Unless we change direction,
we are likely to wind up
where we are headed.
—Ancient Chinese proverb

Like many of you, I get unsolicited manuscripts that make startling and revolutionary claims. In years past they arrived by snail mail and were often handwritten or typed with copious use of capital letters, exclamation marks, and hand-drawn diagrams. More recently they come by email and look more like conventional scientific literature. (Even crackpots know how to use word processors and PowerPoint.) Denials of Einstein’s special relativity seem especially popular.

Although the shortcomings of those efforts are often readily apparent, there is much to admire about the passion and dedication with which they are constructed. Occasionally they merit attention, if only because their authors’ thought processes are not fettered by conventional thinking. Sadly, their deficiencies are often fundamental and betray a lack of understanding of the nature of science and its interconnectivity. They are what I call Crazy Ideas of the First Kind—the most common and least interesting.

Most published science is mundane. It is the easiest to get published and the easiest to get funded at a modest, sustainable level—though no funding is easy to get these days. It is also more likely to be right, precisely because it is incremental. Just as rock-solid financial investments are an important part of any balanced portfolio, so the mundane science is an important part of the science portfolio. But I suspect many scientists, even some who are recognized as leaders in their field, are unwilling to acknowledge their lack of adventurousness. They will protest that they are inventive, innovative scientists, but their measure of that is probably quite constricted because of the fine-scale partitioning that characterizes the modern scientific world. In the landscape of scientific knowledge, most of us are digging deeper holes and maybe an occasional trench to link up with a neighboring hole, but few are venturing across the ridges to the next valley.

Crazy Ideas of the Second Kind come when well-established scientists venture out from their holes and up to the ridges and peaks to survey the landscape. Inevitably, such excursions can look like the actions of a dilettante since it takes less effort to dash up a ridge than to dig a really deep hole. One is then accused of speculation. I occasionally sense from colleagues some disdain for scientific speculation, perhaps because it is cheap: It seems to require relatively little effort and commitment. Indeed, bad speculation is easy, and you can do it at the local bar or Starbucks or while riding a bike. Poor experimental or observational work also often requires less effort than good work. In fact, good speculation is hard, judging by the evident rarity of examples. Good speculation is also not always easy to recognize immediately, because part of what makes it good is something that may be hidden: the failures of alternative speculations, the crumpled sheets of paper in the wastebasket.

Richard Feynman once said that the essence of science is (or should be) “the belief in the ignorance of experts.”1 I think he meant that outsiders may provide an important breakthrough because they are unfettered. The “ignorance” that he refers to, though, must not be complete. It still must allow an appreciation of how science works and the rules that apply, and so it is the ignorance of areas of science other than your own. Residents of deep holes know very well the stuff they have excavated and the walls that surround them but know less well what novelty may lie elsewhere.

And then there are Crazy Ideas of the Third Kind, the most interesting and least common. They arise from a leading eminence in some field who has decided that something is rotten in that field’s fundamentals. In essence, they have decided that their hole is a false claim or has been mined out, even though it may be capacious and well populated.

Importantly, good crazy ideas do not have to be true to be valuable. Distinguished astrophysicist Fred Hoyle and colleagues had the crazy idea that influenza came from space.2 The more general concept of panspermia—of which Hoyle’s idea is a special case—is, however, of considerable interest.

Perhaps an even better example of that line of thinking is Hoyle’s wonderful science fiction novel The Black Cloud (Harper, ca. 1957), wherein an intelligent life-form exists as a dispersed but organized globule that wanders into our solar system. That is a truly engaging though crazy idea: Could life take the form of something that we normally think of as having high entropy? Indeed, some fluid dynamical systems display order—consider Jupiter’s Great Red Spot—and the question of what form life could take remains an open one.

Another distinguished astrophysicist, Thomas Gold, had the crazy idea that natural gas was part of Earth’s starting material rather than arising from biological processes much later in Earth history.3 Geochemists might laugh (some did), and yet the possible delivery of large amounts of reduced carbon to Earth at formation is not such a ridiculous idea. We still do not know Earth’s total reservoir of carbon, since some of it may be very deep. Gold was wrong about natural gas, but the idea is provocative, and that’s good.

More famously, Lord Kelvin had the crazy idea that you could figure out the age of Earth by solving the diffusion equation for heat conduction in a half-space. He knew that Earth is a sphere, but the diffusion time for the whole Earth is so large that a half-space suffices. (For more on Lord Kelvin’s mistake, see my letter, Physics Today, November 2010, page 8.)

Kelvin’s idea is a particularly interesting example because it was not regarded as crazy at the time but would be viewed as crazy now, for reasons that could have been explained to him back then. He was ignoring the geological evidence for the great expanses of time that must have passed, but there were as yet no good clocks for geologic time. He was also ignoring the possibility of convection, and that should not have been acceptable. Crazy ideas are often ephemeral: What was crazy then can be “natural” now and vice versa.

As for Crazy Ideas of the Third Kind, opinions will vary, but perhaps one is the idea that gravity is an emergent phenomenon, an idea often attributed to Andrei Sakharov. The extension of a rubber band, which roughly obeys Hooke’s law, is purely entropic and has nothing to do with the forces between the atoms that make up the material, so one could say that in that case a force law emerges from Boltzmann’s definition of entropy. Or perhaps Roger Penrose and his fundamental discretization of spacetime would be one of the Third Kind. Many great developments in physics began encumbered with ideas that we have now shed—for example, Maxwell’s molecular vortices.

My thesis adviser, Ed Salpeter, would occasionally say to me, “Is it crazy enough to be true?” I think what he meant is that when you’re attempting to explain something important and it has resisted solution for a significant time, then the mundane explanation is unlikely to work, so you should be seeking the “crazy” answer. Although Salpeter almost invariably wrote papers of great solidity and impact, he did coauthor a paper with Carl Sagan on life in the atmosphere of Jupiter.4 It was a good crazy paper, I think. Life in the atmosphere of Jupiter figures prominently in a science fiction novel, The Algebraist (Orbit, 2004), by Iain Banks.

In a somewhat similar spirit, Niels Bohr, responding to a lecture by Wolfgang Pauli, said, “We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct.” The hard part lies in figuring out what is crazy enough.

Phys. Teach.
), p. 319.
Viruses from Space and Related Matters
U. College Cardiff Press
The Deep, Hot Biosphere
Copernicus Books
Astrophys. J. Suppl. Ser.