mstoehr's comments

The author might have done well to read pg's essay on disagreement since his attacks were mostly vague (I too agree that the characterization of London and Paris could have been better supported), and the attacks were executed merely by bringing up an example point and then not attacking it. On the point of cities, I think that there is good economic evidence (not cited by pg) that Cambridge and Boston are very much an intellectual center because some of the greatest universities of the world and they are leaders in terms of patents and scientific citations (from "Who's Your City" by Richard Florida).

This article claims that venture capital is lacking in innovation, but the article (a) sites no evidence to back the claim (b) does not provide support that any perceived lack in innovation might be the result of the recent financial crises (which would be a better-supported conclusion).

The idea that people from these selective schools are too conformist to innovate disregards the fact that most innovations are incremental. Furthermore, if one is taking a risk by innovating in one area of a business, it's better risk management to be more risk averse in other areas of your business. That will allow a greater chance that the business will survive in the longer terms and that you'll be able to test out new innovations and really contribute something.

So, I would guess any skill in conforming would certainly be an asset in innovation, and that this would at least counter-balance any negative effects.

It wouldn't be an internet discussion without at least one ad hominem argument.

It may be "dangerous", but basing causation just on correlation (or statistical data in general) is actually a pretty prominent idea: http://plato.stanford.edu/entries/causation-probabilistic/. Chris Anderson obviously glosses over many tricky details, but Judea Pearl among others have written extensively on it. Ultimately, all these ideas can probably be traced back to David Hume (at least here in the West).

Hank's argument that Chris is suggesting that we don't try to find spurious correlations is rather simplistic since a probabilistic theory of causation can account for "spurious" and "real" correlations quite well. Indeed, the only reason why we know that "spurious" correlations exist is because they eventually show up in the data (i.e. the economist finds out that the stock market does not predict sun spots). Thus, a statistical definition of causation (more or less one that only uses a notion of correlation), can actually be quite robust.

I agree. I mean human minds usually forget things unless they're reminded more than once.

I'm surprised at how strongly held most of the opinions are argued in the forum. The reason why is that I know of very little scientific evidence that would lend people such certainty. Firstly, as I understand it, to date, there has been no longitudinal study of mathematics talent in people who develop in interest after adolescence. Secondly, the neurological basis of learning is a rapidly growing field, but the field right now may not have much to say about the development of mathematics talent. The points that have been made: i.e. that you can't do it may be true, it's just that you probably should take what they say with a grain of salt since they are talking about a subject that is not very well understood.

I would wager, though, that going from having a small knowledge of math to going to a level of knowledge of comparable size to a mathematics researcher is going to be very hard. People who focus on math starting freshman year of high school go through 4 years of high school + 4 years of college + 5-7 years of grad school = 13-15 years before they become research mathematicians. So it might take you 10+ years before you know enough to start contributing.

Additionally, if you read psychological research on expert performance (which you probably should, and Eric K. Andersson is one of the experts in that area so perhaps start with an article by him), it normally takes 10 years to develop expert skills in a field, and that expertise comes about from something he terms "deliberate practice". Check out: (http://projects.ict.usc.edu/itw/gel/EricssonDeliberatePracti...) The Role of Deliberate Practice in the Acquisition of Expert Performance.

Most evidence would indicate that the abilities of a Putnam fellow are probably not out of reach to somebody who uses a strict deliberate practice regimen to develop their working memory (google that with 'mathematics') of and the ability to execute the thousands of tricks that mathematicians employ to solve problems. I am not very confident in this particular assertion, and I believe there is only weak evidence for it, however, there is only weaker evidence against it (and most people who argue against it make use of hand-waving has their primary argumentative technique).

On the actual task of becoming a mathematician I suggest you read some essays by Gian-Carlo Rota (http://web.archive.org/web/20070630211817/www.rota.org/hotai...), in particular look at the "10 Lessons I wish I had been Taught" and the reflections on math and mathematicians. He points out that mathematicians seem to have only a couple of tricks up their sleeve which they apply over and over and over again.

  The points made by yelsgib are good since mathematics is about a community of researchers, and most problems have been looked at by hundreds of researchers.  At the very least you will need to attend conferences at Universities.

This brings me to my final point, which is that if you want to make contributions to the field you'll make it a lot easier on yourself if you attend grad school in mathematics. In general people don't have to pay for math grad school, but it will cost you time. The reason why I say that it will make your life easier is that, firstly, math grad school will induct you into the community of mathematicians. You'll have better guidance than I can give (I am a lowly undergraduate) on how to become a mathematician, and when you get to doing serious research you'll have an advisor who will (hopefully!) guide you through it. One of my friends who is finishing up his P.h.D in analysis points out that he would have no idea whether he was making progress or not if it weren't for his advisor (he's doing research on semiclassical wave functions). Secondly, you'll know whether mathematics is right for you.

And, if you plan on making 'significant' contributions you'll have to do more or less the same preparation that a math grad students goes through and you'll have to put in the same, if not more time as grad students do in preparation to do research.

I admit that I am curious to see what happens if you go through with such a project. It would take a great deal of perseverance on your part as you come across all the barriers I am facing (as a math major) as well as those that come about because of your age and station in life.

My main suggestion is to try to get into correspondence with mathematicians to try to get more guidance. This can be difficult because you are probably just starting out, but you will most likely find one or two gracious ones if you start trying to correspond with mathematics departments.

I lack the experience to be a good person to talk to but I am nearly always willing to discuss this sort of thing so feel free to send me an e-mail to [my sn without the 'm'] [the a with a circle around it] uchicago [period ] edu.

Most econometricians would admit it, it's just that the linear models, and Gaussian models are easier to handle since they require much less data to calibrate, and the results have more or less confirmed economic theory. There is no doubt that economic theory does not have near the predictive power that physical sciences have attained, but that is due in part to how recent new developments have been, and how sparse the data available to economists is. Indeed, estimating all the parameters necessary for non-linear models is significantly trickier. Anybody that developed robust nonlinear economic models could safely bet on receiving a good academic appointment at a top-20 school, and very probably an economic prize.

I can't think of a single econometrician who claims to have all the answers through Gaussian statistics.

These two are my favorite (that are reasonably priced!). Samuelson is definitely a formidable thinker and lays the groundwork for much later economic thinking.

http://www.amazon.com/Worldly-Philosophers-Lives-Economic-Th... http://www.amazon.com/Price-Theory-Milton-Friedman/dp/020206...

However if you go with the Samuelson, Fridman, and Heilbroner you'll be missing out on some key concepts relating to information and games, which are essential for understanding modern developments in economics.

So, I would also look at Myerson's Game Theory http://www.amazon.com/Game-Theory-Analysis-Roger-Myerson/dp/...

Finally, the empirical side of economics is quite important, and it is essential for investigating whether the theoretical conceptions (say in Samuelson) actually hold up. There are many bad texts, and the seminal ones (Greene) are quite difficult in the beginning. So, I recommend a pedagogical text that uses the likelihood approach. Although, this is, by no means, a comprehensive text, you can certainly gain an understanding of a basic econometric study http://www.amazon.co.uk/Econometric-Modeling-David-Hendry-Ni...

That should give you a broad introduction. Also, checkout http://papers.ssrn.com/sol3/DisplayJournalBrowse.cfm, which is an excellent resource with many free papers.

Good Luck!

I somewhat agree with sah in that Roth's essay did not fully address the central point of Graham's essay: the effect that large hierarchical structures have on people. The discussion of ad hominem arguments aside, I would point out that you could phrase Roth's argumentative method as, "you've argued for x given method y, and I can use method y to also prove z, you don't believe z, therefore you can't prove x". A rough sketch might look like this: y --> x y --> z therefore z <--> x (this step is hard to sketch out because it's unclear) ~z therefore ~x.

The difficulty with this argument is a fallacy about implication. Roth states that the "evolutionary argument" supports pg's view, but that he can then use that same "evolutionary argument" to prove an absurd point of view. Then he holds that he has disagreed with pg's central viewpoint.

This method of argumentation is fundamentally flawed because pg's view might be supported by a multitude of arguments, the truth or usefulness of the "evolutionary argument" is not a necessary condition for the truth of pg's view of organizations, bosses, and human nature. Hence, Roth has merely attacked pg's method of proof while leaving the central claim untouched. I have other criticisms of Roth's argument, but even if I am wrong in such criticism the argument would fail to disagree with pg.