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Back in May, Malcolm Gladwell wrote In the air, a piece in the New Yorker about how many big ideas seem inevitable. While we (rightly) attribute the moniker “genius” to many of the people who have invented or discovered important things in history, Gladwell argues that others would have almost surely come up with the same (or similar) ideas in short order, what science historians call “multiples”. A number of examples are tossed around, based on a list compiled in 1922 by William Ogburn and Dorothy Thomas:
Newton and Leibniz both discovered calculus. Charles Darwin and Alfred Russell Wallace both discovered evolution. Three mathematicians “invented” decimal fractions. Oxygen was discovered by Joseph Priestley, in Wiltshire, in 1774, and by Carl Wilhelm Scheele, in Uppsala, a year earlier. Color photography was invented at the same time by Charles Cros and by Louis Ducos du Hauron, in France. Logarithms were invented by John Napier and Henry Briggs in Britain, and by Joost Burgi in Switzerland. […] The law of the conservation of energy, so significant in science and philosophy, was formulated four times independently in 1847, by Joule, Thomson, Colding, and Helmholz. They had been anticipated by Robert Mayer in 1842. There seem to have been at least six different inventors of the thermometer and no less than nine claimants of the invention of the telescope. Typewriting machines were invented simultaneously in England and in America by several individuals in these countries. The steamboat is claimed as the “exclusive” discovery of Fulton, Jouffroy, Rumsey, Stevens, and Symmington.
The idea, then, is that big ideas are “in the air”, or that these “multiples” exist because the collective thinking is being steered in particular directions by previous discoveries and advances, letting multiple people working on the same problem independently find similar solutions. This is actually a fairly obvious idea (how many of us in science are worried about being “scooped” in some way or another?), but it isn’t usually the way we think about the history of science. As Gladwell points out, “[g]ood ideas are out there for anyone with the wit and the will to find them.”
This idea of “multiples” was also used by sociologist Robert K. Merton to classify what genius actually meant. His belief was that a genius was invariably part of many different “multiples”, far more than an average scientist or inventor, and that the genius was no different than you or I except in their efficiency in generating good ideas. Merton’s example was Lord Kelvin, where, after analysis of Kelvin’s 600-odd scientific correspondences, concluded 32 multiples:
These 32 multiples involved an aggregate of 30 other scientists, some, like Stokes, Green, Helmholtz, Cavendish, Clausius, Poincaré, Rayleigh, themselves men of undeniable genius, others, like Hankel, Pfaff, Homer Lane, Varley, and Lamé, being men of talent, no doubt, but still not of the highest order… For the hypothesis that each of these discoveries was destined to find expression, even if the genius of Kelvin had not been obtained, there is the best of traditional proof: each was in fact made by others.
Gladwell relates all of this back to an extremely unique company called Intellectual Ventures, whose goal is to gather together many smart people and brainstorm ideas (in “invention sessions”) with the intention of following up on them themselves (they are apparently working on a new kind of nuclear reactor, and have more nuclear engineers than GE), or licensing their ideas to other companies. They’ve been generating interesting ideas at an amazing pace (some 500 patents are granted each year, and they have a backlog of 3000 waiting to go), bypassing the necessity for a single genius by increasing the number of Hankels, or Pfaffs, or Varleys, working together. These are still very clever people—in their ranks are a chemist from Stanford, doctors, lawyers, career scientists from Livermore who were trained by Edward Teller, etc—but the point is that none of them are Kelvin-style geniuses.
In my mind, this is also the way academic science works. It is increasingly rare to find lone geniuses working on their big ideas, and instead to find teams, often spanning multiple institutions or countries, doing the real interesting science. To make important contributions does not require that you be a Kelvin or a Feynman (they solve things the same way we do anyway) but to surround yourself with other clever people, and to have the wit and will to follow interesting problems.
Comment [1]
I can’t recall offhand, but it was probably in Genius where Gleick, or maybe some famous figure in the history of science, joked about the way Richard Feynman solved problems. It went something like this:
While this is obviously wouldn’t have worked for his brief stint as a biologist, for someone of Feynman’s intellect you might sometimes imagine it to be close to the truth for solving physics problems. In fact, Feynman solved problems the same way we all try to solve problems. From a wonderful essay titled Richard Feynman and The Connection Machine, W. Daniel Hillis recounts Feynman’s internship at a startup computer company:
For Richard, figuring out these problems was a kind of a game. He always started by asking very basic questions like, “What is the simplest example?” or “How can you tell if the answer is right?” He asked questions until he reduced the problem to some essential puzzle that he thought he would be able to solve. Then he would set to work, scribbling on a pad of paper and staring at the results. While he was in the middle of this kind of puzzle solving he was impossible to interrupt. “Don’t bug me. I’m busy,” he would say without even looking up. Eventually he would either decide the problem was too hard (in which case he lost interest), or he would find a solution (in which case he spent the next day or two explaining it to anyone who listened). In this way he worked on problems in database searches, geophysical modeling, protein folding, analyzing images, and reading insurance forms.
This idea of solving little puzzles as the way we do science is something André and I often talked about as undergrads, and it still rings true for me. Turning a large problem into a host of smaller ones makes research seem far more tractable and gives real, shorter-term goals to keep me motivated.
The article also makes mention of “crazy” ideas, and how Feynman was excited by them:
His reaction was unequivocal, “That is positively the dopiest idea I ever heard.” For Richard a crazy idea was an opportunity to either prove it wrong or prove it right. Either way, he was interested.
I think the combination of those two quotes forms a good philosophy for doing science. Crazy ideas are often interesting ideas (if they’re right it could be very exciting!), and after working on a problem and deciding it is too hard, you can’t be afraid to lose interest and try something else.
Comment [11]
George Wald made considerable progress in our understanding of the chemistry and physiology of vision (which just so happens to be the area I find myself in now). He won the Nobel Prize (physiology or medicine) in 1967, and his lecture in Stockholm opened with a beautiful description of experimental science:
I have often had cause to feel that my hands are cleverer than my head. That is a crude way of characterizing the dialectics of experimentation. When it is going well, it is like a quiet conversation with Nature. One asks a question and gets an answer; then one asks the next question, and gets the next answer. An experiment is a device to make Nature speak intelligibly. After that one has only to listen.
Enzymes are the workhorses of the cell. They are proteins which help facilitate reactions, such as RNA polymerase adding nucleotides to form new strands of RNA. The polymerase is the enzyme (E), the nucleotides are the substrate (S), which react to form a product (P), the newly formed RNA strand.
It can often be the case that there are very low copy numbers of enzymes in the cell, meaning only one to a handful of a specific kind of enzyme. It is also possible that there is significant substrate present. You might then wonder, how fast can the enzyme of interest, given basically unlimited substrate, carry out its reaction? Let’s simplify the situation and assume only one enzyme in a cell filled with substrate*. The below treatment was first outlined by Haldane, and then by Leonor Michaelis and Maud Menten.
The enzymatic reaction described above looks like this:
where the concentration of the substrate, cS, comes into play, and it is assumed that the second step, ES reacting to make product P, is irreversible. Thinking of the reaction in terms of probabilities (which we will denote using lowercase p), if the enzyme is unbound there is a probability per unit time cSk1 of binding a substrate, if the enzyme is bound with the substrate there is a probability per unit time of k2 of reacting to form product, or probability per unit time k-1 of returning back to its unbound state. Explicitely,
In the steady-state (dpE/dt = 0), you can solve for the probability of being in the enzyme-substrate complex:
The rate at which product is created is then k2pES as per our original reaction equation, and multiplying by the enzyme concentration (in our case just a single enzyme) gives you the velocity of the reaction.
We can simplify the formula further by introducing these two substitutions:
where KM is called the Michaelis constant, and is a measure of concentration, while vmax is a measure of the rate of change of concentration. Substition gives the famous Michaelis-Menten rule:
This rule helps explain the observed kinetics of some enzyme reactions, such as the mechanochemical cycle RNA polymerase (free link to the paper at the bottom of the post).
So, why the primer on enzyme kinetics?
Because Maud Menten and I are schoolmates, so to speak!
* This treatment is based on P. Nelson’s Biological Physics, Ch. 10.
Comment [3]
Biocurious is written by Andre Brown and Philip Johnson, since 2005. Content of the weblog is licensed under a Creative Commons Attribution-Share Alike 3.0 License.
