7. Fine-tuning — as it really is, not as it is put about

The question: is there in the structure of the universe a fine calibration that shows it was intended?

The answer in two lines: in the laws of physics there are free numerical parameters which the theory does not derive but which are measured and then put in by hand, and some published models find that altering a few of them by small percentages disrupts the production of carbon — and these are peer-reviewed calculations that nobody denies were carried out; how wide the permitted range is, though, is disputed among the specialists themselves, as will appear with Adams and Stenger and Barnes. But moving from them to 'therefore there is a designer' requires a probability distribution over the possible values which we do not have, and the three best-known figures put about in this subject in Arabic are described as other than what they are.

In this chapter I go against most of what has been written on the subject in Arabic, and my going against it is in the argument's favour and not against it. For a figure passed on as other than what it is does not lose itself alone when it is exposed; it takes with it the reader's trust in everything he read before it and after it. And whoever built a conviction on a figure and then opened the reference and found the man who made it saying other than what was attributed to him has not lost the figure but has lost the one who passed it on.

And what is this chapter doing in this book? I say it at the start and not at the end, because whoever leaves it to the end has led his reader to think he is building when he is clearing away. This chapter is a clearing away and not a building: its aim is to get three false figures out of the Arabic literature, and to state the limits of what is left after them. And it tips no scales, nor is it meant to leave any leaning in you. I will say at the end of it what is left in my hand, and I will say with it that it is a question and not an argument — and I will put it under the blade I take to others, in a section named for it.

First: what is actually measured — 'the free parameter'

Begin from the thing there is no dispute about, and set the dazzling figures aside until we come to them.

The laws of physics are not figures but forms: equations saying how one quantity is tied to another. And a form on its own is not enough to calculate anything with — you have to put numbers into it. Some of these numbers come out of the theory itself, and some of them the theory does not know at all: you go and measure it in the laboratory, then come back and write it into the equation by hand. And that is the free parameter.

The example: in a factory there is a control panel with seven dials — heat, pressure, belt speed. And the manual for the machine, a hundred pages explaining in full how the machine works, does not say in a single place where each dial is to be set. Those are figures written by hand on a sheet stuck up beside the panel, and they came from trial and not from the manual. And the manual is not deficient: it describes the machine, and the sheet describes the setting.

*And where this example breaks down*: the range of the factory dials we see with our own eyes — from zero to a hundred, engraved on the panel. And the range of possible values for the cosmological parameters we do not see, and we do not know its limit, and it will appear shortly that this very ignorance is the most serious thing in the whole subject.

And a second example nearer home: 'flour and water and heat' is the rule of bread, and it does not say three to one. You ask the baker: where did the ratio come from? And he refers you to no law of chemistry but to a practice he inherited. The rule is in the book, and the ratio is in the hand.

*And where it breaks down*: the baker gets acceptable bread over wide ranges, so the ratio is elastic. And the claim in this subject is that the acceptable range in some of the cosmological parameters is narrow — and its narrowness is what is disputed, not the existence of the free parameter itself.

So how many of these parameters are there in physics? In the Standard Model of particle physics there are some twenty free parameters — particle masses, the strengths of the forces, mixing angles — and with them the parameters of the standard cosmological model: the density of matter, the cosmological constant, and the amplitude of the primordial fluctuations.

And this last passes in Arabic writing as a name with no meaning attached, so I shall explain it. The universe moments after the explosion was close to complete uniformity: one density almost everywhere. And it is that 'almost' that is meant: within it is a slight variation from place to place of the order of one part in a hundred thousand (written `Q ≈ 10⁻⁵`), and we see it today printed in the microwave background radiation. And this variation is the seed of every structure in the universe: gravity pulls at the slightly denser places so that they grow denser still, until they become galaxies and stars. Had it been much smaller, matter would have stayed a scattered gas that never clumped; had it been much larger, the masses would have collapsed swiftly into black holes. So it is a parameter that is measured and that the theory does not derive from principles — and that alone is what I claim for it here; as for how narrow its range is, that is of a piece with what we dispute throughout this chapter.

And the count itself varies with what you count and how you count it (do you count the neutrino masses? do you count the zeros?), so whoever has put the count forward as a decisive figure has overstated what will not bear overstating.

And here is the first limit on the claim: that a parameter is free in our theory does not necessarily mean it is free in reality. There may be in nature a deeper law not yet discovered that derives it outright, so that the description 'free' falls away from it. And the like of this has happened repeatedly: the wavelengths of hydrogen light were a table measured and written out by hand, until quantum mechanics came and derived them from principles. So the existence of a free parameter is a report about the limits of our knowledge as much as it is a report about the world — and that alone is enough to give pause to anyone who wanted to build something heavy on it. And keep this limit in mind, for I will come back to it in the conclusion to strike down by it a formulation I had written and then saw to contradict it.

Second: three figures corrected, each with the name of its error

Hardly an Arabic page on the subject is free of these three figures. And there is no deliberate falsehood in any of them; in them is a correct transmission and a wrong description, and that is more dangerous than falsehood because it survives review.

(a) '10^120': a gap in estimation, not a degree of tuning

The figure is sound in its own place. Its origin is that quantum field theory, if the vacuum energy in it is computed up to the Planck scale, gives a value exceeding the observed value of the cosmological constant by about a hundred and twenty orders of magnitude. And this gap is the best-known open problem in theoretical physics, and nobody denies it.

But it is not a calibration measured in the universe. It is a gap between two calculations: a theoretical one we know to be incomplete, and a measurement we trust. And among the things that show it is not an observed figure of precision is that it shifts as the place of the cut-off in the calculation shifts: if you stop the calculation at the Planck scale you get something like 10^120, and if you stop it at the electroweak scale you get something like 10^55. And the universe did not change between the two calculations — what changed was our assumption about where our theory gives out.

And this is no annulment of the matter at root, and here is a place where I corrected myself. I had written: 'so the figure measures our ignorance and not any craft in the universe' — and that is a false dichotomy, assuming that the possibilities are either an observed calibration or a measure of ignorance. And there is a third case: there remains in the cosmological constant a real cancellation problem within the theory — it is what physicists call 'naturalness', and it will come in the third section with its concrete example — and its upshot is that the observed value requires a fine cancellation between large quantities. And that is a verdict on the theory and not a probability computed over the world. So what falls is the putting forward of '10^120' as a figure of intended tuning, not the matter itself.

The example: you say to an engineer: estimate for me the cost of building this house without going down to the market. So he reckons with old figures he has and says: a hundred million. Then the actual bill comes: a hundred thousand. So the gap is a thousandfold. What, then, does this gap measure? It measures the error in the estimate, not the builder's precision and not his skill.

*And where it breaks down*: the example rests on our knowing that the estimate is the error — and knowing the right figure and the source of the mistake. And in the matter of vacuum energy we do not know where the error is, and that is why it has been an open problem for decades. So the example shows the shape of the possibility I favour, and does not prove it — and whoever has put it forward as a proof has begged the question, which is the very thing it forbids.

And in this same matter there is another calculation that does hold: Steven Weinberg computed in 1987 an upper bound on the cosmological constant from a clear physical condition — that galaxies do not form if it rises above a known amount.

And here I give the figure I dropped the first time. I had written 'nearer the observed value by orders beyond counting' — and that is the very vagueness I built this chapter on condemning, and whoever pulls down a false figure and does not put the true one in its place has left his reader worse off than he found him. And the truth is: Weinberg's bound stands above the observed value by something like one order of magnitude to three depending on the estimate — that is, by a factor of ten to a thousand — and not by a hundred and twenty orders. And that is the real figure for the argument in this place, and it is less striking beyond all measure than the figure that is put about. And whoever put 10^120 forward and said nothing of this put forward the larger and hid the truer.

And this is a real calculation with value in it — but mind its price: the bound becomes a prediction only on an assumed distribution over the values inside the permitted range, and Weinberg takes that from the multiverse postulate. So it buys its force with the very assumption I say in the third section that we do not have — and had I praised it as sound reasoning and said nothing of this, I should have used two measures within a single premise. And whoever put it forward as evidence of tuning without this qualification put forward half the paper.

Then look at what the man who made it did with it: he put it forward as an explanation by selection within a multiverse, not as evidence for a designer. And Weinberg declares his atheism and does not hide it. So whoever passes the figure on should say that the man who made it put it forward in another direction, and should credit him with nothing he did not say; as for differing with him over the interpretation, that is his right, on condition that he make clear that the interpretation is his own and that he establish it himself. And such a misreporting is exposed in a minute with a search engine.

And I state a rule I shall be held to throughout this chapter: the soundness of a calculation is independent of its author's interpretation, and differing with the man who made a figure over the conclusion is no error in itself — and I differ with Weinberg over his account and take his bound. The error I am arraigning is something else: that a man be credited with what he plainly denies, or that his face be borrowed for an interpretation that is not his.

(b) '2% in the nuclear force': two quantities run together

This is the most widespread of the three and the least checked. The truth is that in the literature there are two different figures for two different quantities, which were fused into a single sentence that no published paper says:

• Oberhummer and his colleagues (2000) computed the effect of altering the strength of the nuclear force between nucleons on the synthesis of carbon and oxygen inside stars, and found a double window: about 0.5% in the strength of the nuclear force, and 4% in the Coulomb force. And the Arabic retelling puts the first forward on its own and says nothing of the second — and dropping half the window, in a chapter built on 'a figure is passed on with its qualifications', is a fault of the kind I am arraigning, so I have set it down.
• And its effect is stronger than what I had written: I said the first time that 'the ratio between carbon and oxygen is thrown out' — and the text of the paper is that the production of carbon or of oxygen in stars falls by a factor of thirty to a thousand. That is a fall of three orders of magnitude, not a shift in a ratio. And the softening was in my opponent's favour, and it is inexact all the same — and exactness runs both ways or it does not run.
• Epelbaum and his colleagues (2013) computed a different matter: the effect of altering the light quark mass — which is a parameter in the Standard Model, a degree deeper than the strength of the force between nucleons — and they conclude that a change of some 2–3% is 'unlikely to be catastrophic' to the formation of carbon and oxygen, and that their worst estimates leave carbon-based life standing with a shift of no less than 0.7%. So the figure is a margin of survival and not a threshold of collapse, and whoever put it forward as a threshold credited them with the contrary of their own sentence. And the formula 'more than 2–3% lands you in trouble' has its source in the NC State University release in Dean Lee's words and not in the body of the paper — and the difference between the two is the very thing this chapter arraigns. And I myself put it forward as a threshold in an earlier version, so I reproduced the error the chapter came to correct.

And the two quantities are not one thing: the quark mass enters into the pion mass, and the pion mass enters into the force between nucleons non-linearly, and the force between nucleons enters into the reaction rate. So carrying a figure from one end of the chain to the other is a distortion even if the order of magnitude is close.

The example: the doctor said to you, 'an extra spoonful of salt a day raises your blood pressure'. And another said, 'an extra two spoonfuls of shop sauce raise your blood pressure'. Then a third came and said, 'two spoonfuls of salt raise blood pressure'. The third sentence is in the mouth of neither of them, and the difference between salt and sauce is not a difference of figure but a difference of the substance being measured. And you do not know — if what has been passed on to you is muddled — which of the two spoonfuls to cut out of your food.

*And where it breaks down*: salt and sauce can be told apart by looking at the plate; and the quark mass and the strength of the nuclear force are told apart only by someone who has read both papers — and that is why the confusion has lasted twenty years.

And the third part of the claim is disputed in the literature. It is often said: 'had the nuclear force been some 2% stronger, the two protons would have bound together, so that all the hydrogen would have burned up in the first minutes, and there would be no water and no stars of our sun's kind'.

And here I set the paper within its own limits. Bradford in 2009 holds that the stability of the diproton does not exhaust the hydrogen in primordial nucleosynthesis — the universe stays at something like 75:25 — so this part of the common claim is overturned. And inside stars it opens a channel converting protons into deuterons faster than weak capture by ten orders of magnitude or more, so that stars of the familiar hot dense kind are ruled out. But his conclusion does not stop there: he holds that cooler and less dense stars satisfy the basic tests of stability, and might last for billions of years at a brightness and a surface temperature fit to harbour life, and that 'an anthropic upper bound to the strong force to ensure diproton instability appears to be unfounded'. So stars remain possible on his account — not stars of our kind. And he makes no claim to finality: 'we do not pretend to provide a definitive answer to this question here', and he notes that raising the strength above 40% leaves the universe with no hydrogen to speak of.

And my error in this place is an error of phrasing and not an error of result. I attributed to Bradford the formula 'no diproton disaster', which is the phrase of Barnes and Lewis (2015), and the two papers meet over the possibility of stars and part over its detail. Then I added to that a heavier error: I wrote in an earlier version that saying 'stars remain possible' was the contrary of Bradford's conclusion — whereas it agrees with it by the text of his own abstract. So I corrected the correction, and did not erase its trace: a man who writes a chapter on honesty in transmission and then errs in it twice owes it, at the very least, to leave the road written down for his reader to learn from.

And the description is corrected as well: I wrote 'so the claim has been refuted in a peer-reviewed journal for years' — and that is stronger than it will bear. One paper, a single author, in a journal that is not among the leading journals of the field. And on the same page I lay down that one must be wary of a paper that alters one parameter and holds the rest fixed, so it will not do for a paper to become 'a published refutation' when it suits me and 'a limited model' when it does not. And the literature on the matter is wider: MacDonald and Mullan in the same year give a stronger estimate of the effect of the nuclear force on primordial synthesis. So what is right to say is: this claim is disputed in print and its detail is a matter of disagreement — not that it has been refuted.

And a third qualification runs on all the sound figures: these models alter one parameter and hold the rest fixed. And that is methodologically sound in its own place, but its result does not read 'had the universe been different it would have collapsed' — rather 'had this one parameter been different and everything else stayed as it is, this process would have been thrown out'. And simultaneous variation may compensate. And Fred Adams in 2019 surveyed the permitted range in the constants of physics quantitatively and found that stars form over a range far wider than what is in circulation, and that several well-known figures in this subject are overstated. And this is a researcher at the heart of the speciality who narrows the claim rather than widening it, and whoever wished to be honest mentioned him.

And on the other side: Victor Stenger holds, in a book published in 2011, that the permitted ranges are wider than is said, and that models of simultaneous variation defeat many of the figures in circulation — and that is a claim about the figures and about the reasoning built on them, not a denial that there are free parameters in the laws; and Luke Barnes answered him in 2012 with a long review. And I do not take up the widest of what Stenger went to, nor do I dress him in a formulation he does not utter — and the method of simultaneous variation is the very one I praise in Adams and make the third item among the things that would overturn me, so it does not become a fault when the man holding it differs with me. And I set down what the review says of itself: that many of Stenger's claims are 'highly problematic' — that is, that they make trouble for his own claims, not that they 'establish the tuning' as I wrote the first time. As for the denial of theology, it is established from his own text: Barnes states outright that he sets out to defend no conclusion resting on the universe's being tuned for intelligent life. And Barnes is a declared Christian — so this is the sentence of a man who differs with your conclusion while holding your creed, and it weighs heavier in the scale than the sentence of an opponent. So the honest weighing is: the phenomenon is a matter of serious research, and most of the figures in circulation in Arabic are wider than the papers they are attributed to will bear — and as for describing the range as 'narrow' or 'wide', that is a verdict requiring a measure which the third section will show we do not have, so I do not pronounce it here any more than I pronounce it in the conclusion.

(c) 'Penrose's probability': a ratio dressed in the clothes of a probability

The figure in Roger Penrose's book is correctly transmitted: 10 raised to the power of 10^123. And the error is in three places at once:

The first: it is not a probability. It is a ratio of volumes in phase space — that is, in the mathematical space in which all the possible states of the universe are represented — between the volume of the states answering to a universe like our own universe's initial state and the volume of all the states. And dividing a volume by a volume does not become a probability unless there is a justified prior distribution saying that the states are drawn with equal weight. And that distribution is what is missing.

The example: you are in a library with a million books in it, and one of them carries its author's signature. To say 'the proportion of signed books is one in a million' — that is entirely correct, and it is a report about the library. And to say 'the probability that the book now in my hand is signed is one in a million' — that is another report, and it holds only if you drew it blind and with equal weight. For if the librarian handed it to you because it was the signed one, the proportion stayed correct and the probability failed altogether. The proportion is a report about the shelves, and the probability is a report about your hand.

*And where it breaks down*: in the library we know the number of books and we know how the book reached our hand; and in the space of the universe's states the measure itself is disputed, so the example shows the difference between a proportion and a probability and does not settle the dispute.

The second: the measure is not normalised except by a choice that is justified. And here I correct a formulation I wrote in the body, by which I contradicted what I had written in the note. I said: 'to take a volume as a proportion of a volume requires the total volume to be finite' — and this is not exact. Ratios of infinities are in fact taken by regularisation: you cut off a finite part, compute the ratio within it, then widen the cut and see where it tends. And the trouble is not that the ratio is impossible, but that it follows the regularisation.

And the example that shows you this with your own eyes, and it was missing from the chapter: what is the proportion of the even numbers to all the natural numbers? The obvious answer: a half. And that is correct if you count in the familiar order: 1, 2, 3, 4, … so that in every segment you find half of them even, and the proportion tends to 0.5. But order them like this: 1, 2, 4, 3, 6, 8, 5, 10, 12, … that is, an odd then two evens, and they are the same numbers, with not one dropped from them and not one added to them. Now if you count in this order you will find in every segment two thirds of them even, and the proportion tends to two thirds. And with a third ordering you reach a tenth, and with a fourth nine tenths. So the ratio was not impossible — it was following the ordering. And the ordering is not in the numbers but in the hand of the counter. And if two men fell out over it and one said 'a half' and the other said 'two thirds', there would be no settling between them until they agreed on why this ordering rather than that. And this is exactly the case with the space of the universe's states: whoever said 'the ratio is 10^(−10^123)' counted in an ordering, and did not demonstrate that his ordering is the ordering.

And Gibbons and Turok in 2008 examined the measure problem in cosmology, and showed that the canonical measure on the space of cosmological solutions diverges — the source of the divergence on their account being the invariance of the expansion in flat Friedmann universes — and that the divergence is lifted by identifying with one another those universes too flat to be told apart by observation, and that identification is a chosen one.

And here I correct a second piece of reporting. I had written of them 'and that the results follow the choice' — and this is the contrary of their text: they hold that the measure, in some of the quantities that matter, takes very little notice of how exactly that identification is carried out. And that on their account is a merit of their measure and not a defect. As for the close of their abstract, that is something else again which I attributed to it wrongly: it is that the likelihood of inflation in single-field slow-roll models is suppressed by a factor of exp(−3N) — and that is their principal result, and it runs against whoever puts inflation forward as doing away with the tuning claim, not with him. So I took a paper that treats the problem and made it a witness to the problem's being intractable. A second qualification: the Gibbons–Turok measure is a measure on the space of cosmological solutions (and its best-known result is that the likelihood of a large number of e-folds of inflation is exponentially suppressed), and not a measure on the initial phase space in which Penrose computes. So citing it on Penrose's question is an approximation and not a fit, and I say so plainly rather than letting it slip past. So what is left of the objection after the two corrections? What is left is the measure problem itself — a problem acknowledged in cosmology, and standing with no need of Gibbons and Turok — and its upshot is that the ratio is suspended on the justification of a measure, and the example of the even numbers is enough to make it understood. As for attributing to them that 'the results follow the choice', that is what they do not say, and I have taken it out.

And the third — the heaviest of them in the scale of honesty: Penrose puts his figure forward for a contrary purpose. He does not offer it as an argument from design; he offers it as a statement of how vast the puzzle is and then asks for a physical explanation of it, and he proposed that explanation in 1979 under the name 'the Weyl curvature hypothesis': a law imposing on any cosmic beginning a geometrical condition that makes the initial entropy low by force of law and not by force of coincidence.

And a third correction in description: I wrote that 'the Creator' on Penrose's page was a tongue-in-cheek figure — and the illustration in his book is illustrative and not tongue-in-cheek: a divine hand placing a pin at a point of phase space, its purpose being to picture how slight the required region is. And my description was an excess in my own direction, and it is the same kind of excess in reporting that I am arraigning. And it is enough for me that Penrose asks for a physical explanation — that alone breaks the claim, and it needs nothing added.

So whoever passed the figure on and credited Penrose with putting it forward as evidence for a designer has credited him with what he plainly denies. And whoever wishes to differ with Penrose over the conclusion, that is his right — differing with the man who made a calculation is no error in itself — but he must then establish the evidence himself, and not borrow for his interpretation the face of the man who made the figure.

And with it a third claim that goes against the facts: that 'science has no explanation, so nothing is left but design'. The physical explanation has been on the table since 1979, and from the man who made the figure himself. And it may be wrong — the Weyl curvature hypothesis has not been established — but the existence of a candidate on the table defeats the claim that 'nothing is left but'.

And I do not exempt the Weyl hypothesis from what I shall apply to others. It is a law, and of a law it is asked: and why this law rather than another? So the argument that 'the question moves and is not cancelled' — which I shall shortly brandish against the cosmic generator — applies to the Weyl hypothesis to the letter. And I mention it here for one limited purpose only: the defeat of the claim that 'nothing is left but design', not its being preferred over anything else. And whoever saw that I welcomed it and refused the generator on the same argument saw something that was in me, and I have taken it out.

Third: the measure problem — why 'the narrow band' does not become a small probability

This is the strongest objection in the whole subject, and the least mentioned in Arabic writing. It was framed by Timothy and Lydia McGrew and Eric Vestrup in 2001 in the journal *Mind*, and its framing in one line:

The claim that 'the range permitting life is very narrow' presumes that we know the total range within which the value could have fallen. And if that range is infinite, then there is no uniform normalisable probability distribution over it at all — so the ratio the proof rests on is undefined, neither small nor large.

The example: your friend says to you, 'I have thought of a number. What is the probability that it is even?' So you ask him: from one to ten? And he says: no, from all the numbers without limit. At this point your answer does not become small — the question becomes unanswerable. Because 'an equal-weighted choice out of an infinity' is a phrase with nothing answering to it: any distribution you lay down will weight one region above another, and there is nothing in the question to say which region.

And a second example that shows you the thing with your own eyes: you throw a pin at a map hung on the wall and ask: what is the probability that it lands in Egypt? The answer requires you to know the edges of the sheet first: how large is its whole area? As for a sheet with no edge, it gives you neither a small ratio nor a large one — it gives you no ratio at all. And the area of Egypt has not changed in either case.

*And where the two examples break down*: the pin is thrown by a hand with habits and a bias, so the distribution is not uniform even on a bounded sheet — a reminder that 'equal-weighted randomness' is an assumption to be justified and not a natural state. And breaking down harder than this: the example of the even numbers that came in the second section shows that the thing is no absolute impossibility — you can compute the ratio by regularisation, and come out with a half or with two thirds according to your ordering. So the incapacity is an incapacity to justify and not to calculate, and it is conditional on the absence of a justified measure and not absolute. And whoever said 'the calculation is impossible' went too far; what is right is 'the calculation is suspended on a choice that has not been justified'.

And the proponents of the argument have answered, and the answer is to be set out honestly and given its due — for it is the heart of the whole dispute, and the first time round I short-changed it with four lines.

Robin Collins restricts the range to what he calls 'the epistemically illuminated range': you do not compute over an infinite range — that being a futility he acknowledges — but over the range within which our present theories are able to say something intelligible. And what lies beyond it is neither small nor large; it is outside the circle of speech.

And take his concrete example, which is Collins's own example of the gravitational constant. What is the range of values our physics is able to speak about for the strength of gravity? Collins says: its reasonable upper limit is for gravity to reach the strength of the strong nuclear force — that is, some 10^40 times what it is — and above that we have no theory to speak with. Then he asks: and how wide is the range within which stars remain possible? And he puts it at about three thousandfold. So the ratio is not 'one in infinity' — it is one in about 10^36, and that is a defined figure that can be computed. And with this the distribution becomes normalisable again and the ratio becomes defined again. And this is a real answer and not an evasion, and it must be read before it is answered.

*And where it breaks down — and this is the sharpest thing in the dispute*: the boundary of the range is a decision and not a discovery. Why was the strong force the ceiling? Why not the Planck mass, so that the range widens by many orders and the ratio shrinks accordingly? And why not a narrower scale, so that the ratio grows until it no longer astonishes? And whoever altered the boundaries altered the result, and the boundaries are not in nature but in the reach of our theory today — that is, the figure that comes out changes with the advance of physics and not with any change in the universe, and that is the very trouble with 10^120 coming back by another door. And there is no settling of this matter to this day, and it is in my view the most important open point in the whole subject.

And this is a two-edged weapon — and I got its two edges wrong, so I put them right. I had written: 'so the missing measure is missing on both sides together, and its absence halts the calculation and weights nobody' — then I added: 'so whoever supposed that McGrew grants naturalism a victory has read him as others have read Penrose'. These two sentences I withdraw. As for the second, it fastens on the reader a charge of bad reading with no evidence, after pages in which I had built up credit in honest transmission — so I spent the credit on something other than what earned it. And nobody said that McGrew 'grants naturalism a victory'; McGrew says: the argument does not stand. And the falling of an argument is no victory for the other side — and that is true — but it is a real result and not a tie, and I made it a tie with a stroke of the pen. As for the first — the claim of symmetry — it is the heaviest of my errors in this chapter. The absence of the measure does not bear equally on the two sides, and the reason is simple: the serious opposing position is not 'there is no tuning here and nothing calling for a question' — that is a position held neither by McGrew nor by Carroll nor by Oppy. The serious opposing position is: the phenomenon is a real puzzle, the argument built on it does not stand, and I do not know what the answer is. And 'I do not know' needs no measure at all — it is needed by the man who wants to extract a weighting out of the phenomenon. So the burden is on the one who builds, and the absence of the tool prevents the building and does not prevent the abstaining. And I was the builder, so the absence tells against me and not against him. And what remains true of the sentence after the correction, and it is narrower than what I wrote: whoever used the measure problem to establish a positive claim in the other direction — as by saying 'so it has turned out that the tuning is nothing' or 'so the probability of naturalism has become high' — has used the tool for what it does not serve, because it defeats the calculation and does not yield a result. And this is a small limit, not to be traded for the symmetry I claimed.

And let us not overlook that physicists have another sense of 'tuning' than the philosophers' sense: with them it is naturalness — and the first time round I left it an abstract paragraph with no example, so it passed without effect. And here is its concrete picture:

The example of the Higgs mass, and it is the mother of examples. The observed mass of the Higgs particle is about 125 gigaelectronvolts. But quantum field theory says that this mass receives quantum corrections from every particle it interacts with, and the size of these corrections is proportional to the highest scale up to which the theory runs — and had it run up to the Planck scale (10^19 gigaelectronvolts) the corrections would have been larger than the observed mass by about seventeen orders of magnitude. So how did the mass stay small? By the enormous quantities meeting so that they cancel one another out, and there being left of them a slight difference which is what we see — to a precision of about one part in 10^32 in the square of the mass. And this is a state of affairs that physicists find objectionable and they call it 'the hierarchy problem', and they say: there has to be a deeper structure that makes this cancellation automatic rather than coincidental. So look at the nature of this verdict: there is in it no probability computed over the world, and no distribution over the possible values. It is a verdict on the theory: that it looks more like an equation whose numbers were written in so as to come out at a known result, so that one supposes there is something simpler underneath it. And it is a methodological hunch, and hunches are disappointed: supersymmetry was founded on this very objection, and the Large Hadron Collider searched for it for years and did not find its particles in the range that was hoped for. So naturalness is itself liable to error — and that is a lesson running on anyone who builds something heavy on 'this figure looks odd', on me and on my opponent alike.

And running the two senses together — the philosophers' tuning, which wants a probability, and naturalness, which passes a verdict on the structure of the theory — is among the strongest causes of confusion in the whole subject.

Fourth: the multiverse — it is set out, and it is not mocked

Much of what is written in Arabic treats the multiverse hypothesis as a contrivance invented to escape the inference. And this description is not correct, and whoever said it weakened his own position. And its best-known forms were not put forward for that purpose at all:

• Eternal inflation is a consequence of models put forward for quite other questions (the horizon problem and the flatness problem in cosmology), and it then appeared that some formulations of them do not stop producing new regions.
• The string landscape is a consequence of counting the possible solutions in string theory, and Leonard Susskind put it forward in 2003 in that setting.

So the hypothesis is not made for the occasion, and that has to be said even if we differ with it.

And the example that shows what it does explain: you found in the street a ticket winning a million. Now if you know that a printing house in the district prints a million tickets every day and scatters them in the roads, the astonishment is wholly gone and there is nothing left to be explained. And if in all history only one ticket had ever been printed, the astonishment would stay exactly as it is.

*And where it breaks down*: as for the printing house, you see its door and hear its noise and pay its electricity bill. And postulating a printing house from which only a single ticket ever reaches us is itself the matter in dispute and not its resolution — and that is the most cogent objection brought against the hypothesis.

So what does it explain and what does it not explain?

It does explain: that some universe exists with values permitting life. For if the samples are very numerous and the values vary across them, the existence of one that answers is to be expected.

And it does not explain — on the best-known objection to it — that this universe I am in should be the one that answers. And this is what is called the inverse gambler's fallacy: that you see the dice come up six six times running at one table and infer that there are many tables in the hall being thrown at, and that your own throw is no wonder because one of the tables was bound to produce this. And the inference is wrong: the multitude of tables raises the probability that the throw occurs somewhere, and does not raise the probability that it occurs at your own table.

And the attribution of this objection is set right. The form of the fallacy was framed by Ian Hacking in 1987 — but he framed it against one particular form: Wheeler's successive universes, that is, those following one another in time. And he expressly exempted the form of simultaneous universes on Carter's manner. And the man who generalised the objection to the multiverse as a whole is Roger White in 2000. And I had written 'Hacking framed this … against the multiverse claim', so I credited him with a generality he did not hold — and that is of the kind I am arraigning, so I have taken it out.

And the opponents of this objection have a strong answer that must be set out: that observation here is not like observation at the table. You cannot observe a universe other than one that permits your existence, so the datum in your hand is not 'this universe is tuned' but 'the universe I could exist in is tuned' — and that is a proposition whose probability the multiverse does raise. And the dispute over this very point stands among philosophers to this day, and there is no settling it, and whoever told you it is settled in one side's favour has abridged for you what has not been abridged for the people of the subject.

And two objections remain against the hypothesis which the foregoing answer does not remove:

The first: the question moves and is not cancelled. The generator that turns out universes has in its turn laws and parameters. So whoever accounted for our universe's calibration by a machine producing all the calibrations is still left to ask: and why does this machine have these laws? So the hypothesis moves the question up one storey, and that is a gain if the upper storey is simpler, and it is no gain if it stands in as much need of explanation as the storey below.

And here I must draw the weapon on myself, having sheathed it before. If the generator is asked, 'and why is it of this character?' — then the designer is asked the same question: a mind with a will and knowledge and power, choosing these values rather than those. So why is he of these attributes? And why did he want a carbon universe rather than another? The answer on offer is that God is necessarily simple — with no parts in him and no composition — so that the question 'and why this composition rather than that' does not arise against him. And this is Richard Swinburne's claim, and it is a real answer and no evasion. And it has been strongly disputed: the substance of the known objection is that a mind knowing everything and able to do everything and willing this rather than that is not a simple thing in the sense that would exempt it from the question; for willing this particular universe is a specific content whose cause is asked for. And I attribute this to no particular chapter in anyone: I have not set it against any place in `Arguing about Gods`, so I put it forward as a well-known objection and not as a documented report. And I do not settle this dispute — this is not the place for it, and it belongs to the enquiries of the chapter that follows. I only lay down one thing: that the regress objection is not a weapon with one direction, and that whoever draws it against the multiverse and then sheathes it over his own postulate is using two measures. And I did it in the first version of this chapter, and this is the mending of it.

The second: that it is not a settled matter inside physics itself. Eternal inflation is a live disagreement among cosmologists; Ijjas and Steinhardt and Loeb published in 2013 a critique of the inflationary model from inside the speciality.

And the incident set right, for I had made two additions to it. First: the 2013 paper is pure critique — three objections to the plateau models and then a discussion of the Higgs, closing with the statement that the coming searches for polarisation patterns and non-Gaussianity will be decisive. And there is no mention in it of a cyclic alternative. Steinhardt's cyclic alternative is in other works. And my saying 'that is, a universe with no beginning' was an inference of my own and nobody's text, and Steinhardt's cyclic models are not all of them without a beginning — so I have taken the two sentences out. Second: I said 'and a large team of physicists answered them' — and those who answered this paper are three: Guth and Kaiser and Nomura. And 'the large team' — thirty-three signatories — answered an article by Steinhardt and his two colleagues in a general magazine in 2017, and not the 2013 paper. So I carried a description from one incident to another, which is the very kind of error this chapter rests on.

So whoever built on 'the multiverse' a building of certainty — for it or against it — built on a matter still under investigation.

And there is a third candidate I overlooked, and it deserves mention more than much of what I did mention, because it is the only one claiming to derive the values outright rather than postulate them: cosmological natural selection in Lee Smolin. Its picture is that every black hole gives rise to an offspring universe with values close to its parent's and a slight deviation; so universes that produce many black holes leave more progeny, and their values come to dominate the whole after generations. And the result on his account is that our universe's values are tuned for producing black holes and not for producing life — and that life is a side effect, because what makes a black hole makes heavy stars and carbon along with it.

And the best thing in it is that it yields a prediction that can be overturned: Smolin says that any small change in the parameters ought to reduce the number of black holes — so whoever found a single change that increased them would bring the theory down. And it has in fact been disputed (Vilenkin and others), and it is not widely accepted in the field, and the mechanism for generating offspring universes is itself not established. But mentioning it is obligatory, because I said in this chapter that the field lacks a candidate that derives the values rather than postulating them — and this is a candidate that does so, and overlooking it made my claim wider than the facts.

And this is the limit of what I say in this branch: I cannot say that the multiverse is false, nor can I say that it resolves the matter. I say that it is a serious postulate with its sources in physics, and that there are serious objections to it which have not all been answered. And whoever wanted more of me than this was asking for a settling I do not have.

Fifth: the anthropic principle — sound, not to be denied, and no answer to the question

The anthropic principle in its weak form is a proposition that cannot be denied: no universe is observed except one that allows an observer to exist. However strange the values we see may be, it was never possible for us to see any others; for had they been otherwise we should not have been here to see.

An example: a survey came out saying that seventy per cent of people are sitting at home at midday. It was carried out by ringing landlines between ten and two — so whoever was at work was never asked at all. The result is perfectly true as a description of those whose telephone was answered, and false as a description of people. The fault is not in the counting but in the door by which one enters the sample.

*And where it breaks down*: in the survey we know who was excluded and how, so the correction is in our hands. In the cosmological question we are inside the sample and hold no record of those who were never asked — so the principle is a warning that keeps us from naive astonishment, and gives us no reckoning by which to correct.

So how far does this principle reach? It reaches one place and stops there: it accounts for why we see what we see, not for why what we see came to be. The difference between the two is what the whole subject turns on.

And the example that shows the difference — it is the philosophers' famous one, and its source is John Leslie and Richard Swinburne, and I put it in its exact terms: a man was sentenced to death, and a hundred rifles in the hands of skilled marksmen were lined up against him, and all of them were fired, and he found himself alive. And he was told: there is no ground for your astonishment, since had they hit you, you would not have noticed anything at all; for you cannot observe yourself dead. And the sentence is true word for word — and Leslie and Swinburne hold that even so the matter is not to be closed with it. The man is entitled to ask: and why did all hundred of them miss? So his question is about the event, and the anthropic answer is about the condition of the observing, and the second, on their account, does not answer the first.

*And where this example breaks down — and here I correct an attribution I turned completely on its head*:

I had written: 'Elliott Sober says the survivor's astonishment is warranted…' — and Sober says the opposite. His published position is that the observation selection effect is at work in the firing-squad case as well, so that surviving is no witness to intent; and his formulation is that the probability of the tuning given design and the selection effect equals its probability given chance and the selection effect, both of them coming to unity. And the one who says the astonishment is warranted is his opponent: Jonathan Weisberg, in a published reply of 2005 whose title is about the firing squad itself. And the nastiest thing in the error is that it inverts the work of the paragraph: it is headed '*and where this example breaks down*' — that is, it is brought forward against the firing-squad example — and what I attributed to Sober strengthens the example rather than breaking it. So the structure says one thing and the attribution says the contrary, and nothing reveals this but opening the source.

And here is what is right in both places:

• Sober's argument against the example: observation selection is at work in the firing squad as it is in the universe, so the example will not serve as a witness that the astonishment is warranted.
• And Sober's second objection, the objection from 'intentions and abilities': we have no independent knowledge of the intentions of a supposed designer nor of his abilities, so we cannot derive from the design hypothesis a prediction to set against any other. And this is an argument against the design argument and not for it — and I had grafted half of it onto a head taken from Weisberg, so that the paragraph came out a hybrid that neither of them holds.
• And Weisberg replies to Sober: that the difference between the two cases is real, and that in the firing-squad case there is an independent background — we know the marksmen, we know their skill, and we know that they have intentions — which makes 'they missed on purpose' an intelligible hypothesis to set against others.

And this is a standing dispute among philosophers, not a place for silencing anyone — and the breaking of the example does not establish that the alternative to it is design.

And a quieter example shows the same idea: every fish in the fisherman's boat is longer than twenty centimetres, so he writes in his notebook: there are no small fish in this sea. Then he looks at the mesh of his net and finds it is twenty. The net accounts for what is in the boat, and does not account for why there are fish in the sea at all.

*And where it breaks down*: the fisherman can step out of his boat and change his net and fish again with a finer mesh, and so correct his notebook. And we have no second net, and cannot step out of the sample to look at it. So the example shows the structure of the fault and does not show the way to mend it — and that is exactly why the question stays open.

Sixth: two questions that ought to have been put in this chapter and were not

I wrote the chapter the first time with two gaps in it that nobody drew my attention to but a doubting reader. And they are of one kind: two questions that come at the argument from within it, and my silence about them made the field emptier than it is.

(a) If it was tuned for my sake, why is it so hostile to me?

A universe some thirteen and a half billion years old, and what we know today to bear life is a single place, and all the rest of it — by everything we know — is void, or stars that burn, or radiation that kills. And I put forward no percentage, because I do not have the denominator of the fraction: what has been measured is that we have found no second one, not that we have swept and come out with some particular fraction — and a claim that does not specify what it is dividing by what is not tested at all, and I laid that down against my opponent, so I hold myself to it. So whoever says that this machine was built to produce what we are in is asked about the maker's efficiency before he is asked about his existence. And if a factory the size of a continent were put before you turning out a single loaf, the first thing that would occur to you is that it is not a bread factory.

And the argument has two answers to this, which are set out as they deserve:

• The first: that the fine-tuning argument does not claim that the universe is designed for life economically, but claims that the necessary conditions for life to exist are met, and met strikingly. And the vastness is no surplus in those conditions: a universe that produces carbon needs generations of stars, and generations need time, and time in an expanding universe means size. So the vastness is required by the chemistry and is not an extra laid on top of it — and this is a real answer in physics, not a verbal escape.
• And the second: that the question 'why at such poor efficiency?' is not an objection to the tuning, but an objection to the designer's attributes — and it belongs to the problem of evil and of wisdom, not to this chapter.

And this second answer is right in its classification and does not deliver wholly. For if the argument is an argument of probabilistic weighting — and so it is with Collins himself — then everything that lowers the probability of the data on the design hypothesis enters the scale, and is not taken out of it by classification. So the question stands, and I have set it down because it ought to have been set down.

(b) 'Chance' and 'brute fact' — and I discussed the weaker of the two

I had written in the conclusion: 'and the word chance does not answer it, because chance denies intent and does not deny a cause'. And that is an equivocation I fell into, and it is one of the fallacies I put on trial.

For 'chance' in this subject is two words and not one:

• The first, the everyday one: 'nobody intended it'. And this is a sense which truly explains nothing — because it is a report about the absence of intent and not about the presence of a cause. And this is the one I discussed.
• And the second, the philosophical one that the serious opponent means: brute fact — that is, that these values are a primitive occurrence with nothing beneath them to account for them, not because the account is hidden from us but because there is no account. And what I said before does not touch this sense at all, because the one who says it claims no account, that his account might then be called incomplete; he denies that there is anything to be accounted for.

So the matter comes down to a single question that I never once mentioned in the chapter, and it is the hinge of the whole dispute: does everything have an explanation? And this is what philosophers call the principle of sufficient reason. Whoever grants it is bound to seek an explanation for these values — a generator, or some deeper law, or a will. And whoever refuses it, or restricts it to some occurrences and not others, is free to stop at 'they are so' and is bound to nothing.

An example: you ask, why is the speed of light this much and no more? And you are told: it is a conventional unit of measure, so ask about something else. Very well: and why is the fine-structure constant about one in a hundred and thirty-seven? Either there is a deeper answer — which is what the physicists hope for — or this is the end of the chain. And whoever demands a cause for everything ends at one of three: an endless regress, or something with no cause, or a stopping of the demand itself. And I do not dismiss the first with a stroke of the pen: to say that 'chains come to an end' is a claim in metaphysics and not a self-evident postulate, and it has been disputed, and whoever holds an endless regress is not obliged to name a terminus so that he might be asked about its identity. And if it is granted that the chain does stop — and that is a supposition, not a result — the disagreement becomes one about the identity of what stops it: some make it God, and some make it the laws of physics themselves, and both then stop at a limit that is not accounted for by anything above it. And this is a weighting in the presentation of the question and not something the question compels, and I laid down a few lines back that whoever refuses the principle of sufficient reason or restricts it is bound to nothing — so it will not do for me to take that back here.

And I state plainly that I do not settle this question here — it belongs to the cosmological argument and not to fine-tuning, and its place is another chapter. I set it down only because my silence about it left me discussing the weakest form of the opposing position and then announcing that it does not suffice — and that is the building of a straw man.

The conclusion: what is left after all this?

What is left is something quieter than the figures. And I do not say 'firmer than them' nor 'harder to overturn' — I had written both, and then saw that what is left in my hand is vaguer and not firmer, and that the difficulty of overturning it comes from its vagueness and not from its strength. And I myself laid down in this chapter that a claim which does not specify its form is not tested at all — so vagueness may not become a virtue when the turn comes round to what is in my own hand.

That there is in the structure of the universe a fact that calls for looking into. The laws of physics are not closed equations that produce their own numbers; there are empty places in them that are filled from outside. And some of these places, on our best models today, if moved on their own within the range those models have tried, throw out processes on which the chemistry of life depends.

And I do not say 'a narrow range' — narrowness and width are relative to a measure which the third section established that we do not have; and whoever says 'it is not wide' after declaring that the ratio is 'neither small nor large' has taken back in half a line what was bought with a whole section. It is rather a range that was tried in particular models and what came out in it was recorded — and that is a statement tested by opening the paper, whereas the other is a statement tested by nothing.

So the question that is left is not 'what is the probability of that?' — that is a question we do not have the tools to answer, as has gone before — but: why are the laws of such a form as to fall into order under mathematics and to admit of being known?

And I avoid here the form I wrote the first time: 'why do these laws have free parameters at all?' — for I laid down in the first section that a parameter's freedom is a report about the limits of our theory as much as it is a report about the world, and the description may fall away from it tomorrow as it fell away from the spectra of the atom. And to build a final question on what may fall away is to build on shifting sand — so I withdrew the form and kept the question in a shape that does not depend on the parameter staying free.

And I call this question by its name and do not dress it in the clothes of fine-tuning: it is at bottom Eugene Wigner's question about 'the unreasonable effectiveness of mathematics in the natural sciences' — a paper published in 1960 — and with it a layer of the cosmological argument. It is not fine-tuning, and nothing of the calculation that has gone before in this chapter rests on it. And whoever brings it in at the last line after clearing the field of every opponent has smuggled in an argument that was never set out and never tested — and I did it, and this is an acknowledgement of it and a placing of it where it belongs rather than in the place of what I demolished.

*And where my conclusion breaks down*

In this chapter I have run the 'and where it breaks down' lens over twelve examples — the factory, the bread, the house, the salt, the library, the numbers, the pin, and Collins's example of the gravitational constant, the ticket, the survey, the firing squad and the net — and one example was left without the lens, and it is my own: 'a factory the size of a continent turning out a single loaf'. *And where it breaks down*: a factory's cost is measured against a limited resource, so extravagance in it is a report of incapacity or of some other purpose; and whoever supposes a maker whom size costs nothing does not have this side of it brought against him. So the example shows the objection and does not establish it, and its force lies in the question of wisdom and not in the question of fine-tuning.

And even so I left the section that carries what is in my own hand without the lens. And a discipline that lapses just where its cost falls on me is the first thing a writer is accused of, so here is that lens over my conclusion:

• It breaks down first in that the question may be a bad question. 'Why do the laws admit of being written in mathematics?' may have this answer: because mathematics is the language we developed to describe regularity, whatever it may be, so that had the universe been regular in some other way we should have developed another language and called it mathematics. And this is a real answer, one that makes the astonishment an astonishment at our own handiwork — and it has been said.
• It breaks down second in that it yields no weighting. 'There is a question left over' is not a premise in a syllogism. And whoever grants the question entire is bound by that granting to nothing in matters of belief — nor is he bound to answer.
• It breaks down third in that it falls on the other party as it falls on me: whoever says 'these are the laws and there is no explanation beneath them' has answered with brute fact, and I have no instrument that overturns his answer — exactly as he has no instrument that overturns my question.

And I state plainly what this whole chapter does not establish, for a declared limit is of more use than a claim spread wide:

• It does not establish a designer. The most that is in it is that here is a fact that calls for looking into, and the personal explanation is one of the candidates and not the only one.
• Nor does it establish — were the weighting to come out for a designer — that he is one, nor that he is powerful, knowing and good, nor that he still is. And Robin Collins, who has the strongest philosophical formulation of the argument, states plainly that it is an argument of weighting and not a proof that establishes, and that it weighs against single-universe naturalism alone.
• Nor does it establish any particular religion, nor prophethood, nor a law. And the move from 'there is something particular about the structure of the universe' to 'so this book is from God' is a step that needs evidence of an altogether different kind, and has nothing to do with this subject.
• Nor does it say that physics is helpless. Graham Oppy — an atheist who has surveyed the arguments for God's existence critically — holds that the arguments do not carry in either direction, that is, that they do not oblige anyone who does not grant their premises. And that is a description nearer the truth than any party's claim of victory. And I have taken from Oppy in this chapter a single place — this one. I had counted a second place for him in the fourth section (the critique of Swinburne on simplicity) and then did not establish it against any particular chapter, so I withdrew the count. And whoever takes from a man only what agrees with him has cut him short.

And the claim this chapter loses if it loses, and I say it because whoever hides it has cheated his reader: if some deeper theory should one day appear that derives these parameters from first principles — as the spectra of the atom were derived after having been tables measured and written out by hand — then every inference in this chapter that rests on 'the free parameter' falls, and that is most of it. And this is a live possibility, worked on by serious physicists for decades, some of whom hold that it is the right direction.

And after it one question remains, whose limit I state plainly: why is there anything ordered that admits of being known? And this is a question no theory in physics brings down, because it is not of the kind physics settles — so it counts neither for me nor against me in the scale of testing. And whoever counts it a gain left to me after every loss has counted what does not count in the scale. I had written that 'every deeper theory will come with parameters of its own and so put the question back' — and that is a sentence which cancels what I had declared three lines above would overturn the chapter, leaving it proof against every future result while it claims to have exposed itself to falling. So I withdrew it.

And what overturns what is in this chapter today, not tomorrow?

An argument all of whose overturning tests lie in the future has no content today that can be tested. So here are four that overturn, all of them within reach of anyone who wants them, today:

• My claim about the three figures is overturned by opening the papers. If a reader finds in Oberhummer the figure of 2%, or in Epelbaum that 2–3% is a threshold of collapse and not a margin of survival, or in Penrose that he puts his figure forward as an argument from design — then the whole of the second section falls. The references are all in the tail of the chapter with their digital identifiers and their places; and where a page number or an international number could not be given, the fact and the reason are stated plainly in its place — and the chapter reference holds where editions differ.
• And my claim about the measure problem is overturned by a justified measure. Whoever puts forward, over the space of parameters, a measure justified independently of the result wanted, brings the third section down and the ratio comes back defined. And that is published work going on today.
• And my claim about the narrowness of the range is overturned by a survey that varies the parameters together. Adams's survey is a step along that road and has narrowed many claims; and whoever widens the survey and finds wide windows under simultaneous variation has brought down what is left.
• And Smolin is overturned — or falls — today: whoever finds one small change in the parameters that increases black hole production has brought his theory down. And I mentioned him because he is the only candidate who put his neck under the sword that plainly.

So whoever has built his faith on a figure has pledged his faith to a paper not yet published. And the sentence cuts both ways, and I say it against myself first: whoever has built his denial on a figure from the other side — on an article he trusted without opening its source — has pledged his denial to the very same paper. And in this subject there are no safe figures for anyone.

As for what I myself came away with from writing this chapter, I say it about myself and not as advice to anyone: I went wrong in it in five places of transmission which I noted where they occur and have not erased — Bradford (twice: a statement attributed to him that belongs to Barnes and Lewis, then a correction that turned his conclusion round), and Epelbaum (I put their margin of survival forward as a threshold of collapse), and Gibbons and Turok, and Sober, and Ijjas and his colleagues — and in a straw man's wording that I put on Stenger ('he denied the phenomenon at root', whereas his claim is about the figures), and in three descriptions in which I was harder than the paper will bear, and in a claim of symmetry by which I gave myself what I do not deserve. And every one of them happened to me while I was writing a chapter about honesty in transmission, and nothing revealed them to me but opening the sources after the writing and not before. So the rule I learned here was not for the reader: it was for me.