### Square This Circle

Obama asserts 2 propositions vigorously:

1. I will not negotiate with the Republican Party leadership in Congress. (With Republicans in Congress mind you. Mullahs, Putin-whole different story.) (Given Democratic comparisons of the Republicans to suicide bombers, the Taliban, etc., perhaps this is a corollary of the “We don’t negotiate with terrorists” principle.)

2. I have bent over backwards to work with the Republican Party.

The scary thing is that I am pretty sure that Obama believes this. It’s not an act. He sees no contradiction whatsoever between these irreconcilable beliefs. He believes he’s been totally flexible and accommodating. Totally.

Look. I think that Obamacare is a disaster, but that the Republicans played this like idiots: they aren’t known as the Stupid Party for nothing. Ted Cruz was a debating star at Princeton who thought that studying with alums of “lower Ivies” (like Penn) at Harvard Law was beneath him, but he strategized this like the holder of a diploma from a penitentiary correspondence school. If anything, this strategy has cemented Obamacare, rather than undermined it.

But the most important cause of the current impasse is that a hardcore partisan president is partisan out of near religious conviction in his righteousness, and the near religious conviction that his opponents are evil. He is willing to compromise on things he doesn’t really care about-and Syria and Iran fall into that category-but it’s a zero sum game to him on domestic matters. He doesn’t want to win: he wants to extirpate his enemies. Beginning to understand this, the Republicans have every incentive to double down. Meaning that the conflict and crisis will only metastasize.

Every day I pray more fervently that Adam Smith (“much ruin in a country”) and Bismarck (“a special providence for . . . the United States of America”) are right. We’re testing both.

Ooops. I once again pasted redundant stuff. Please disregard the stuff about Goodwin.

Comment by Vlad — October 10, 2013 @ 12:30 am

You know, Vlad, it is hard for me to conform to the fact that instead of doing what I ought to do now, I am doing what I don’t have to do. But may this be a last attempt at that…

You want to present that you do what you do because of the complexity of the issues and, in particular issues surrounding the path of mathematical research.

Let me first assert that my injection into this process is not about a particular statement of yours. I usually read what you and many others write and I don’t interject even if I strongly disagree.

But with you I indeed observe a pattern – not an isolated case. You distort your opponent’s argument more often than not and start taking largely your own invention apart. And it is not about my statements on mathematics. You do the same on other subjects – in particular you have done it in this thread before the argument on math started.

For example, it can be attributed to your description of the political impasse between the Republicans or Democrats, or your allegory on getting a car or attributing yourself the rights of a parent in this particular case.

Now, if everyone does it, it is too bed. If you observe me doing it, please bring it to my attention.

Now, you claim that I make things personal. But what do you think your arguments sound like for those who ascribe to the opinions you “take apart?” At the end, if someone is emotionally or otherwise vested into something, everything becomes personal isn’t it? For example, when I claim that the “global warming” argument is a hoax (and I strongly believe in it) it is taken very personally by those who ascribe to the opinion. So, let’s start directly from the personal statement and say, “it is stupid of you to ascribe to a hoax like the global warming argument.” 😉 Clearly I am not talking about you here.

My strongly held opinions are part of who I am. They shape my personality or are a direct consequence of it. And it doesn’t matter if you assault me or my strongly held opinions. It doesn’t mean I don’t change my opinions the same way it doesn’t mean that I don’t change myself. So, you have the liberty of assaulting me personally and, if you wish, calling me illiterate. Just have the courtesy of demonstrating it.

Now on a couple of specific issues.

To call linear programming “Kantorovich’s Linear Programming” is astounding to me. Linear Programming is not Kantorovich’s more than calculus is Leibnitz’s. I have no idea if Kantorovich had come-up with an algorithm to solve LP problems earlier than Dantzig. I read that allegedly Kantorovich had done it earlier but his work was kept in secret by the Soviets until Dantzig published his work. Well, if somehow it turns out tomorrow that someone in Germany had done it during the WW1 and it was kept secret till our days, would we need to attribute LP to him? What kind of strange chain of thought does this represent?

Finally, LP is not Kantorovich’s invention while Kantorovich might’ve even been the first to come-up with a solution (I have no direct knowledge on it and am willing to accept that it is very possible). But then, why do you use the language “Kantorovich’s LP” instead of using the term “Kantorovich’s solution of LP, which was historically the first solution?”

And what is this hang-up with Nobel Prize, Fields and other medal recipients?

More importantly, doesn’t the merit of Kantorovich’s story shed further light on our discussion of the goals and justifications of mathematics?

It appears that there was a specific applied problem associated with the supply chain optimization during WWII in Russia and Kantorovich apparently studied the problem and came up with a novel method to solve it. Fine. Who would be willing to argue with something like this?

Abstracting from the case of Kantorovich, this is the point I have made – justification of mathematics is in its ability to solve problems in natural sciences, economics, etc. Healthy mathematical research is motivated by the need to solve some real problems. And it can take a lot of research and sometimes the research might not be immediately recognizable as contributing to the solution of the posed problem.

However when the process of research instead of converging to a solution is diverging away from it, it is a manifestation of corruption – whether intellectual or otherwise – especially when this divergence takes place not because of the uncertainty of the path or lack of knowledge of the right path but because the original problems are not important anymore and the process turns into a [bottom-up] pyramid scheme of a type or an academic “you scratch my back and I’ll scratch yours.”

This type of research takes place not only on the edge of algebra and quantum physics but also in other disciplines as well, including in finance. And it is a shame.

Comment by MJ — October 10, 2013 @ 2:05 am

> And the prediction that the majority of voters share my concern and that this shutdown will cost the Republicans seats in the next year’s House elections – that’s an analysis, not a “prophecy”.

http://www.nytimes.com/2013/10/10/us/business-groups-see-loss-of-sway-over-house-gop.html

WASHINGTON — As the government shutdown grinds toward a potential debt default, some of the country’s most influential business executives have come to a conclusion all but unthinkable a few years ago: Their voices are carrying little weight with the House majority that their millions of dollars in campaign contributions helped build and sustain.

Their frustration has grown so intense in recent days that several trade association officials warned in interviews on Wednesday that they were considering helping wage primary campaigns against Republican lawmakers who had worked to engineer the political standoff in Washington.

Such an effort would thrust Washington’s traditionally cautious and pragmatic business lobby into open warfare with the Tea Party faction, which has grown in influence since the 2010 election and won a series of skirmishes with the Republican establishment in the last two years.

Comment by Vlad — October 10, 2013 @ 2:19 am

See, Vlad, this is my point… Who cares what the majority of voters think? We are analyzing here, right, not running for an office.

I am out of here… 🙂

Comment by MJ — October 10, 2013 @ 2:58 am

@Professor

I hadn’t heard of Godwin’s Law previously-very funny.

Comment by pahoben — October 10, 2013 @ 10:19 am

@MJ,

I don’t understand your insistence on ad hominem attacks. I also don’t understand why you take this topic – paths of mathematical research – so personally. It seems to me that you are carrying a big chip on your shoulders against math Olympiads, pure math and math awards.

I am sorry that I don’t seem to be able to articulate my position on pure math in a way that you would understand me, no matter how many times I try. I am also sorry to see you dissect my

every little inconsequential phrase, like “Kantorovich’s linear programming” in which I accidentally omitted two words (I meant to write: “Kantorovich’s work on linear programming”), get “astounded”, and throw a long hysterical fit over it.

> But then, why do you use the language “Kantorovich’s LP” instead of using the term “Kantorovich’s solution of LP, which was historically the first solution?”

Because I wasn’t discussing the historical attribution of LP. What I was trying to say was:

“Kantorovich’s work on linear programming, designed to solve practical problems in the economic planning, couldn’t have happened without pure math results in linear algebra that preceded it.“

The reason why I choose Kantorovich for my little example was because you also come form Russia. If this little example “astounds” you, I will be happy to replace “Kantorovich” with “Dantzig” or with “von Neumann” or with “ 20th century mathematicians”. What difference does the name make if my point is:

“Work on linear programming, designed to solve practical problems in the economic planning, couldn’t have happened without pure math results in linear algebra that preceded it.“

> justification of mathematics is in its ability to solve problems in natural sciences, economics, etc. Healthy mathematical research is motivated by the need to solve some real problems.

When Euclid and his predecessors worked on the factorization of integers, did they expect that more than 2300 years later their work will become crucial to cryptography, or were they motivated by intellectual curiosity? How do we know that the problems and models that are of major interest to modern pure mathematicians and have no practical application today, will not become indispensable in real life 2,10 or 100 years from now? As long as these problems naturally arise as generalizations and continuation of the previous development of “mainstream” pure math, they are likely to be good science and may find application.

Interestingly, Norm Zadeh thinks the reason why most professors (including applied mathematicians) are paid to do research is to keep their minds sharp in order to do what they are REALLY useful at: teaching.

Sorry for repeating the same thought for the 3rd or 4th time. Enough said.

> This type of research takes place not only on the edge of algebra and quantum physics but also in other disciplines as well, including in finance. And it is a shame.

I agree. There are a lot of artificial “research” areas and cliques that thrive off of them. Speaking of Zadehs, I once stumbled upon a whole army of “researchers” whose work was in translating all existing math results into the language of fuzzy logic. In the 1980s there was a big uproar over zero-knowledge researchers gradually taking over most of papers accepted for top conferences in theoretical computer science.

However, sometimes it is the “practical” applications of math that are much more damaging than esoteric pure research. In finance, exotic derivatives were developed and then traded on the false belief that Black-Scholes-like models were good descriptors and safe ways to model, price and hedge financial uncertainty. In reality, when being calibrated for things like volatility, these are often self-referential models (you use market price to compute volatility and then use this volatility to ”prove” that the market price agrees with the model), unless they rely on historical data, which will work OK until the next crisis, at which point it will blow up. That’s what happened to LTCM, D.E.Shaw etc. Math models also gave legitimacy to credit derivatives, when in reality we have no reliable way of assessing credit risks. Even though derivatives are advertized as hedging risk-control instruments, most of their buyers buy them as casino bets in order to actually increase risk and exposure. And mathematicians end up giving the veneer of legitimacy to this irresponsible gambling.

Comment by Vlad — October 11, 2013 @ 2:21 am

Jeez, Vlad, just when I want to be a “goner” you keep dragging me back… It’s like the mafia, once you are in, you won’t be let out 😉

The earliest I can respond to you on merits is perhaps Monday. Meanwhile, I might be carrying a chip associated with pure mathematics on my shoulder. It is a heavy chip to carry. But if Arnold and Novikov carried it (and it would be ridiculous to compare myself with them), who am I not to carry it? 😉

As to Olympiads, my indignation on this subject is associates with your correlation of quality education with successes in Olympiads. Let me repeat it. Under the best case scenario Olympiads create quasi-culture in mathematics and their coefficient of usefulness is extremely law in terms of producing good mathematicians. The corresponding statistics might serve as a proof. In fact, I think Olympiads succeed more in ruining young lives and careers – such as in the case of Perelman perhaps.

Do you notice how many self-admitted misplaced statements you make in one discussion? In some cases misplaced expressions, in other cases wrongly places sentences in terms of where they had to fit, etc.? (And I am not insinuating that I don’t do it.)

Maybe it is not simply an artifact of an unedited text but there is some Freudian element to it? 🙂

Comment by MJ — October 11, 2013 @ 5:12 am

…extremely “low,” of course.

Comment by MJ — October 11, 2013 @ 5:16 am

@Vlad

How old are your children?

Similar story with risk in the oil and gas industry. Stochastic economics packages supplanted traditional economic analyses some years ago. The problem is no one knows the appropriate input distributions for many of the input variables for exploration projects. The results are now nontransparent fantasies with great looking power point slides that imply much more knowledge than is there.

Comment by pahoben — October 11, 2013 @ 3:06 pm

@MJ,

> Vlad, I have to focus on work now and will only respond to the “personal” issues.

> You know, Vlad, it is hard for me to conform to the fact that instead of doing what I ought to do now, I am doing what I don’t have to do.

> Jeez, Vlad, just when I want to be a “goner” you keep dragging me back… It’s like the mafia, once you are in, you won’t be let out

You know, MJ, you are overestimating my power to “drag” you anywhere. I think both you and I are engaged in this on our own free will. And I do get your message that you have more important things to do. Believe it or not, so do I. However, I find thinking about the foundations of math and math education interesting enough for me to talk about in my spare time. So please stop whining.

> Do you notice how many self-admitted misplaced statements you make in one discussion? In some cases misplaced expressions, in other cases wrongly places sentences in terms of where they had to fit, etc.? (And I am not insinuating that I don’t do it.)

Yes you do it. Profusely. Including giving wrong names to your mathematical heroes, misspellings and inadvertent omissions of words. I just find it below my dignity to point them out to you and simply ignore them. You, on the other hand, dwell on my inadvertent mistakes and even engage in clinical psychoanalysis of my personality.

> Maybe it is not simply an artifact of an unedited text but there is some Freudian element to it?

Maybe. Or it may be that given that I write very long comments, I save time by typing very fast, cut-and-pasting very fast, compacting my phrases, and not proofreading the final text before posting it. Most other blogs allow you to edit your recently posted comments, and Craig should consider allowing such edits here as well.

> Under the best case scenario Olympiads create quasi-culture in mathematics and their coefficient of usefulness is extremely law in terms of producing good mathematicians.

I don’t know what math culture you were growing up in, but to me, Olympiads had no effect on my studies. My school (sponsored by Gelfand, Dynkin and their students) didn’t give any special classes to prepare us for Olympiads. After it was destroyed by the authorities for political reasons, I went to another math school, and there was no preparation either. Our teachers didn’t even tell us when the Olympiads were held. However, the 5 or 6 students in the class who were interested in math (and thus good at it) went to them on our own. Nor did I prepare for the Olympiads on my own.

Their only importance to me and other Jewish students was that top Olympiad victories allowed one to get into good math universities without having to go through the entrance proceedures in which the admissions committees made it virtually impossible for Jews to get in. But my parents solved this problem by emigrating soon after my 9th grade. However, I find it hard to imagine a student interested in math (or physics or chemistry), who wouldn’t want to take the Olympiad in their subject just for the pleasure and the challenge of it. I, for example, competed in art/drawing olympiads even though I had no desire or ability to become a professional artist.

Here in the USA there are special “math Olympiad camps”, and top high schools offer classes called “Advanced Problem Solving “, but they end up being the only places that teach schoolchildren REAL math, with proofs and rigor.

> The corresponding statistics might serve as a proof.

What “statistics” are you referring to?

> I think Olympiads succeed more in ruining young lives and careers – such as in the case of Perelman perhaps.

First of all, Perelman’s career wasn’t “ruined”. Quite the opposite. He became an immortal name in mathematics and the most famous and celebrated “math genius” (along with Newton) among the average “mainstream” (as you call it) public. Are you referring to his eventual decision to drop out of Steklov Institute and out of sight? This is probably due to the same cause as his mathematical brilliance: Asperger syndrome. The other side of the coin. Why do you think that his participation in Olympiads influenced his lifestyle and personality?

About teaching calculus vs. mastering historically more traditional topics of mathematics such as trigonometry, geometry, etc. Geometry serves the great purpose of explaining to children how real math works: axioms, definitions, rigorous proofs. However, teaching classic plane geometry for 3 years is an overkill, as it is neither central to modern math nor important as an application. Trigonometry, if studied in too much detail, is hardly inspiring and much less useful/important to both mathematicians and average people than calculus, which is vitally important to all scientists, engineers and medical doctors. No wonder calculus is a prerequisite for US medical schools.

Medical, social science, education researchers, if unfamiliar with things like area under the curve and integration, waste months of their life trying to rediscover these basic notions and when they rediscover them, they and their colleagues often treat them as earth-shattering inventions. For example, an NYU (!!!!!) researcher Mary Tai with a PhD in Education“discovered” for herself the simple idea behind the definite integral, and her paper about her “discovery”, published paper in a mainstream refereed (!!!) medical journal, created a mini-revolution among her colleagues and has been referenced by 200 other medical papers, whose authors, evidently, had never had calculus and didn’t know how to go about measuring areas under a curve. She even gave Riemann integral a modest name: “Tai’s model”:

http://care.diabetesjournals.org/content/17/2/152.short

Doctors rediscover Riemann integral (200 citations)

https://plus.google.com/112065430692128821190/posts/1qr5LKbJ98J

A Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves

Mary M Tai, MS, EDD

Astract

OBJECTIVE To develop a mathematical model for the determination of total areas under curves from various metabolic studies.

RESEARCH DESIGN AND METHODS In Tai’s Model, the total area under a curve is computed by dividing the area under the curve between two designated values on the X-axis (abscissas) into small segments (rectangles and triangles) whose areas can be accurately calculated from their respective geometrical formulas. The total sum of these individual areas thus represents the total area under the curve. Validity of the model is established by comparing total areas obtained from this model to these same areas obtained from graphic method (less than ±0.4%). Other formulas widely applied by researchers under- or overestimated total area under a metabolic curve by a great margin.

RESULTS Tai’s model proves to be able to 1) determine total area under a curve with precision; 2) calculate area with varied shapes that may or may not intercept on one or both X/Y axes; 3) estimate total area under a curve plotted against varied time intervals (abscissas), whereas other formulas only allow the same time interval

Just think about it: until her publication, many medical (and education?) researchers miscalculated total area under curves “by a great margin”!!! I shudder to imagine how many patients died because their doctors relied on results of researchers unfamiliar with basic calculus and statistics… 🙂

http://science.slashdot.org/story/10/12/06/0416250/medical-researcher-rediscovers-integration

I peeked at one or two of the articles citing this paper:. Rather than saying: “we used the trapezoidal rule to approximate XYZ”, everyone in the field now says “we used the Tai procedure”.

> There is no reason to force down the throats of the general populace what could be viewed as a university level calculus class in USA. The result is not overly positive – only a very small percentage of students in high school manage to learn it.

I have been helping with calculus to a below-average high school senior who had a C- prior grade, who is taking a regular (not Honors) class in calculus. Once I started explaining calculus to him, his grade went up to A- and he has no problem understanding even the concept of the limit. People grossly underestimate the ability of average students to understand math and calculus, if they get explanations instead of rote memorization of facts.

Comment by Vlad — October 11, 2013 @ 7:50 pm

@Vlad

I sent my son to a Catholic High School and he didnt thrive. When he entered college it was liked a switch was flipped and he is a senior now and has done better than I could hope for in college. He now loves mathematics. He will have an engineering degree with a 3.9+ GPA. He is doing graduate work in simulation and gets some cycles on the supercomputer in Austin. He also has everything in place to go to med school if he chooses. There are a lot of very bright kids that follow a similar path in the US. As soon as a bright kid is motivated to learn math they can go through the usual high school math curriculum in short order. For me my primary and secondary education years were horrific but I liked university. Kids that dont do math may never be professional mathematicians but can still be quite successful technically. Brains mature differently. As long as the native ability is there it has a good chance of working out pretty darn good in the long run

Comment by pahoben — October 12, 2013 @ 7:30 am

Heck I have fraternnal twin girls that turn one next week. I cant even keep them interested in Dr Seuss alphabet biook after J ( big J liitle J what begins with J). They are much more interested in destructive testing of my iphone.

Comment by pahoben — October 12, 2013 @ 8:49 am

As young as they are they engage in competition. As best I can tell they are engaging in a poop contest.

Comment by pahoben — October 12, 2013 @ 8:57 am

This obamacare roll iut is absolutely hilarious. The people that are able to register (largely eager lefties) have typical comments like holy crap I supported obamacare but didnt know I would have to pay for it. The populace of the blue states are so out of touch with reality it is comical (okay in a sad kind of way).

Comment by pahoben — October 12, 2013 @ 9:37 am

@pahoben,

I have twin girls too. Alphabet at the age of 1 – isn’t that way too early? when they are talking to others, they constantly interrupt each other, because they have the same stories to tell.

> For me my primary and secondary education years were horrific but I liked university.

Well, the USA is famous for good colleges and bad schools. But if you want to become a mathematician, you do need to start way before college.

Comment by Vlad — October 12, 2013 @ 8:02 pm

You are right but trying to keep them occupied and out of mischief is a demanding task. Only two arms is a poor design.

Comment by pahoben — October 13, 2013 @ 8:53 am

@Vlad Indeed you got my message… I am working on developing an algorithm with a great prospect for applications in gerontology 2300 years from now … 😉

Comment by MJ — October 14, 2013 @ 8:19 pm

MJ, great. I hope you are having fun and have the personal savings to do it. However, I personally would work on something really fundamental and natural. Such research is much more promising even for future practical applications than very specialized ad hoc research with no immediate practical applications.

Comment by Vlad — October 15, 2013 @ 12:34 am

Vlad, have a drink 😉

Comment by MJ — October 15, 2013 @ 1:45 am

MJ, seems that it is you who is carrying a big chip on his shoulder (against Olympiads, awards, pure math) and should relax. Just let it be.

Comment by Vlad — October 16, 2013 @ 6:43 pm

@Vlad I really have no appetite to get into a “debate” with you on something so stupid and idiotic as this subject so dear to your heart. I also understand that you can’t let it go. But if what I have said so far has not been enough for you to grasp some simple things, doubling the volume of this thread down would serve no worthwhile agenda.

So, now, have your last word and move on with your life to something more meaningful – as late as it can perhaps be for you.

Comment by MJ — October 16, 2013 @ 8:18 pm

MJ, best wishes on exorcising your demons.

Comment by Vlad1 — October 23, 2013 @ 3:46 pm