Six Numbers in Search of a Theory

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As the public spokesperson for the Skeptics Society and Skeptic magazine, I participate in a series of collegiate debates around the country with theologians and intelligent design advocates on the existence (or lack thereof) of a deity or intelligent designer, which may or may not be one and the same. In my opinion, the single best argument my debate opponents have is the apparently fine-tuned characteristics of nature. Indeed, they quote no less a personage than Sir Martin Rees, Britain’s Astronomer Royal, who argues in his 2000 book, “Just Six Numbers,” that “our emergence from a simple Big Bang was sensitive to six ‘cosmic numbers.’ Had these numbers not been ‘well tuned,’ the gradual unfolding of layer upon layer of complexity would have been quenched.” These six numbers are:

Ω = 1, the amount of matter in the universe, such that if Ω were greater than one, it would have collapsed long ago, and if Ω were less than one, no galaxies would have formed.

e = .007, how firmly atomic nuclei bind together, such that if epsilon were .006 or .008, matter could not exist as it does.

D = 3, the number of dimensions in which we live, such that if D were 2 or 4, life could not exist.

N = 1036 , the ratio of the strength of gravity to that of electromagnetism, such that if it had just a few less zeros, the universe would be too young and too small for life to evolve.

Q,= 1/100,000, the fabric of the universe, such that if Q were smaller, the universe would be featureless, and if Q were larger, the universe would be dominated by giant black holes.

λ = 0.7, the cosmological constant, or “antigravity” force that is causing the universe to expand at an accelerating rate, such that if λ were larger, it would have prevented stars and galaxies from forming.

Change these relationships, and stars, planets, and life could not exist. Thus, this is not just the best of all possible worlds, it is the only possible world.

One answer to this argument comes from string theory, which holds that the fundamental constituents of matter are vibrating strings of extremely small scale, perhaps even at the unimaginably small Planck length, or 10-35 meters. According to one model of string theory, there could be 10500 possible universes, all with different self-consistent laws and constants. That’s a 1 followed by 500 zeroes possible universes (12 zeroes is a trillion!). Also, through string theory there may be an underlying principle behind all the fine-tune equations and relationships that will be forthcoming when the grand unified theory of physics is discovered. In a unified theory there will not be six mysterious numbers, there will just be one.

For many years now I have invoked string theory as my authority from whence this unification may come. I may now have to look for another source. According to two new books, there is much to be skeptical about in string theory.

In “Not Even Wrong” (Basic Books, 291 pages, $26.95), the Columbia University mathematician Peter Woit invokes Wolfgang Pauli’s famous critique of a paper: “This isn’t right. It’s not even wrong.” String theory, Mr. Woit argues, is not only based on nontestable hypotheses, it depends far too much on the aesthetic nature of its mathematics and the eminence of its proponents. In science, if an idea is not falsifiable, it is not that it is wrong; it is that we cannot determine if it is wrong, and thus it is not even wrong. In an engaging, albeit challenging, narrative, Mr. Woit recounts the history of string theory, concluding: “Since 1973, the field has failed to make significant progress, and in many ways has been the victim of its own success.”

Mr. Woit is not alone. No less a physics god than the late Caltech Nobel physicist Richard Feynman cautioned, “Now I know that other old men have been very foolish to say this is nonsense. I am going to be very foolish, because I do feel strongly that this is nonsense! I can’t help it, even though I know the danger in such a point of view. So perhaps I could entertain future historians by saying I think all this superstring stuff is crazy and is in the wrong direction.” More succinctly, Feynman quipped: “String theorists don’t make predictions, they make excuses.” What did he mean by this stinging rebuke?

I don’t like that they’re not calculating anything. I don’t like that they don’t check their ideas. I don’t like that for anything that disagrees with an experiment, they cook up an explanation — a fix-up to say, ‘Well, it still might be true.’ For example, the theory requires ten dimensions. Well, maybe there’s a way of wrapping up six of the dimensions. Yes, that’s possible mathematically, but why not seven? When they write their equation, the equation should decide how many of these things get wrapped up, not the desire to agree with experiment. In other words, there’s no reason whatsoever in superstring theory that it isn’t eight of the ten dimensions that get wrapped up and that the result is only two dimensions, which would be completely in disagreement with experience. So the fact that it might disagree with experience is very tenuous, it doesn’t produce anything; it has to be excused most of the time. It doesn’t look right.

That was in 1987. According to Mr. Woit, not much has changed since. Echoing Feynman, Mr. Woit concludes: “The fundamental reason that superstring theory makes no predictions is that it isn’t really a theory, but rather a set of reasons for hoping that a theory exists.”

If anyone would be sympathetic to the struggles of bringing to fruition a revolutionary idea like string theory it would be Lee Smolin, the Yale University and Pennsylvania State University physicist who went on to co-found the innovative Perimeter Institute of Theoretical Physics, located in Quebec and “dedicated to extending theories of space, time and matter.” In “The Trouble with Physics” (Houghton Mifflin, 392 pages, $26), Mr. Smolin argues that string theory has unjustly used up a disproportionate amount of time, resources, money, and young physicists, which, at this point, could be put to better use on other topics that have a better chance of bearing experimental fruit. “String theory now has such a dominant position in the academy that it is practically career suicide for young theoretical physicists not to join the field.”

The failure of string theory “is not so much a particular theory but a style of doing science that was well suited to the problems we faced in the middle part of the twentieth century but is ill suited to the kinds of fundamental problems we face now.” According to Mr. Smolin, there are five such fundamental problems for which we need a new style of science to solve:

1. Combine general relativity and quantum theory into a single theory that can claim to be the complete theory of nature. This is called the problem of quantum gravity.

2. Resolve the problems in the foundations of quantum mechanics, either by making sense of the theory as it stands or by inventing a new theory that does make sense.

3. Determine whether or not the various particles and forces can be unified in a theory that explains them all as manifestations of a single, fundamental entity.

4. Explain how the values of the free constants in the standard model of particle physics are chosen in nature.

5. Explain dark matter and dark energy. Or, if they don’t exist, determine how and why gravity is modified on large scales.

“These five problems represent the boundaries to present knowledge. They are what keep theoretical physicists up at night. … Any theory that claims to be a fundamental theory of nature must answer each one of them.” String theory, says Mr. Smolin, has failed to do so.

Yet, for Mr. Smolin, the deeper problem is not string theory per se; it is in the social structure of science itself. In a penultimate chapter on “how science really works,” Mr. Smolin sings the praises of thinking outside of the box, including and especially the staid and delimiting box of academia. The system is set up to create scientists who are risk-averse, and granting tenure doesn’t help: “Too much job security, too much power, and too little accountability for older people. Too little job security, too little power, and too much accountability for younger people in the prime of their creative, risk-taking years.”

Mr. Smolin concludes that we must do two things: “We must recognize and fight the symptoms of groupthink, and we must open the doors to a wide range of independent thinkers, being sure to make room for the peculiar characters needed to make a revolution.” How can you spot one of these young revolutionaries? Easy. Find someone already doing science this way, or “find at least one accomplished person in the candidate’s field who is deeply excited about what the candidate is trying to do,” and, just to be sure, “find at least one professor who thinks the candidate is a terrible scientist and bound to fail.”

This brings to mind the first of Arthur C. Clarke’s famous three laws: “When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong.”

But is he not even wrong?

Mr. Shermer is the publisher of Skeptic magazine ( and a monthly columnist for Scientific American. His latest book is “Why Darwin Matters,” available from Times Books.

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