:00

@akbarov:

I mainly referred to the FAQs for 'procedural' things, e.g., who is a moderator who is not, how the site is run in genral. Explained somewhat to the end, and in the point on the reputation points. This is not really relevant to the question, but possibly to some of your inferences on the MO-community in general.

Something else that is in the FAQs that could have been helpful, is this:

What if I don't get a good answer? In order to get good answers, you have to put some effort into the question. Edit your question to provide status and progress updates.

For example somebody mentioned of having overlooked your clarification regarding your question given in a comment.

Specifically you said in a comment this:

The Mendeleev table claims, for example, that the first electronic orbit can have only 2 electrons, the second - 8, the third - again 8, the fourth - 18, and so on.

Which I find quite helpful in understanding what you are after. So, once you noticed there is some confusion what you are asking for you could have added things like this in the question. Now, not doing this, is certainly not breaking some rule. All I am trying to say is that I think some people really found it difficult to figure out what you are asking for, and perhaps you could have helped them a bit more, and by doing so accelarated the process of arriving at a version that more people appreciate/understand.

I think the question in principle is good for MO, it is just that it took some time to collectively figure out what it was.

Finally, and a bit unrelated, I am not sure how you can say that you agree with me that MO is better than Russia, as I said nothing on Russia. (And would not as I have not detailed knowledge.)

grp comments on "Should a mathematician be a robot?" (17026)

2011-11-11T12:21:38-08:00

The closing of the question is determined by what some part of the community feels is not appropriate for the forum. This does not mean the question is bad, or unrelated to mathematics, or strongly violates the guidelines of the FAQ. It means some part of the community does not think it appropriate.

I think your question is not appropriate, partly because it is interdisciplinary (and so likely not going to find a good answer among this community), not sufficiently focussed (asking for an axiom system to describe a diverse and complicated set of characteristics such as listed in my copies of the periodic table, using an unstated and perhaps undiscovered set of primitives; I don't think "Mendeleev table" and "quantum mechanics" to be sufficiently precise descriptions for this forum), and for me most importantly, not well motivated. (What are you going to do with it?)

You can spend time attempting to argue with me on the points above; I advise you that such would be a waste of time, as I already have my mind up on these points and how they are applicable to questions posted on MathOverflow. As it turns out, there is another point: the question and your pursuit of it on this form is subjective and argumentative (just judging by the resulting thread). This is another reason for closure.

Should mathematicians be robots? I don't know, but that has nothing to do with what is considered appropriate for MathOverflow. I do not say your question is bad. It strikes me as a worthy question, and there are questions close to your question which may be appropriate for MathOverflow. In any case, congratulations on getting interest and responses to it. If you want to work with the MathOverflow system instead of fight it, I recommend your next post be here on meta.mathoverflow.net, asking if the next question you propose can be made appropriate for MathOverflow.

Gerhard "Ask Me About Question Asking" Paseman, 2011.11.11

Sergei Akbarov comments on "Should a mathematician be a robot?" (17025)

2011-11-11T12:08:55-08:00

@Todd Trimble:

"I entered a vote to close"

I agree.

Todd Trimble comments on "Should a mathematician be a robot?" (17023)

2011-11-11T11:57:22-08:00

@akbarov (Sergei): I am reluctant to enter this debate, but at the time I entered a vote to close, I think I considered the question a kind of category error: the periodic table is part of empirical science, not part of mathematics. Alexander Woo has formulated this more elaborately, I believe. I will not follow him in applying the word 'crank' however (too strong, too heated), and much has happened since the first closing, and anyway I prefer not to argue because the question has indeed been reopened, and I'm not sure how much time I have to devote to a debate. I am sorry however that you seem to be experiencing MO in such a negative way.

Sergei Akbarov comments on "Should a mathematician be a robot?" (17022)

2011-11-11T11:43:32-08:00

@Todd Trimble: thank you very much.

@Alexander Woo: following your reasoning, naive questions, like "what time is it?", must also be a sign of crankdom, since only a person who never heard about Big Bang can ask them.

Sergei Akbarov comments on "Should a mathematician be a robot?" (17021)

2011-11-11T11:18:51-08:00

@quid: every time when somebody suggests me to look at FAQ, I am reading it again and try to understand what I did wrong. And every time I do not understand. If you think it is indeed important in my situation, I ask you to explain which rule I broke. But of course I agree with you that MO is much better than Russia. :)

As to this:

"'Mendeleev table' is not defined and neither is 'proof' and there is sufficient room for reasonable interpretation"

-- this is the usual situation when you try to axiomatize something. For example, the notion of probability was not accurately defined before Kolmogorov gave his axioms. This does not mean that mathematicians could not ask questions each other about probability before Kolomgorov published his work, and discuss some unexplained effects after he did this.

@Mariano: I compare what I see here with the usual behaviour of russian bureaucrats. Of course, MO is better, but some details are the same, for example, the way how my question was closed: nobody (of those who were closing) explained me what was wrong, nobody suggested to reformulate, nobody informed how I can appeal (by the way in FAQ the last question is not explained, isn't it?). All this information I received later from Dmitri Pavlov, who as it turned out is neither a moderator, nor the one who closed my post.

Todd Trimble comments on "Should a mathematician be a robot?" (17019)

2011-11-11T11:05:51-08:00

It's a made-up word, referring to <a href="http://en.wikipedia.org/wiki/Crank_%28person%29">crank</a>.

Sergei Akbarov comments on "Should a mathematician be a robot?" (17017)

2011-11-11T10:31:44-08:00

@Alexander Woo: excuse me, what is crankdom? I did not find this in dictionary.

Mariano comments on "Should a mathematician be a robot?" (17016)

2011-11-11T09:15:56-08:00

Sergei,

a triple of observations:

your question was really an outlier in the context of MO. Surely you can see that questions involving proving anything regarding the real physical worlds and, much less, the periodic table, do not exactly abound. I suggest that you not base your opinion of the site based on your experience regarding such a question, for it is really not representative of anything. In my humble opinion, your question was off-topic—this is no obstacle to certain great users of ours who have the amazing capability of turning off-topic and/or blatantly bad questions into what they might have been in optimal conditions and answer them all in one big swoop.
your comments regarding politeness and generosity of the community simply startle me. One of the most amazing things of MO is the immense display of generosity and politeness it offers! I have been reading through the site for a long time now with steady frequency and I still marvel, every day, at the energy, good will and good manners that most of its active participants put into it.
the site is run more or less in a communitarian way. Any user gets voting powers, long-term users get closing powers, even longer-term users get deletion powers. The moderators are are very, very small set of users (three or four?) who only in rare cases get involved in those matters.

Mariano comments on "Should a mathematician be a robot?" (17015)

2011-11-11T09:01:38-08:00

Wouldn't it be easier to say that generally naïveté, in the 21st century, is a sign of crackdom? :=)

Alexander Woo comments on "Should a mathematician be a robot?" (17014)

2011-11-11T07:57:07-08:00

Dear Sergei,

1) It is true that mathematics nowadays, especially in the United States, runs by the principles of Geselleschaft and not Gemeinschaft, but it is such a large enterprise that there is no choice.

2) To me, in the 21st century, naive realism, naive Platonism, and naive Pythagorianism are all signs of crankdom. For me, the way your question was phrased set off this alarm.

quid comments on "Should a mathematician be a robot?" (17013)

2011-11-11T07:28:01-08:00

(cont.)

You also say:

This means that a little dialogue between moderator and questioner must take place, and in this dialogue the questioner must be informed how he can appeal against the decision of moderator.

If I oversee the situation correctly the only person having anything to do with this question that is a moderator is Scott Carnahan (look for diamonds in the list of users to see the moderators and/or read the FAQs for further information). Everybody else is in some sense just somebody using the site long and intensely enough to have been (automatically, based on the point count) assigned certain moderating duties (or granted the privileges if you prefer to think of it this way, but let me tell you getting into this closing-business can be quite unfunny at times so IMO it is at least as much a duty as a privilege). That being said, it is common that when somebody asks something and people close it they leave a comment to explain why (in some sense this was also done in your case) and how to appeal is not always made explicit but only since it is assumed it is clear that you can do so by comments and/or creating a discussion here on meta. And, as you see people paid attention to your appeal.

More generally, the most important things on how the site works are explained in the FAQs and linked documents (did you read these?; what I mean is that for practical reasons it is not reasonable to expect that each and every individual gets an individual explanation about the basic guidlines/rules of the site/community; by contrast it seems more reasonable that there are publically available guidlines/rules). In case you feel some important piece of information is missing there it is my experiecne that if you bring this to the moderators attention (here your really need a moderator or I believe technical the administrator), by posting here for example, then if they agree this is a useful suggestion it will be added. I know from personal exprience that they even pay attention to pseudonymus users.

So, while I can understand why you are not quite happy how your question was treated, I would also say that there were reasons intrinsic to the formulation of your question that caused some of the initial 'problems' about which you are unhappy. And, perhaps you should also keep in mind that it is now open; so you see, you can appeal, and the appeal was even successful.

Regarding the organizational form of MO you say it is feudalism; occassionaly some people said it is an oligarchy; one could also say it is a meritocracy. Yet, the truth is, it is a dictatorship! User Number One, the man with the two diamonds, can decide everything and if he wishes to tomorrow we are all dead (as MO users). This is not meant so seriously, but technically I think it is correct.

quid comments on "Should a mathematician be a robot?" (17012)

2011-11-11T07:27:42-08:00

I so far stayed out of this discussion as the subject of the question is/was quite far removed from things I have a meaningful amount of knowledge about, however since now this is taking a very genaral turn some remarks:

Sergei Akbarov, you suggest that:

Before closing a question, a moderator should verify that the questioner indeed does'not understand what he wants.

I would say it is also, or even more, important to make sure that others can understand what the questioner wants. For a highly ill-formed question the questioner can still know very precisley what she or he wants, but nevertheless it could be completely incomprehensible for anybody but the questioner. In such a case to me the only useful course of action is to ask the questioner to rephrased, make more precise,... what she or he wants to ask, and posibly close the question in between (with the idea that it is then reopened once clarified). Look, it seems to me some people simply at first (mis)understood your question as one being not about mathematics but rather physics/chemistry, so off-topic here (and I can assure you from observation that for example Greg Kuperberg is a very helpful and tolerant person on this site, so to me it is really a given that he simply could/did not understand what you want, or what he thought you wanted was not on-topic). Then you explained that, no, it is actually more mathematical then they understood it, then it was not quite clear to some what was meant precisely. Then some more explanation happened, until some people agreed that it is now precise enough to be understandable. While the main purpose of the site is to allow people to ask question and get answers, another purpose is also to allow others to learn something by reading what is written; so one really also needs to make sure it is somewhat easy to understand what is meant.

Regarding your question, I would say that at least to me the problem was/would have been [I did not interact with it in any way] with 'proof the Mendeleev table'. What should this mean? What even is the Mendeleev table? In some sense I assume you do not refer to some specific original historical document from the 19th century but what nowadays goes by this name, but these tables are not unique and change over time. So, what exactly? And, what is 'a proof'?

You yourself and others later gave meaningful interpretations of this, and still others anticipated (guessed?) the intent correctly. But, I think it is at least not completely unfounded to say that a question for a 'proof of the Mendeleev table' is not a precise question, as 'Mendeleev table' is not defined and neither is 'proof' and there is sufficient room for reasonable interpretation. (What if there were something that worked until atomic number 42, is this then a 'proof' of 'the Medeleev table'?)

In this sense in my opinion your question in it original form simply does not meet your point 2., as 'proof the Medeleev table' is not sufficiently precise, and can mean quite different things to different people (as experimentally verified).

(cont.)

Sergei Akbarov comments on "Should a mathematician be a robot?" (17011)

2011-11-11T04:05:15-08:00

So you see how this happens. As I told before, this comes from the idea that only a specialist can understand a specialist. As a corollary, if somebody asks you something, and you see that he is not a specialist, you should not waste your time on ceremony - get rid of him, and you'll be right. I lived almost all my life in a country where this principle is followed through: in Russia you can't demand an answer from a specialist if you are not a specialist in this field as well. Moreover, this principle is interpreted as a tool for "defending specialists" (this is the widely accepted idea, but of course in practice it means defending the leaders of the professional communities, and not just scientific communities, but first and foremost the bureaucratic ones). It implies not only that

-- questions from non-specialists can be ignored just on the ground that the questioner is not a specialist,

but also that

-- even if you are a specialist your question must be sufficiently convenient, it can't contain any possibility of critical interpretation, otherwise it will be ignored as well, or, if you insist, the community starts the procedure of your (step-by-step) disqualification (this happens from time to time in Russia with judges, policemen, teachers, etc. -- you can just listen the news).

I claim that this is the only official principle that manages the social life in modern Russia. Of course, there are others, like the idea that "only loyal person can be appointed to the post", but things like that will never be openly recognized by professional communities -- they are always hidden.

Practically this leads directly to the feudal organization of the society. The details of how this works in Russia you can learn from the Vladimir Shlapentoh book "Contemporary Russia as a Feudal Society" (or again from news). The chain of implications here is the following:

"only a specialist can understand a specialist" =>
"it is necessary to protect specialists from non-specialists" =>
"if A asks B, then it is B's group of specialists (in fact, B and B's boss) who decides whether A is a specialist in their field, and only if the answer is positive, B acknowledges his duty to answer the question" =>
"nobody acknowledges his duty to help anybody but his group and his leader" =>
"the society is divided into groups with leaders, and the relations between the leaders are regulated by an hierachy according to the idea of loyalty".

The last situation is called feudalism. The difference with the western society is that in the West the principle of "protecting specialists" does not dominate yet, and in a situation of controversy A can appeal to the rest of the society -- some tools for this are provided by the competing idea of human rights (which claims that outsiders must have also some possibility to influence on what happens).

So my point is the following. If you contemplate promotion of communication between mathematicians, of establishing horizontal connections in scientific community, you should realize that leaving only possibility 1 (among 1-2-3 above) for this communications is a road to the inverse direction. To avoid falling into feudalism, we should encourage interdisciplinary questions, or questions looking like them, instead of closing them immediately. For this I suggest the following:

1. Before closing a question, a moderator should verify that the questioner indeed does'not understand what he wants. This means that a little dialogue between moderator and questioner must take place, and in this dialogue the questioner must be informed how he can appeal against the decision of moderator.

2. If logically a question is formulated correctly, it is not nice to close it. And the questions like "is this an axiomatic system?", or "what is the definition of this notion?", must be legal.

Sergei Akbarov

Sergei Akbarov comments on "Should a mathematician be a robot?" (17010)

2011-11-11T04:04:48-08:00

Thanks to all for the response, and excuse me for the delay.

Special thanks to José, who gave a quotation of Feynman. José's interpretation indeed would have been a good question, but I must confess, it is not what I wanted to ask. I had in mind the axiomatization of quantum mechanics, so Ryan understood me correctly, although I do not share his idea that "the question is clearly not focused enough". I do not see a way to focus it more clearly, than it is already focused. (I would not protest againts Scott's reformulation, but I am sure this would not solve the problem of "acrimonious string of comments ".) Ryan says that I could cut my question into a sequence of more specific questions, but I do not see how this could be done. I must say also, that I do not agree with Andreas Blass: I think that questions like "what is the definition of atom?" must be legal at least in the situation where questioner sees mentioning of atoms in mathematical texts. Anyway, if there are no objections, I will edit my original post, quote there Feynman (with reference to José) and give reference to Scott, Andreas and Alexander.

I started this thread in Meta (and put it to this category -- Etiquette), because people's reaction to my original post reflects a problem which I find to be very important and urgent - the problem of interdisciplinary communication.

The problem is the following. When somebody (let's call him A) asks a specialist (we call him B) a question concerning his discipline, then there are only three possibilities for A to count on a reasonable answer:

1) A can try to formulate his question in the language of B's discipline, and B will give an answer in this special language (so this is the situation, when both A and B actually are specialists in this field),

2) A can count on their common language, the langauge, that unites A and B (I would call this situation "polite specialist", since it does'n require from B any efforts, he should just recall some words which he had been taught, but maybe did not use them for a some time),

3) B can try to understand A's language, then translate his question into the language of his discipline, find an answer, and retranslate it again into the language that A understands (this can be called a situation of "a generous specialist", since this line of behavior can require some efforts from B).

I claim that the modern scientific society moves step-by-step to the top of this list (remark: I am speaking about communication, not about the situation of business, where A pays B money, or A and B are in some other mutually beneficial relations, like partnership, friendship, etc.). In my life the situations 2 and 3 occured only when I was a student in USSR. This does not mean that I am a supporter of the communist idea, but the unpleasant truth is that when we lived under communism, the idea of solidarity between mathematicians was much more popular than now. I could telephone any mathematician in the USSR, no matter who he was and where he lived, and he willingly was answering my questions. After the fall of the iron curtain almost all these mathematicians emigrated, and what is pity, almost all of them do not reply when you try to contact them.

I deduce from this (and from my own expirience of communication with western mathematicians) that the situation in the West is even worse. My experiment at theoreticalphysics.stackexchange shows that you can't count on generocity of specialists (situation 3). My post here in MO shows that even counting on politeness of colleagues (situation 2), of whom everyone undoubtedly had been taught the language you try to use (everyone of us knows what axiomatic system is, isn't it?) -- is too idealistic. Of course, I am extremely grateful to those three persons who managed to give their answer before my question had been closed, Terry Tao, Denis Serre and Physicist (and after reopening it to Jeff Harvey, who added his opinion) -- but I hope, you understand, that my impression of what I saw here would have been much more pleasant if I had not been mocked at two websites before coming to Meta.

Mariano comments on "Should a mathematician be a robot?" (16991)

2011-11-09T07:23:41-08:00

@Gerry, well, if Hilbert has asked an off-topic question on MO, it should have been closed.

I would surely read regularly Hilbert's blog, though!

thei comments on "Should a mathematician be a robot?" (16987)

2011-11-08T22:51:13-08:00

"@Pete: this is Motl we're talking about. Life's too short..."

He *is* the only one who answered, the answer has been upvoted and is consistent with the remarks on TP.SE. So one can presume that no other physics poster there thinks that the answer needs improving.

Nilima comments on "Should a mathematician be a robot?" (16985)

2011-11-08T21:09:43-08:00

Gerry, hopefully if OP Hilbert posted his problems on MO, he'd be politely told this wasn't a forum for open problems. Maybe the 4th and 6th would be shut down as 'too localized'. This is, of course, all tongue-in-cheek.

DavidRoberts comments on "Should a mathematician be a robot?" (16984)

2011-11-08T21:05:35-08:00

+1 Gerry

More seriously, I think Scott's reformulation is about as good as it can get.

Gerry Myerson comments on "Should a mathematician be a robot?" (16983)

2011-11-08T20:42:24-08:00

Alexander Woo, I suspect that if, in some parallel universe, Hilbert had posted his 6th problem to MathOverflow instead of presenting it to the ICM, it would have been swiftly closed as "not a real question."

Scott Carnahan comments on "Should a mathematician be a robot?" (16981)

2011-11-08T19:38:50-08:00

I agree that there is an interesting question hidden here, but I protest at the actual wording: "I wonder if there is a mathematical proof of the Mendeleev table?" Perhaps someone suitably brave can edit that. I am loath to engage the poster, in light of the rather acrimonious string of comments stuck to the question.

Here's one possibility: "Do we have the mathematical means to give a sufficiently precise description of the chemical properties of elements from quantum-mechanical first principles, such that the Mendeleev table becomes a natural organizational scheme?" This seems to avoid the sticky business of proving a table. Maybe one should add a note that we might as well make the simplifying assumption that the nucleus is just a very small ball of charge with comparatively large mass and small magnetic moment.

José Figueroa comments on "Should a mathematician be a robot?" (16980)

2011-11-08T17:43:54-08:00

On the question of whether or not Chemistry was "solved" by quantum mechanics (which is one possible reading of the response this question got in TP.SE before it got migrated), let me quote RIchard Feynman from his lectures, more precisely lecture 19-6 in the volume on quantum mechanics:

... it is going too far to say that quantum mechanics has given a precise understanding of the periodic table.
It is possible, however, even with a sloppy approximation -- and some fixing -- to understand, at least qualitatively,
many chemical properties which show up in the periodic table.

Even Feynman, a physicist not famous for his insistence on mathematical rigour, recognises that there is a mathematical problem involved in "understanding" (Physics-speak for "deriving") the chemical properties described in the periodic table from Schrödinger's equation.

Alexander Woo comments on "Should a mathematician be a robot?" (16979)

2011-11-08T17:22:59-08:00

Instead of looking at this question, let's think about a much more well known one - Hilbert's Sixth Problem, which says "Axiomatize all of physics."

A lot of water has gone under the bridge in mathematics, physics, and philosophy since 1900. Nowadays, I think a lot of mathematicians, physicists, and philosophers, if not blinded by the prestige of Hilbert, would say that the question is (very sophisticated!) nonsense and the mere asking of such a question shows such monumental (and subtle!) philosophical confusion about what mathematics and physics are that one doesn't quite know where to begin to untangle this confusion.

One major problem with Hilbert's problem, and with this question, is that it is phrased in a way that makes very little sense outside of a philosophical framework which is both Platonist and Pythagorean - one which takes it as at least plausible that the world is metaphysically mathematical, where mathematics actually is the structure of the world. (I should backtrack - it also makes sense in a philosophical framework which is very strictly Kantian Idealist - in which mathematics actually is the structure any rational being imposes on experience.) Nowadays, to a large extent because of quantum mechanics, many of us think of mathematics as merely a source of models which approximate experimental results, not as the stuff the world is made of, but merely as a tool that we can use to organize our descriptions and predictions about what we observe, and many of us think of theoretical physics as choosing among (and helping the development of) mathematical models for this purpose, not as finding the correct description of the world.

Because Hilbert was Hilbert, people have taken the trouble to try to interpret the Sixth Problem in a way that makes sense (roughly "Axiomatize various particular physical theories," which actually might be what Hilbert really meant anyway), but unfortunately for the this questioner, the questioner doesn't have Hilbert's standing.

Noah Snyder comments on "Should a mathematician be a robot?" (16977)

2011-11-08T15:38:18-08:00

When I was teaching group representation theory I spent a day or so trying to sort out whether you could work out the basic structure of the periodic table just from the representation theory of SO(3), because my vague recollections of QM were that this might be plausible. Sadly you can't do this, but my point is just that this is a natural mathematical question that I might have asked at MO myself.

Ryan Budney comments on "Should a mathematician be a robot?" (16974)

2011-11-08T14:21:50-08:00

@Pete: you see this kind of behaviour often enough in physics. The assertion that "X explains Y" does not mean they've actually done the explaining, let alone testing the explanation, it's an assertion that "I believe you can explain everything in Y given X as a starting point and enough creativity and time". The statement is to be taken like a meta-physical law, in that it has been tested in many different ways so it seems to be true, at least often enough for people to think it's true. :)

Yemon Choi comments on "Should a mathematician be a robot?" (16973)

2011-11-08T14:16:47-08:00

@Pete: this is Motl we're talking about. Life's too short...

Pete L. Clark comments on "Should a mathematician be a robot?" (16972)

2011-11-08T14:11:15-08:00

@Ryan: There is a sense in which quantum mechanics "fully, quantitatively and comprehensively" explains chemistry, biochemistry and biology? A useful sense?? Come on.

Will Jagy comments on "Should a mathematician be a robot?" (16971)

2011-11-08T14:09:32-08:00

The question is open now.

Ryan Budney comments on "Should a mathematician be a robot?" (16969)

2011-11-08T14:04:24-08:00

I think there's a sense in which what he's saying is true. He's likely referring to the work of people like Pauling in the late 20's and early 30's. Of course, "comprehensively" is an over-statement, presumably this is in the standard physics undergraduate jargon for "a talented person seeing Pauling's set-up, with some sweat and years of work could work this out..." the idea being there's something of a framework, an edifice to work with.

There's of course still lots of physical chemistry to be done.

I agree the diversity of the number of reactions is strange. IMO it's a sign the question is clearly not focused enough. Everyone has their own take on what it's supposed to mean. So the question should really be re-written, taking one of these more focused directions, and possible ways of misinterpreting it.

Pete L. Clark comments on "Should a mathematician be a robot?" (16967)

2011-11-08T13:52:38-08:00

I agree with Jose's point of view and have cast the fourth vote to reopen. Here are some additional comments:

Although I am very (very!) far from being an expert on this material, it is hard for me to see how the OP's question can be interpreted to be a standard under/graduate level textbook question. This would seem to imply that there is some textbook in which the atomic structure of the 100-and-some known elements is derived from some system of axioms for quantum mechanics (such axiom systems do exist -- the OP has given a reference), but even I know there is no such textbook. (Right??) Let me also say, without wanting to wade too far into name-dropping, that since Terry Tao read the question, took it seriously and gave a nice answer in the spirit in which the question was intended, perhaps we could also take the question seriously and not nitpick the setup so much.

I confess I am more interested in the reaction that the OP got to his "experiment" to post the question on the theoretical physics SE site. Namely, it got migrated to the lower-level site and received an array of comments about how this was not a research level question, e.g.:

"I agree it is off-topic, this is a "standard textbook question", quoting the FAQ – Squark"

"I agree this is off-topic, to attract our atention please flag such questions. To be complete - this is textbook material, not current research. As secondary issue, not many physicists would describe quantum mechanics as an axiomatic system, and derivation of much (but not all) elementary chemistry as a process of deduction. Being phrased in the wrong language, it is not likely to be productive. – Moshe"

So the physicists say this is a standard textbook question, but one of the world's leading mathematicians (Tao) says this is a very difficult question and gives a link to recent research on the problem! The end of Moshe's comment above seems much more relevant (though, I must say, completely contradictory to what he says just before it): the game of deriving things rigorously from axioms is one that mathematicians like to play much more than physicists. Thus the OP's question, although obviously interdisciplinary in nature, has its most natural home on a site for research level math questions...i.e., this site.

Although I would like to convey a message more nuanced than "Wow, this question has inspired some physicists to say some really weird things", nevertheless...this question has inspired some physicists to say some really weird things. For instance, Lubos Motl's answer to this question on the lower level physics site begins with this paragraph:

"Yes, quantum mechanics – even non-relativistic quantum mechanics for several electrons orbiting nuclei – fully, quantitatively, and comprehensively explains all of chemistry (including biochemistry and, in fact, biology). This fact has been known since the late 1920s."

Wow! Is this serious, or am I missing some satirical slant here?

Ryan Budney comments on "Should a mathematician be a robot?" (16965)

2011-11-08T13:20:19-08:00

I feel like we're in a situation where contributors want to answer a different question than the one asked. Moreover, it's hard for me to imagine what I described as being unfair when there's still such freedom of interpretation regarding just what the actual question is. Perhaps people should ask the questions they want to ask, rather than reinterpreting questions to fit what they want?

José Figueroa comments on "Should a mathematician be a robot?" (16963)

2011-11-08T13:07:45-08:00

I think that there is an interesting mathematical question here, but which is not related to the axiomatisation of quantum mechanics. There are interesting mathematical questions about well-known equations: Navier-Stokes being perhaps the most famous example, but there are other equations, such as Schrödinger's equation, which are of physical relevance (just as Navier-Stokes, by the way, which is indeed part of the thrust behind its study) and which will most certainly require new mathematics to understand. The atoms in the periodic table are presumably close in some sense to stable solutions of the multi-electron Schrödinger equation. It would be a fine MO question, in my opinion, to ask about progress in the analytic or numerical treatment of the multi-electron Schrödinger equation and whether anything qualitatively like the periodic table (by which I do indeed mean the orbital structure of the electrons) can be gleaned from its study.

I agree that the original question did not read like that, but this is perhaps explained by the fact that the OP is a mathematician and not a (mathematical) physicist.

Ryan, what is a taught component of any degree involving quantum theory is the hydrogen atom, which is the simplest possible instance of this problem. It is unfair to characterise this very complicated problem as a "undergraduate/grad level QM topic" as I hope that Tao's answer illustrates.

Ryan Budney comments on "Should a mathematician be a robot?" (16961)

2011-11-08T12:53:44-08:00

Jose, the question specifically raises the issue of formal axioms for quantum mechanics. So I don't think it's silly to think that's the mode it was intended to be in. If you want to interpret it as an undergraduate/grad level QM topic, isn't the question on the wrong forum? I mean, wouldn't it be fair game to ask for surveys of any physics, engineering or chemistry argument that involves some mathematics -- what makes this topic specially suited for MO?

Andreas Blass comments on "Should a mathematician be a robot?" (16960)

2011-11-08T12:46:51-08:00

José Figueroa's interpretation of the question would have been a good question, and I agree with him that Terry Tao has done a good job of answering it. But I don't see this interpretation in the original question with its emphasis on axioms and mathematical proof. My first reaction to the question was that the periodic table is not a mathematical statement and therefore not susceptible to mathematical proof. Returning to the question now, I see that, rather far down in the long list of comments, there is a more specific statement of what is to be proved, namely facts about the number of electrons is various shells of atoms. (I think of the periodic table as including also information about some chemical consequences of those electron numbers, at least that elements in the same column have somewhat similar chemical behavior.) But even in that comment, there was still a mention of unspecified additional properties. Furthermore, a mathematical proof would still require a mathematical definition of (or postulates about) notions like "atom" and "shell".

José Figueroa comments on "Should a mathematician be a robot?" (16942)

2011-11-08T11:29:27-08:00

I really don't understand the controversy with the original question. Perhaps it is not a mathematics question, but it certainly is a sensible mathematical physics question. The periodic table, by which one means the existence of atoms with certain properties which for the purposes of this discussion are not essential to recapitulate, is an empirical fact. Atoms exist and they do indeed exhibit the properties ascribed to them in the periodic table. This is beyond dispute. Furthermore, the simplest atom (hydrogen) is pretty well understood theoretically. Indeed we teach this to undergraduates: a typical undergraduate course in quantum mechanics includes a derivation of the spectrum of bound states in the hydrogen atom and there is a reasonable agreement with experiment. Later in a more advanced course, one learns how to incorporate relativistic corrections, solves the Dirac equation and gets even better agreement with experiment. Since (relativistic) quantum mechanics is so successful with the hydrogen atom it is a sensible question to ask how it fares with more complicated atoms. That is how I understood the original question. It seems not at all controversial and frankly, I'm a little taken aback by the hostility with which it has been met. I think all this talk about which formal system,... to be pretty spurious and if anything shows a certain lack of magnanimity when it comes to interpreting the question. Terry Tao seemed to have read the question in the way that it was intended and I don't think one can do better than his answer. It is a difficult problem under current investigation, but the sheer complexity of multielectron atoms makes progress difficult. For what it's worth, I think the question should be reopened and Tao's answer accepted.

Ryan Budney comments on "Should a mathematician be a robot?" (16941)

2011-11-08T11:17:28-08:00

Yeah, the forum is supposed to be about specific mathematical problems. You're asking a very interesting question but it's a wide-ranging question that brings in issues beyond mathematics, primarily the choice of an axiom system, and the definition of terms in that axiom system, such as atom and periodic table.

Your question is very much in line with the broader context for why we're on this planet as mathematicians, but this forum isn't here to be everything for all mathematicians. Your question is so big that it invites too much discussion with the fussy-business of nailing down an axiom system and specific terms. The forum tries to be about relatively small technical, precise issues rather than wide-ranging discussion type questions.

I think you could perhaps cut your question into pieces that might be appropriate for this forum. I've got to run and teach a course, but perhaps there's some nice and more managable bits your question could be cut into.

Sergei Akbarov comments on "Should a mathematician be a robot?" (16939)

2011-11-08T10:58:43-08:00

Ryan: If what you write -- "choose the definitions so that everything is tautologically true" -- was published somewhere with the title like "Justification of the Mendeleev table", that would be an example for me as well. I would not blame a reader who gave me such a reference. I did not understand, "nailing down a framework" is also my duty, when I ask something here?

Ryan Budney comments on "Should a mathematician be a robot?" (16937)

2011-11-08T10:46:19-08:00

That can't be quite true -- if any system of definition will satisfy you, you could just choose the definitions so that everything is tautologically true. Presumably you want some level of physical significance? Nailing down just one precise framework for the question would be a significant task.

Sergei Akbarov comments on "Should a mathematician be a robot?" (16935)

2011-11-08T10:24:45-08:00

Ryan, I do not give definitions, because any system of definitions will satisfy me. Why can't the reader write: "in this system of definitions a version of Mendeleev table is proved, see... ", or ".. is not proved...", or "the problem is that atoms are not defined yet, that's why the Mendeleev table is not yet justified..."? And I indeed need a reference, you told before that the problem is open, where did you read this?

Tom, can you explain simply (just for future), why was this concrete question closed? The moderators (I call them so, because as far as I understand they closed my question, although I do not know who of them is actually a moderator) wrote initially that this is a physical question, a chemical question, a senseless question, a non-mathematical question, and I tried to explain that this is not true, finally they told me that I can ask people to explain this here. So I ask people here.

Tom Leinster comments on "Should a mathematician be a robot?" (16932)

2011-11-08T09:47:34-08:00

Ryan is right when he says that "the intention for MO is for it to be about precise mathematical questions that have specific answers."

The wider question of what a mathematician "should" be is quite different from whether akbarov's question is appropriate for MO. There are many questions that are mathematically interesting but not appropriate for MO. The fact that an MO question is closed does not mean that it is mathematically uninteresting.

Ryan Budney comments on "Should a mathematician be a robot?" (16931)

2011-11-08T09:40:02-08:00

You've mentioned a system of postulates for QM, but you have not given a precise definition of what the "periodic table" is. For example, which version of the periodic table? Do you allow for any atoms that aren't in some version, and what formal language do you use for this? Do you have a formal definition of an atom, and what is it? for example, in your formal language, what is the definition of uranium?

Sergei Akbarov comments on "Should a mathematician be a robot?" (16930)

2011-11-08T08:34:49-08:00

Ryan, I do not understand this: "to be about precise mathematical questions that have specific answers". I see a "system of postulates" in a book written by well-known mathematicians. In their book they do not consider a question, that I find to be interesting. I ask specialists if it is already proved that the answer to this question follows from this "system of postulates". The answer to my question is either "yes, it is", or "no, it isn't". Why isn't my question precise?

And about this: "we're a long way from having any kind of formal justification of the periodic table from QM". Is it explicitly written anywhere? I need a reference (that's why I asked this question).

Ryan Budney comments on "Should a mathematician be a robot?" (16929)

2011-11-08T07:41:17-08:00

I'm pretty sure Dmitri Pavlov is not a moderator. But in a sense everyone has some kind of moderation role on MO.

I think the objection is you haven't made a precise mathematical question. I think you've asked a very suggestive question which is quite nice in a way, but the intention for MO is for it to be about precise mathematical questions that have specific answers. As has been pointed out in the comments and answers, in near any interpretation of your question we're a long way from having any kind of formal justification of the periodic table from QM. Similarly, well-known open problems are not encouraged on MO.

Sergei Akbarov comments on "Should a mathematician be a robot?" (16928)

2011-11-08T07:22:49-08:00

Dear colleagues,

Recently I asked a question in MO about axiomatization of quantum mechanics, it's here: http://mathoverflow.net/questions/80146/is-the-mendeleev-table-explained-in-quantum-mechanics-closed It was almost immediately closed as "off topic". Three moderators reacted to my protest, and one of them, Dmitri Pavlov suggested to continue our talk here, in Meta. That's why I write here. From what moderators wrote me I understood that questions like "is this an axiomatization of quantum mechanics?" are not accepted here. Mark Sapir even wrote that my question is senseless (however, he lately removed all his comments). This is very interesting for me, because this is a sign of some philosophy, and I even think that I understand the philosophical idea that moderators have in mind when justifying their actions -- this must be the idea that before asking questions to specialists you should first prove that you are a specialist in this area as well. It can be called a "philosophy of robots" (I tried to explain this in that thread, you can look).

I am a partisan of the idea that misunderstangs between people are always results of philosophy, so I would be happy if somebody will explain me the idea of why questions like mine are "off topic" here.

Sergei Akbarov