Big bad scientific publishing groups

Mike Dunford (The Questionable Authority) launched into a tirade against big scientific publishers whose pricing structures have forced many university libraries to cut back on journal subscriptions, thus hampering the ability of many scientists to work effectively. He makes this comparison:

[T]he situation that I've described with journal prices is similar to the gasoline analogy I presented. Both are necessities (at least under certain circumstances). Both have been increasing in price. And the providers of both are making large profits, while their customers suffer.

That's where the analogy ends, though, because scientists are not only the end customers for journals, they're also the people who provide the content. For free. If you want to continue the analogy, you'd have to pretend that during the whole time that gas prices and profits have been rising you were spending five or ten hours a week working on an oil rig, and that you're doing it without pay.

…

The relationship between publishers and the scientific community is not a partnership. It's parasitic.

More on healthcare

Last week, Jonathan Oberlander was interviewed on NPR's Fresh Air about his article in the 21 August issue of NEJM (New England Journal of Medicine) covering the health care policy positions of the two major Presidential candidates. In both the article and the interview, Oberlander outlines the details of each candidate's plan and offers a balanced view of the pros and cons of each. Definitely worth a read and a listen.

One of those days

You wake up, skim the headlines delivered to your inbox, and end up reading about Russian skittishness about NATO ships in the Black Sea followed by this interview (emphasis mine):

AMY GOODMAN: Can you talk about significance of this, in terms of nuclear warfare in Russia? Do we have anything to fear along those lines?

COL. SAM GARDINER: Absolutely. Let me just say that if you were to rate how serious the strategic situations have been in the past few years, this would be above Iraq, this would be above Afghanistan, and this would be above Iran.

On little notice to Americans, the Russians learned at the end of the first Gulf War that they couldn’t—they didn’t think they could deal with the United States, given the value and the quality of American precision conventional weapons. The Russians put into their doctrine a statement, and have broadcast it very loudly, that if the United States were to use precision conventional weapons against Russian troops, the Russians would be forced to respond with tactical nuclear weapons. They continue to state this. They practice this in their exercise. They’ve even had exercises that very closely paralleled what went on in Ossetia, where there was an independence movement, they intervene conventionally to put down the independence movement, the United States and NATO responds with conventional air strikes, they then respond with tactical nuclear weapons.

I feel so much safer, now that the Cold War has ended.

Tell me a story

Via Alex Palazzo (The Daily Transcript), one of the best commencement addresses I have ever heard, delivered by Robert Krulwich at Caltech earlier this summer. In it, he issues a challenge to those working in science and engineering:

When you are asked "What you are working on?", should you think, "There's no I way I can talk about my science with this guy, because I don't have the talent, I don't have the words, I don't have the patience to do it. It's too hard. And anyways, what's the point?"

…

[In writing his Principia,] Issac Newton didn't care to be understood by average folks. But here's the argument I want to make to you guys this morning. You're not going to hear this advice often; I suggest you may never here it again. When asked about your work, do not do what Isaac Newton did. No, no, no!

When a cousin or an uncle or a buddy comes up and asks you "So, what are you working on?", even if it's hard to explain, even if you know they don't really want to hear it (not really), I urge you to give it a try. Because, talking about science, telling stories to regular folks, is not a trivial thing. Scientists need to tell stories to non-scientists because science stories, and you know this, have to compete with other stories about how the universe works and how the universe came to be. And some of those other stories -- Bible stories, movie stories, myths -- can be very beautiful and very compelling. But to protect science and scientists (this is not a gentle competition), you've to get in there and tell yours, your version of how things are and why things came to be.

…

[T]here is a tension here among scientists between two kinds of truth: math and narrative. But the job that we face, and I should come clean with you and tell you what's really on my mind here, is to put more stories out there about nature that are true and complex -- not dumbed down -- but still have the power to enthrall, to excite, to remind people there's a deep beauty, a many-level beauty, in the world. And what scientists say is not their off-hand opinion; it's hard won information. It's carefully hewn from the world. It's not the bunch of ideas from a tribe of privileged intellectuals who look down on everybody…But it's my sense that if more scientists wanted to, they could learn how to tell their stories with words and pictures and metaphor, and people will hear and remember those stories and not be as willing to accept the other folks' stories. Or at least, there will be a tug of war. And I think the science stories will, surprisingly, win.

Basics: Groups, Rings, and Fields

In talking about Keith Devlin's call to stop teaching multiplication as repeated addition, I mentioned that multiplication is one of two basic operations defined for a type of algebraic structure called a ring. However, I realized I never explained what that statement means, and in this article, I hope to remedy that by explaining what rings and their related structures (groups and fields) are and why we care about them.

Background concepts

Before getting into groups, rings, and fields, we have to first understand the concepts of sets and binary operations. Mark Chu-Carroll has written a great introduction to set and set operations, but I'll provide a condensed version here.

Intuitively, a set is a well-defined collection of mathematical objects (e.g., numbers, matrices, or functions). We use the term "well-defined" so we can tell whether some arbitrary object is a member or element of a set; the notation "a ∈ S" simply says that object a is an element of set S. A set is non-empty if it contains at least one element.

I should point out that a formalism called axiomatic set theory provides a stricter definition for the term "set" that helps avoid certain paradoxes that would otherwise occur when working with sets. However, for purposes of this article, the simple and intuitive definition of "set" provided above will do.

A binary operation or binary relation on S (represented by a symbol like ◊) is a rule for taking two elements from a set S (call them a and b) and combining them to get a third object (call it c); we write this as "c = a ◊ b". Notice that there is no intrinsic requirement for c to be an element of S. However, if combining any pair of elements of S using the operation ◊ always results in an object that is also an element of S, then we say that "S is closed under ◊". Mathematically, we say "S is closed under ◊ if and only if for all a ∈ S and b ∈ S, a ◊ b ∈ S."

A algebraic structure consists of one or more sets closed under one or more binary operations that satisfy certain conditions.

Defining groups, rings, and fields

One of the simplest algebraic structures is a group, which consists of a non-empty set S and a binary relation on S (written as ◊) that satisfies the following conditions:

1. Closure under ◊: For all a, b ∈ S, a ◊ b ∈ S.
2. Associativity of ◊: For all a, b, c ∈ S, (a ◊ b) ◊ c = a ◊ (b ◊ c); i.e., the order in which we apply ◊ doesn't matter.
3. Existence of an identity element: There is some element e ∈ S such that for all a ∈ S, a ◊ e = e ◊ a = a.
4. Existence of inverse elements: For every element a ∈ S, there is some element a^-1 ∈ S such that a ◊ a^-1 = a^-1 ◊ a = e. The element a^-1 is called the inverse of a.

A group defined in this way is written using the notation (S, ◊).

There are two things to notice. First, the definition of a group requires us to provide or define the operation ◊; in other words, saying "Set S is a group" without saying anything about some binary relation on S is a meaningless statement. Second, the definition of a group does not require ◊ to be commutative; that is, we don't require that a ◊ b = b ◊ a for all a, b ∈ S. If ◊ does commute, then the group (S, ◊) is called a commutative, or Abelian, group.

A familiar example of a group is the set of integers Z = {…, -2, -1, 0, 1, 2, …} under ordinary addition (i.e., the addition taught in elementary school). For this group, the identity element is 0, and the inverse element of a given integer, a, is the negative of that integer, −a.

Like a group, a ring is a type of algebraic structure, but defined using two binary operations. The ring (S, ⊕, ⊗) consists of a non-empty set S, a "ring addition" relation ⊕, and a "ring multiplication" relation ⊗ and satisfies the following conditions:

1. Closure under ⊕: For all a, b ∈ S, a ⊕ b ∈ S.
2. Closure under ⊗: For all a, b ∈ S, a ⊗ b ∈ S.
3. Commutativity of ⊕: For all a, b ∈ S, a ⊕ b = b ⊕ a.
4. Associativity of ⊕: For all a, b, c ∈ S, (a ⊕ b) ⊕ c = a ⊕ (b ⊕ c).
5. Existence of an identity element for ⊕: There is some element z ∈ S such that for all a ∈ S, a ⊕ z = z ⊕ a = a. The element z is called the additive identity or the zero element of the ring.
6. Existence of inverse elements for ⊕: For every element a ∈ S, there is some element x ∈ S such that a ⊕ x = x ⊕ a = z. The element x is called the additive inverse of a.
7. Associativity of ⊗: For all a, b, c ∈ S, (a ⊗ b) ⊗ c = a ⊗ (b ⊗ c).
8. Distributive law of ⊗ over ⊕: For all a, b, c ∈ S, a ⊗ (b ⊕ c) = (a ⊗ b) ⊕ (a ⊗ c) and (b ⊕ c) ⊗ a = (b ⊗ a) ⊕ (c ⊗ a).

As noted above with the definition of a group, saying "S is a ring" without defining both the ⊕ and ⊗ relations is a meaningless statement. Also, notice that the ring multiplication relation ⊗ need not be commutative; because of this, the order in which we write the terms in the distributive law (#8) above matters. If ⊗ is commutative, then the ring is called a commutative ring.

A field is a ring that satisfies two additional conditions:

1. Existence of an identity element for ⊗: There is some element u ∈ S, u ≠ z, such that for all a ∈ S, a ⊗ u = u ⊗ a = a. The element u is called the multiplicative identity or the unity element of the ring. Note that the multiplicative identity and the additive identity cannot be the same element of S.
2. Existence of inverse elements for ⊗: For every element a ∈ S, a ≠ z, there is some element a^-1 ∈ S such that a ⊗ a^-1 = a^-1 ⊗ a = u. The element a^-1 is called the multiplicative inverse of a.

The set of integers Z under ordinary addition and ordinary multiplication, written (Z, +, ×), form a ring. In this ring, the integers a and −a are additive inverses of each other, 0 is the additive identity, and 1 is the multiplicative identity. However, (Z, +, ×) is not a field because, except for the case a = 1, the multiplicative inverse of a ∈ Z is not a member of Z; e.g., the multiplicative inverse of 2 is 1/2, which is not an integer.

The set of real numbers R under ordinary addition and ordinary multiplication is a field (and thus a ring as well). The additive inverses, additive identity, and multiplicative identity are the "same" as those for integers. However, unlike the integers, the multiplicative inverse r^-1 of every non-zero real number r ∈ R is itself a member of R.

What Devlin was talking about

Looking at the definition of a ring above, you can see (fairly easily, I hope) what Devlin meant when he said that multiplication is not repeated addition, but is instead another "basic operation" you can perform on numbers. Nothing in the definition of a ring requires us to assert that ring multiplication is repeated ring addition; in fact, the definition of a ring requires no relation between multiplication to addition, except through the distributive law.

Devlin's arguments boil down to this: Because rings are typically the structures through which mathematicians understand the numbers we commonly deal with (e.g., the integers, rationals, reals, and complex numbers) and because of the way a ring is defined, teachers should not introduce a concept (multiplication = repeated addition) that really isn't there.

Why care about groups, rings, and fields?

From a pure math perspective, proving statements using only the definitions above automatically tells us the properties of a large range of mathematical objects of interest. For example, using only the definition of a field, we can show that the additive and multiplicative identities must be unique, as must the pairs of additive and multiplicative inverses (i.e., each element of a field has a unique additive and a unique multiplicative inverse). Thus, even though the rules for adding and multiplying numbers, matrices, and functions differ, we know that so long as these sets and their operations form a field, the uniqueness properties of identities and inverses must hold. Without such broad theories, every time a new field is defined, we would have to go back and prove these uniqueness criteria using a different set of rules.

Moreover, the theory underlying these structures has played a key role in the mathematical development of modern science, ranging from physics and chemistry (which rely on group theory to understand the symmetries found in nature) to computer science and electrical engineering (which rely on group theory to develop the coding systems used in encryption and digital communication systems). Without these algebraic structures, many of the results that present day scientists and engineers depend on would have been difficult, if not impossible, to derive and understand.

What the heck is multiplication anyways?

Speaking of misusing words, Keith Devlin issued a call to teachers to stop teaching multiplication as repeated addition, and instead, to teach multiplication simply as one of the basic operations we can apply to numbers. The crux of Devlin's argument is the following:

Multiplication simply is not repeated addition, and telling young pupils it is inevitably leads to problems when they subsequently learn that it is not. Multiplication of natural numbers certainly gives the same result as repeated addition, but that does not make it the same. Riding my bicycle gets me to my office in about the same time as taking my car, but the two processes are very different. Telling students falsehoods on the assumption that they can be corrected later is rarely a good idea. And telling them that multiplication is repeated addition definitely requires undoing later.

Of course, Devlin is right in that what multiplication really is is one of two operations defined for a algebraic structure called a ring. He is also correct in asserting the need to undo the perception of multiplication as repeated addition, especially when it comes times to multiply things like complex numbers, matricies, or functions.

However, Mark Chu-Carroll and Jason Rosenhouse both highlight a key problem: Devlin really doesn't really provide any real answers as to what to teach elementary school students when they first encounter multiplication. They correctly point out that taking an approach other than "multiplication is repeated addition" would likely fail to build students' intuitions about what multiplication is and how to carry out the mechanics of the process.

To a certain extent, I disagree with Devlin that continually "redefining" the rules of multiplication leads to frustration and "thinking mathematics is just a bunch of arbitrary, illogical rules that cannot be figured out but simply have to be learned"; like Jason Rosenhouse, I think most of the frustration comes from the fact that mathematics forces us to think using specific abstractions we aren't entirely comfortable with. Moreover, I (and I suspect many others) do eventually stop considering multiplication to be repeated addition without really thinking about it. For me, this unconscious transition happened when I started working with formulae that involved units, such as those from physics. By that point, it was no longer clear how repeatedly adding two kinds of units (e.g., mass and acceleration) gave a third kind of unit (e.g., force), and multiplication became a basic operation performed on two numbers to get a third number.

On the other hand, like Devlin, I'm not a fan of the lie to the children approach to teaching, primarily because doing so leaves "brain bugs" that are notoriously hard to get rid of. Going back to Devlin's argument, defining multiplication as repeated addition implies that the inverse operations are related as well, i.e., that division is repeated subtraction; as we discovered one day at work, this leads to enormous complications when trying to explain certain things, like why dividing by zero is undefined. Another good example Devlin points to is the teaching of exponentiation as repeated multiplication; because this "definition" has been beaten into my head, I have tremendous difficulty understanding what matrix exponentiation (i.e., e^A where A is some matrix) really means.

I'm not entirely sure as to what to make of all this. Devlin wrote a follow up article, saying essentially "however you teach it…, don't do anything that is counter to the way the mathematicians do it." While I agree in principle, I'm still not sure how to translate this to the classroom. So far, the only good solution I can think of is simply to attach and repeat a caveat like this when teaching multiplication:

Aside from addition, the other thing we can do with numbers is to multiply them. When working with the counting (natural) numbers, multiplying works like adding over and over again. But multiplying and adding over and over again are not always the same thing, as you will see in higher grade math.

Not the way to recruit new engineers

Via Chad Orzel, this laughably silly billboard:

Matthew Yglesias provides the only comment necessary: "If anything, characterizing the sex-engineering link in this manner seems overwhelmingly more likely to reduce interest in engineering than to reduce interest in sex."

Articles on teaching evolution

The New York Times recently ran two good articles on the teaching of evolution. First, Olivia Judson's op-ed makes arguments for teaching evolution. Two of the arguments Judson made I especially like. The first is the scientific argument that evolution is one of, if not the, organizing principle of modern biology:

[Evolution] provides a powerful framework for investigating the world we live in. Without evolution, biology is merely a collection of disconnected facts, a set of descriptions. … Add evolution — and it becomes possible to make inferences and predictions and (sometimes) to do experiments to test those predictions. All of a sudden, patterns emerge everywhere, and apparently trivial details become interesting.

The second is a more philosophical argument as to why we should bother doing science in the first place:

It’s that the endeavor [of studying evolution] contains a profound optimism. It means that when we encounter something in nature that is complicated or mysterious, such as the flagellum of a bacteria or the light made by a firefly, we don’t have to shrug our shoulders in bewilderment.

Instead, we can ask how it got to be that way. And if at first it seems so complicated that the evolutionary steps are hard to work out, we have an invitation to imagine, to play, to experiment and explore. To my mind, this only enhances the wonder.

This sense of wonder, this sense that if we imagine and play and experiment and explore enough, we can really figure out how this universe is put together, is the main reason why I, and many like me, became a scientist in the first place. And it's also one reason why I react so strongly against Creationism: because saying "God did it, and that's all there is to it." is vacuous and intellectually unsatisfying, and ultimately robs us of this sense of wonder.

The second NY Times article is more depressing, covering the efforts of David Campbell, a Florida high school teacher trying to teach evolution to a group of skeptical kids. It really quite impressive to see how Campbell walks that fine line of teaching the science while trying to avoid alienating kids entirely by "[forcing] them to look at themselves in the evolutionary mirror".

I had the unfortunate experience of having a high school biology teacher who was a Creationist. While picking apart his arguments in class was good fun (especially when it came to that asinine second law of thermodynamics "argument"), it really was disturbing to have a science teacher publicly deny and denigrate to core principles of the science he was purportedly "teaching".

I can somewhat understand why people are scared (if that is the right word to use) of evolution, and of science in general. Science tells us certain uncomfortable facts about the reality in which we live, that perhaps we aren't as unique as we imagine ourselves to be, being fairly ordinary animals living on a fairly ordinary planet orbiting a fairly ordinary star in the corner of some fairly ordinary galaxy.

But science does not say that we cannot make ourselves special. And it certainly does not say, contrary to what Creationists seem to believe, that we should abandon all moral and ethical precepts. Science merely is a tool by which we can understand how the universe works.

Hat tip to Jason Rosenhouse (EvolutionBlog) for pointing out the Judson op-ed.

The color of stars

Phil Plait (Bad Astronomy) explains why there are no green stars. The short version:

[T]he only way to see a star as being green is for it to be only emitting green light. But as you can see from the graph above [showing the broad spectrum of emitted light], that’s pretty much impossible. Any star emitting mostly green will be putting out lots of red and blue as well, making the star look white. Changing the star’s temperature will make it look orange, or yellow, or red, or blue, but you just can’t get green. Our eyes simply won’t see it that way.

That’s why there are no green stars. The colors emitted by stars together with how our eyes [and brains] see those colors pretty much guarantees it.

For those who are really interested, Matt Springer (Built on Facts) explains the Stefan-Boltzmann distribution, which provides a reasonable approximation for the intensity of a given wavelength of light given a star's temperature.

Dealing with sexual harassment

Instead of suing, try the female guppy's approach:

...the [female guppies] are segregating the sexes by choosing to spend time in areas where there are high numbers of predators. The brightly-coloured males are far more likely to attract the predators than the dull brown females, so they keep their distance.

Science link dump

In no particular order, five pieces of interesting science:

• Overly well fed oysters compromise their immune systems in pursuit of sex.
• Stopping beams of protons energetic enough to melt half ton blocks of copper at the Large Hadron Collider.
• Calculating the bite force of two species of sharks (the great white shark and the now extinct megalodon) using finite element methods.
• Increasing endurance without exercise by using drugs to alter muscle metabolic processes.
• Studying Drosophila to understand one purpose of sleep: the integration of sensory data and experiences into memory

Energy policy explained

Via CR McClain (Deep Sea News), Stephen Colbert explains off shore drillling and other aspects of energy policy:

Choice quote (towards the end): "Hey, it's your choice. [You can either play] the game that doesn't exist yet [alternative energy] or the one that destroys your furniture [offshore drilling]."

Why even bother

Ed Brayton (Dispatches from the Culture Wars) writes about how the Pentagon may ignore tribunal verdicts and continue hold Salim Hamdan even after his prescribed sentence has been served. I have seriously wonder sometimes whether our government is run by a bunch of six year olds: "Oh no, I don't like the way this game is going, so let's change the rules."

One quote from the Washington Post article succinctly summarizes my feelings about the situation:

"We had a court. We had a jury. It was a military jury. They heard the evidence. They gave him five months," Hollander said. "That ought to be his sentence. Either we believe in American justice or we don't."

Enabling the Georgian War

Juan Cole writes in Salon about how the Bush administration's cavalier attitude towards international law is coming back to haunt the U.S.:

An emboldened Russian Prime Minister Vladimir Putin sarcastically likened Russia's actions [in Georgia] to Bush's foreign policy.

…

In the run-up to the Iraq war, Bush officials repeated ad nauseam the mantra that Saddam Hussein had killed his own people. Thus, they helped create a case for unilateral "humanitarian intervention" of the sort Putin says Russia is now pursuing.

…

Indeed, Putin's invoking Bush's Iraq adventure points directly to the way in which Bush has enabled other world powers to act impulsively. With his doctrine of preemptive warfare, Bush single-handedly tore down the architecture of post-World War II international law erected by the founders of the United Nations to ensure that rogue states did not go about launching wars of aggression the way Hitler had. While safeguarding minorities at risk is a praiseworthy goal, the U.N. Charter states that the Security Council must approve a war launched for this purpose or any other, excepting self-defense. No individual nation is authorized to wage aggressive war on a vigilante basis, as Bush did in Iraq or Russia is now doing in the Caucasus.

This, of course, is the same "moral high ground" argument used against allowing torture. Once that U.S. cedes that ground, it is only a matter of time before another state attempts to use that argument in a manner we don't entirely approve of.

Just in time for the start of school

A new hobby:

"You keep using that word."

"I do not think it means what you think it means." Meghan Daum writes in the Chicago Tribune about misuse of the word "nonplussed", which in the common parlance, has come to mean "unfazed, unperturbed or unconcerned", even though its proper definition (as provided by the Oxford English Dictionary) is "surprised and confused". Similarly, the word "peruse" is commonly used in the sense of "to skim or to read over quickly" even though its proper definition is "to read thoroughly or carefully."

This phenomena, of course, is simply the evolution of language through what linguist Mark Liberman calls "change by mistake", though embarrassingly, I have to admit to misusing both these words.

I bring this up because (1) it's amusing and (2) it serves as a reminder as to how difficult processing language can be, especially from a computational (read "natural language processing") standpoint. In a world where words can acquire meanings quite contrary to what appears in a dictionary, how are humans, let alone computers, expected to truly understand the semantics of an ambiguous statement such as "He was nonplussed by the situation."? In a world where we are allowed to take a Humpty Dumpty-esque approach to language ("When I use a word, it means just what I choose it to mean -- neither more nor less."), I'm not entirely convinced that we will ever reach a point where NLP has anything but domain specific applications.

The biology of the very small

Moselio Schaechter (Small Things Considered) describes some of the smallest eukaryotes in the world, the picoeukaryotes. These organisms are so small that they contain only one each of the major organelles (chloroplast, mitochondrion, Golgi body, etc.); however, they play major ecological roles by producing a large fraction of the photosynthetic output at the bottom of oceanic food chains.

Elsewhere on the web, Ed Yong reviews a Nature letter describing a virophage named Sputnik, which acts as a parasite on a larger mimivirus, hijacking the host virus' machinery to make copies of itself.

Finally, Mo (Neurophilosophy) describes kuru, a prion induced neurodegenerative disease characterized by loss of motor coordination and spread, in large part, by "ritualistic mortuary cannibalism". The article provides a great introduction to prion diseases (and other diseases caused by protein misfolding such as Alzheimer's). It also raises the question of whether we may see a sudden outbreak of Creutzfeldt-Jakob disease (the human manifestation of BSE or "mad cow disease"), given the discovery of the long incubation period (up to 50 years) of kuru and related diseases.

Now, go read.

Is anyone really surprised?

On Sunday's All Things Considered, host Andrea Seabrook interviewed Masha Lippman, a columnist and political analyst. The last part of the interview has this very telling Q&A:

Andrea Seabrook: Does the way this conflict has unfolded reveal anything about the power relationship between Prime Minister Vladimir Putin and President Dmitry Medvedev?

Masha Lippman: Indeed. During this conflict, Prime Minister Putin, from the statements that he's made, he sounded like he was the higher authority compared to the President of the country. And even though, formally, he's acting on orders of the President, [Putin] certainly looked as if the decisions were his. He was the first to appear on the Russian television. He certainly has looked through this conflict so far as the person who's taking decisions.

Really now? Is anyone all that suprised that Medvedev is pretty much Putin's puppet? As John Oliver once quipped on The Bugle shortly after Medvedev's election: "Meet Russia's new president -- Vladimir Putin."

Wikipedia for gene annotations

The people over at 23andme describe a proposed project to develop a gene wiki, built on top of Wikipedia. The idea is to provide a gene annotation resource similar to the Entrez Gene that exploits the collective knowledge of "the community", instead of relying on only a few curators. Of course, such a project will be plagued by questions of accuracy, though a 2005 Nature study suggests Wikipedia comes close to the accuracy of Encyclopedia Britannica (not that the NCBI curated databases are entirely accurate in the first place). It will be very interesting to see how this project develops.

For reference, here's the link to the PLoS Biology paper proposing this project.

[Via Coturnix]

Interesting biology

PZ Myers reviews a Nature paper on snake fang development and evolution, while Ed Yong reviews a PNAS paper on binge drinking tree shrews that somehow manage to stay sober.

And in news that illustrates the dynamic and self-correcting nature of science, the 2005 publication of the recovery T. rex soft tissue (see PZ Myers' review) may have been wrong. A recent PLoS ONE paper suggests that the observed structures, originally believed to be blood vessels and red blood cells, may in fact be a bacterial biofilm; Grrlscientist and Tara Smith offer reviews, while the Panda's Thumb post offers discussion, including comments from the first author on the PLoS paper.

On glass

Chad Orzel (Uncertain Principles) points to a New York Times article on the nature of glass and the glass transition. Understanding the structure of glass and how the glass transition occurs is one of the large remaining problems in condensed matter and solid state physics.

Glass, of course, is a solid, insofar as it holds it shape without a container; yet, it exhibits the properties of a liquid in that it lacks any long range molecular structure. To quote the article:

When a liquid solidifies into a glass, [the] organized stacking [of a crystal] is nowhere to be found. Instead, the molecules just move slower and slower and slower, until they are effectively not moving at all, trapped in a strange state between liquid and solid.

Further complicating the issue is the fact that the transition temperature and final structure of a glass is dependent on the rate at which the liquid is cooled. The complexity of the problem has led one physicist working on the problem to joke, "There are more theories of the glass transition than there are theorists who propose them."

In any case, the article provides a great summary of the questions involved in glass and glass transitions and the current theories proposed to address them. Definitely worth a read.

Interesting fact about π

Matt Springer (Built on Facts), in responding to a post on "Good Math, Bad Math", highlights an interesting property of π, namely, that it is (widely believed to be) a normal number.

Roughly speaking, a number x is said to be normal in base-b if its digits exhibit a uniform distribution, such that the asymptotic probability of every length k string occurring within the representation of x in base-b is 1/b^k. For example, for a number normal in base-10, the probability of observing a given digit '0' through '9' is 1/10, while the probability of observing a string of length 3 ('000' through '999') is 1/1000.

We can observe this using the first 1.25 million digits of π from Project Gutenberg and a simple Perl script. If π is a normal number, then the observed frequency of each digit '0' through '9' should be around 10%, which is precisely what we see:

Digit	0	1	2	3	4	5	6	7	8	9
% observed	10.01	9.97	10.01	10.03	9.99	10.03	9.95	10.00	10.00	10.02

Using this same script, we can also observe that within the first 1.25 million digits of π, length 3 strings occur at a frequency of about 1/1,000 and length 4 strings at a frequency of about 1/10,000; this is in line with our expectations that π is a normal number.

Of course, this exercise doesn't actually prove that π is a normal number. To date, no one has proven that π and other "interesting" numbers like e, which we strongly suspect are normal numbers, actually are.

One final comment: While the digits and finite length strings in π appear in a uniform distribution, π and the digits within it aren't actually "random" or "randomly distributed", at least not in the algorithmic sense. This is because fairly simple formulas that will generate the digits of π, though those are the topic for another discussion. I mention this only to highlight the fact that being pedantic about vocabulary does matter when talking about math.

The liberal media

The 13 June 2008 episode of On The Media has an interview with Frank Scandale, who, as editor of The Record of Bergen County, New Jersey, launched a six month "self-examination" after the paper was accused by its readers of being too liberal. The interview itself is interesting, but this quote in particular caught my attention, as it provides a great explanation as to why people tend to think of the media as being "liberal":

BROOKE GLADSTONE: You know, it's been argued that the values of journalism naturally line up with the values of liberalism, in that journalists question authority – at least they're supposed to do that when they're doing their job – that they challenge institutions, that they dig deep into places where they're not supposed to go, that this is sort of part and parcel of the craft.

FRANK SCANDALE: I totally agree. Two points to make is I've written a column basically espousing what you just said, that we tend to be those kinds of people.

I have a letter here from a fellow who said he used to be a newspaper reporter, editor and columnist, and he said, yep, you guys have a liberal paper, albeit one I have never read. How can I know this? Well, and I say this with tongue in cheek, it would never occur to a conservative paper to engage in such introspection.

The short version of this, of course, is Stephen Colbert's quip at the White House Correspondents' Dinner, "Reality has a well-known liberal bias."

Meta funny

To Billy, Steve, and all others sending me LOLcats pictures, I give you this:

[Via Greg Laden's blog]

What does "universal health care" mean anyway?

On the 18 July 2008 broadcast of On The Media, Trudy Lieberman discusses how the press has done a poor job covering the politics and language of healthcare. In particular, she addresses one of the key misconceptions I've heard quite a bit; namely, that when Barack Obama speaks about "national" or "universal" healthcare, he really isn't talking about creating a system like the National Health Service in the UK. Instead,

TRUDY LIEBERMAN: Essentially, what Obama would like to do is craft a plan that builds on private insurance coverage from Aetna, Cigna, Blue Cross and the like, and add to that a public program, a national insurance exchange people might be able to go to and buy coverage. If this entity, this health insurance exchange works, then people will have another option.

Let me say what the lead of an AP story was that I think came very close to describing what Obama is doing; that Obama was proposing universal access to coverage. Access is the key word, as opposed to automatic coverage as a matter of right.

Indeed, in her posting "One Step Forward, One Step Back" on the Columbia Journalism Review blog, Lieberman notes that Obama's position "leaves unanswered the knotty question of whether people will actually be compelled to buy a policy. If they will not, it’s hard to figure where the universality comes in."

Not that McCain's plan is much better:

TRUDY LIEBERMAN: Basically, McCain wants you to pay taxes on the employer provided insurance that you get. And when that happens, he’s going to give tax credits to people, 5,000 dollars for families, 2,500 dollars for individuals, to go into the individual market to buy their own coverage.

It’s likely young, healthy people will leave the employer plan and go into this individual market, leaving only the sick people left in the boss’ insurance, and that will send the premiums through the roof.

What this will do eventually is force a large crack in the employer provided insurance market, and ultimately, people will have to go to the individual market to buy their coverage.

Both the CJR post and the On The Media segment are worth reading/listening to.