To find the best possible solution to a problem, scientists have to avoid the trap of the ‘local maximum.’
If we could start from scratch, we’d be better off, no doubt, using metric units instead of inches and feet, duodecimal (base 12) numbers instead of decimals, and Dvorak keyboards instead of QWERTY. But in parts of the world where inches, decimals and QWERTY are the standard, people have built habits of thought and devices around them, so switching would be far from painless. These are homely examples of a profound issue that haunts both science and the human condition: the specter of local maxima.
To understand local maxima, imagine a climber who is trying to reach the highest point in a mountain range. No matter where she starts, she can get higher for a while by following a simple rule: always ascend. Eventually she will reach a peak. But there is no guarantee that the peak she reaches this way is the highest in the range. She has reached a local maximum but not necessarily the global maximum. Higher peaks may lie elsewhere, separated by valleys and mountain passes. To get to them, she’d have to go down for a while and maybe wander a bit, before ascending.
In physics and its applications, one often encounters the problem of exploring a landscape of possible outcomes. We might know the sequence of amino acids within some protein, for instance, and look to determine the possible shapes that the protein, responding to internal stresses, can fold into. By starting with some guess and considering small changes, we can home in on a stable structure. But a radically different starting point might have led to a different answer.
In “mad-cow disease” and the human disease kuru, among others, proteins that normally perform useful functions take on an alternative shape that leads to formation of plaques and devastating cell damage. The diseased form is difficult to reach, starting from the normal form, but one misfolded molecule can form a template for others. The alternative shape is effectively stable, once formed, because it is a sort of local maximum.
Local maxima can be difficult for evolution, or for human societies, to escape. Without the disruptive effect of an asteroid, dinosaurs might still be roaming the Earth, leaving mammals as an oppressed race of nocturnal vermin. Without the disruptive effect of the Black Death in Europe, the Renaissance and the modern world in general might have been substantially delayed.
In our own lives, the choice of whether to abandon a comfortable local maximum can be wrenching. If my life is pretty good already, should I consider changing jobs, emigrating to a different country or going to back to school? Voltaire warned that “the best is the enemy of the good.” But Omar Khayyam urges us on:
Ah Love! could thou and I with Fate conspire
To grasp this sorry Scheme of Things entire,
Would not we shatter it to bits—and then
Re-mould it nearer to the Heart’s Desire!
Psychologists tell us that, as a rule, people become more content as they age. A plausible explanation is that as the prospect of making dramatic improvements in one’s life recedes, so does anxiety about taking on the associated labor and risks. Omar’s fiery resolve passes into Voltaire’s cold comfort.
Originally appeared on April 30, 2020 on The Wall Street Journal website as ‘Good Enough Versus Even Better‘
Frank Wilczek is the Herman Feshbach Professor of Physics at MIT, winner of the 2004 Nobel Prize in Physics, and author of the books Fundamentals: Ten Keys to Reality (2021), A Beautiful Question: Finding Nature’s Deep Design (2015), and The Lightness of Being: Mass, Ether, and the Unification of Forces (2009).