General

Re: Greatest mathematician of our times is dead.

Jeremiah Dyke — Fri, 26 Nov 2010 07:06:46 GMT

Taleb has a new book coming out within the next month and he has some great thoughts on TED TV

Again, as fancy pants as economists like to be with their maths, their ignorance of chaos theory is telling.

Agreed, even some pop-knowledge of nonlinear dynamics would prevent great men like W. Block from saying bonehead things like "the government is responsible for us not being able to predict the weather"

Re: Greatest mathematician of our times is dead.

Giant_Joe — Thu, 25 Nov 2010 19:54:21 GMT

FWIW, I'm about 250 pages into "The Black Swan"

I'm loving it.

Re: Greatest mathematician of our times is dead.

Prateek Sanjay — Mon, 08 Nov 2010 15:28:22 GMT

Clayton:

I think I'll soon delve into alternative problem solving techniques

Note that there is a political dimension to this. Mathematician Gregory Chaitin has been pretty vocal about the neglect of computability and its implications. This has been a serious problem in mathematics since 1931 when Kurt Godel published his paper on the limitations of formal logic. Chaitin doesn't identify the political reason but after becoming acquainted with Austrian economics, I realized what the political reason for this resistance is. Computability theory (of which AIT is a sub-field) places limits on what can be known and what can be calculated. It tells us that there can be no Theory of Everything in mathematics, let alone physics or economics. In other words, it is an irrefutable devastation of all Utopias.

Clayton -

You just blew my mind. That man's work may have been the most important work of the 20th century, and if it got swept under the rug, we all have just lost the chance to learn the most humbling and useful lesson mankind ever needed to learn.

The most amazing thing is that the traditional Christians were ahead of us, going back to the days of the oldest Christian scholars, in explaining that all formal logic and scientific reasoning is limited. http://www.chroniclesmagazine.org/2007/04/01/dead-monkeys-and-the-living-god/ Perhaps the ultimate blame lies in the 17th century "revolution" in thinking of many people that they could eventually create a rational scientific utopia with billions of enlightened mortals with infinite power of reasoning.

Re: Greatest mathematician of our times is dead.

Giant_Joe — Mon, 08 Nov 2010 05:39:03 GMT

Note that there is a political dimension to this. Mathematician Gregory Chaitin has been pretty vocal about the neglect of computability and its implications. This has been a serious problem in mathematics since 1931 when Kurt Godel published his paper on the limitations of formal logic.

Yup, I'm aware of this stuff. :) It kind of boggled my mind at first. But then I realized that since we are limited beings, how would we be able to know everything there is to know? (which includes things we are incapable of knowing)

Re: Greatest mathematician of our times is dead.

thelion — Sun, 07 Nov 2010 22:59:49 GMT

RIP Benoit Mandelbrot.

-------------------

On seperate note:

I would agree with R. Penrose, actually, who is more radical in the sense of noncomputability, than G. Chaitin, who wrote somewhere (I browsed his books in our library) that he believes a real AI can be created by conventional methods.

In the near future, actually, I predict rather a more pressing problem in conventional computing, is multi-core construction (which is done basically to avoid requiring non-mainstream heat dissipation methods) might actually impede some calculations that we actually can do, due to the impossibility of efficiently breaking and recombining certain tasks.

Re: Greatest mathematician of our times is dead.

Clayton — Sun, 07 Nov 2010 20:11:26 GMT

I think I'll soon delve into alternative problem solving techniques

Note that there is a political dimension to this. Mathematician Gregory Chaitin has been pretty vocal about the neglect of computability and its implications. This has been a serious problem in mathematics since 1931 when Kurt Godel published his paper on the limitations of formal logic. Chaitin doesn't identify the political reason but after becoming acquainted with Austrian economics, I realized what the political reason for this resistance is. Computability theory (of which AIT is a sub-field) places limits on what can be known and what can be calculated. It tells us that there can be no Theory of Everything in mathematics, let alone physics or economics. In other words, it is an irrefutable devastation of all Utopias.

Clayton -

Re: Greatest mathematician of our times is dead.

Clayton — Sun, 07 Nov 2010 20:01:39 GMT

Can you concisely state what the problem of induction is?

Yes. Why should the future be like the past?

That the universe has behaved in an orderly, lawlike manner in the past does not constitute evidence that it will in the future. Hume shows the way. If you say that we can believe that the future will be like the past because past futures have always been like past pasts, Hume's reply is that you must still assume that the future will be like the past to get from that observation to the belief that future futures will be like future pasts.

Restricting oneself to strings*, Solomonoff induction resolves this problem by asking what are the future states of the most likely Turing machines, given the output string which has been seen so far. By weighting these future states, we can assign meaningful probabilities to the future behavior of whatever is generating the output we are observing. Nick Szabo has written a pretty nice summary of the idea, here.

Clayton -

*In the computer theoretic sense, i.e. a string of characters drawn from a finite alphabet

Re: Greatest mathematician of our times is dead.

Clayton — Sun, 07 Nov 2010 19:44:19 GMT

If I get caught up in doing AI work, (it's a possibility) I'll be looking into that stuff you mentioned, Clayton.

I'm surprised the AI community hasn't invested more interest in this.

Clayton -

Re: Greatest mathematician of our times is dead.

abskebabs — Sun, 07 Nov 2010 19:08:34 GMT

I remember when I was studying the calculation argument, I coudn't help but feel there would be problems similar to those expounded in chaos theory for any social planner who attempted to plan a complex economy without prices. My memory is fuzzy though, so I don't remember the details, I should look over my old notes.

I think chaos theory would be a great educational tool(or at least something for most of the econ grad students who are ex physicists to consider) in ilustrating to economists the limitatons of calculational methods. We have long known in physics only a small subset of problems can be solved analytically, with most others requiring computational methods. Yet chaos theory has made us even more humble in recognising the limitations we cannot avoid in principle for predicting the evolution of complex systems.

Again, as fancy pants as economists like to be with their maths, their ignorance of chaos theory is telling.

Re: Greatest mathematician of our times is dead.

I. Ryan — Sun, 07 Nov 2010 19:05:22 GMT

Clayton:

I think it's not an exaggeration to say that the problem of induction has been solved, by Ray Solomonoff.

Can you concisely state what the problem of induction is?

Re: Greatest mathematician of our times is dead.

Giant_Joe — Sun, 07 Nov 2010 18:55:47 GMT

*bump*

Some good info in this thread. I came back to it to write down some names. Given the benefits I've gained from my anti-mainstream views of politics, economics, and nutrition, I think I'll soon delve into alternative problem solving techniques and alternative finance.

If I get caught up in doing AI work, (it's a possibility) I'll be looking into that stuff you mentioned, Clayton.

Thanks again, people.

Re: Greatest mathematician of our times is dead.

DMI1 — Tue, 19 Oct 2010 00:57:55 GMT

@patreek Sanjay: I've been looking for some good books on Heuristics! Can you tell me which ones you read?

Re: Greatest mathematician of our times is dead.

bcyclwutztht — Mon, 18 Oct 2010 23:44:56 GMT

@PrateekSanjay

What Joseph Schumpeter did for business studies, what George Polya did for mathematical method, what Benoit Mandelbrot did for statistics, what Friedrich Hayek did for economics, (and what Gary Taubes recent work did for nutrition!) all are a small part of destroying Anglo-American orthodoxy, and bringing back the superior continental European thinking. The German, Central European, and French underground thinkers, if popularized, could devastate the entire pyramid of nonsense taught in American and British universities and in other nations that imitate them.

I'm not a philosopher, and I'm not an expert on method, so I don't know what you're referring to regarding the "underground thinkers". Is it rationalism?

With Hayek, there appears to be an important distinction regarding Hayek vis-a'-vis his representing Austrian economics---in particular its methodology.

Here's a few words on Austrian method from Hoppe (from "Murray Rothbard: Economics, Science, and Liberty"):

First, Rothbard is the latest representative of the mainstream within Austrian Economics.* As in other intellectual traditions, various interconnected branches can be identified within the Austrian School of economics. Rothbard is the latest exponent of the main rationalist branch of the Austrian School, starting with the School’s founder Carl Menger, and continuing with Eugen von Böhm-Bawerk, and Ludwig von Mises.

...

*Among academia in general, currently Friedrich A. Hayek is by far the most prominent Austrian economist. It is worth emphasizing, then, that Hayek is not a representative of the rationalist mainstream of Austrian economics, nor does Hayek claim otherwise. Hayek stands in the intellectual tradition of British empiricism and skepticism, and is an explicit opponent of the continental rationalism espoused by Menger, Böhm-Bawerk, Mises, and Rothbard.

Re: Greatest mathematician of our times is dead.

Clayton — Mon, 18 Oct 2010 20:33:06 GMT

@Prateek: I'm not familiar with Keynes's work on probability but I would be surprised if Keynes was a friend to Bayesianism. Frequentism is usually the view held by those with a positivist bent.

Clayton -

Re: Greatest mathematician of our times is dead.

Prateek Sanjay — Mon, 18 Oct 2010 20:29:27 GMT

In the Black Swan, Taleb explained what he meant when he uses certain words, and he tends to give them his own definition.

Taleb is an "academic libertarian", a believer in breaking academic orthodoxy. Not a libertarian per se. However, he does give credit to the Austrian School for some ideas with which he is in agreement.

Clayton, I remember Murray Rothbard mentioning that Richard von Mises' theories on probability debunked many of Keynes' theories on probability. Of course, while Ludwig and Richard rarely agreed, both were supposedly quite brilliant and original thinkers, and you can just see that continental Europeans have so much natural superiority to Anglo-Americans on so many fronts. It's not that Keynes' Treatise on Probability was a bad work at all; it may have been his main strength, since it was also helped by the fact that he was a person of philosophical background.