Guest Post: Phillip Helbig reviews “Lost in Math”

[Phillip Helbig worked in cosmology and gravitational lensing at Hamburg and Jodrell Bank Observatories and the Kapteyn Astronomical Institute. Although no longer employed in academia, he regularly attends conferences and writes book reviews for The Observatory, as well as the occasional journal paper. Phillip is a regular commenter on this blog.]

I've read a huge number of popular-science books, and my first impression is that Sabine's book is very well written. One could also think that Sabine is a native speaker (or, rather, a native writer) of English. The style is breezy without rambling, and direct quotations make it clear what the illustrious interviewees actually said, without any filter of interpretation (but see below for a caveat). Sabine's own position is very clear; this is almost an op-ed. Whether or not one agrees with her, this approach is preferable to introducing one's own biases into what might appear to the uninitiated as an objective description.

Enough praise; now for the critique. Let me emphasize, though, that I agree with everything which I don't discuss here, which is most of the book. In the interest of stimulating discussion, I'll concentrate on those few areas where I see things differently.

It is not always clear what needs to be explained. In discussions of fine-tuning and so on, one often reads about numerical coincidences, which imply that two numbers are roughly the same, but also about small (or large) numbers, which allegedly also need an explanation. (Since the inverse of a large ratio is a small ratio, I will speak only of small numbers in what follows.) It needs to be clear what is even potentially puzzling: it is always ratios near 1. In other words, if the smallness of some quantity is the result of a near cancellation, then that implies a ratio near 1 of the quantities which almost cancel; if the number is just small in relation to some other quantity because it has nothing to do with that other quantity, then it certainly needs no explanation.

Another aspect of the presentation I disagree with is the claim that the standard model has been "souped up" with dark matter and dark energy, as if these were some sort of epicycles, fudge factors brought in so that theory and observations match. On her blog, Sabine has often pointed out that general relativity says nothing about the sources of gravitation, so while dark matter might be interesting or even mysterious because we don't know what it is, it is not some sort of addition to general relativity. The same goes for the cosmological constant. Yes, Einstein initially introduced it as a fudge factor, and later abandoned it, but the universe is independent of the contingent history via which we have learned about it. From a mathematical point of view, one could just have easily included the cosmological constant from the beginning. Indeed, in other areas of physics, what is not forbidden actually happens, and if someone claims that something doesn't happen, that some quantity is 0, etc, then the burden of proof is on the person making the claim. Actually, what is interesting is that no fudge factors have had to be introduced. Despite a huge amount of cosmological data, a model with just a few parameters---all of which were known even back when there was almost no data---which was derived when there were some data but considerably less than now still fits the observations.

I have tremendous respect for George Ellis. However, I don't always agree with him, even on matters of science. I think that Sabine lets him too easily off the hook because they seem to agree on many issues. Ellis dismisses the idea that we could be living in a simulation, but is careful to point out that science cannot disprove the existence of God. One could just as well say that we cannot disprove that we are living in a simulation and dismiss the idea of God. Strictly speaking, one can disprove neither, but can use various arguments to discuss the probabilities of both. Also, after criticizing certain ideas as being non-scientific, Ellis says of one of his own ideas, that nothing is physically infinite: "There's no way I can prove it.... But we should use it as a principle." This isn't the place to argue with Ellis; my point is that if Sabine could be obstinate enough to stay in Weinberg's office even after he had essentially asked her to leave, she should have called out these two obvious contradictions on the part of Ellis. I think that this is a good example of confirmation bias. (Interestingly, Tegmark is also critical of the idea of physical infinity but, in contrast to Ellis, is a strong proponent of the multiverse.)

My main disagreement with Sabine concerns fine-tuning. I think that this is due to an unnecessary attachment to probability. Many normally think that fine-tuning and low probability go hand in hand. As Sabine points out, though, without knowledge of the underlying probability distribution, one cannot say whether an anthropic explanation involving the multiverse leads to likely values. But is that even necessary? One can discuss fine-tuning for life, in the sense that slight changes of various parameters (within the otherwise allowed range) would lead to a universe incompatible with life. There can be absolutely no debate that the universe is fine-tuned in this sense. Whether the values we observe for the physical constants are likely in some sense is unknown, but also irrelevant. One must be careful not to confuse fine-tuning in the particle-physics sense of lack of naturalness (discussed above) with the case of values being within a small region of possible parameter space (regardless of how likely that small region is by some definition.) As an aside, it is not true, as Sabine claims on p. 114, that fine-tuning goes away if one considers many changes simultaneously. A good discussion of fine-tuning, which also rebuts many common objections, including that one, can be found in the book by Lewis and Barnes.

It is also beside the point whether, also mentioned on p. 114, somewhere in parameter space there is another region compatible with life; the point is that most of it is not. A good comparison is with the "coincidence" that the Earth is just at the right distance of the Sun for the existence of life. The explanation is simple: there are many solar systems with planets at various distances from their stars. By chance, some will be at the right distance for life. It is also completely irrelevant how likely these are, as long as the probability is non-zero. The same goes for the multiverse. Given the multiverse (perhaps a daunting proposition), then fine-tuning is not puzzling at all. A good case for the multiverse is made by Max Tegmark. (Lewis and Barnes mention the multiverse in a book about fine-tuning; Tegmark does the opposite.) I think that most examples of fine-tuning are real; again, the book by Lewis and Barnes is a good summary. In one famous case of alleged fine-tuning I disagree, and that is the flatness problem. I wrote an entire paper about that, so I won't say much about it here. I'm also sure that most of the people who have thought much about the multiverse don't make this simple mistake.

Suppose I flip a coin a hundred times and it comes up heads every time. It seems that Sabine would say that this outcome is just as probable as any other outcome (which is true) and therefore that there is no reason to assume that the coin is not fair (which is false). I think that most people would disagree with Sabine, and I agree with those people. If one must discuss probabilities in conjunction with fine-tuning, or vice versa, what is relevant is not the probability per se, but rather the probability relative to some situation which is important to us.

A common theme in Sabine's book is that fundamental physics, having become "lost in math", has not made much progress in recent decades. This is a correlation, but is there a causation? Perhaps the problems are just really hard theoretically, and experimentally nothing is accessible at the moment. In neither case would this be the first time that something like this has happened. Thus, while I sympathize with the main theme of the book, I don't think that there is a watertight case for the claim.

Perhaps other approaches will be more successful, but the burden of proof is on those who make such claims. Yes, maybe progress is difficult due to lack of funding for those thinking outside the box, and without funding, it is difficult to prove whether an alternative approach would pay off.

Does beauty distract us from truth? Perhaps, in some cases, but in these I claim (probably agreeing with Sabine here) that it is not beauty per se, but rather a false sense of beauty. Aesthetics in some sense, perhaps something similar to Pirsig's "quality", has been a useful guide in some cases. At the end of the day, though, the route to truth doesn't matter; a successful theory is a successful theory regardless of the path trough which it was arrived at.

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Some comments from me:

First, as you can see, Phillip unfortunately used his review to propagate his own notion of fine-tuning. I therefore want to warn you that this is not the way most physicists use the word and therefore not the way I use the word in my book. Please don't let yourself get confused.

Second, Ellis correctly points out that the simulation hypothesis is not science because you cannot disprove it. This is totally in line with him saying that science cannot disprove god. And, yes, Ellis puts forward metaphysical principles, but in contrast to the other physicists I spoke to, he is aware that these are unprovable.

Third, I discuss the issue of fairness in the interview with Weinberg using the example of poker. It's a useless objection because we have equally little idea what counts as "fair" in the multiverse as we know the probability distribution. Neither of those are notions that make sense scientifically.

Fourth, I address the often-raised claim that progress has slowed down because "the problems are just hard" right in the beginning of the book. To sum it up once again: no one can tell how much of the slow-down is due to the problems being harder, but certainly using flawed methodologies will not help.

Fifth, I don't think there is anything like a "false sense of beauty". You decide what is beauty for yourself. Just don't mistake your sense of beauty for a scientific criterion.