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## What do you know? – A Fine-Tuned Critique of Ikeda and Jefferys (Part 2)

This is my second critique of the work of Ikeda and Jefferys (IJ) on the fine-tuning of the universe for intelligent life. IJ insist that we must always condition on everything that we know is true. Here, I’ll raise a few case studies in need of clarification. I should warn that I’m somewhat less certain about this part than the previous one. The fog is probably in my own head.

### A. Magneto saves the day

This is a variation on John Leslie’s firing squad parable. You are sitting with your grandpa on his porch. Grandpa says, “I have a confession. I’m Magneto.” You: “What? You’re one of the Xmen? You can manipulate metals at will?” Grandpa: “Yes. That’s right”. You: “Right. Sure. Prove it.”

Grandpa pulls a set of keys from his pocket and makes them levitate two inches above his hand. “Yeah, nice magic trick, Grandpa”, you say. But then, up on the hill overlooking the porch, a freight train derails! Its carriages tumble toward the house. And, just your luck, this train happened to be loaded with TNT and samurai swords. The ensuing explosion sends several tonnes of rather pointy metal hurtling towards the porch. You instinctively flinch. A few seconds later … you’re alive! You turn in shock to see that every inch of your Grandpa’s house has shards of metal sticking out of it, except for two perfect silhouettes of you and your Grandpa. He looks at you, and smiles. “Not bad, huh?”

Now, like the nerd you are (you’re reading a science-themed blog, so there’s no point denying it), you want to formalise your conclusion.

$L$ = you are alive

$F$ = all the shards of metal from the explosion followed paths that were “you-friendly”.

$N$ = the shards of metal followed essentially straight paths from the explosion to their final resting place. The “Grandpa is Magneto” hypothesis implies that Grandpa can violate $N$.

Now, the fact that you are alive means that all the shards missed you.

$P(F|NL) = 1$        (1)

Also, the probability that all the shards missed your body, given that they travelled in straight lines from the explosion, is very small:$P(F|N) \ll 1$. But, according to IJ, we must condition on L. Thus, we find:

$P(N|FL) = \frac{P(F|NL) P(N|L)} {P(F|L)}$       (Bayes theorem)

$= \frac{P(N|L)} {P(F|L)}$                   (using 1)

$\ge P(N|L)$                               (since $P(F|L) \le 1$)

It follows that you cannot conclude anything at all about your Grandpa’s abilities. Observing that all the shards of metal missed my body has somehow made it not less likely that they simply followed ballistic paths from the explosion. This conclusion holds independently of the extent and violence of the explosion: suppose another train hits the wreckage and the whole debacle happens again, suppose a malfunctioning tank wanders past, the monthly meeting of the society for blind snipers gets out of hand, several satellites fall out of orbit, an angry neighbour throws a frying pan. And still you have no evidence at all of your Grandpa’s ability. Surely, this is nuts. If you see Grandpa Magneto cause a shard of metal to swerve wildly so that it hits the door instead of the window, then this is evidence of his abilities. But if it hits the door instead of your head, then you can’t conclude anything, even if Grandpa makes the shards in the door spell out the sentence: “I’d like to see Rev. Bayes do this!”.

I’m not sure if the problem here is that we are conditioning on $L$, or if this formulation is incomplete, as I alleged of IJ’s formulation of the fine-tuning argument (see part 1).

(Note that we might wonder why Grandpa didn’t stop all the shards of metal from hitting his house. This is a good question, but it isn’t an objection: it does nothing to reduce the strength of our conclusion that Grandpa has the abilities he claims. Neither can we object that any arrangement of metal shards is improbable.)

### B. Make your own universe

It’s 3042 and the annual universe building competition is about to kick off. First prize goes to the universe which first produces life intelligent enough to speculate that it was created as a result of a universe building competition1. You are going to compete, having spent years up to your eyeballs in equations, sorting through all the possible physics of your universe, trying to find the ones that will support the evolution of intelligent life. (No cheating! You can’t put intelligent organisms into the initial conditions.) Nervously, you hit the big red button and your universe (call it Lucia) has its “In the beginning …” moment. Success!!! Intelligent life forms – we shall call them Lucians. Soon enough, they speculate on all manner of theories of the origin of Lucia.

Now, in such a universe, the fact that physics permits the evolution of life is the direct result of your hard work and ingenuity. You sit back and wait for the Lucians to develop science, discover the laws of nature and marvel at the cleverness of your physics (where physics = physical laws + initial conditions + constants of nature).

But what’s this? One rowdy Lucian is trying to convince them that the fine-tuning evident in the laws of nature is no evidence at all that physics has been carefully chosen to permit the evolution of life. Given that life exists, he argues, the fact that the physics of Lucia supports life follows inevitably. Thus, life-friendliness supports (or at least does not undermine) the hypothesis that Lucia is governed by naturalistic law.

Fuming, you hit the small white button next to the big red one – the intercom. A heavenly voice booms across the Lucian cosmos.

What do you mean, “given that life exists”?! Talk about being taken for granted – I’ve been working my fingers to the bone up here, you ungrateful sods. Do you think this is just any old universe? That I just closed my eyes and picked at random? Do you have any idea how hard it is to blow up a star and make the remains into DNA? Of course you’re governed by naturalistic laws – they’re my sodding laws! Unbelievable. And to think I was going to introduce you to my son.

Someone who merely stumbled into your basement and found Lucia could reasonably conclude that it is unlikely that its physics were chosen at random. The Lucians have exactly the same information, and should be able to make exactly the same inference.

______________________________

I’ll repeat my warning at the start: I wouldn’t call these counterexamples. There’s every chance that they are just puzzles to be solved by clear thinking.

1. Incidentally, if this scenario is true of our universe, I may have just won the competition for our creator. The downside is that, with the competition over, our creator has no motivation to continue sustaining our universe. My sincerest apologies if I have consigned our universe to some transcendent trash bin.

More of my posts on fine-tuning are here.

### 8 Responses

1. lukebarnes,
your grandfather thought experiment reminds me of a paper by V. Palonen entitled Bayesian considerations on the Multiverse explanation of cosmic fine-tuning (see the link below).
In short he argues that Multiverse hypotheses don’t explain fine-tuning. He also provides a version of the firing squad thought experiment to make (part of) his point.
I am curious to read your thoughts on this. If you find the time to read it that is.

Click to access cornell-palonen-v.pdf

Cheers

2. […] More technical response to Ikeda and Jeffreys’ Bayesian probability critique: 1, 2. (DM, kindly take notice. This critique, by reasonable extension,  also applies to Sobers’ […]

3. […] I would like to add that Dr. Barnes has also written an incisive online critique of Mike Ikeda and Bill Jeffery’s widely cited paper, The Anthropic Principle Does Not Support Supernaturalism, which is cited by Professor Stenger in his book, in order to show that even if some observation were to establish that the universe is fine-tuned, it could only count as evidence against God’s existence. Part 1 of Dr. Barnes’ reply is here; Part 2 is here. […]

4. […] Dr. Barnes’ ARXIV paper, The Fine-Tuning of the Universe for Intelligent Life (Version 1, December 21, 2011), is available online. Readers who dislike technical jargon can find a non-technical overview of key excerpts from Barnes’ paper in my blog post, Is fine-tuning a fallacy? (January 5, 2012). I would like to add that Dr. Barnes has also written an incisive online critique of Mike Ikeda and Bill Jeffery’s widely cited paper, The Anthropic Principle Does Not Support Supernaturalism, which is cited by Professor Stenger in his book, in order to show that even if some observation were to establish that the universe is fine-tuned, it could only count as evidence against God’s existence. Part 1 of Dr. Barnes’ reply is here; Part 2 is here. […]

5. […] I understand that Loftus is a big fan of Professor Victor Stenger, an American particle physicist and a noted atheist, who is also the author of the recent best-seller, The Fallacy of Fine-Tuning: How the Universe is Not Designed for Humanity (Prometheus Books, 2011). Stenger’s latest book has been received with great acclaim by atheists: “Stenger has demolished the fine-tuning proponents,” in the words of one gushing Amazon reviewer. Unfortunately for Loftus, however, the claims made in Stenger’s book have been completely demolished in a critical review by Dr. Luke A. Barnes, a post-doctoral researcher at the Institute for Astronomy, ETH Zurich, Switzerland. In his review, Dr. Barnes takes great care to avoid drawing any metaphysical conclusions from the fact of fine-tuning. His main concern is simply to establish that the fine-tuning of the universe is real, contrary to the claims of Professor Stenger, who asserts that all of the alleged examples of fine-tuning in our universe can be explained without the need for a multiverse. Readers who are daunted by the technical jargon in Dr. Barnes’ online ARXIV paper, The Fine-Tuning of the Universe for Intelligent Life (Version 1, December 21, 2011), may prefer to peruse a non-technical overview containing key excerpts from Barnes’ paper in my blog post, Is fine-tuning a fallacy? (January 5, 2012). I would like to add that Dr. Barnes has written an incisive online critique of Mike Ikeda and Bill Jeffery’s widely cited paper, The Anthropic Principle Does Not Support Supernaturalism, which is cited by Professor Stenger in his book, in order to show that even if some observation were to establish that the universe is fine-tuned, it could only count as evidence against God’s existence. Part 1 of Dr. Barnes’ reply to Ikeda and Jeffery is here; Part 2 is here. […]

6. Thank you for your post. However, I believe there is a minor error in reasoning in the scenario you present.

The assumption is made that P(F|NL) = 1. However, this assumption is poorly motivated in your scenario. To see this, consider more deeply the justification given: “the fact that you are alive means that all the shards missed you.” This is incorrect since one can imagine many counterexamples where you are hit by shards to various degrees but are left with a marginal amount of life. For example, your body could be so filled with metal shrapnel that you have only 9 seconds of conscious life remaining. Or you could have 9.9 seconds remaining. Or 9.99 seconds. Etc. In any of those scenarios, both N & L would be true, yet F is not. There are countless similar scenarios, and they are more probable than the “friendly” alternatives (given N). Therefore, P(F|NL) << 1.

In other words, it would indeed be ridiculous to observe "every inch of your Grandpa’s house has shards of metal sticking out of it, except for two perfect silhouettes" without concluding that something unnatural occurred. If you did see such "perfect silhouettes," concluding something unnatural happened *would* be justified using Bayesian reasoning. You would realize how unlikely two perfect silhouettes were — you certainly wouldn't assume P(two perfect silhouettes|NL) = 1.

7. […] responded to Ikeda and Jeffrey’s article here and here. Their reasoning is valid, but is not about fine-tuning. I show how the fine-tuning argument, […]

8. on June 9, 2018 at 5:07 pm | Reply Miguel Castro

Hello Dr. Barnes,

I have a criticism of your “Grandpa Is Magneto” example. I found it interesting and humorous in a good way. However, I think that, far from leading us to a “conclusion that Grandpa has the abilities he claims,” we should actually trust the Ikeda-Jefferys Theorem (IJ) over our “intuitions” and conclude that Grandpa likely doesn’t have those powers after all, or that, at best, we can’t tell if he has them. The IJ Theorem tells us that, despite our first-impression intuitions, it is no more likely (and possibly less likely) that Grandpa has the powers than not. I believe that this (the IJ Theorem’s conclusion) should be the correct inference however unlikely my survival after the “train explosion,” and however much our first-impression intuitions may disagree with the IJ conclusion. In fact, those first-impression intuitions can be superseded by more reliable intuitions once we think a bit more carefully. But regardless of at-first-blush intuitions vs. more-carefully-thought-out intuitions, it should not be our intuitions that ultimately produce our conclusions, but well-reasoned arguments instead.

My criticism is twofold. First, the Magneto example is disanalogous to IJ’s formulation, despite the superficially identical labels F, L, N (particularly F), and this might subject the Grandpa Magneto example to “straw man” condemnations. However, even under the same definitions used in the Magneto example, we cannot conclude that Grandpa has the powers that he claims to have. Second, while piling on more examples (besides the original “train explosion” example) may entice us to fallacious thinking, they still do not get us to a reasoned conclusion that “Grandpa has the powers.”

The disanalogy

First, note that “F” in the Magneto example is disanalogous to IJ’s “F” in the following important sense. IJ define F as: “[The] conditions in [the] universe permit or are compatible with life existing naturalistically (emphasis mine). On the other hand, you (Dr. Barnes) define F differently. I’ll label your definition as F* to distinguish it from IJ’s F. You define it as: F* = “all the shards of metal from the explosion followed paths that were ‘you-friendly.’ “ If I’m not mistaken, the shard paths can be either natural trajectories or Grandpa-influenced unnatural trajectories, as long as they are “life-friendly.” So, your F* is defined as “life friendly” regardless of whether the life-permitting “friendliness” comes from Grandpa’s power or from unaided natural laws. However, IJ make the crucial distinction that their F stands for “Naturalistically Life-Friendly.”

In this way, IJ’s F captures well what we think of as “Fine Tuning,” whereas your F* is simply “Life-Friendly, with or without Tuning.” After all, Fine-Tuning Argument (FTA) proponents rely only on naturalistic principles and observations. In that sense, FTA proponents “play by the rules of science” since they don’t resort to any kind of miraculous sustenance of natural laws, but quite to the contrary, they rely on empirical observation and natural principles, and don’t assume miracles.

This means that, while IJ’s F is possible under ~N so that P(F|~N) >= 0, IJ’s F specifically disallows miraculously-sustained life, per the FTA. However, the F* in your example does allow for miraculously-sustained life. Letting M = “the presence of miracles” so that the conjunction ML stands for “miraculously-sustained life,” we can write this as:

P(F|ML) = 0, while P(F*|ML) >= 0.

Moreover, P(F*|F) = 1, but P(F|F*) <= 1. In other words, while F entails F*, F* does not necessarily entail F. This leads also to:

P(F*) >= P(F).

Clearly, F and F* are not logically equivalent, so in that sense your example is disanalogous to IJ’s formulation.

Yet the IJ Theorem still works with F*

We can also see that:

P(F*|L) = P(F|L) + P(F*|ML) P(M|L),

P(F*|L) >= P(F|L).

Now, the partial inequality in the IJ Theorem’s conclusion, P(N|FL) >= P(N|L), hinges on the value of P(F|L). We might think that substituting F* in place of F in the IJ inequality could undermine the IJ Theorem, because P(F*|L) >= P(F|L). Of course, this would still not invalidate the IJ Theorem, because the Theorem refers to F, not to F*. However, we can see that even using F* does not get us to P(N|F*L) < P(N|L). In other words, we cannot say that learning even the more ambitious F* will undermine N.

To see this, note that it is still true that P(F*|LN) = 1 (from the entailment P(F*|F) = 1 above). The IJ inequality using F* now reads:

P(N|F*L) = P(F*|LN) P(N|L)/P(F*|L) = P(N|L)/P(F*|L) >= P(N|L).

The partial inequality is still respected despite P(F*|L) >= P(F|L) because the most that P(F*|L) can be is 1. (In fact, one might even argue that P(F*|L) = 1. The reason is that P(L) = P(L|M) + P(L|~M), and F*, by definition, permits life either by miraculous or non-miraculous means. But we don’t need this result.) In any case, even if P(F*|L) reaches its maximum of P(F*|L) = 1, we are still left with:

P(N|F*L) = P(N|L),

so that N is not undermined even by F* which is more ambitious than the original F.

Fixing the disanalogy recovers IJ’s inequality

But, as mentioned before, the IJ Theorem deals with F, not F*. Now, to make your (Dr. Barnes’) F* fully analogous to IJ’s F, we could modify it as follows:

F = all the shards of metal from the explosion followed paths that were naturalistically “you-friendly.”

In other words, all the “friendly” paths must be consistent with unaided physical laws (even if in fact Grandpa had used the powers). In this case, F would now be fully analogous to the one used in the IJ Theorem, whose result would in turn remain unchanged, so that P(N|FL) >= P(N|L), and indeed P(~N|FL) <= P(~N|L). This means that observing that the shard paths didn't hit me would tell me either nothing about Grandpa's power, or possibly that it is less likely than not that he has the powers he claims to have–my "intuitions" to the contrary notwithstanding.

Shards, fallacies, and rethinking intuitions

It is indeed very unlikely that I would survive the explosion if the shard trajectories had followed their normal course, P(F|N) << 1. At first blush, I may be tempted to infer, intuitively, that a lack of Grandpa powers, N, must also be very unlikely: P(N|F) << 1, and that in fact P(~N|F) is close to 1. But as IJ point out and you (Dr. Barnes) fully agree, this is a fallacy. In other words, we cannot conclude that P(F|N) << 1 entails P(N|F) << 1, regardless of its intuitive appeal.

But if we think about this, we may see that our first-blush intuition was not reliable. The problem is that learning that the shards followed exactly the paths that would have been consistent with the (unassisted) normal laws of physics unaided by Grandpa’s powers does nothing to raise the likelihood that Grandpa has those powers. It is still possible that Grandpa had–and in fact did use–the powers, but we have no way of differentiating between that and normal unassisted physical law upon observing that the trajectories, while “friendly,” looked just as if they had been “unassisted” by Grandpa’s powers (even if they were in fact “assisted” by Grandpa’s powers). This is despite how unlikely it is that I have survived the explosion because, intuitions to the contrary, it is not the case that P(F|N) << 1 entails that P(N|F) << 1. This is, in fact, a fallacy in intuitive thinking (a type of Prosecutor’s Fallacy, I believe), not a reliable guide to a correct conclusion.

Upon further reflection, we can see that our observation may even undermine the “Grandpa has powers” claim. This is because if Grandpa had the powers, there would be many, many, many more possible “friendly” trajectories that the shards could have taken to avoid killing me than “friendly” but unaided physics-like trajectories. For example, the trajectories that would otherwise kill me, could have curved in midair, not conserving momentum. They could’ve slowed down more than it would be warranted by air friction–not conserving energy–and they could’ve stopped before hitting me. They could’ve shot up and exploded like fireworks, without hitting me. They could’ve buried themselves in the ground, thus not hitting me. They could’ve been suspended in midair. They could have hit me, and I could’ve died if they stayed inside me, yet Grandpa could magically extract them from my wounds using his powers, so they wouldn’t kill me, etc. etc. All of these cases would correspond to friendly trajectories which were not physical, but which were aided by Grandpa’s powers. There is a virtually infinite number of such friendly trajectories when we allow them to be unconstrained by physical law–many more than friendly trajectories that are actually constrained by physical law.

So the question remains, why expect, if Grandpa had powers, that the trajectories would just so happen to appear to follow normal physical law after all? In fact, if Grandpa had the powers, we should think it quite an unlikely coincidence that the “friendly” trajectories just happened to line up perfectly with the extremely unlikely “friendly” unaided physical trajectories, when there were so many more available “friendly” unphysical trajectories that could have come from Grandpa’s powers.

Of course, it is possible that somehow Grandpa is trying to hide his powers from me, but this seems unlikely, especially since he seemed to want to communicate to me that he had the powers, and even appeared to revel in showcasing his powers.

It is also possible that Grandpa wants to show off his ability to exert his powers even while not appearing to violate physical law. But, in that case, we would have no way to distinguish his hidden powers from unaided physical law, nor would we be able to gain explanatory power. In other words, if Grandpa had the powers but always hid them, we would never be able to tell, nor would we be able to explain anything that wouldn’t be explainable through unaided physical law. So again, the “why-do-they-look-just-like-physical-trajectories” question remains.

Granted, it is very unlikely that I would have survived, namely: P(F|N) << 1. But this doesn't entail a misplaced intuition that P(N|F) << 1, as we saw before. And it is at least as unlikely, if not more unlikely, that the "friendly" trajectories under Grandpa having the powers, just happened to follow paths that lined up exactly with unaided physical law.

Other examples and the “Surely this is nuts” fallacy

In the last section of your Magneto example, Dr. Barnes, you seem to be attempting to defend the intuition that P(N|F) << 1, after all (and thus P(~N|F) is close to 1), by offering several other examples beyond the original "train explosion" example which you analyzed. The purpose, it seems to me, is to prop up our (possibly fallacious?) intuitions instead of relying on reasoned analysis. (Of course, I could be totally wrong, and I invite you to correct me if I am.) The examples are: "the whole debacle happening again," "blind snipers getting out of hand," "several satellites falling out of orbit," "angry neighbors throwing frying pans," "Grandpa Magneto causing a shard of metal to swerve wildly" etc.

Those (rather extreme) examples should, of course, be analyzed on a one-by-one basis, instead of marshalled to a rushed (possibly fallacious?) conclusion. It seems clear to me that, except for the very last one, none of them would override the IJ Theorem’s conclusion, despite our intuitions. Each example (or all of them at once, for that matter), could be framed exactly as the original “exploding train” example, and we would be forced to conclude, via the IJ Theorem, either that we can’t know whether Grandpa has the powers, or that he more likely than not doesn’t have the powers. Our intuitions to the contrary notwithstanding.

The very last example that I cited, “Grandpa Magneto causing a shard of metal to swerve wildly” (which I presume is through Grandpa’s unnatural powers) would constitute an observation of a miracle or suspension of natural law, which lies outside the purview of the IJ Theorem, and indeed of the FTA. If we were very confident in this observation, namely P(M) is close to 1, then we would have an immediate disconfirmation of N, since P(N|M) = 0. So indeed, it would “surely be nuts” to not accept that Grandpa had the powers if we indeed verifiably observed the miracle with a high degree of certainty (i.e., if we were “surely not nuts” while witnessing the miracle). But again, this last example is nothing like what FTA proponents advance, since they rely on empirical observation and physical phenomena, not on ratifications of miracles. So this last example is inapplicable here.

Is IJ incomplete or is conditioning on L “the problem” ?

You also state, Dr. Barnes, that you’re “not sure if the problem here is that we are conditioning on L, or if this formulation is incomplete as [you] alleged in part 1 I don’t think that there should be any “problem” with conditioning on L. Arguably, there are good reasons to do so. While analyzing counterfactuals not conditioned on L might be interesting, I would think that ignoring the self-evident observation of L, would leave the analysis incomplete if we in fact didn’t condition on L. I think what would be prudent is to ensure that we’re not fabricating “problems” because of the lure of the “P(N|F) must be small” fallacy. That, it seems to me, would constitute a real “problem.” If you are aware of any reason why conditioning on L is either disallowed, or not well-motivated, a reference would be greatly appreciated.

In addition, I’m not aware that you have actually provided, either a definition of what you mean by IJ’s formulation being “incomplete,” or an argument for your assertion that IJ’s formulation is incomplete. While you provided a different formulation in part 1, I don’t think that offering a different formulation, by itself, constitutes an argument for IJ’s incompleteness. I may address your alternate formulation vs. IJ’s later, time permitting. Until then, if you know of an argument demonstrating, or attempting to demonstrate, that IJ’s formulation is incomplete, I would greatly appreciate a reference.

The moral

The moral here is that “at-first-blush” intuitions are demonstrably prone to fallacies and can be wrong, and that we should trust the conclusions of a properly framed and correctly derived line of reasoning instead of (and in spite of) our intuitions.

That is precisely the lesson to be drawn from the IJ Theorem. Unless, of course, there is a flaw with it, but it doesn’t seem like the “Grandpa Magneto” example uncovers any flaws in the IJ Theorem itself by pitting “first-impression” (and likely fallacious) intuitions against the IJ Theorem’s more sensibly derived conclusions. It is not apparent to me that IJ’s formulation is “incomplete” either, or that it suffers from any “problems” by conditioning on the self-evident observation that life exists in our universe, L. The virtually self-evident and transparent simplicity of IJ’s Theorem, it seems to me, gives a great deal of strength to its evisceration of the FTA. As far as I can tell, the IJ Theorem is unassailable.

In conclusion: It seems to me that the Ikeda-Jeffery’s Theorem is alive and well and is not overturned or undermined by “first-impression intuitions” about the “Grandpa May Have Magneto Powers” example. If anything, this example should draw a lesson form the IJ Theorem and what it teaches us about unchecked intuitions leading to fallacious inferences.