WOLFRAM JUST WON'T GO AWAY

The NYT has just given Wolfram an interview. Either you can see all this as the greatest exercise in self-publicity in history, or you can accept that despite the arrogance, despite the infantilism, and despite the failure to recognize others who have something to say on the subject, this show is going to run and run, because, at the bottom line, there is something really, really interesting. And whether he's right or wrong, I kinda agree with this:

I'm probably more nervous about people trying to apply what I've done in the book too quickly, rather than too slowly. It would be bizarre if my attempts to sort of change the direction of quite a bit of science were, you know, immediately absorbed and understood by people who had spent decades working in some different direction. In academia, there is this common statement: New ideas have either been done before, or they're wrong, or both. And it's kind of charming to me that people send mail about some things in my book, say, ''We've said this before.''
But I don't think they've understood what I've said. In fact, if they did understand, their first response would be, ''That can't be right.'' People's responses are being documented in a very obvious way. There are newsgroups and postings. I find it rather interesting. But so far, I'm just collecting the data. The thing one learns about the history of science is that these things take awhile. And one waits.
Source: New York Times:
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ONLY PART OF THE PICTURE

The Economist is rightly worried again about the impact of the present bear market, but the background thinking needs to get a bit clearer why the problem in Japan has gone as it has.

Stockmarkets around the world are unusually jumpy, with dramatic falls in share prices followed by sudden recoveries. But the underlying trend still seems to be down, raising fears that the global economic recovery could yet be undermined.THESE are not times for nervous investors. The recent sharp fluctuations in the world’s stockmarkets have brought the doom-mongers out in force. They point to the relentless downward slide in share values since their peak in 2000 in America, earlier in London and more than a decade ago in Japan. The collapse in share prices has sent many investors scurrying for cover in safer assets like bank deposits or bricks and mortar; and workers due to retire have begun to worry about the safety of their pension funds. Stockmarket volatility has been matched by swings in currency values—if there’s panic around, foreign-exchange dealers don’t like to be left out.

The market hysteria, coupled with a relentless air of gloom among many in the financial and corporate sectors, is enough to make even the most balanced economist pause for thought. Long-time market observers know things are rarely as bad as they seem—but could the current bear market be one of the exceptions?
So far, the bear market has not had too dramatic an impact on America’s admittedly modest recovery this year. The data is mixed, and there are still worries about business investment levels—which Mr Greenspan regards as key to a sustained upturn—and about wobbly consumer confidence. But unemployment has not risen as far as some had forecast—not yet, at any rate—and labour market figures released on July 3rd showed a further fall in initial unemployment claims from those who have recently lost their jobs.

For those determined to look on the black side, though, the spectre of Japan looms large. In late 1989, the Nikkei share index peaked at almost 40,000: the ensuing collapse was swift—within three years the index had fallen to less than half that, and it hovered around that level for the best part of a decade before plunging again in the middle of last year. Most worrying of all, for those now watching the decline of American shares, the Japanese economy has been in the doldrums ever since its share bubble burst.
Source: The Economist
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ITALY'S NATIONAL ACCOUNTING

The Italian mystery deepens. Now it seems we're using Enron style special purpose vehicles to move debt off balance sheet to meet EU stability pact requirements:

Italy and the European Union Commission clashed Thursday over controversial accounting practices, another sign of increasing tensions over Europe's strict budget rules.

Like other European countries, Italy has promised to balance its budget by 2003 and has been leveraging state-owned assets to help it reach its goal. Wednesday, the Commission's statistics arm, Eurostat, outlawed this practice, ruling that borrowings secured on future government revenues can no longer be pushed off the national balance sheet.Under the Italian financing program, Rome parked state assets such as real estate and lottery revenues in special-purpose vehicles, which then issued debt. Since the government didn't issue the bonds itself, the debt didn't end up in the national accounts and inflate the deficit.
Source: Yahoo News
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Now if Italy had a nicely balanced population structure, then probably none of this would matter. But this isn't the case, so one day this debt is going to make itself felt on balance-sheet, and then this particular bubble is going to burst. Don't say you haven't been warned.

Incidentally, following the story I blogged earlier this week, Italy's Interior Minister has now resigned following his comments that the assasinated government economic adviser was a pain in the neck. I don't really know what the definition of a 'banana republic' really is, but if there was such a thing would the current Italian administration fit the description?

PRIME NUMBER PATTERNS

After all the stir caused by Wolframs rule 110, here's another puzzle about our universe whose understanding might help us get things a little clearer: Riemann's Zeta function.

The Riemann hypothesis, first tossed off by Bernhard Riemann in 1859 in a paper about the distribution of prime numbers, is still widely considered to be one of the greatest unsolved problems in mathematics, sure to wreath its conqueror with glory — and, incidentally, lots of cash. Two years ago, to celebrate the millennium, the Clay Mathematics Institute announced an award of a million dollars for a proof (or refutation) of the hypothesis.

Whether in pursuit of glory, cash ("prizes attract cranks," one mathematician sniffed) or pure mental satisfaction, more than a hundred of the world's leading mathematicians came to New York City recently to attend an unusual conference at New York University's Courant Institute. While most math conferences are devoted to presenting completed work, this one was held for mathematicians to swap hunches, warn of dead ends and get new ideas that could ultimately lead to a solution......
As in all sports, it helps to know the rules of the game. Riemann made his hypothesis in the course of a 10-page paper he wrote on the distribution of prime numbers that is considered to be one of the most important papers in the history of number theory, a history that stretches back more than 2,500 years..............Despite the random occurrence of individual primes, the primes themselves were found to follow a remarkably simple distribution. In 1792, when he was 15, Karl Friedrich Gauss decided to examine the number of primes less than a given number. He discovered that the primes became, on average, sparser the further out he looked and that this dwindling obeyed a simple, logarithmic law. He had no idea why this was so, but it was intriguing.

In 1859, Riemann, who had been a student of Gauss, took up the question of the distribution of primes in his only paper on number theory. With that paper he revolutionized the field, as he had the fields of geometry (his math became the basis for Einstein's theory of gravitation) and several other branches of mathematics. What Riemann discovered was a way of using the properties of a relatively simple function to count the primes.

While the real numbers can be thought of as points on an infinite line, the complex numbers are points on a plane. One axis of this complex plane corresponds to the real numbers, and the other corresponds to the "imaginary" numbers — which were introduced so that negative numbers could have square roots, and are no more imaginary than real numbers. A function like Riemann's zeta function is simply a rule that takes a point on this plane and sends it to some other point.

Riemann showed that if he knew where the value of his zeta function went to zero he would be able to predict the distribution of the primes. He was able to prove that aside from some "trivial" zeros — located at -2, -4, -6, and so on and thus easily included in his equations — the zeros of the zeta function all lay within a strip one unit wide running along the imaginary axis.

Somehow the distribution of these zeros mirrored or encoded the distribution of the prime numbers. Riemann guessed that all of the zeros ran along the middle of the critical strip like the dotted line on a highway. Nobody is sure why he made this guess, but it has proven to be inspired. Over the past few decades billions of zeros of the zeta function have been calculated by computer, and every one of them obeys Riemann's hypothesis.

Source: New York Times
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The problem is to know whether this zeta function for primes has any significance, and if so, what is it?