The real work that needs to be done is in attacking the fundamental assumptions of "expectations" modelling in economics. I mentioned above that Samuelson's assumptions underlying the Law of Iterated Expectations were "innocent-looking", which they are, but they're actually extremely restrictive. Importantly (and this is a topic I've harped on about before), they're only valid for expectations of *ergodic* processes. What the hell is an "ergodic process" when it's at home? Ergodicity is a statistical property. A data generating process is "ergodic" if the data that it generates is "well-behaved" in the sense that you can take a sample of it and that sample will be in some way representative of the whole. Imagine a random number generator, spewing out numbers, and yourself sitting in front of it, writing the numbers down. After 1000 numbers, you calculate the mean of the observations. If the random number generator is driven by an ergodic process, you now have a decent estimate of what the mean will be after 10,000 observations. With ergodic stochastic processes, collecting more data gets you a better and better estimate of what the underlying parameters of the process are, as the "noise" cancels itself out in some statistically well-defined way. But imagine if you were in front of the machine, and you kept on collecting more and more data, but the average after 1000 numbers was completely different from the average after 10,000, which was nothing like the average after 100,000 and so on. Imagine further that it *never* settled down, no matter how much data you collected. That would be a strongly nonergodic process; over time periods of around a week to a month, lots of weather data appears to be nonergodic, which is why medium term weather forecasting is so difficult. It's clear here that to talk about "expectations" of the future states of a nonergodic system are meaningless; people might have opinions about the future, but there aren't the solid linkages between these views and the actual data which one would need to call them "expectations". Certainly, there isn't enough to support the trick used by economists in using the expectations operator to make dynamic processes static so that they can be modelled tractably. So what? Well, so this: Most processes which are characterised by positive feedback are nonergodic Most economic processes of interest are subject to significant, destabilising positive feedbackGo read the whole post and while you're over there go read the whole blog and it's archives as well. There's plenty of great stuff there too.
Surprising observations of a star swiftly orbiting the cloudy heart of the Milky Way Galaxy have verified with near certainty the existence of a central black hole, a theoretical object that still eludes direct detection. Astronomers watched the star for a decade, tracking two-thirds of its path around the galactic center. No object has ever before been seen so close to the center of any galaxy, nor has any other object previously been observed making more than a small fraction of its orbital trek around a galaxy. "We could not believe our eyes," said Thomas Ott, an MPE researcher who co-led the study along with Schoedel and MPE director Reinhard Genzel. "We suddenly realized that we were actually witnessing the motion of a star in orbit around the central black hole, taking it incredibly close to that mysterious object."
The Peopling of the Pacific Ann Gibbons Archaeologists, linguists, and geneticists struggle to understand the origins of the bold seafarers who settled the remote Pacific Islands Polynesia, with its dramatic volcanic islands rising out of the South Pacific, was the last area of the world to be settled by people. The fossil and archaeological trail shows that humans first set foot in Fiji only 3000 years ago, then sailed on within 500 years to Samoa and Tonga, and later reached Easter Island, Hawaii, and the fringes of remote Oceania, exploring a realm stretching 4500 kilometers. But just who was in those outrigger canoes has long been a mystery. Even Captain James Cook mused about the islanders' origins on his last voyage from 1776 to 1780, noting the resemblance of language, customs, and appearance among the tall, fair Polynesians on such farflung islands as New Zealand, Tahiti, and Easter Island. And he proposed his own theory that they had come from Malaysia or somewhere in the islands of Micronesia, such as the Marianas or Caroline Islands, where they had "affinities with some of the Indian tribes." From such observations, Europeans such as French voyager JulesSebastienCesar Dumont d'Urville got the idea that these islanders could not be the descendants of the generally shorter, darkskinned Melanesians living in islands of New Guinea, the Bismarck Archipelago, and the Solomon Islands. In 1832 Dumont d'Urville classified the people of the Pacific into three groups: Polynesians ("many islands"), the diverse Melanesians ("dark islands"), and Micronesians ("little islands"). This superficial classification stuckeven though the geographic terminology eventually changedand ever since, many researchers have looked beyond the Melanesians of Near Oceania for the ancestors of the Polynesians who populate Remote Oceania (see map). For example, until recently many geneticists and linguists have looked to the "express train" model. In this view, the ancestors of Polynesians came from Taiwan, where farmers speaking Austronesian languages set sail 3600 to 6000 years ago, largely bypassing the indigenous Papuanspeaking people of Melanesia as they swept out into the Pacific and left behind a trail of distinctly decorated pots. Although this model was often touted as an interdisciplinary synthesis, in fact it is no favorite of archaeologists, many of whom have for years preferred a more "integrated" model, with at least some mixing between Melanesians and Austronesian speakers from Southeast Asia (a vast area that ranges from the coast of southern China to the islands of Indonesia and the Philippines). And now a flurry of studies of the Y chromosomes of Polynesians also favors the "slow boat" model, in which the ancestors of Polynesians originated in Asia but moved slowly through Melanesia, with time for genetic mixing among the peoples before the colonization of the rest of the Pacific. But even as these different kinds of data begin to point the same way, researchers are still groping for a true synthesis of the archaeological, linguistic, and genetic data. Each discipline tends to frame ideas in its own way, and at the moment each data set tends to favor a different homeland for the original voyagers. "I have to write a review myself of the spread of early farmers, and it's very difficult," says archaeologist Peter Bellwood of the Australian National University in Canberra. "It's the genetics that is causing headaches." Read on...
The National Aeronautics and Space Administration (NASA) space shuttle has imaged a mysterious ancient bridge between India and Sri Lanka, as mentioned in the Ramayana. The evidence, according to experts is in the Digital Image Collection. The bridge, which was discovered only recently, was named as Adam’s Bridge. It is made of a chain of shoals, 30 km long, in the Palk Straits between India and Sri Lanka. The bridge reveals the mystery behind it. The bridge's unique curvature and composition by age reveals that it is man-made. Legend as well as Archeological studies have it that the first signs of human inhabitants in Sri Lanka date back to the primitive age, about 17,50,000 years ago. And the bridge is almost equivalent.Update: Actually there's a tad more to this, Adam's Bridge (or Rama's Bridge) really exists and is a
...chain of shoals, c.18 mi (30 km) long, in the Palk Strait between India and Sri Lanka. At high tide it is covered by c.4 ft (1.2 m) of water...According to Hindu legend, the bridge was built to transport Rama, hero of the Ramayana, to the island to rescue his wife from the demon king Ravanna.And NASA really did image it (in the mid 1990's). The original story appears to have been lifted from the real Pravda wannabe VNN who in turn lifted it from INDOlink.
Captain James Cook's place in Australian history is safe after a man who claimed an early shipwreck on Fraser Island admitted he made a mistake. Archaeologist Greg Jefferys thought he had discovered the remains of a ship which showed that European mariners had discovered the east coast of Australia before Captain Cook's arrival in 1770. He based his claim on what he believed were the muzzles and barrels of cannons uncovered in the sand at the northern end of the island, off the Queensland coast. But he said today that what he had found was actually davit supports from a ship wrecked on the island in the 19th century.Oh well, got a little over-excited there...
You know you are in China when you decide to take a walk through a park on your university campus and encounter students shouting out English texts to a tree. Alternatively, if it's raining or cold, you can find them in deserted corridors barking at the wall. Beware of these students, for they have entered the crazy world of "Crazy English". Li Yang, the creator of the "Crazy English" method of learning, has built up a huge following by touring the country and delivering lectures which demonstrate his technique. Thousands turn up and join in the mass-chant "Crazy! Crazy! Crazy!" He turns the audience into parrots, repeating his mantra "I love humiliation! I embrace hardship! I welcome failure! I pursue success!" Everyone yells English phrases in unison. It's a great big pep talk, and he sends the crowd home on a high. Then you and I give them weird looks as we walk through parks and deserted corridors.
It appears likely the attack will result in the greatest single loss of Australian lives overseas during peacetime.
He stakes his claim in the first few lines of the book: "Three centuries ago science was transformed by the dramatic new idea that rules based on mathematical equations could be used to describe the natural world. My purpose in this book is to initiate another such transformation...." Usually I put books that make claims like these on the crackpot shelf of my office bookcase. In the case of Wolfram's book, that would be a mistake. Wolfram is smart, winner of a MacArthur Fellowship at age twenty-two, and the progenitor of the invaluable Mathematica, and he has lots of stimulating things to say about computers and science. I don't think that his book comes close to meeting his goals or justifying his claims, but if it is a failure it is an interesting one.
Wolfram goes on to make a far-reaching conjecture, that almost all automata of any sort that produce complex structures can be emulated by any one of them, so they are all equivalent in Wolfram's sense, and they are all universal. This doesn't mean that these automata are computationally equivalent (even in Wolfram's sense) to systems involving quantities that vary continuously. Only if Wolfram were right that neither space nor time nor anything else is truly continuous (which is a separate issue) would the Turing machine or the rule 110 cellular automaton be computationally equivalent to an analog computer or a quantum computer or a brain or the universe. But even without this far-reaching (and far- out) assumption, Wolfram's conjecture about the computational equivalence of automata would at least provide a starting point for a theory of any sort of complexity that can be produced by any kind of automaton. The trouble with Wolfram's conjecture is not only that it has not been proved—a deeper trouble is that it has not even been stated in a form that could be proved.
Jakarta: Charred and limbless bodies were strewn across the road as terrified foreign tourists, some with clothes on fire and drenched in blood, stumbled through the carnage of the Bali blast. In seconds the bustling nightspots in the popular Legian resort overnight were transformed into an inferno which left at least 150 people dead and many more injured. The bomb erupted at about 11pm (0100 AEST) just as the nightclubs were beginning to fill up, and the restaurants and roads were brimming with people eating or strolling.
Mariana Islands (Guam) from Johann Ludwig Gottfried's Historia Antipodium Newe Welt Frankfurt, 1640