Apologies to any Pynchon readers for the delay...

I have to apologize for the fact that I haven't posted any new Pynchon material recently. I still am working on the essay/science primer for Against the Day, however the task has turned out to be more formidable than I first anticipated. The problem is this: there is so much material that could be included in a primer on vectors, quaternions, space-time, etc., much more than I have the time or, in some cases, expertise to cover. In order to keep things focused on the truly relevant science, I must finish a second reading of the book.

I'm well on my way through that second reading, furiously taking notes, and I'm working on various portions of the essay, but it will probably be at least a month before I finish and can post my results.

In the meantime, I highly recommend this book, which I'd bet was one of Pynchon's sources on quaterions and vector analysis (as you can imagine, there just aren't that many books out there on the history of vector analysis): A History of Vector Analysis. It looks like it's hard to find - I picked up a copy from my local university library. I'll leave you with a few choice excerpts from the book that relate to what Hamilton was trying to accomplish with quaternions, and how his efforts were viewed:


p. 37, from an 1857 review of Hamilton's work on quaternions:

"It is confidently predicted, by those best qualified to judge, that in the coming centuries Hamilton's Quaternions will stand out as the great discovery of our nineteenth century."

[In reality, quaternions were eclipsed by vector analysis only a few decades later.]

p. 23-24: From an essay published by Hamilton in 1837, a section called "On Algebra as the Science of Pure Time" (to understand this passage, recall that imaginary numbers are multiples of the square root of -1):

"The thing aimed at, is to improve the Science, not the Art nor the Language of Algebra. The imperfections sought to be removed, are confusions of thought, and obscurities or errors of reasoning; not difficulties of application of an instrument nor failures of symmetry in expression...

"For it has not fared with the principles of Algebra as with the principles of Geometry. No candid and intelligent person can doubt the truth of the chief properties of Parallel Lines, as set forth by EUCLID in his Elements, two thousand years ago... The doctrine involves no obscurity nor confusion of thought, and leaves in the mind no reasonable ground for doubt, although ingenuity may usefully be exercised in improving the plan of argument.

"But it requires no peculiar scepticism to doubt, or even to disbelieve, the doctrine of Negatives and Imaginaries, when set forth (as it has commonly been) with principles like these: that a greater magnitude may be subtracted from a less, and that the remainder is less than nothing; that two negative numbers, or numbers each denoting magnitudes less than nothing, may be multiplied the one by the other, and that the product will be a positive number, or a number denoting a magnitude greater than nothing; and that although the square of a number, or the product obtained by multiplying that number by itself, is therefore always positive, whether the number be positive or negative, yet that numbers, called imaginary, can be found or conceived or determined, and operated on by all the rules of positive and negative numbers, as if they were subject to those rules, although they have negative squares, and must therefore be supposed to be themselves neither positive or negative, nor yet null numers, so that the magnitudes which they are supposed to denote can neither be greater than nothing, nor less than nothing, nor even equal to nothing. It must be hard to found a SCIENCE on grounds such as these..."

[Note in this upcoming section that Hamilton speculates that with geometry as the science of space, perhaps algebra could become the science of time:]

Hamilton asks "whether existing Algebra, in the state to which it has been already unfolded by the masters of its rules and of its language, offers indeed no rudiment which may encourage a hope of developing a SCIENCE of Algebra: a Science properly so called; strict, pure, and independent; deduced by valid reasonings from its own intuitive principles; and thus not less an object of priori contemplation than Geometry, nor less distinct, in its own essence, from the Rules which it may teach or use, and from the Signs by which it may express its meaning..."

He suggests that "the Intuition of TIME is such a rudiment... The argument for the conclusion that the notion of time may be unfolded into and independent Pure Science, or that a Science of Pure Time is possible, rests chiefly on the existence of certain priori intuitions, connected with that notion of time, and fitted to become the sources of a pure Science; and on the actual deduction of such a Science from those principles, which the author conceives that he has begun."

Hamilton here draws a comparison between Euclidean geometry as a pure science of space, and his efforts to make algebra a pure science of time. Historically, and in light of Against the Day, it is interesting to note that Hamilton wrote this before Non-Euclidean geometry became widely known (after 1860, according to Crowe), and long before experiments suggested there was anything wrong with our intuitive notions of time which Hamilton wanted to rely on. In essence, Hamilton's quaternions and Euclidean geometry are part of a classical world that came to an end during the time frame of Pynchon's book. (In the long run, vector analysis and quaternions themselves, instead of being a science of time, became an algebra dealing with space.)

Introducing Indy Science Blogs Part 2

I didn't get a chance earlier to introduce all of the fascinating blogs on the newly launched Indy Science blogs. So here are the rest of the introductions:

If you like robots, astronomy and rocketry, check out Ed at Robot Guy.

Barry Leiba is a researcher at IBM, and he writes about life, politics, and technology issues at Staring at Emtpy Pages.

Emily DeVoto is an epidemiologist who writes about health care and its relationship to the media at The Antidote - check out her recent post on evidence based medicine.

And The Rational Fool writes about...well...er, a whole lot of things - India, bioethics, economice, science, and Richard Dawkins - go check it out.

It's a diverse group, so you're guaranteed to find something you're interested in. Subscribe to the RSS feed and keep up with what's going on in the world of health and science.

John Tierney's Science Blog at the NY Times

John Tierney, a conservative/libertarian/who knows? columnist at the NY Times has started a science blog. I'm usually not very optimistic about pundits commenting on science - the results are rarely good, with one of the worst cases being Gregg Easterbrook. The pundits usually have a muddled grasp of the technical issues and view scientific debate through a deep partisan tint.

However, the NY Times science section has much higher standards than opinion magazines like Slate and The New Republic, and so far Tierney's blog looks interesting. I recommend checking it out.

Is Systems Biology Teaching Us Anything New?

What I find most exciting about basic molecular biology today is the prospect of building a quantitative understanding of how a cell works. Many other scientists are excited about this as well, leading to the current popularity of what's being called 'systems biology.' The idea is that maybe we can understand the design principles behind a cellular process - how the behavior of a cell emerges from all of those detailed physical interactions among proteins, nucleic acids and other components of the cell. If that sounds vague to you, well, that's because it is vague. It's a nice sentiment, but I think biologists still have a hard time defining just what it is we want to learn.

Think of this problem from a historical perspective: biology has several profound organizing theories that have been fantastically useful as explanations for what happens in biological systems. As the geneticist Dobzhansky famously put it, nothing in biology makes sense except in the light of evolution. The same thing holds true for genetics (you don't have adaptive evolution if you don't have genes encoding traits that are passed on from one generation to the next), biochemistry (all organisms are made of molecules that obey the laws of physics and chemistry - not some mysterious substance that transcends physical laws), and molecular biology (DNA makes RNA makes Protein). Each of these theories has been successful by those criteria that define a good scientific theory; for example, they have explained previously mysterious phenomena, they have predicted completely new phenomena that have since been verified, and they have opened up huge new avenues of research. Each one of these theories has changed the way the entire community of biologists operates.

Will systems biology do that? I hope so, but I don't know. It hasn't yet. Let's take the cell division cycle, for example, since it's a process that's near and dear to my heart. It's also a process that is crucial for understanding human disease, notably cancer. How can systems biology help us understand the cell cycle? How can it help us understand and cure cancer?

A recent paper in Nature, from Michael Laub's lab, reports the identification of an "integrated genetic circuit." This is a very nice paper, with a clear set of experiments, that identifies certain interactions among key cell cycle proteins that control division in the bacterium Caulobacter crescentus. The interactions identified in this research explain how it is that a key cell cycle regulator protein, called CtrA, is cyclically switched on and off during the various stages of the cell cycle.

The authors aren't claiming that they are producing a quantitative model, but they use the language of systems biology, notably by calling their set of novel interactions an "integrated genetic circuit." So what then is a non-integrated genetic circuit? How does a biological integrated circuit relate to the integrated circuit used in electronics?

Ultimately, this study, and many others like it, are largely filling in the molecular details of a specific process, something molecular biologists have been doing for decades. Feedback loops and regulatory interactions are valuable, but not new. In some cases, we are getting enough detailed data to build some primitive computer models, but these models are largely descriptive - reproducing what extensive experimental work has already shown.

So is systems biology ever going to amount to something like the paradigm-shifting initiation of molecular biology in the 50's and 60's? Are there any Really Big Questions left in biology, or are we now just finding better, faster ways to fill in the details? I think there are big questions left, but they're still poorly defined and often lost in the flood of genomic research. One telling gap in our knowledge is the origin of living cells from nonliving systems - we can't build a cell from scratch. We don't have the theoretical tools to understand, rigorously, how the first cells could have arisen from available components on the early earth, for example. This suggests that there is more we need to understand about how physical systems can cohere together to produce something that can adapt to its environment and reproduce. Not just molecular details, but new concepts of how physical systems organize themselves.

For now I'm just raising questions, but in future posts I'll discuss how we might go about finding some answers.

Introducing Indy Science Blogs

This blog is part of the newly launched Indy Science Blogs - a group of science bloggers that coalesced in the wake of a mass rejection email from Science Blogs. Science Blogs didn't have the courtesy to blind cc the addresses of all the recipients, exposing our email addresses to dozens of strangers. Some of us strangers got together and formed the brand new Indy Science Blogs.

There are some great blogs at Indy Science Blogs. Visit the site, or check out some of my links to the right to see all the blogs. I'm just going to highlight a few:

The Beauty Brains has fascinating articles on the science of beauty products - if, like me, you like the intersection health and chemistry, or if, unlike me, you use many beauty products, check out this great blog.


Susan, a science writer over at Hug the Monkey writes about how "a single hormone called oxytocin is responsible for life's most fulfilling emotions: love, trust and commitment." Amazingly enough, it is possible to write a blog about a single hormone. Susan has some fascinating material on how the biology of the brain shapes who we are.

Trisha at Women's Health Research News writes about research relating to birth control, pregnancy, osteoporosis, and just about any other health issue that concerns women.

And Sibin at Context Switch is a PhD student in computer science who writes about whatever strikes his fancy, and happens to like Thomas Pynchon as well.

There are more blogs I haven't mentioned - head on over to Indy Science Blogs to see the rest.

And for you newcomers here - what's this blog about? You should know two things about me:

- I am almost completely HTML illiterate, which is why this blog doesn't have any fancy bells and whistles.

- Infant twins + seven-year old = not enough time left for blogging. It's been a hectic year, but now that sleep is more available in our house as the twins get older, I will pick up the pace here at Adaptive Complexity.

Here I write about my interests in the hope that some of those interests overlap with your interests:

- the future of basic research in biology - what do we want to learn now? Is systems biology any good?
- conveying the latest research in genomics to the public who should know about the exciting things that are being done with their tax money.
- science in the media
- science in literature - not science fiction necessarily, but usually the kind of stuff you find in books by Thomas Pynchon or Richard Powers
- book reviews of popular science books
- defending science against absurd claims by anti-evolutionists and other cranks.

So have a look around, and come back for more if you like what you see. And go check out Indy Science Blogs!