In one corner, we have Moore’s law. In the other corner, there is Carlson’s curve.

Moore’s law— named after Gordon Moore, co-founder of Intel—famously predicted over 40 years ago that the transistor density of integrated circuits would double about every two years. So far, it’s been right.

Carlson’s curve—named after biologist Rob Carlson—refers to a graph showing the diminishing cost per base of sequencing DNA over time. Like transistor density, DNA sequencing prowess is similarly exponential, and showing no signs of slowing down.

Of course, neither of these is a fundamental law of nature, only empirical observations, and reality will inevitably deviate from the prediction someday.

So one naturally wonders, if it were a contest, which will hold steady the longest?

If one assumes a conventional mathematics of exponential growth, Moore’s law will be repealed first because it started first (approximately 1965 and 1990 for the two cases), and such a curve always levels off.

Deviations from a standard exponential would most likely come from new discoveries or technological innovation. For Moore’s law, the physical constraint of moving electrons in circuits is certainly limiting, as is the near certainty that a transistor can’t be smaller than a single atom. However, quantum computing or DNA computing might overcome these inherent limits of silicon chips.

For DNA sequencing (or DNA synthesis for that matter), the cost of chemical reagents and the ability to physically resolve DNA fragments cheaply are clearly limiting at some point. However, rapid advances in robotics, miniaturization, and “lab-on-a-chip” technologies can be expected to continue for the foreseeable future.

Based on nothing but the intuition that cost is easier to overcome than physics, my bet is that halving the price tag of DNA sequencing will outlast the course of integrated circuit doubling. Doubtless, readers can present counter-arguments, which I of course welcome and encourage.

Astute readers will recognize that “all the world’s a stage” is a classic metaphor. Shakespeare, in fact, created metaphors by the bushel, this particular one from As You Like It.

Without consulting a dictionary, I would say that a metaphor is a comparison that shows how two things not fundamentally the same have at least one thing in common. The actual dictionary says much the same thing, albeit with more precision. Thus, while not physically a stage, the Bard tells us that much drama is acted out in the world.

The periodic table, that veritable icon of science, has itself been used as a metaphor for countless ideas. So much so that I’ve posted more blogs than on any other subject on what Mendeleev (unintentionally) begat.  (See posts from 14 February 2008, 25 February 2008, 14 April 2008, and 2 October 2008).

And now, combining idioms, comes the Periodic Table of Metaphors, courtesy of artist Christoph Niemann.

Like all periodic tables, the metaphors are aligned into groups with similar properties. There is Group I, “The Classics” (e.g., worm in an apple, hammer and nail, train entering a tunnel), and Group VI, “The Toxics” (piles of money, light bulb, piggy bank). Presumably you want to steer clear of these.

There is also Group IV, “The Zombies,” but since this includes the double helix I think I’d have trouble avoiding it. My favorite is Group III, the “Editors’ Faves” (Swiss army knife, brain, crown of thorns). Presumably I’d have no trouble getting published if I claimed that the Chemical Heritage Foundation is a brainy Swiss army knife.

But the real value of this version of the periodic table, at least according to Niemann, lies not in figures of speech, but in creating conceptual metaphors. There’s no way to describe what he has in mind so visit his Web site to see for yourself. Then announce your ideas so our drama can have “all the men and women merely players” (Shakespeare, ibid).

Moore’s law states that the number of transistors in integrated circuits doubles about every two years. This is why computers keep on getting smaller, why memory chips keep increasing in storage capacity, and why digital cameras keep having more megapixels.

But can Moore’s law hold forever?

Of course not, even though it has held steady for nearly half a century. It’s hard to imagine a transistor being smaller than a single atom, and even Gordon Moore himself has pointed out that exponentials always crash at some point.

The limitation at the moment is the photolithography process that lays down circuit diagrams on silicon chips. Current technology can produce features as small as 45 nanometers. But suppose you could use carbon nanotubes (about tenfold smaller at 4nm in diameter) as the mask for the lithographic process?

You can, at least in principle, thanks to new work from Columbia University chemists. Liu et al. deposited carbon nanotubes on silicon to mask the wafer for etching by hydroxide ions (Journal of the American Chemical Society (2 June 2009), doi: 10.1021/ja903333s). They cajoled the reaction sufficiently to get trenches about 4–6 nanometers deep, but alas ten times as wide.

The authors speculate that the resolution could be improved by clamping down the wandering tendency of the carbon nanotubes through clever chemistry. This would then yield the hoped-for tenfold increase in masking potential over current photolithography.

So Moore’s law may continue to hold for some time to come. With luck, we’ll postpone the inevitable exponential crash just long enough to come up with Moore’s law 2.0.

Who were the most accomplished chemists of the 20th century? Of course such a question is unanswerable in any truly objective way, but that uncertainty doesn’t diminish our interest in speculating about “the answer.”

A couple of engineers at UCLA proposed a methodology for naming the 10 highest achieving physicists for the 20th century prior to World War II (the heyday of modern physics). Their approach is to equate accomplishment with fame, the latter as evidenced by hits on physics Nobel Prize winners in a Google search.

You could surely debate all manner of reasons why this is a wholly bad measurement tool, but the authors do offer some evidence for its veracity. You can check the arguments and the results for yourself, but no doubt you won’t be surprised to see Einstein at the head of the list.

Naturally I wondered about the test being applied to chemists. Here’s the result of the Googleized highest achieving chemists prior to mid-century, starting with number 1: 

1. Marie Curie
2. Fritz Haber
3. Otto Hahn
4. Sir William Ramsey
5. Francis W. Aston
6. Wilhelm Ostwald
7. Emil Fischer
8. Heinrich Wieland
9. Carl Bosch
10. The Svedberg

(For readers who think they know the history of chemistry: for how many of these chemists can you describe their work?)

If you add in the second half of the 20th century, Linus Pauling would break in the list as number 9 and Robert Woodward as number 6. In my book Pauling is in the running for number one, throwing some doubt on the method.

But guess who appears on the top ten lists in both physics and chemistry? Marie Curie, who is also the only woman on either. Go, Marie!