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The Poincaré conjecture, I

Tuesday, August 29, 2006

We've said a bit about the circumstances surrounding the proof of the Poincaré conjecture, but little about the conjecture itself. What is it?

In the most general terms, it is about the question: When is a topological object "the same" as a sphere?

In order to give a mathematical answer to such a question we first have to precisely define at least three terms: "topological object", "the same", and "sphere".

Mathematicians define a topological object as a set of points that satisfy certain axioms. ("Points" themselves are left undefined. The notion of "set" can also be axiomatized, but the intuitive idea is sufficient here; more detail would take us too far afield.) Intuitively, you can think of topological objects as the sort of things studied in high school geometry -- lines, surfaces, solids, etc. Axiomatization of high school ("Euclidean") geometry itself is more complicated than actually taught in high school -- it's more than just Euclid. It was done by David Hilbert in 1899, but details aren't for the faint-of-heart. (Hint: He needed to use 19 axioms.)

The Poincaré conjecture doesn't concern topological objects in full generality. Instead, it's about objects of a certain kind, which mathematicians call "manifolds". I intend to go into more detail about manifolds in another article, but it's not necessary to be more precise at this time. Just keep thinking about lines, surfaces, solids, and higher dimensional analogues. (If you really want to know right now, take a look at this or this.)

In order to add some intuitive content to the notion of manifold, we can consider how "sphere" is defined. The simplest sphere is two points (+1 and -1), sometimes written (a little ostentatiously) as S0. The zero refers to "dimension" -- a point is 0-dimensional. The meaning of "dimension" here is wrapped up in the definition of manifold, but it's just the intuitive thing. An example of a 1-dimensional manifold is a (possibly curved) line. Another example is a circle. A "standard" circle is the set of points in a plane (which itself is 2-dimensional) that satisfy the equation x2 + y2 = r2, where (x,y) is a point in the plane given by x and y coordinates, and r is the radius.

Now, topologically, the size and exact shape of an object is not important. Topology is sometimes called "rubber-sheet geometry" because exact sizes and shapes don't matter. Any transformation of an object on a rubber sheet resulting from stretching or bending is considered to be "the same" object, as long as the sheet isn't ripped. So any figure on a rubber sheet which is "the same" as a standard circle (of radius 1) is just another example of a 1-dimensional "sphere" (a "1-sphere").

When speaking topologically, mathematicians are often deliberately ambiguous. Technically, a circle (on a flat plane) of radius 1, given by the equation above, is a particular manifold, while any stretched, squashed, or twisted version is a different manifold. But topologically they are all "the same" or "equivalent", and any particular instance is referred to simply as a 1-sphere, or S1 for short.

Continuing in the same vein, a "standard" 2-sphere is the set of points (x,y,z) in 3-space defined by the equation x2 + y2 + z2 = r2. Anything that's "the same" as a "standard" 2-sphere is itself usually referred to as a 2-sphere, S2.

One can similarly define n-spheres, Sn, for any integer n≥1. Note that n is the dimension of the object as a manifold, but it is defined in terms of points in a space of dimension n+1. That is, the points themselves each have n+1 coordinates, yet the equation that specifies the points reduces the dimension of the resulting manifold by 1.

Finally, what do we mean by "the same"? As noted, two objects are considered "the same" if there is a transformation that stretches, compresses, or bends the overall space, without tearing it, and carries one object into the other. (That's not quite right, since a manifold need not be defined as embedded in a "Euclidean" space of a particular dimension, but it's close enough, absent a more precise definition of "manifold".)

With those preliminaries out of the way, we can return to the original question: When is a topological object "the same" as a sphere?

For concreteness, consider the case n=2. When is a manifold topologically the same as S2, which is just what we ordinarily think of as a sphere in 3-dimensional space (but a hollow one, like a globe, without the solid interior).

The game is rigged. All the precise definitions of "manifold", "the same", and so forth are arranged so that everything that is topologically the same has the same (topological) properties. So anything that's equivalent to the 2-sphere S2 must have all of its properties. Having each of the properties is a necessary condition for equivalence. So let's list some of them.

  • S2 is a 2-dimensional manifold (a surface).
  • A sphere is just a single piece, not 2 or more disconnected pieces. Topologists say it is "connected".
  • A sphere is finite and bounded. It does not extend infinitely in any direction. Topologists say it is "compact".
  • A sphere has no "boundary". That is, there is no "edge", as there is on a 2-dimensional disk, for example.

Unfortunately, it turns out that this set of necessary conditions isn't enough to be sufficient to ensure that a manifold meeting the conditions is topologically equivalent to a 2-sphere. The simplest example of a nonequivalent manifold meeting the conditions above is a (2-)torus, which is the surface of an ordinary 3-dimensional donut. (Ummmmm, donuts!)

How can one visualize the reason this is so? Well, just think of drawing a circle on a torus. In some cases you can imagine the circle contracted to a point without ever leaving the surface or breaking the circle. But in other cases, if the circle goes either around or through the central hole, this is impossible. Because of this circumstance, a torus is not topologically equivalent to a 2-sphere, where a circle can always be contracted to a point.

The condition that any circle drawn on a 2-manifold can be contracted to a point without breaking the circle or leaving the manifold must be met by any manifold that is equivalent to S2. This condition is necessary. The neat thing is that you do get a sufficient set of conditions for equivalence if you add this last condition to the earlier ones. This fact was (implicitly) proven in the mid 1800s by Bernhard Riemann, who gave a simple classification of 2-dimensional manifolds.

In 1904 it occurred to Henri Poincaré to wonder whether an analogous set of conditions applied to 3-dimensional manifolds. (The case of dimension n=1, essentially just closed loops, is fairly trivial.) He conjectured that, with the appropriate definitions, the answer would be yes. That is, if the right conditions are met, a manifold is equivalent to the 3-sphere S3. This is the Poincaré conjecture. At first he even thought, incorrectly, he could prove it.

Others later conjectured that an analogous result holds in any dimension n≥3. In the next installment, we will discuss how to generalize the necessary concepts to higher dimensions, and recount the history of the conjecture up to the present time.

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Miscellaneous links, 8/24/06

Saturday, August 26, 2006


We start off with some sites which have great collections of information in their respective subject areas.



Comparative Mammalian Brain Collections
As it describes itself, "This web site provides browsers with images and information from one of the world's largest collection of well-preserved, sectioned and stained brains of mammals. Viewers can see and download photographs of brains of over 100 different species of mammals (including humans) representing over 20 Mammalian Orders." Building upon this extensive visual information, there are also overviews of topics like brain evolution, brain development, brain architecture, and brain function.

BCI-info
One staple of much science fiction writing is the idea of Brain-Computer Interfacing (BCI) -- connecting living brains with computers and other electronic or mechanical devices. There are obvious mundane applications, such as brain diagnostics and control of prosthetic devices like artificial retinas and artificial limbs. Then there are more speculative applications like brain augmentation by connection to specialized computers, interfaces to large databases, teaching machines, and perhaps even storage and retrieval of individual memories. Put some sort of communications capability in the loop and you have electronic telepathy. But this isn't just science fiction. BCI research is actively going on. That's what this site is about: "BCI-info is an open international platform for Brain-Computer Interface research intended to provide information for scientists, patients, students, the media, and people from the general public interested in BCI technology."

Introduction to Linguistics
Would you like a quick, easy introduction to linguistics so you could get a grasp of what's common to most human languages and understand some of the issues that people like Noam Chomsky and Steven Pinker write about? Try the course put together by Sophia A. Malamud at the University of Pennsylvania. See the class schedule to access the course lectures.

The Virtual Embryo
Embryology and developmental biology are two of the most active areas in the life sciences. You need to understand the basics in order to appreciate hot topics like stem cells and evolutionary developmental biology ("evo-devo"). This site provides a great resource for learning about them. Topics covered include gametogenesis, embryonic development, the genetic regulation of development, organization of multicellular embryos, and cell differentiation. There are plenty of links to relevant external resources as well as a tutorial on devlopmental biology.

And here are some shorter articles about interesting recent research.



DNA or RNA? Versatile Player Takes a Leading Role in Molecular Research
RNA is chemically very similar to DNA, except that its backbone is made of a slightly different sugar molecule, one of its four bases is different from the analogous base in DNA, and RNA molecules are usually single-stranded, in contrast to double-stranded DNA. RNA was first understood in the form known as messenger RNA, which transcribes the information in a gene in order to construct a protein. However, there is another type of RNA that is chemically the same but has a different function. This is sometimes known as regulatory or "silencing" RNA. It is produced in the same way as messenger RNA, as a transcription of a special type of DNA gene. But its function is to regulate the production of proteins from messenger RNA. Silencing RNA is usually only about 20 base units long, but it performs its regulatory function by attaching to a complementary segment of messenger RNA, thereby inhibiting the construction of a protein.

Monster Tumors Show Scientific Potential in War Against Cancer
A teratoma is a cancer-like growth, consisting of a mass of partially differentiated cells. Teratomas can be quite large, and sometimes include mature tissues such as teeth and hair. Some teratomas originate from egg cells which begin to develop as if they had been fertilized, but without the developmental programming to progress like a normal embryo. They can be useful in stem cell research because they may be a good source of such undifferentiated cells. Since they also contain a variety of differentiated cell types, they can be used in cancer research as a test bed for new drugs.

Diving deep for answers
Sea anemones are primitive animals of the phylum Cnidaria. Other cnidarians include corals (belonging to the same class as anemones) and jellyfish. They seem to be the most primitive animals that have distinct types of tissue, such as mouths and tentacles and stinging cells. Cnidarians originated at least 600 million years ago, even before the Cambrian explosion. The study of sea anemones should help understand the evolutionary process which allows more complex animals with multiple tissue types to develop.

And the Evolutionary Beat Goes On . . .
Evolution is often thought of as a process that goes on only over long periods of time, like hundreds of thousands of years. But smaller changes can occur much more quickly, as in the coloration of insects in order to better hide from predators. Some recent research has demonstrated simlar rapid changes in humans that have occurred in the last 10,000 years. Such changes include responses to variation in diet. Others have to do with skin color, disease resistance, fertility, and reproduction. In each case, scientists have identified corresponding changes in human DNA that can be dated to recent times.

Large and small stars in harmonious coexistence

Friday, August 25, 2006

Large and small stars in harmonious coexistence (8/14/06)
This is a Hubble Space Telescope image of one of the hundreds of star-forming stellar systems, called stellar associations, located 180,000 light-years away in the Large Magellanic Cloud (LMC). The LMC is the second closest known satellite galaxy of our Milky Way, orbiting it roughly every 1.5 billion years. Earlier ground-based observations of such systems had only allowed astronomers to study the bright blue giant stars in these systems, and not the low-mass stars.




Star forming region in the Large Magellanic Cloud
Click for 1280×1280 image

Is it "weird" to have principles?

Wednesday, August 23, 2006

This post isn't really about the Poincaré conjecture, so the conjecture isn't mentioned in the title.

Nevertheless, what I'm talking about, of course, is the Perelman affair, and especially the media narrative on it, as related in the previous post. As you can see from the popular media articles referenced there, the narrative is very much focused on Perelman's supposedly odd behavior: mysterious, reclusive, and all that.

Perhaps it's even typical of brilliant mathematicians? Nope, it's not. I've known plenty of brilliant mathematicians, and most are pretty "normal". Often a little bit eccentric, perhaps, but still pretty normal. In fact, most would (figuratively) kill for the honor that Perelman turned down. And that, it turns out, is a large part of the problem.

Since this story has actually been brewing for some time, it should come as no surprise that a few savvy journalists have had an in-depth article all ready to go. And that is what Sylvia Nasar and David Gruber offer in their article Manifold Destiny appearing in the lastest New Yorker. ("Manifold" isn't a typo; it's a pun.)

It's an excellent article, but you'll be disappointed if you expect to learn much about the Poincaré conjecture from it. Instead it's mostly about Perelman and the intrigues of a number of other mathematicians involved in the quest to solve the Poincaré conjecture. As Nasar and Gruber tell the story, it's very reminiscent of other stories of intense competitions to solve major scientific problems. One thinks, for instance, of the story of how the structure of DNA was determined, as recounted in Jim Watson's Double Helix. In short, it's largely about ambition and ego and jockeying to receive credit for the solution of a major problem.

Nasar is very qualified to write about the mathematical psyche, as she's well-known for her book A Beautiful Mind about another mercurial mathematician, John Nash, who even plays a small part in the Poincaré conjecture drama.

Nasar brings on another bit-player in the drama, another top Russian geometer, Mikhail Gromov, to summarize at the very end, Shakespeare-like, what the play's all been about:
Mikhail Gromov, the Russian geometer, said that he understood Perelman’s logic: “To do great work, you have to have a pure mind. You can think only about the mathematics. Everything else is human weakness. Accepting prizes is showing weakness.” Others might view Perelman’s refusal to accept a Fields as arrogant, Gromov said, but his principles are admirable. “The ideal scientist does science and cares about nothing else,” he said. “He wants to live this ideal. Now, I don’t think he really lives on this ideal plane. But he wants to.”

In other words, Perelman isn't some nerdy nutter. There's a principled logic to what he has done in refusing the Fields medal. It's a statement of his objection to the ego-centric way that the game of high-stakes mathematics (and science in general) is often played. This may be a quixotic gesture, but it's not daft.

Sadly, the villain in this drama, at least as Nasar and Gruber tell it, is another famous mathematician, Shing-Tung Yau, known especially in connection with Calabi-Yau manifolds, which are so important for superstring theory. Ironically, Yau seems to have gotten the short end of the stick, much earlier in his own career, in a credit struggle for his work on Calabi-Yau manifolds.

If the portrayal is accurate, it's sad. I crossed paths with Yau in the early 70s at Stanford, when he was at the beginning of his academic career. He seemed like a very decent, easy-going person then, though I hardly knew him. Perhaps the appearance was different from the reality, but I suppose I'll never know. Just as likely, if not more so, is that Perelman is right -- covetousness of honors and the high esteem of others is not good for us. And yet, how many brilliant scientists can put forth the great efforts usually required for high achievement without some degree of ego and strong motivation?

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The Poincaré conjecture: press accounts

Wow. When a mathematics story makes the news, it really makes it big. Sometimes.

Unfortunately, most of the emphasis seems to be on the personality of Grigory Perelman and how, like, weird he is portrayed as being.

One commentator, who calls his blog "Freakonomics" (yeah, I know, same as his book) compares Perelman and the Unabomber: What Do the Unabomber and Grigori Perelman Have In Common? The list is long: both are (or were at some time in their lives) mathematicians, bearded and long-haired, reclusive, and scholars/teachers at -- get this -- U. C. Berkeley.

Jesus. (Speaking of hirsute guys known for decidedly unnormal behavior.) It's stereotype-o-rama. Shouldn't we mention Rasputin as well? I mean, he was also Russian (like Perelman), though not, as far as I know, interested in mathematics.

But let's not dwell on this sort of thing, OK? Now, where was I? Oh, yes, press accounts of the (apparent) solution of the Poincaré conjecture.

It must be said that this isn't exactly news. It came to the attention of the mathematical community in 2003, when Perleman lectured on his results at MIT -- see here. The news even leaked out to the general public in 2004, as in this ABC News/Reuters story.

Of course, it's all getting attention now, since just recently others have filled out and prepared for publication most of the necessary details of Perelman's proof, as was noted here (near the end, via Peter Woit's blog) two weeks ago. There was also much speculation that, for his work, Perelman would be offered a Fields Medal at the International Congress of Mathematicians meeting Tuesday (8/22), and that he would neither accept the award nor even be at the meeting.

The New York Times picked up on this in a story on August 15 by Dennis Overbye. And on Tuesday the speculations proved correct, which is when the news flood really rolled in.

I'm not going to dig further into the press accounts in this post. That's for later, when I'll also try to say a lot more about the Poincaré conjecture itself, which is what really matters. (I'll leave the tabloid stuff about Perelman for others -- watch for the Broadway play next year, and the movie starring Tom Cruise the year after that.)

But for now, I just wanted to provide, for your reading pleasure, some of the other press accounts that showed up in the past 24 hours or so...


More to come. Stay tuned.

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Curmudgeons unite!

Tuesday, August 22, 2006

Or maybe it should be subtitled, "Why Mensans have less fun"...

Personality predictors of intelligence change from younger to older adulthood
An ability to be open to new situations may predict intelligence earlier in life, says a new study, but disagreeableness may predict intelligence later in life.

Wait. It gets better:
In the cognitively superior older group, who outperformed both the cognitively comparable older adults and the younger adults on every ability tested, “agreeableness was found to have a contrary relationship with general knowledge suggesting that a disagreeable nature may go hand in hand with better vocabulary and knowledge retention in older age,” said Baker. This result supports previous research that suggests that those who are highly intelligent may be more aloof and independent.


Cranky? You may be smarter than you think

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NASA Finds Direct Proof of Dark Matter

Monday, August 21, 2006

I've written about dark matter a number of times, most recently here. A more extensive article is here.

The gist of things is that, although there has been much indirect evidence for dark matter, there have also been many skeptics, both among astrophysicists and in the general public.

Uncomfortable with the idea of dark matter as a postulated solution to a number of astrophysical puzzles, the skeptics have devised a number of alternative explanations for the various anomalies -- often by attempting to modify long-accepted principles of Newtonian gravity and general relativity.

But heedless of the skeptics, evidence for dark matter just keeps piling up. Here is the latest, just released today, and it is a lot less indirect than previous evidence:

NASA Finds Direct Proof of Dark Matter
Dark matter and normal matter have been wrenched apart by the tremendous collision of two large clusters of galaxies. The discovery, using NASA's Chandra X-ray Observatory and other telescopes, gives direct evidence for the existence of dark matter.

"This is the most energetic cosmic event, besides the Big Bang, which we know about," said team member Maxim Markevitch of the Harvard-Smithsonian Center for Astrophysics in Cambridge, Mass.

These observations provide the strongest evidence yet that most of the matter in the universe is dark. Despite considerable evidence for dark matter, some scientists have proposed alternative theories for gravity where it is stronger on intergalactic scales than predicted by Newton and Einstein, removing the need for dark matter. However, such theories cannot explain the observed effects of this collision.


For more commentary, see this at particle physicist Clifford Johnson's Asymptotia.

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Longevity genes and cancer

Sunday, August 20, 2006

Scientists have identified a number of genes that seem to have some effect on an animal's longevity. Mostly they have been found in small, short-lived creatures whose longevity is easily studied, such as mice, fruit flies, or roundworms (C. elegans), though they frequently have analogues in humans. See here for an earlier discussion.

Of course, any gene which is important for inhibiting cancer, such as the well-known p53, will tend to improve longevity, for obvious reasons. But surprisingly, there are some longevity genes which don't have such an obvious relation to cancer, and may lengthen expected life span even when cancer is present.

Longevity genes fight cancer at its source
Over the years, biologists have discovered a handful of genes in roundworms, mice and flies that bestow a dramatic increase in lifespan on the organism that carries it – sometimes up to twice their normal life expectancy.

These genes are involved in diverse biochemical pathways including those for growth hormones, insulin, food intake and caloric restriction. But it is thought that they are all have a role in how the body responds to stress.

Julie Pinkston at the University of California in San Francisco, US, and colleagues, wondered if these longevity genes had something else in common: the power to fight cancer – a notoriously age-related disease.

Pinkston manipulated a C. elegans gene to make the worm more susceptible to cancer, and she also introduced a mutated version of the daf-2 insulin-like receptor gene, known to be longevity-enhancing. Worms with both mutations, even though they developed tumors, still lived twice as long as unmutated worms. Apparently the mutated daf-2 was doing something in addition to preventing tumors from forming.

The something else seems to be related to apoptosis:
Daf-2 seemed to protect against the lethal cancer by stimulating apoptosis – programmed cell death – which tumour cells usually avoid, the researchers say.

It's understandable that a gene which stimulates apoptosis helps fight cancer. The question is whether stimulating apoptosis also has harmful side effects. Apparently not so much in this case, if longevity is doubled anyhow.

But there's more to it than that:
One hallmark of cancerous growth is a rapid acceleration of cell division. Daf-2 also decreased the number of cell divisions in the roundworms by 50% compared to what was expected for those with the gld-1 gene, Pinkston says.

Other longevity-releated gene mutations are known in C. elegans, and when these mutations were present, the longevity effect also occurred:
The team then used the same process to test three other known longevity genes in turn against the life-shortening gld-1 gene. These three double-mutant worms also lived longer than normal roundworms. Each of the three genes (eat-2, isp-1 and clk-1) suppressed cell division, even though they did not appear to increase apoptosis.

Again, it would seem that suppressing cell division with these mutations is a net benefit for longevity, despite the need for some cell division outside of tumors. Perhaps they simply cause an animal's life cycle to proceed at a slower pace.

But roundworms are rather simple animals. One wonders how such an effect would play out in a human...

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Other references:

Longevity genes fight back at cancer
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What does it take to be a star?

There probably isn't much explanation needed about this, but it's an important detail that astronomers have been trying to nail down for some time: A concentration of cosmic gas must amount to 8.3% of the Sun's mass, or it will never be a star, just a brown dwarf.

Mass cut-off between stars and brown dwarfs revealed
The observations provide the most accurate measurement ever made of the mass boundary between lightweight stars and "failed" stars called brown dwarfs – the dividing line is at about 80 times the mass of Jupiter, in line with theoretical predictions.


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Unsolved problems in mathematics

Tuesday, August 8, 2006

I just noticed this page in Eric Weisstein's excellent Mathworld site: Unsolved Problems. It's a nice list of 16 problems in mathematics -- some of which date back two hundred years or more -- that have defied the efforts of many mathematicians to find a solution. Everyone is familiar with the feeling, of course.

Curiously, however, most of the problems concern number theory, in the general sense that they deal primarily with questions involving integers. More precisely, 11 of the 16, by my count. No doubt this is because such problems can be explained to anyone who knows what an integer is, without reference to any "higher" mathematics.

I won't discuss them here, since the Mathworld site itself is an excellent encyclopedic reference to just about any topic in mathematics you might care to name. For that reason alone it's worth perusing the site if you aren't already familiar with it. Each problem, with related concepts, has its own page of explanation on the site.

However, there's a hell of a lot of mathematics out there that's not concerned primarily with integers, and a correspondingly large number of unsolved problems. Does the site have more to say about such? Yes, it does. A little poking around reveals an index page: Mathematical Problems, and beneath that five lower level index pages that deal either with unsolved problems, noteworthy unsolved problems of the past that have subsequently been solved, or important conjectures that have been found to be mistaken.

One of the lower level indexes, Unsolved Problems, lists no fewer than 223 individual pages (as of today) describing a great variety of unsolved problems. Aha. Now there's something to sink one's teeth into.

Another lower level index lists 17 "Prize Problems" -- problems considered important enough by someone to put up a substantial sum of money to be awarded to the first person who provides a valid solution. If you'd like to try your math skills, 16 of these are (as far as I'm aware) still unsolved. The 17th is Fermat's Last Theorem, which, as you know, was resolved in 1993-95 (primarily) by Andrew Wiles. I wrote quite a bit about this here.

Yet another index page covers Problem Collections -- lists of diverse unsolved problems compiled by various mathematicians. Oddly, one of the most well-publicized recent lists of this kind -- the Millennium Problems of the Clay Mathematics Institute -- is not included. This is especially odd because the Instutite offers a prize of US $1,000,000 for a solution (positive or negative) to each of its seven problems. Five of these problems are listed among Mathworld's Prize Problems -- but two (Navier-Stokes equations and Yang-Mills theory) are not.

There's one Millennium problem which deserves special comment here -- the Poincaré Conjecture. I won't even attempt to describe it in this post, though it's not too hard to explain what it's about, but less easy to explain why it's so important. The reason it's worth special comment here is that it has (apparently) just recently been resolved after kicking around for about 100 years since Henri Poincaré called attention to it. See this post from Peter Woit's blog for some of the latest news. See here and here for technical background.

What's going on with the Poincaré Conjecture definitely deserves a lot more discussion than a few sentences in this post. Looks like I'll have to make a project out of that -- as soon as I figure out what actually is going on...

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Recent technology news, 8/6/06

Monday, August 7, 2006

If your main source of information is the traditional media, then "technology news" is all about PCs, large-screen TVs, high-density DVDs, digital cameras, cell phones, MP3 players, and other electronic gadgets.

Stuff for consumers to gorge themselves on, in other words. Buy, buy, buy. Then buy some more, when the new models come out next year. Gotta keep the economy wheezing along, y'know.

Bletch.

In fact, there's plenty of interesting technology news that comes out every week. Only it's about stuff that won't be available on the shelves at Best Buy or Circuit City for maybe 10 years, or not oriented towards consumers at all. Stuff that may affect our lives just as significantly as cell phones, if only indirectly -- in much better health care and medicine, for example.

The following is just one week's worth of such technology news. I wish I had time to report on this kind of thing every week, but at least this is a sample.


Bayesian Mathematics Breathes Perception Into Robots
Robots have been around for decades. But you still can't buy one to prepare and serve dinner or help Grandma clean her house and do her wash, because existing robots are too stupid. They can "see" just fine, like a digital camera. But they have only the barest understanding of what they see. Robotic vision is a big problem. It's an "artificial intelligence" problem in which progress is slow, in spite of orders of magnitude improvement in computer speeds over the past several decades. What's holding things back isn't speed, but lack of adequate algorithms -- understanding of how humans comprehend their sensory inputs. The research discussed in the present article concerns a mathematical technique called "Bayesian reasoning" -- "a model for rational judgment when only uncertain and incomplete information is available."

AI Reaches the Golden Years
Here's another perspective on the AI problem. The occasion for the article is the 50th anniversary of a famous workshop at Dartmouth where the term "artificial intelligence" was coined. You'd think that there should have been a significant amount of progress in 50 years, something commensurate with the progress in computers that makes the comparison between 1950s computers and contemporary ones like the relation of cuneiform tablets to high-density DVDs. Sadly, no. One of the main participants in the Dartmouth workshop, Marvin Minsky, said in 2003, "AI has been brain-dead since the 1970s." (I took an intoductory course in AI from Minsky a mere 40 years ago.) Perhaps that's too harsh a judgment, but the main problem is still "commonsense reasoning". However, we may be closer to the advent of "real" AI than to the founding of the subject. Stanley, the self-driving "autonomous vehicle" developed at the Stanford AI Lab which won the Darpa Challenge in 2005, may indicate that vehicles with at least some such capabilities may be on our roads in, oh, just another decade or two.

The Quest for the $1,000 Human Genome
AI will arrive eventually, but a bet I'd be a lot more confident making for the nearer term is the "$1000 genome" described in this article. The idea is that for the (arbitrarily chosen) price of a mere $1000 the genome of any particular individual could be sequenced. This means, in particular, that all of the potential disease-related genes of the individual would be known, along with genes that affect (for better or worse) individual reactions to therapeutic drugs. The first complete human genome sequence was produced by the government's Human Genome Project at the cost of only $3 billion (and almost simultaneously by the Celera Genomics company for only $300 million). This was essentially complete just 3 years ago, in 2003. Now it is estimated a complete sequence would cost only $10 million -- a factor of 30 improvement over the Celera work in only 3 years. But a cost reduction by a factor of 10,000 is still needed. How long will that take? 15 years, maybe, 20 at most? Together with the evolving knowledge of what genes make us more susceptible to cancer, Alzheimer's disease, diabetes, etc., this will make a really significant difference in our lives. Heck, it might be worth the price even at $10,000. After all, if you're diagnosed with cancer, you're probably talking medical bills above $100,000 or more. Knowing your actual genome might help dodge the cancer entirely. How much is your life worth?

Team Invents Fast, Flexible Computer Chips On Plastic
The range of small, hand-held electronic devices now available, like MP3 players, advanced cell phones, and digital cameras, is certainly impressive. Such devices now have the computational ability and memory capacity of computers that occupied entire rooms only 30 years ago -- a thousand times the memory capacity in some cases. This is an aspect of "ubiquitous computing", where computers disappear into the innards of common objects like coffee makers or telephones. But this trend has a lot farther to go, and it is due to be accelerated when electronic circuits no longer need to be fabricated on silicon chips but instead can be "printed" onto more convenient materials such as glass, plastic, or other flexible substances. The research described in this article is aimed at this goal.

A New BEC Magnetometer
A Bose-Einstein condensate is a state of matter that exists only at temperatures very near absolute zero. It forms when a large number of individual atoms (which must be "bosons") all fall to the lowest quantum state. BECs have been created in the laboratory only since 1995, and have remained largely of theoretical interest -- until now. The article reports on "the first application for Bose-Einstein condensates (BECs) outside the realm of atomic physics." In this case, the measurement of very small magnetic fields. There will certainly be other applications, such as in nanoscale optics and, quite possibly, in quantum computing.

Rice Scientists Unveil 'Nanoegg'
The article is about "asymmetric specks of matter whose striking optical properties can be harnessed for molecular imaging, medical diagnostics, chemical sensing and more." This is just one of a very large number of recent developments in the field of nanotechnology. Traditional media have carried many alarmist articles about the potential health dangers of nanoparticles that come in contact with human bodies. Much of that alarmism is rather beside the point, since (as here) the potential applications use nanotechnology safely encapsulated within high-tech medical or industrial devices that the pubic has no actual interaction with.

Connect the Quantum Dots
A quantum dot is another product of nanotechnology which already has significant applications, such as biomedical sensing devices and the blue lasers used in high-density DVD recording. They may very well be used, also, in quantum computing. A quantum dot is an aggregate of 100 to 100,000 atoms confined to a region with a diameter of 2 to 10 nanometers. Such an aggregate behaves like a single atom, which can assume discrete energy levels. This means that, among other things, quantum dots can absorb and emit distinct wavelengths of light, and hence are capable of flourescing with specific colors. The article here is about the use of quantum dots to replace conventional organic dyes in biomedical applications.

Add Nanotubes And Stir
Yet another, and well-publicized, product of nanotechnology is found in carbon nanotubes. A vast amount of research and development work is going on in this area. One application is nanoelectronics, where nanotubes are used to construct electronic devices at nanometer scales. They are also being used to make composite materials by mixing them with organic polymers. Such composites can have exceptional strength, toughness and electrical conductivity. The problem is that the composites have to be made with great care. The research here is about using just the right amount of force in mixing the composite in order to achieve the desired properties.


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Tangled Bank #59

Wednesday, August 2, 2006

Welcome to Tangled Bank #59 at Science and Reason.

I assume you all know what this is about -- why else would you be here? (But if not, you can read more here.)

Before we begin, I have a question for the audience. As far as I can tell, from just noting links to carnivals at other science blogs, as well as a little more focused research at the Blog Carnival index, there doesn't seem to be any carnival of bloggers writing about the physical sciences in general -- mathematics, physics, astronomy, cosmology, chemistry, Earth science, and all that. Or about advanced technology as a whole -- stuff like nanotech, artificial intelligence, robotics, quantum computing, etc. The Tangled Bank is wonderful for the life sciences and allied fields like medicine, neuroscience, biotechnology, etc. It even graciously accepts articles from the physical sciences and technology, though they are few in number. But still....

The question is: are there readers out there who'd like to see a similar carnival for physical sciences and technology, as well as bloggers who'd like to contribute? If so, I'd be willing to work on organizing such a thing. All that's needed are bloggers who'd like to contibute articles (or nonblogging readers who find articles by others to recommend). If interested, contact me: cgd AT scienceandreason.net. I can host the first couple or three editions. Volunteers to host are also welcome, of course.

Check back here at Science and Reason in a week or three to see what, if anything, comes of this. If it happens, there will be a link for more, somewhere on this page.

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And now, to this edition's submissions. They're ordered loosely by date of receipt, as modified arbitrarily and capriciously by stream of consciousness.

GrrlScientist at Living the Scientific Life reviews Birds of Washington State, by Brian Bell and Gregory Kennedy. I guess she really liked it, as she says it "is the most user-friendly bird field guide I've seen." She also notes that "To encourage beginners to learn the proper vocabulary, scientifically accurate descriptive terms are often used as well, and are defined with a reference illustration in the glossary." I wish that could be said for all science books aimed at a general audience.

Speaking of birds, how can we not raise the subject of bird flu? Fortunately, Tara Smith of Aetiology reports on a study about how easy it is for humans to become infected with a type of avian influenza (not H5N1). The tricky part is, they may not show any symptoms of infection, which is both good and bad.

Since birds are natural predators of bugs, even if butterflies could read, they might not be too keen on bird books. However, we have predation (partially) to thank for the marvelous variety of life forms, including butterflies. David Winter of Science and sensibility examines detailed questions about evolution and speciation driven by predation in his article Did forest islands or Dr Moreau's Island generate the present day distribution of Heliconius?

More about bugs. André Brown -- a physics grad student interested in biology -- writes at Biocurious about a large deceased insect he found on campus. Though he has no pretensions of being an entomologist and couldn't identify the bug, he applied the tools of his trade -- in this case, an atomic force microscope -- to the wings of the subject at hand. In Insect Wing Nanostructure he shares the resulting image and the questions it raises.

Jeremy Bruno at The Voltage Gate offers another essay in a series on why spiders aren't insects, and in the process gives a clear introduction to cladistics.

Darren Naish at Tetrapod Zoology invites us to learn more about peccaries (which aren't insects either). Very educational. I mean, did you know that "Collared peccaries release an odour like cheese or chicken soup"? No word on what they taste like, though.... Limburger? Consommé of Rhode Island Red?

Let's talk more about comestibles. Budak, at The annotated budak (natch), warns us of the impending crisis possibly facing bananas, while holding out hope due to the efforts of small-scale growers devoted to varieties less familiar than the common (U. S.) supermarket banana.

Regarding another sweet -- but healthy -- treat, Joe Kissel at Interesting Thing of the Day writes about honey as medicine. Besides soothing sore throats, it may help to heal wounds, prevent tooth decay, and perhaps even reduce the risk of heart disease.

And still on the topic of stuff to eat, Coturnix at Blog Around the Clock educates us about why, from an evolutionary point of view, peppers are hot stuff. As to why some humans are especially fond of incindiary edibles, check back later... an article on that is promised.

Jim Cambias at Science Made Cool ponders the reasons that motivate people to engage in the Search for Extraterrestrial Intelligence (SETI). A number of good reasons are adduced (William Proxmire be damned). But it seems to me that there's a simple and obvious reason -- the same as what motivates most pure science -- curiosity. And maybe a less obvious reason, too: humans seem to be encumbered with an inferiority complex (perhaps well-deserved) that goads them to seek sentient beings "higher" or more advanced than humans. Same thing that explains religion and Star Trek fandom too. Y'know, you read the daily news and think surely there has to be something out there smarter than humans....

We see this same fascination with space aliens in the occasional temptation to interpret mysterious archaeological finds as alien artifacts. Or at least, as prehistoric astronomical devices. Martin Rundkvist at Salto Sobrius is inclined to take a skeptical attitude towards such interpretations.

But another archaeologist does not eschew the romance of the subject. The most estimable Oxford University Press, without which our reading choices would be much diminished, has its own blog -- affording authors the opportunity to tout their latest labors of love. Veteran archaeologist Brian Fagan does so in a bittersweet reflection on the contrast between famous archaeological sites as they were on his first visit and now, when they suffer from an excess of cultural tourism.

Speaking of extraterrestrial life, has any reader not wondered what forms the critters of an alien planet might assume? Perhaps there are clues in the very alien life forms that were crawling around in our own seas more than half a billion years ago during the "Cambrian Explosion". I was first really aware of these through Simon Conway Morris' book Crucible of Creation. Some stunning illustrations by Yukio Sato in that book. Could extraterrestrial creatures be much weirder than Anomalocaris, Wiwaxia, or Hallucigenia? You need not buy the book to see what I mean. Just take a look at this illustration by Carel Brest van Kempen at Rigor Vitae.

One thing you notice in these illustrations of Cambrian critters is that most have symmetries, at least approximately, of some sort or another. Some are rotationally symmetric about an axis (though seldom with discrete rotations like the 5-fold symmetry of many starfish). A very few are spherically symmetric. Only a small number have little or no symmetry (like a saguaro cactus). But the most common (approximate) symmetry is mirror symmetry across a plane -- bilateral symmetry. How such symmetry arises in the animal's development from a roughly spherical blastula is a fascinating topic. It comes about from the breaking of the original symmetry due to the asymmetric expression of genes. And that's what PZ Myers of Pharyngula discusses in his article, Ancient rules for Bilaterian development.

But returning again to extraterrestrial life, Steinn Sigurðsson at Dynamics of Cats is vexed by the possibility that alien cows don't fart. This is a problem, you understand, since Steinn is concerned with biosignatures which might be detected on an extrasolar planet to indicate the presence of life. Methane is an example. Unfortunately, that would be possible only with carbon-based life. What signatures could we look for to indicate life with some non-carbon chemistry?

Motivated by this story by Nicholas Wade in the New York Times, Hsien-Hsien Lei at Genetics and Health invites you to respond to a poll on the question: how much would you pay for your DNA sequence? (And incidentally, for the uninitiated, there's a trick to getting permanent links to NYT articles -- here.)

Dougal Stanton gives us a nice, elementary introduction to hash functions. <rant>Apologies to Dougal, but as a mathematician I can't help venting about a pet peeve of mine: writing about mathematics without actually showing, you know, any real math. The metaphor of "fingerprints" is very good for giving an intuitive sense of what hash functions are about. But how much would it hurt to add a paragraph with a simple example of how such a function is computed? It need not involve anything more than simple arithmetic. Must we really perpetuate the misapprehension that "math is so haaaaard"? </rant>

Phil Plait of Bad Astronomy asks the question on everyone's mind these days: Is the government trying to kill us? Actually, he's thinking about the apparent circumvention of good science in the process by which the FDA approves new drugs. Let me just submit that there may be a difference here in the way that the drugs of large pharmaceutical companies are treated vs. the drugs of small, impecunious biotech companies (which can't wield sufficient inside influence). Yet the FDA has also been known to deal roughly even with large pharma companies, as for instance the rocky road to approval experienced by the cancer drug Erbitux of Bristol-Myers and ImClone. No big deal, you say? Well, it was enough to land the CEO of ImClone and his pal Martha Stewart in the slammer (for financial, not scientific, misbehavior).

"Life extension" as a scientific study has an aroma of controversy about it, not unlike, say "artificial intelligence". Not just about its aims and methods, but even about its status as a science. Writing at the pro-life-extension Fight Aging site, "Reason" argues here for investing in explicit life extension research. Related essays here and here and here supplement the argument.

An appreciative reader nominated Peter Pesic's essay on why the sky is blue. The question is older, and the answer less clear-cut, than you probably suppose.

John Wheaton, of Wheat-dogg's world, is a teacher of physics. In Gravity deniers and the gravity of ignorance he describes his experiences interacting at another blog with science skeptics -- people who mistrust or deny even fundamental and well-accepted principles of physics and gravity. His reflections suggest that, while knowledge is power, ignorance is also very powerful. Although skepticism is a fundamental part of the scientific method, another part of the deal is that skepticism has to yield in the face of accumulated evidence that supports a particular model of the world. Unfortunately, this cannot help convince people who don't understand the model and are ignorant of the evidence. Doesn't matter whether it's the theory of gravity or the theory of evolution.

Pedro Beltrão, at Public Rambling, has metathoughts of a different kind about the scientific process. He's concerned about the waste and inefficiency of different research groups working on the same problem with little communication among them. In Opening up the scientific process he sketches how some kind of "open science" might work.

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That's all folks. The next edition of Tangled Bank will be August 16 at FrinkTank. Submissions may be sent here.
 

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