Martin Rees: Just Six Numbers: The Deep Forces that Shape the Universe (Weidenfeld & Nicolson, 1999) It’s hard to tell whether chicken or egg takes pride of place, but Rees uses the worst of all possible arguments to plump for the multiverse theory. The previous sentence may be hyperbole, but the argument really is pretty bad. Rees’ premise is a summary statement of certain parts of our current model of the physical universe. That model contains theorems and primary observations that make use of constants, dubbed the universal or cosmological constants, which express facts about the state of the physical universe, facts such as the ratio between electromagnetic and gravitational force. That these constants are what they are is not logically necessary, since it is possible to assert without contradiction that a given constant could have a different value from the value it is observed to have. Proceeding along these lines Rees notes that, if one of the universal constants were hypothetically to have a different value and if all the other truths in our physical model were to remain unchanged, then there would be consequential and in many cases significant differences in the state of the physical universe. Observers, i.e. people, would not, under the right circumstances, have evolved. Animals as we know them would not have been able to sustain their own weight. Carbon and oxygen would not have been formed. Or stars, or galaxies. The universe would have collapsed in an instant or have spread out so thinly that the ordinary guy would consider it nothing at all. To highlight these consequences is not to exaggerate, nor need it even be intentionally inflammatory, but it is emotionally tinged. Read incorrectly these conclusions might lead the naive to think that we have to do something quick to make sure the constants don’t change. Something like appeasing the gods, a fear that goddists are only too happy to stoke when they rush to conclude that the universal constants are what they are because of supernatural “fine tuning.” The implication is we shouldn’t make god mad or else it might – much like a disgruntled engineer at Com Ed  decide to reset one of the critical switches that keep the universe humming. Rees expresses surprise that the constants are exactly such that we the elect could emerge. “Many scientists take (the line…that there’s nothing to be surprised about), but (that line) certainly leaves me unsatisfied.” (p. 164) Apparently it was a close shave. Rees’ conclusion is that we should look for an explanation for our good fortune. As noted, the view that the fact that universal constants are what they are is no more surprising than any other observed fact is dismissed by Rees as a matter of personal preference. But among explanations, he says, there are only two currently on the table. Either the big guy planned it all from the beginning (Why it chose a universe configured according to exactly this physical model would remain a mystery since an infinite number of other configurations would lead to the same result), or there exist (or have existed) (Or could exist, but in my opinion all the alternative physical models would have to be actualized in the multiverse to make Rees’ argument a real lockdown. Otherwise all he does is reduce the surprise by some insignificant, at least compared to infinity, amount. Rees confesses that an “infinite” number of alternative universes may, in his view, exist (p.4) In fact he throws around the concept of infinity like a drunken set theorist. He presumably means mathematical infinity, and, as the first three sentences of this parenthesis indicate, there is a sense in which he must mean mathematical infinity. However, when you introduce mathematical infinity into physical theory all hell breaks loose. We shall see below one way this happens.) an infinity of other universes each with its own set of physical laws such as to exhaust all possible configurations of physical law (Interestingly there is nothing in the multiverse speculation to exclude that a subset of all the universes in the multiverse also containing an infinite number of alternative universes could have exactly the same physical laws as our own). Accordingly there (possibly) must exist at least one universe with the exact set of physical laws we call our own. Under these circumstances, it is a matter of mathematical necessity that our universe exists. The surprising fact that the roulette ball should land on number 7 is reduced to the unsurprising fact that 7 is on the roulette wheel, or the unsurprising  indeed necessary  fact that 7 is a real number. Moreover, some of the inhabitants of that universe could make the observations that we do and ask the questions that we ask. It is much less surprising that those inhabitants should be us. Indeed if they weren’t us, we wouldn’t have known about it. (In a mathematical type proof a step would be: Let the inhabitants be us.) If every universe is actualized in the multiverse, then the exclamation, “How fortunate the universal constants are such as to be conducive to our existence!” is reduced to the near tautology, “A universe with observers is a universe that can produce observers.” Rees’ basic premise, as I mentioned, is just the current physical model. However, the subordinate premises that there is something “impressive” about the fact that the universal constants are what they are and that there are only two explanations for that fact  those premises are much more difficult to sustain. Let’s put the notion of impressiveness or surprise in some perspective. Since surprise is a matter of personal preference (or individual impulsive reaction), any observed fact could be surprising to somebody. You pays your money, you takes your chances. I’m sure there is someone (probably more than one) out there who is surprised that the sun rose this morning. In fact the deductive (and presuppositional) links between the sun rising this morning and the universal constants being what they are  indeed the links that bind all the theorems of our model of the physical universe  means that to be surprised about one is ultimately to be surprised about all. Surprise that one aspect of our physical model is what it is turns out to be surprise that the entire model is what it is. So there is no special reason to focus one’s “surprise” on the universal constants in isolation. There is no difference from Newton’s “surprise” that apples fall. Scientists look for explanations for everything (to the extent that they can) and the apparent good fortune that the universal constants are what they are does not deserve special notice. Indeed, if we picture the apple’s location on the tree branch as the center of a circle, then there are (ideally) an infinite number of other trajectories that apple might have taken other than the one we so geocentrically refer to as down. However, there is a big difference in the sorts of explanation our surprise might call up. Scientific explanations lie within the realm observation or are derived from physical theory. Creationist “explanations” are neither observable nor a part of physical theory. They are a different kind of animal from scientific explanation and are such that they cannot be proved (certainly not by surprise). However, they may be disproved on logical grounds (e.g. they might be such that they cannot be formulated in a way that is both nonobservational and makes sense). The Reesian and by extension creationist demand for an explanation of why the universe is this way rather than that way is indistinguishable from the supposedly philosophical issue of why there is a universe at all. Rees abjures the latter. “…physics can never explain what ‘breathes fire’ into the equations (governing physical reality  WD), and actualizes them in the real cosmos.” (p. 145) And, in a classic misunderstanding of the Tractatus, “the fundamental question of ‘Why is there something rather than nothing?’ remains the province of philosophers. And even they may be wiser to respond, with Ludwig Wittgenstein, ‘whereof one cannot speak, one must be silent’.” (Ibid.) The same can be said about the question of why are the equations just this way. Many writers on the subject sex up the idea of surprise by the socalled anthropic principle. This frames the surprise as surprise that the universe is so configured that it should contain inhabitants that are surprised that it is so configured (Cf. Rees p. 10.) Psychedelic, man! The anthropic principle, however, is just a bit of rhetoric and not an argument. It is certainly not an independent observation. Define “inhabitants who can be surprised etc.” as “people.” Now, people are in the universe only if the current physical model, or some insignificant variation of the current physical model, is true. Therefore, the anthropic principle comes down to saying that it is surprising that our current physical model is true. Now substitute “People are in the universe” with “the observed facts.” In this case the hypothetical becomes: If the observed facts are what they are, then the current physical model is true. This is no more than a condition for any true physical theory. So let us replace the rhetorically charged anthropic version (“It’s just supercallifragilistic that god should have designed the universe as a home for his chilluns!”), with “It is surprising that the current physical model should be consistent with the observed facts.” A bummer, I know. As we shall see below, what would really be surprising would be if someone were to knowingly construct a physical model that is inconsistent with the observed facts. Anthropocists introduce an additional level of reference, and thereby greater confusion, into the basically uncomplicated notion of prior conditions for the observed facts. They gloss wonder that the universe is as it is, where the embedded clause is assumed to be true by observation, as wonder that we can wonder that the universe is at it is, a version that doesn’t say a great deal more. In fact it says less. Anthropic arguments confuse two different sorts of propositions. Although we assume the universe is indeed F in both versions (by observation), and so the anthropic version avoids an improper implication, the anthropic version does nothing but make the first version needlessly complicated. For example, the form of the first is, “It is wonderful that the universe is F.” The form of the second is, “It is wonderful that we can wonder that the universe is F.” Metaphysical anthropocists think they are asserting the first sort of proposition, while in fact they are asserting the second sort. An important difference between the two is that the first can be asserted by someone (or something) that is not part of the universe referred to in the embedded clause (where “the universe” is a proper name of some universe), while, for the purposes of the anthropic argument, the second (where “the universe” is supposed to be but, as far as the form of the proposition is concerned, doesn’t have to be the proper name of the universe inhabited by the speaker) cannot. At equivalent levels the first sort of proposition says something about some universe, while the second sort of proposition says something about our wondering. A proposition of the second sort would not necessarily entail a corresponding proposition of the first sort. It may be wonderful that we can wonder that the universe is F but at the same time it may not be wonderful that the universe is F, since there is ambiguity about the referent of “the universe” in this context. But the essence of anthropic arguments is to try to derive propositions of the first sort from propositions of the second sort. Rees skirts this kind of error when he asserts (p. 10) that the size of “the” universe “is actually entailed” by our existence. "Surprise" is also an emotive term, a psychological term that does not (barring neurophysiological analogy) stand for a physical concept. Actions in accord with surprise belong within the sociology of physical scientists but not within physical theory proper. While perhaps good as an element for a scientist’s autobiography, it adds nothing to physical theory. It is not a physical observation. But just how surprising is it that the universal constants are what they are, namely that our entire current physical model is what it is? For my money, it is not surprising at all, since any alternative would be just as surprising. If they are all surprising, then none of them are surprising. More accurately, “surprising” is not a meaningful adjective to apply to the universe (as is “unsurprising” the purported attitude of Rees’ hardheaded straw man). There are ex hypothesi an infinite number of alternative configurations of physical laws. Why wouldn’t each one of them be equally surprising (at least to us; some of the configurations wouldn’t have any inhabitants to be surprised) if it were actual? And if all of them are surprising, is there any meaning to the term “surprising” in this context? Would “improbable” be a better alternative to “surprising” as some have suggested? The idea here is that it is improbable that the universe should be configured the way it is because there are so many alternatives. While Rees goes to town with being impressed, he, perhaps wisely, avoids the superficially more sober idea of the improbability of the configuration of the universe as understood by our current physical model. For, to bring probability into this mess is to commit an elementary error in the mathematics of probability. There are not just a lot of alternatives, there are an infinite number. So any probability calculus in this instance would involve division by infinity, which  since for any real number r, r/∞ = 0  is tantamount to saying that it is not true that the cosmological constants are what they are which contradicts our assumption. The idea of cashing in the appearance of design as the reality of improbability rigorously defined is a spectacular freshman mistake. And I venture to speculate that any like attempt will meet with similar ignominy. But unless surprise or beingimpressedby can be anchored in some, so to speak, primary quality, i.e. some property possessed by the universe itself and not solely a qualification of an observer of the universe (“Appearing designed” is distinct from “in fact having been designed.” The former is evidence we muster to support our argument that the latter is the case. It is a sort of secondary quality. Something can appear designed to one person and not appear designed to another person. In fact, if one can speak of tertiary qualities, then “appearing designed” is closer to “good” than it is to “green.” Both “good” and “appearing designed” as opposed to true secondary qualities, rely on values on the part of the beholder. If approached by some creationist with wild hair and rolling eyes who asks whether the facts are just coincidences, you may reply that the difference between a fact and a coincidence is the attitude of the observer  and then offer to have him anesthetized.), that is to say unless the secondary qualities that form the basis of the assertion that the universe exhibits evidence of design can point to some specific objective correlative in the universe, and preferably a rigorously definable correlative such as a probability ratio, then the assertion that one simply “feels” the secondary qualities is arbitrary at best and most likely irrational. I regret to say that, despite all his degrees and accomplishments, Rees is in this case being both arbitrary and irrational. Note this is not a matter of physical measurement but purely an issue of mathematical probabilities. There is no demand that every one of the countably infinite number of possible cosmological constants be identified by an empirical procedure like a measurement. In fact by definition only one is instantiated. For that reason my argument does not court something like the Pythagorean confusion between arithmetical quantities and measurable quantities. In fact it is those who try to impose probability on the observed values of physical measurements without recognizing that probability introduces a countable infinity of possible values who reintroduce the Pythagorean confusion (Cf. J.E. Raven’s discussion of this issue, pp. 371372). The infinities involved are no more perplexing than the infinities we use every day in calculating velocity and acceleration at a time. I reference the real numbers because, to take just one example, even transcendentals like π are used in the most elementary geometrical reasoning. However, the only property needed to make my point is density so we can restrict our measurements of the universal constants to the rationals. It should go without saying that, since I am using a concept of infinity derived from the density of the rational numbers, the infinity I am referring to is countable and need not involve one of the Cantorian transfinite infinities or anything having to do with the mathematical Continuum Hypothesis. Cantorian issues do arise for those who believe that ∞/∞ is definable, a group that doesn’t include an overwhelming number of physicists. Those who are uncomfortable with mathematical infinity can easily substitute the tried and true “indefinite” for all occurrences of “infinite” in this discussion. If you’re driving along the highway and a tire goes flat, you slow down. The system comprised of your car and yourself as driver undergoes a state change and reacts by a compensating change to achieve a new equilibrium (where equilibrium means not crashing into the divider). If you’re fucking some hooker and your condom breaks, you could go limp. That is, if your psychology is such that you are affected by this minor sexual trauma. Change an assumption about your psychology and you keep banging away until the hooker pushes you off. Say we made a thought experimental change in the psychology of a depressive. Under ordinary circumstances, if we give him a hit of Prozac it’s smiles and hugs all around. But suppose we hypothetically change biochemical laws such that Prozac does not eliminate depression, but has no effect at all on a person’s mood. Is this possible? Yes, because its description entails no logical contradictions. The point is that a single change in a system does not of itself lead to a completely different system. We must also specify that no compensating changes occur such that some description of the system that interests us remains unchanged. The same is true for the physical system we call the universe. Changing one feature of that system may lead to certain consequences. But if compensating changes also occur, then those consequences would not occur. A change in the value of a given universal constant would lead to the consequences Rees predicts only if all (or enough of) the other constants and physical laws remained unchanged. He says as much at a number of loci. Under Rees’ thought experiment of a change in the value of the ratio of electromagnetic to gravitational force, he says “Conditions for complex evolution would undoubtedly be less favorable if (leaving everything else unchanged) gravity were stronger.” (p. 34) And, discussing the percentage of mass loss in the fusion of two hydrogen atoms into helium, he says, “Stars could still form in such a universe (if everything else were kept unchanged) but they would have no nuclear fuel.” (p. 55) If the proportion of gravity and total restmass energy were different, “but the other cosmic numbers were unchanged,” (p. 128), one consequence would be that stars could not form. And so on. If we speculatively assume a change in one facet of the current model, we must also assume that a significant portion of the rest of the model remains unchanged for the imagined consequences to ensue. After all in a universe with a significantly stronger force of gravity there could also be a biochemistry that permits the creation of skeletons with the load bearing strength of steel Ibeams. This really takes much of the drama away from unwarranted focus on the universal constants. Once we start speculating and stop observing there are too many alternative scenarios (Try an infinite number of them) for our speculation to make much sense. If we weren’t so poor, we’d be happy now. Did some fine tuning make you poor? Unless you beg the question and assume that everything is fine tuned, the answer is: None. Rees is also guilty of what one may call perspective manipulation. That is, arbitrarily choosing a point of view that increases the appearance of improbability. For Tante Léonie going into the next room is a journey of a thousand miles. Rees does not commit the undergraduate mistake of some of his theological epigones (Cf. Stenger p. 145) of choosing dimensional measurements as examples of the hand of god. But even probabilities expressed as ratios look very different depending on what alternatives we choose to highlight. Do the values of the universal constants represent a lucky shot in a sea of possible failure or one of many, many possibilities of success? Is Gulliver a giant or a pygmy? It depends on how you look at things. A couple of examples will suffice. The constant that generates most of Rees’ alarmist speculation is the ratio between electromagnetism and gravity: N. According to Rees, this is 1/10^{36}. (Rees doesn’t distinguish clearly between the strong force and all three electromagnetic forces, the strong force, the weak force and electromagnetism, but he seems to mean just the strong force. Published measurements of the ratio of electromagnetism, the weak force and the strong force to gravity go as high as approximately 1/4.1 x 10^{42}. Current estimates of the ratio of the strong force alone to gravity range anywhere from 1/10^{36 }to 1/10^{38}.) After you put down Just Six Numbers you have the panicky feeling that the gravitational constant might just have something to do with global warming. It’s hanging on a razor’s edge and if it were to shift even just a teentsy bit we would all be squished as flat as pancakes or flung into the endless void to meet Captain Kirk. Rest assured, dear reader. The universal constants don’t shift, or if they did, it wouldn’t have anything to do with armchair speculation. What Rees actually says is, “If N (the ratio) had a few less zeros, only a shortlived miniature universe could exist: no creatures could grow larger than insects, and there would be no time for biological evolution.” (p.2) How much is a few? Gravitation is feebler than the forces governing the microworld by the number N, about 10^{36}. What would happen if it weren’t quite so weak? Imagine, for instance a universe where gravity was ‘only’ 10^{30} rather than 10^{36} feebler than electrical forces. Atoms and molecules would behave just as in our actual universe, but objects would not need to be so large before gravity became competitive with other forces. The number of atoms needed to make a star… would be a billion times less in this imaginary universe. Planet masses would also be scaled down by a billion. Irrespective of whether these planets could retain steady orbits, the strength of gravity would stunt the evolutionary potential on them. (pp. 3334) A difference of 10^{6}?! That’s a lot less. If my dick were a million times larger than it is I would not be the greatest porn star in history because it would be 158 miles long plus or minus a couple of miles. Even fully erect this is too long. I would definitely be on a lot of “No” Lists. The point is, when we are speculating, we can choose any randomly huge number and, depending on our rhetoric, make it look like the original measurement was finely tuned. Rees actually says that the munchkins would have to grow two meters to play in the NBA but makes it sound like they would only have to grow a micron or so. Well, you may say, the variation is large, but it is a mere pittance from a cosmological perspective where a trillion is considered chump change. But science deals with facts not perspectivally biased value judgments. The statement that it’s a close shave that the universal constants should have exactly the value that they do, that they are finely turned (An issue independent of the question of whether they are tuned at all), is a rhetorical statement. It is a value judgment that is not part of physical theory. But even if the universe flared and sputtered like a Roman candle, that wouldn’t mean that “we” or some version of us couldn’t find a home in it. Let me engage in a bit of speculation about time. To us the present age of the universe seems like a very long time. The period from the Big Bang to some sort of heat death is even longer. This is mostly because we compare these times in our minds to the length of a human lifetime or to the course of recorded history. Multiply either time by say 10^{100} and the actual time would appear pretty damned short by comparison. The same perspectival prejudice is in play when we assume that a universe where N is much larger would be ridiculously short lived. But assuming enough physical laws were different in that universe, it could evolve conscious entities constituted by a physics and chemistry unlike anything we know. Those entities’ few blips of Planck time could to them appear just as endless as any Sunday afternoon in our “middlesized” universe. Maybe that universe even contains a Rees Doppelgänger who expressed satisfaction that N was not something absurd like 1/10^{36}. Rees helps us understand the fine tuning of the ratio between gravity and the expansion force of the universe or Ω by means of a graph (p. 98): He shades a portion of the trajectory of the universe around the flat universe to indicate the “permitted” range for expansion speed to accommodate the observed facts (e.g. the existence of humans). Now any harassed sales manager can tell you that a graph can be dressed up to make sluggish sales look like they were increasing exponentially. Note the permitted range looks awfully small compared to all the white around it. Ain’t necessarily so. The area of any expanding bounded range is going to look small depending on how we set up the graph. For example, the graph is cut off before the widening of the permitted range can really kick into gear (admittedly the present age of the universe). Blow up a segment of the graph sufficiently far from the origin and the permitted range can be made to look quite large. It will look really proportionally large at the origin where all the values converge. More importantly the representation of the ratios between the shaded and unshaded portions of the graph can be adjusted at will. However, graph magic and perspective manipulation is not the only issue. The permissible range for values for Ω is actually a segment of the real number line. Rees says, “…at one second after the Big Bang, Ω cannot have differed from unity by more than one part in a million billion (one in 10^{15}) in order that the universe should now, after ten billion years, be still expanding and with a value of Ω that has certainly (“certainly” – strange expression. Either it has departed or it hasn’t  WD) not departed wildly from unity.” (p.99) Sounds like a long shot unless you’ve spent time in Vegas where one chance in 10^{15} is practically even money. Take a segment of permissible values for Ω in the second after the Big Bang. Say the range from a difference of one part in a million billion plus or minus one from unity to a difference of one part in a million billion from unity. Sounds pretty small from our “middle sized” perspective (There’s that damned perspective again). But it’s not small. It’s huge, gigantic, XXXL. It is in fact just as big as the real number intervals that lie outside of this interval. Because the real numbers have the property of density, the interval from a million billion minus one or a million billion plus one to a million billion has an infinite number of values. So do the intervals lying outside this range. And infinity (as long as we we stick to the countable) equals infinity. So if you really wanted to apply the probability calculus to the chances (i.e. possible events as represented by the denominator of a random variable) for “successful” vs. “unsuccessful” values of Ω one second after the Big Bang (which you pointedly cannot do when you are dealing with an infinite number of chances), your result might look like ½, i.e. a single flip of the coin, what you might call a “gross tuning.” That is, if we were dealing with finite real numbers as allowable values for the frequency of a given event out of all possible events, i.e. the numerator and denominator of the random variable. But we're not. The random variable would in fact end up being infinity over infinity plus infinity (∞/∞ + ∞), which, since countable infinity equals countable infinity, reduces to ∞/∞ which is disallowed. (There is a version of ∞/∞ that relies on a distinction between countable and uncountable infinities. Even this version of ∞/∞ yields a type of infinity, which is tantamount to being disallowed, since the range of acceptable probability outcomes is from 0 to 1.) ε is another example. Rees asserts (p. 55) that the permissible range of values of ε for complex chemistry to emerge is 0.0060.008 (or 4%, p. 56). This is also a segment of the real numbers that has the property of density. But since probability calculus does break down when you are dealing with an infinite number of alternatives to a given event, it doesn’t make sense to speak of probability at all. “Fine tuning” is a meaningless term. (Note the concept of one out of an infinite number of alternatives to an event is different from an infinite number of random variables in a sample space such as appears in probability density functions. One value over an infinite number of chances is disallowed, whereas you can have an infinite number of valuechance combinations (the random variable) as long as the chances are finite in number. There is no probability of any kind that one side will land face up if the die has an infinite number of faces. But the waiting time at a stop light could be expressed by a probability density function.) To repeat, when we deal with an infinite number of chances the calculus of probability breaks down (In a good way. Division by infinity indicates that to speak of probability in situations like this is to talk nonsense.) However, and this is where Rees breaks down, probability calculus is the only vaguely rigorous way proposed so far of approaching the finetuning hypothesis, the only way that doesn’t incorporate rhetorical and emotive terms like “surprising” or “impressive.” Would probability be applicable if the value of a constant could be expressed accurately as a single real number and not a set of permissible values? The answer is “No” because the set of alternatives, i.e. the divisor in the ratio, is still infinitely large. In other words, if the numerator of the random variable is infinity (i.e. the number of possible values for a given cosmological constant equals infinity), the ratio or random variable becomes ∞/∞, which is disallowed. If the value of a given cosmological constant is a single real number, then the ratio becomes r/∞ which rates the probability that the actual cosmological constant is the actual cosmological constant as zero, a contradiction. Furthermore, let’s get real about these constants. The values of the universal constants are not magical talismans. More apropos, they are not axiomatically generated. They are the result of measurements. And measurements have a margin of error. So to achieve the same result for any of the universal constants that I did for Ω just take any segment within the margin of measurement error and you still end up with a phony ratio of infinity to infinity. You end up with no meaningful concept of probability. Would there be any merit to an argument to the effect that Rees and his creationist buddies do not rely on mathematical infinity, that in physics we at best deal with a real world ersatz for mathematical infinity (which works down to “indefinitely large,” that is when a physicist asserts that the cosmos is infinite he means it is indefinitely large, viz. that, not unlike the Lucretian spear thrower, we cannot find its boundary. Stenger lucidly explains (p. 123) one concept of infinity for empirical physics, though he is wrong in assuming that real distances are not accurately represented by the nondenumerable continuum.) and the paradoxes of mathematical infinity? In a word, no. There is no merit to this argument. The assignment of probability values to the actual state of the universe is not an observation. Nor is it deduced by physical laws from actual observations. Rees in fact evokes mathematical infinity and not empirically observable infinity (indefinite largeness) when he argues (p. 173. Cf. also. P. 179.) that alternative values for Ω and λ require an infinite number of alternative universes. (The only correction one might add to his comments is that our universe is not a member of a “small and atypical” subset of the set of all universes. In terms of how the problem is set up, the subset of universes of which ours is a member is not small. It is infinitely large.) Probabilistic speculation about alternatives to the actual state of the universe is different from the classical dice throw example where the sample space is defined by the observed number of faces of the die and the observable – either observable or generated from observation by mathematical induction  number of tosses. The infinitely large random variable represented by a segment of the real numbers is not observable and, even if it could be generated by mathematical induction, that would still result in division by infinity (Remember a sample space and the denominator of a random variable are not the same thing.). The idea of alternatives to the actual state of the universe is pure speculation to which mathematical techniques are improperly applied. What is the probability that mushrooms have souls? Does not compute. A random variable in a typical simple probability calculation is expressed as a rational number where the numerator expresses the frequency of an event in a given sample space and the denominator expresses the sum of all possible events. In a properly defined finite sample space the sum of the numerators should equal the denominator of each of the random variables, which in turn should be the same for each value of a random variable. The sum of all possible events cannot be infinity. The situation is simple when we are dealing with tosses of two headed coins and only slightly more complicated in the case of continuous random variables. In the latter case the function that is the integrand of the probability function is often a formula with a finite denominator. In a speculative “calculation” of probability, on the other hand, the denominator of the “random variable” is always going to be infinity because that’s what speculation is all about. If asked, for example, what else could ε be but 0.07, the proper speculative response would be, “Well, anything.” That answer knocks out coherent talk about probabilities. I suppose this is what 18^{th} century materialists meant when they described the facts as necessary and what contemporary scientists mean when they say that “brute” facts just are. “Necessary” is a misleading way of asserting that the facts of the universe are not the result of humanoid volition for obvious reasons since it introduces meanings of “necessary” that are unrelated to the issue. It also seems to imply that things could not have been otherwise in some logical or strong physical sense. I think that what I explained above is what Hume and the French materialists meant to say when they asserted that the universe was “necessary" and not designed (I like what one of those materialists, La Mettrie, had to say about the matter: “…toutes ces choses…qui nous étonnent si fort, ont été produites, pour ainsi dire, à peu près par le même mélange d’eau et de savon, et comme par la pipe de nos enfants.” And: “Dénuée de connaissance et de sentiment (la nature) fait de la soie comme le bourgeois gentilhomme fait de la prose, sans le savoir, aussi aveugle lorsqu’elle donne la vie, qu’innocente lorsqu’elle la détruit.” p. 234). The proper way of expressing this is that the concept of probability does not apply to the observations of physical theory at all. It is falsely assimilated to the coin toss model where the number of alternatives expressed by the denominator of the random variable is finite. In the speculative arena there is no limit on the number of alternatives. The die has an infinite number of faces. Interestingly enough Rees makes a similar point in commenting about the spread of earthly biology to other galaxies. “Manifestations of life and intelligence could eventually affect stars or even galaxies. I forbear to speculate further, not because this line of thought is intrinsically absurd but because it opens up such a variety of conceivable scenarios – many familiar from science fiction – that we can predict nothing.” (p. 81) All one need add is that any probability scenario whose random variable is represented by a segment of the real numbers is intrinsically absurd. All this fits rather well with our natural intuitions about what probability is all about. Consider the fact that we apply probability to future outcomes and not to past events. In manufacturing, traffic control and gambling we are interested in the mathematical chances that a certain outcome will occur. We have close to no interest in the chances that a past event could have been different. After the event our money has been won or lost. The probability of a fact is 1. This doesn’t really have much to do with time from a purely mathematical standpoint, since we can always speak of probability at a time. That is, we can tag a probability distribution P as P_{t} where t = a specific time. However, it has everything to do with the fact that we simplify the description of a probability distribution to ensure, among other things, that the denominator is not infinity. We have, for example, simplified the description of coin flip examples to outcomes where the coin would land heads or tails (i.e. m/2^{n} where n is a finite number of flips). We cannot calculate and do not ask what are the chances that the coin’s temperature on landing will be n^{o }C when the answer to the question “What are the choices” is “Anything.” An equally illuminating illustration lies in fiction and imaginary events. What are the chances that the events in the Odyssey (or perhaps the Bible would be more to the point) could really have happened? Disallowed. It is fiction. You can imagine it, but you can't assign a numerical value to its possibility. You can't compare it to what really happened. As I write the probability is zero. Before Homer’s birth any probability was mathematically inexpressible because a well formed sample space could not be defined. Alternatives to what the universal constants actually are (which is different from what we believe them to be based on our best measurements) should best be treated as fiction. The probability of such alternatives in the past is zero. The probability that they could be different now is mathematically inexpressible. It is no different from trying to express the probability that one of Douglas Adams’ characters is really really rattling around somewhere in the universe at this moment. Schlick (pp. 391 ff.) proposes a a not very helpful different basis for a related objection. Since any general statement about the applicability of probability to nature is itself probabilistic, he says, we cannot apply it without further testing as to its validity. So, even assuming that the formal probability that the universal constants are what they are is one in a billion or whatever (i.e. assuming that all logically possible states of the universe can be put into a onetoone correspondence with one billion natural numbers), we would still have to actually observe a billion different universes to be assured that the mathematical probability actually applies to reality. Make of this argument what you will. It doesn't convince me. The formal statement that there are no more than a billion possible configurations of the universe is not probabilistic. It simply sets an upper limit on the size of the sample space. On the other hand, if the specification of the size of the sample space is an empirical and not a formal mathematical statement, then Schlick has a point. I'm pretty sure Rees believes his sample space is formally defined. He just wildly underestimates its size. Back to surprise and being impressed, which are Rees’ emotive versions of probability. Empirical scientists are less surprised when a measurement is consistent with current theory and other measurements (After all, that’s what they were looking for), although they will insist that the conforming measurement be repeated and verified, especially if the fit is too neat. When they are surprised (Perhaps “dismayed” would be a better word), is when measurements don’t fit. So it would be more surprising if the constants were such that, in contradiction to the observed facts, we could not evolve. That would lead to a welldefined scientific problem rather than the vague imperative that everything needs explaining. Remember the equations in which the universal constants appear are in a very real sense observations (even those that are only deductions from direct observations). Anomalous observations require explanation in a different way than the way that any phenomenon at all requires an explanation, for the unexplained persistence of the anomalies means that there is a contradiction in the physical model. All Rees really asserts is that the universal constants need explaining in the second sense. But he strongly hints (and scientific boneheads like John Leslie outright assert) that they also require explanation in the first sense. They don’t. The currently accepted values of the universal constants do not lead to contradiction in the current model. As any Monte Carlo croupier can tell you, “Et cette circonstance, seraitelle si peu fréquente qu’il dût prendre sur lui de la considérer comme une exception” Or was that Lautréamont? Rees’ own book gives several examples of what happens when competing observations are not consistent with each other. One example lies in the anomalies that led to the hypothesis that there exists something like dark matter in the universe. The speed of the motion of cosmic bodies should be determined by the ratio of gravitational force to the centrifugal force of orbital motion among other things. However, the actual observed speed of cosmic bodies is inconsistent with the value of this ratio. The observations are inconsistent with the known laws. (Rees treats the subject on pp. 82 ff.) Now this is what scientific surprise should be. It is “surprising” because inconsistency is unacceptable. Assume, on the other hand, that the observed speed of cosmic bodies had been consistent with the accepted model. The gist of Rees’ argument is that that would have been surprising because it fit so well. But if both p and ¬p are surprising then neither is surprising. It’s the famous night where all cows are black. In fact the discovery of an observational anomaly (the speed of cosmic bodies, the orbit or Uranus, the perihelion of Mercury) is the exact opposite of the consistent physical model that Rees calls surprising. So a consistent theory can’t be surprising practically by definition. When confronted by an observational anomaly scientists set out to search for a compensating factor so the model can be rendered consistent. They do things like predict the existence of dark matter or an unobserved planet or in extreme cases clean house (special relativity). Why then should it be surprising that the model becomes consistent again? That’s what we were looking for. The fallacy of marveling at a conclusion you did your darnedest to draw is a special kind of fallacy I call the easter egg fallacy. It’s like expressing joy and surprise at finding something in the garden you placed there the previous night. The real surprise would be if you didn’t find it the next morning. The scientists in the family would look for compensating factors (Thieves? Wind storm? Faulty memory?). The specific cosmological form of this fallacy lies in discovering that something does what it was supposed to do. Say a man created from scratch a tool that was perfect for planing wood. He then set it aside and forgot about it. Years later he or his children stumbled on the item and marveled that here lies a thing just perfect for planing wood. How miraculous is that? Not miraculous at all, of course, since that is what the man created it for. It is no more miraculous than if he had not created the tool and years later he or his children stumbled on its components and marveled that here was a bunch of stuff that couldn’t plane wood in any way. The tool is the easter egg. (A particularly brain dead creationist might pipe up at this point and say this example is all about design. The universe is a tool (Actually in my opinion godot is the tool). But obviously the tool is our physical model. Why should we be surprised that in all its precision it is consistent with the facts? That’s what we devised it to be.) I should like to wander off the creationist path for a moment here and speculate that the easter egg fallacy is in fact rather widespread. Philosophers have been seduced by the fallacy ever since they considered true propositions and opined that there is some mysterious and particularly difficult to define relation between a situation in the world and the utterance of a true proposition reporting that situation. But why should it be surprising that the utterance of a proposition bears the relation of truth to the world (in Fregean terms, that the proposition’s referent is truth)? That’s what we devised it to do. It’s not like we found the word “danger” beneath a rock and discovered that it began flashing on and off whenever tigers came by. Perhaps more likely when h. heidelbergensis saw a predator he began exclaiming in a particularly agonized way to warn the wife and kids to dive into the cave. Once he noticed he didn’t have to tear his hair out and stamp his feet on the ground every time, but just utter the same sequence of sounds, even in a whisper, then the word “danger” or “Gefahr” or whatever was born. If you dig a bit into what is said on the subject, you can conclude that philosophers make a further error that underlies the easter egg fallacy in that they tend to carry around in their heads a potentially misleading picture of what language is. They talk and write as if language and the universe were two large contrasting structures, each independent of the other, perhaps somehow created separately, like two giant citadels facing each other across a river (Wittgenstein’s Tractatus makes this implicit misleading picture explicit). The relation between the two citadels is that one is a (rough) mirror image of the other. Taken literally, this picture is not only misleading, it is wrong. Language was not created independently of the universe it reports on. A more likely scenario is that bits of language were devised precisely for the purpose of reporting situations in the world, for the purpose of being true. Such a bit of language would be “Danger!” This might have evolved into “Danger, tiger approaching” and “We are at this moment in a dangerous situation. A tiger is approaching.” The last utterance contains sentences with truth values. In the course of the evolution of utterances a point was crossed where a potentially infinite number of true statements could be generated from a finite number of elements. There is an interesting issue in what actually constitutes the difference between the second quotation, which looks like an unabashed name of a situation, and the third quotation which asserts something about the situation. But I think that if we replace the mirrorcitadel picture of language with this more accurate picture, we are less likely to cause ourselves mental cramps when we address issues like truth and meaning or perhaps even to look upon the predication issue as particularly important. Back to cosmological models: We research to find the generalizations that describe the universe and are consistent with particular observational statements. We are then amazed that we can deduce observed conditions from these generalizations. What's so amazing? That's what we were looking for. It's like creating easter eggs and then "discovering" them in the lawn. Another interesting side note is that once the notion of dark matter began to gain acceptance, dark matter could be used to explain other anomalous observations, such as the unexpectedly high temperatures in the interior of the gas giants (Jupiter, Saturn, Uranus, Neptune) in our solar system (Charles O. Choi, “Neighborhood Darkness” Scientific American, January 2009 pp. 2425), or the abnormal bending of light by distant galaxies (Rees, p.85). Again concern arises and should arise among scientists not when observations are consistent, such as the consistency between the cosmological constants and the development of human life (Remember forces are postulates whose values are calculated and recalculated – adjusted – in the model to accommodate observation. When scientists were developing the equations that gave values to the cosmological constants, why the fuck would anyone have suggested values that he knew were inconsistent with the observed facts?), but when they are inconsistent. A solution is sought in the form of a search for missing observations or supplements to theoretical gaps. The source of this way of doing things is the basic logical requirement for consistency, a requirement that is not limited to scientific modeling. A fundamental axiom of all science is (to use standard notation) ¬(p & ¬p). Its contradictory (p & p) is, of course, trivially true, but it is precisely certain propositions of this kind that Rees calls “impressive.” Rees notes (p. 85) that an alternative to the dark matter hypothesis would be to revise the inverse square law for the calculation of gravitational attraction between bodies. Consider, however, that a revision of that law would entail a revision in the ratio between gravitational force and electromagnetic forces, namely N. But, if we settle on a new value of N, then it would turn out that the former value wasn’t so impressive at all, since it wasn’t even the actual value. But if that value wasn’t impressive, why should we consider the new value to be any more impressive? The cosmologist certainly doesn’t want to be like the duckling that follows the first moving object it sees. Perhaps what is impressive is that there are any constants at all, viz. that the physical universe behaves regularly according to unvarying laws. We already saw that this is no more than being impressed that the sun rises every morning, an object of wonder stripped of all the cool trappings of anthropocism and low numerical probability. Furthermore, it might not even be true. Cosmologists and physicists treat seriously the hypothesis that the laws of physics could be different at very large and very small distances. And if mushrooms suddenly began to fly we might have to accept the possibility that the universe in that case does not behave according to regular laws. What we do know is that scientists would begin to search for an explanation of flying mushrooms that would restore of the uniformity of nature (perhaps some mushroom loving dark energy). And, of course, the “impressive” uniformity of nature says no more about its “design” than does the nonuniformity of nature. These are just two black cows. Another example of an observational anomaly is the observed acceleration of the expansion of the universe. If gravity continues to have an effect at a time when the initial force of the Big Bang should be diminishing and if nevertheless the universe continues to expand at a faster and faster rate, then something is missing in either our observations or our theory. It is as if you threw a ball in the air and, instead of eventually returning to earth, it continued its upward motion long after the force of your toss had been exhausted. Not just continued upward but traveled faster and faster as you watched it soar. Solutions to this conundrum include a search for hitherto undetected particles of the dark matter kind or the revival of the cosmological constant λ that Einstein originally proposed to reconcile a supposedly static universe with the contractive force of gravity. What is important in the present context is not which solution will eventually be found true, but that the anomaly should motivate a search for new data, or, failing the success of that, a modification in our physical model. If Rees is correct that it is impressive that the majority of physical theory should be consistent with observed data, then it should not be disturbing that there is this or any lacuna. The inconsistency of cosmic acceleration with an uncompensated force of gravity should just be evidence that there was no intentional design to the universe. On the other hand, if we hypostatize a force solely to account for cosmic acceleration, then it is not so impressive that the numerical value of that force should be exactly what is needed to balance the contractive force of universal gravitation. To be astounded that something we made up, so to speak, to begin with is what it is – that constitutes an instance of the easter egg fallacy. Rees commits a particularly egregious example of this fallacy when, after explaining that a force such as λ could explain the fact of an accelerating universe, he proceeds to warn what would happen if λ were out of control : If λ isn’t zero, we are confronted with the problem of why it has the value we observe – one smaller, by many powers of ten, than what seems its ‘natural’ value. …a much higher value of λ would have had catastrophic consequences: instead of becoming competitive with gravity only after galaxies have (had) formed, a highervalued λ would have overwhelmed gravity earlier on, during the higherdensity stages….then there would be no galaxies. Our existence requires that λ should not have been too large. (p. 111) Talk about begging the question! These are just a few examples we can find in Rees. In fact part of the basic methodology of the physical sciences is to assume the uniformity of the universe and, if an anomaly is found, to find new observations or devise theoretical modifications to restore uniformity to the model. To then express the secondary quality of “being impressed” that the most up to date model expresses uniformity is like a logician who devises a system that contains the axiom “If p then p” and then is “impressed” that a theorem of the system, assuming appropriate rules of wellformedness and substitution, should be “If (If q then q) then (If q then q)”. Moreover the design proof of the existence of godot and the miracle proof cannot both be valid. For if both the uniformity of nature and observational anomalies are evidence of the “hand of god,” then we have no concept of what an uncreated and by extension a created universe would look like. It is as if someone said that conclusive proof of causality at a distance and conclusive proof against causality at a distance both proved the existence of ether. We would have no concept of the circumstances under which ether did not exist. Or if “Lord Cavendish died by poison” and “Lord Cavendish did not die by poison” are both proof the butler did it, then, using these two facts only, we have no concept of what it would mean for the butler not to have done it. There is, of course, nothing about the constants being what they are that requires an explanation unless the explanation comes in the standard scientific form of specifying an observable antecedent condition that causes them to be what they are or to fit into a broader pattern of regularities. But this kind of explanation is different in kind from the metaphysical explanation of a designer or its concocted opposite number, pure chance. Pure chance incidentally is just as meaningless as design in that “as a result of pure chance” is defined as “undesigned.” Pure chance in this sense is just another goddist fabrication. Now a multiverse theory might be regarded as legitimately specifying antecedent conditions if on independent grounds it were found to be valid. But the constants being what they are does not by itself constitute an argument in favor of the multiverse. There’s something wrong when every outcome of a random sample appears to show the work of an “invisible hand.” For example, I had just finished fucking a girl one night (I forget her name) and, lying back after one too many draws on the water pipe, I began a reverie about the fortuity of that segment of the great chain of being that led us from widely divergent starting points to eventual coupling and eternal love. The chances were definitely against us. We had grown up at opposite ends of the world and shared little in the way of common history. But we did meet; and how wonderful was that? If I hadn’t decided to come to England for a few years, if one of her friends hadn’t visited Oxford, if he hadn’t been an unabashed Mersenne who liked to form intellectual contacts, if I hadn’t taken a few days to get acquainted with his circle….If, if if. The strings that attached our heterogeneous beginning to the moment of union were tenuous indeed. What are the chances that I would get in the pants of the perfect woman for me? One of out 10^{37}? Why hadn’t I made the hideous mistake of coupling with Sally or Mary or Heather? I shared my thoughts with my companion and, since she was just as stoned as I was, she looked as if the universe had just opened up before our eyes. Of course, I immediately realized that, had I coupled with Sally or Mary or Heather instead of what’s her name, I could have and probably would have been led along exactly the same train of thought. What an amazing coincidence that I should, out of the billions of other possible life courses, been led more or less directly to the sweet little pussy of Miss Sally. It cannot be chance. It must have been fate. If I were religious, I would call it design. Of course, this miraculous coupling could have happened with anybody and it would have had exactly the same likelihood or lack thereof. (Barring statistical simplifications such as, for example, specifying exact numbers of various populations). Each one of the uncountable alternatives is equally miraculous. Which of course means none of them are. The problem, as we have seen, lies in assimilating the encounter to an improper model of probability. It is, so to speak, a category mistake to submit these chains of events to the chance/fate, chance/design, chance/multiverse model. Because I did no more than imagine a potentially infinite number of alternative life courses, the denominator in the probability calculation is undefined. My little reverie worked so well at getting a second night with this broad that I used it again. Several times. I recommend it. Part of the point can be made without involving mathematical infinity. If the chances of (name your team) winning the Super Bowl are m/n, then there is nothing special about any particular team having m/n chances of winning the Super Bowl in a given season. The expression of this pure mathematical structure says nothing about the New York Jets that distinguishes that team from the others. In the same way, simply stating that the observed universe had m/n chances of coming about says nothing special about this universe, even though, since it is the home team and we are fans of the home team, we like to think that there is something wonderful in the fact that it (figuratively) won the cosmological Super Bowl. If it turned out that the universe persisted as a seething mass of unruly plasma, then that fact would be just as wonderful. Indeed it is just possible that some of that plasma could express satisfaction that the universe was configured in just such a way as to contain only plasma  that no horrid and sluggish particles were allowed to form. There are also problems with the picture of explanations that Rees suggests. The proposed “fine tuner” explanation is no different from all the external agent explanations that have interfered with real scientific theory from, shall we say, the beginning of time. It really is nothing more than a rehash of the godascauseoftheuniverse metaphysics (and the particularly idiotic debate over whether god worked its magic just once, at the beginning, or continuously every time the sun rose) that Laplace finally put out of its misery. Thinking along these lines represents a regression to the second of Frazier’s famous three stages of human thought, namely the animistic, the theistic and the scientific. What characterizes the first two stages is that they locate the cause of natural phenomena in humanlike volition on the part of entities not subject to verifiable observation. Scientific explanation, on the other hand, looks for causes in natural occurrences that ultimately are just as observable as the phenomena to be explained. The unobservability and the volitional nature of the ostensible cause are problems for the animistic and theistic ways of thinking. Scientists have long recognized how reliance on the unobservable makes for bad theory. It is not emphasized often enough how bad the volitional aspect of animistic and theistic theories really is. Volitional theories are nearly content free. They don’t say much more than that somebody or something wanted it that way. They do not help locate uniformity and regularities and they do not produce any predictions (much less testable predictions). They are barren. In this light the finetuner explanation of the universal constants is different in kind from a real explanation. It is not an alternative to a scientific explanation because it is not in competition with scientific explanations. Both could be true. The ball could have gone into the basket both because of the laws of physics and because coach willed it to go in. (But to say only that coach willed it to go in won’t help much in practice (sports psychology aside), and it could lead to disaster in the next game.) In this respect Rees seems to have been seduced by the volitional goddists who are only too willing to rush in with their bullshit whenever there is a theoretical lacuna (which is all the time). In a broader way and from a scientific perspective, looking for an explanation for the universe represented by our entire current physical model in an unobserved cause outside what the model, or a welldefined more inclusive model, could represent, is a nonstarter. It is so to speak 10^{43} units away from asking why there is something rather than nothing. Scientists have a name for such an inquiry. They call it metaphysics (Rees rather agrees, p. 145). (By way of aside, metaphysics properly practiced by licensed philosophers without the pollution of myth or logical error, does not correspond to what your common run of scientist understands as metaphysics.) Obviously the unobserved creator theory is such a non starter. The multiverse theory, or at least the way Rees uses it, is a fence sitter. Rees appears to consider the reasons proposed for creationism as a good argument for the multiverse theory. If you accept that the actual state of the universe requires some sort of special explanation, then the multiverse theory and creationism are redundant. And Rees obviously prefers the multiverse explanation. By now I think we understand that the grounds proposed for demanding some sort of special explanation of the actual state of the universe are logically incoherent. But, as opposed to creationism, this does not qualify the multiverse theory as scientifically invalid. In the first place there are other perhaps sound reasons for embracing a multiverse theory. And the multiverse theory is falsifiable in a way creationism is not (Cf. Rees, p. 167).The crucial question is whether there are any observations that can give it credibility and whether it can be made to harmonize with a physical model that also includes the model that describes our universe. I am puzzled that Rees does not admit of possible explanations other than the category mistake represented by goddism and the multiverse idea that he adopts as his own. So many options suggest themselves. It is not logically impossible, for example, that we should crack the first instant of Planck time and form a model of the conditions obtaining prior to the emergence of the presently configured universe. (It is perhaps more likely that we will come up with a cosmological model consistent with observation that does not rely on uniform expansion.) And the physically impossible may not be so, even though at this time we can’t figure out how. In fact to slide from the assertion that the actual state of the universe could have been otherwise or even from the mathematically incoherent version that the actual state of the universe is improbable in any rigorously definable sense of “improbable” to the use of the phrase “finetuned” is rhetorical sleight of hand. To put it more bluntly, it begs the question. It is a category mistake. This is because “finetuned” is performative in nature (My use of “performative” is obviously different from Austin’s). It implies an agent. It assumes somebody did it when Lord Cavendish could very easily have died of a heart attack, and improperly reduces the question to whether the maid or the butler did it. Even if there were a logically coherent way of asserting that the actual state of the universe is impressive or improbable, one would still have to show why this implies that it is finetuned. The two are not equivalent. Rees considers himself “impressed” by John Leslie’s firing squad metaphor. The idea is that if a condemned man, facing a firing squad of fifty trained marksmen, remains untouched by every one of their bullets, he should not just consider himself lucky. He should look for some explanation. Perhaps that sawbuck he slipped to the sergeant had something to do with it. Rees should know better. This is a terrible metaphor (more precisely, it’s an analogy)! The only reason we look for corrupt platoon leaders or subversive grunts or some other intentional or volitional behavior on the part of an agent is because volitional behavior is already built into the situation. We assume that the marksmen intend to hit the condemned man. The question is partially begged; it would be completely begged if we sought intentional or volitional behavior on the part of some otherwise unobserved agent when it comes to “choosing” the cosmological constants. The more appropriate analogy would be to a situation where fifty rifles fired at random (Perhaps they were stacked too close to the camp fire). Or else if a fellow was giddily close to a crate of fireworks that exploded unexpectedly. If he were not hit, he would consider himself lucky. But he wouldn’t say to himself, “Hmmm, this is more than just luck. Someone must have known that I would be at just that spot when the fireworks went off and so stacked them intentionally such that I wouldn’t be hit.” Or if he did say that to himself, Dr. Freud would like a moment with him. I hope all this won’t give the little ones nightmares. Rees did write a clear and entertaining introduction to some of the basic concepts of cosmology. But that his pedagogy should become mixed up with a deadend issue like creationism….Surprising.
