Science is hard, but it may still be easier than it ought to be.
A few years back, Hersch Rabitz, an expert in quantum phenomena and the former chair of Princeton’s chemistry department, was trying to solve what should have been a difficult problem — formulating the exact laser pulse needed to control a quantum process. When his group attempted to isolate a single variable and measure the effects, as scientists are taught to do, the problem was intractable.
Making matters seemingly worse, if a single variable is akin to one musical note, Rabitz says the pulses needed to fully solve the problem were more akin to a full musical composition — needing to hit a huge number of frequencies at exactly the right time. And yet, in this case the complex solution was far easier to achieve. Again and again, to Rabitz’s great puzzlement, he was able to start with a multivariable pulse and make adjustments until he was dialed into a solution that achieved the desired effect.
“You could liken the discovery of shaped laser pulses to sitting at a piano and attempting to play a Beethoven sonata without the score,” Rabitz says. “It’s just basically impossible. We can’t solve the quantum mechanical equations reliably enough to design the pulse.” And yet in practice, “it turned out to be remarkably, startlingly easy to do in the laboratory with a smart algorithm guiding the laser.”
Rabitz’s laser pulse experiments set him to thinking about whether there were other seemingly intractable scientific problems that might actually have workable solutions. He thought back to his days as a college chemist: “Many physicists are confused by how easily chemists pull off their magic,” he says. “But once you’ve taken ten chemistry courses or so, you get so smart that if someone asks you to make a reasonable molecule, it is remarkably easy.”
Rabitz wondered whether the solubility of so many challenges in chemistry might be another overlooked facet of an overarching principle affecting every aspect of the large set of scientific and technological challenges known as control problems — where systems (be they laser pulses, chemical reactions, biological processes, or industrial procedures) can be optimized to produce a desired outcome.
Rabitz’s coalescing theory is what he terms the Universal Operating Principle for Optimal Control in the Sciences — UOP for short. The principle is akin to other scientific notions like the Principle of Least Action, which states that, to use a very specific and practical example, water will find the most efficient way to flow downhill.
Rabitz’s principle is also best described in terms of landscapes. Think of the Rocky Mountains’ endless, fractal-like jagged surfaces, with no apparent pattern and no predictable path to the highest point. “The problem with discovering a [properly tuned] laser pulse is a challenge as there are approximately 1,000 variables. We were puzzled because the expectation was that the objective landscape . . . should look terrible. Yet when we struggled through the mathematics, the result we came to was that it doesn’t look like the Rocky Mountains in 1,000 dimensions.”
Instead, the landscape of potential values was remarkably smooth — it was free of jagged valleys and it was relatively easy, to use the three-dimensional-metaphor, to discern which direction you had to travel in to reach a higher altitude. “We originally didn’t even believe the result because it was rather remarkable. But we then realized it really explained the success of the experiments.”
According to Rabitz, if a control problem is well-posed, if there is some ability to move about the landscape of possible adjustments, and if there are sufficient computational or experimental resources dedicated to the problem, then there is hope of reaching an optimal solution. The question of resources at first seems self-evident: why wouldn’t a problem be soluble with enough resources? But there are entire classes of problems which simply grow more and more complex the more you invest in trying to solve them. Rabitz’s principle offers hope that problems that seem insoluble in their simpler forms might in fact become tractable given more resources — and more variables. According to Rabitz, the UOP implies that “complexity is your friend, not your enemy.” This notion is so deeply counterintuitive it has the potential to reshape vast areas of scientific inquiry.
TESTING THE THEORY
For a principle to be called universal it needs to apply across the board, not just in an obscure corner of laser-pulse-friendly quantum phenomena. So Rabitz and his team have been looking for testable examples of how the UOP might apply in other realms. They used a publicly available database of spectroscopy data for known molecular compounds and used it to create a landscape of chemical possibilities. Their initial results showed a generally smooth and orderly set of contours, spiked with a handful of outliers that didn’t fit the general scheme of things. But upon investigating the outliers to find out why the principle hadn’t applied, the investigators discovered that all corresponded to errors in the source database. A further test on a data set dealing with proteins showed again the UOP’s remarkable ability for identifying inadvertent human errors.
Among the most fascinating implications of UOP, both for scientific theory and scientific practice, is in the realm of biology, where many of the sorts of tests you would like to do in theory are hampered by time — you can’t set up an experiment that will involve a hundred million years of evolution.
“Scientists do evolutionary experiments on bacteria and viruses because they mutate fast,” Rabitz says. “They perturb the genome or environment that the bacteria is living in and observe the regrowth of fitness. . . . Almost all of the findings are consistent with the UOP, that creeping back to the top of the fitness landscape is easy and the species don’t get stuck.”
Rabitz continues: “One of the major conclusions of our work in evolution is that, frankly, life is easy — notwithstanding the billion years [it takes] to create it. In the case of chemistry and quantum mechanics, there’s a scientist who decides what the objective is — it’s all under the scientist’s guidance.” In contrast, Rabitz says, “evolution is driven by survival of the fittest. Mother Nature is using random stochastic variations and mutations. If you have the right environment and give Mother Nature enough time, survival of the fittest takes over. The Universal Operating Principle as a theorem says that these two disparate areas . . . have a common physical and mathematical foundation.”
IMPOSSIBLE NO LONGER
As Rabitz and a growing network of colleagues refine, adapt, and investigate the notion of a Universal Operating Principle, the scope and implications of its ideas will themselves develop over time — reaching, perhaps, their own peak of optimal efficiency. But by encouraging scientists to ask different kind of questions, and expect a different kind of results, Rabitz and his colleagues will likely continue to uncover a new range of impossible problems that prove surprisingly easy, given the right framework and — strangely enough — sufficient complexity.