An anthropic bias?

The book by Nick Bostrom, Anthropic bias: Observation Selection Effects in Science and Philosophy, London, Routledge 2002 (ed. on line 2020), is certainly of great interest, even for those who investigate the origin and nature of consciousness.


Bostrom’s approach

This volume discusses the vexed question of the so-called “anthropic principle”. According to this principle our universe is characterized by certain parameters because these are the only ones compatible with “our” existence (in this sense it is a “fine-tuned” universe).

For “our” existence – Bostrom clarifies (in chap. 1) – it mustn’t be understood the existence of Homo sapiens, as living species, even if originally (in 1974) Brandon Carter had called this principle ambiguously “anthropic”. It must be understood the existence of “observers” of the universe itself (or also, as sometimes Bostrom writes, the existence, on Earth or elsewhere, of “intelligent life”, in general). In short it is the question of why our universe not only exists, but is also “observable”.

Although, as I will discuss later, “observer” and “consciousness” do not necessarily have the same meaning, the question of the origin of an observable universe and the question of the origin of consciousness are clearly linked.

Regarding the origin of our universe, as an observable universe, the macro-theories that Bostrom discusses can be reduced to two:

  1. our universe is observable (hosts intelligent and conscious life) because of an intelligent design (i.e. something that has our appearance as goal) or
  2. it is as it is by chance.

Bostrom does not take the first hypothesis seriously: intelligent design is rejected, among other things, with the following argument: in order to support it, we must prove that our universe should be the nicest possible, a feature that Bostrom considers obviously implausible. This argument is formalized, albeit hypothetically, resorting to the Bayes theorem, in chap. 11 with these words:

If our universe is not of the sort that one might have suspected a creator to create if he created only one universe (if our universe is not the “nicest” possible one in any sense, for example), then the conditional probability […] on any creator-hypothesis involving the creation of only one universe might well be so slim etc.

Bostrom considers more reliable (probably the only one worthy of a scientific treatment) the second hypothesis, that is that the universe arose by chance.

And why, then, is it so fine-tuned as it aimed at our existence or, better, the existence of observers?

Bostrom’s thesis is basically as follows: our universe appears “miraculously” fine-tuned because of a (trivial) observation selection effect: we certainly could not observe a universe where there were no observers! In general, according to Bostrom, if we want to do science we must take into account these observation selection effects (this is the great lesson of the anthropic principle, reinterpreted as “anthropic bias”): things (laws of nature, laws of evolution, initial conditions, etc.) appear to us in a certain way rather than in another on the basis that they can be observed by us. Laws of nature or initial conditions not compatible with the birth of intelligent (and conscious) life on Earth obviously cannot be “discovered”. This does not exclude (but, according to Bostrom, rather suggests) that there are infinitely more things, which, “by construction”, we will never know, precisely, those that we cannot observe.

In particular, accepted this non-theological and non-teleological perspective, which gives relevance to pure chance, the hypotheses are again two: or 1) our universe is the only existing universe or 2) it is one among countless or infinite other “universes”, the only observable one (or one of the few or many observable), which is why we observe this universe and not others.

Bostrom seems to favour this second hypothesis.

The argument is basically this: it would be really strange that only one universe has arisen randomly and that just this is fine-tuned and also hosts intelligent life, especially if we assume that this, in itself highly unlikely, would have been impossible in a universe even slightly different from ours. So, the multiverse hypothesis is much more likely.

This thesis is not only argued discursively, but also resorting to logical and mathematical tools, essentially to Bayes’ theorem and its derivatives. It is supported, in particular, by a central assumption in the book, the Self-Sampling Assumption (SSA), which, in its first form (introduced at the end of chap. 3 and subsequently improved and corrected), sounds as follows:

One should reason as if one were a random sample from the set of all observers in one’s reference class

To understand what Bostrom means by this assumption, one can mention its use in traffic analysis, as does Bostrom itself (in chap. 5). If you end up stuck in a queue where one lane is slower and one is faster, the fact that you’re probably in the slowest lane isn’t due to a goddamn “Murphy’s Law,” as you might think, but to the trivial circumstance that the slowest lane is also the one where the greatest number of vehicles is located, so probably yours too! In this example you are a “sample” taken from the set of all drivers who are in traffic (reference class). It seems more likely that you are in the slower lane than the faster one simply because there are more vehicles in this lane.

How does this assumption apply to the “anthropic principle”? Bostrom (in chap. 4) makes several thought experiments to illustrate this; then (in chap. 5 and following) he applies this assumption to several open scientific questions, variously connected with the anthropic principle, such as the origin of this universe, Boltzmann’s explanation of the time’s arrow, the evolution of intelligent life on Earth and possibly in other planets etc.

Here, for example, is how the SSA is applied in the Incubator gedanken (introduced in chap. 4 and resumed in chap. 10). Imagine tossing a fair coin: “If the coin falls tails then it creates one room and a man with a black beard inside it. If the coin falls heads then it creates two rooms, one with a black-bearded man and one with a white-bearded man. As the rooms are completely dark, nobody knows his beard color. Everybody who’s been created is informed about all of the above. You find yourself in one of the rooms. Question: What should be your credence that the coin fell tails?”. In the absence of any other information, if we were one of these newly “created” men, our credence of tails should be 1/2. However, if the lights are switched on and we discover that we have a black beard, according to the SSA our credence of tails should become 2/3.

The reasoning, expressed without recourse to mathematics, could sound like this: in the absence of other information the probabilities of head and tails are equal, but this is no longer true when I discover that I have a black beard: in fact, if the coin had fallen head, I could have had a white beard: therefore it is more probable that it has fallen tails. Indeed, what applies is Bayes’ theorem: the initial probabilities of a given event E may increase or decrease (so that they become final or conditional probabilities), if another F event occurs or does not occur or if a particular H theory is true or false. In the Incubator gedanken, knowing that I have a black beard (new event) gives me additional information (in favor of one theory rather than another) that makes me change my estimate of initial probabilities.

How does this SSA apply to scientific issues in which the anthropic principle is involved?

For example, Bostrom uses this SSA to argue (chap. 5) that it is theoretically possible to experimentally test which kind of view in quantum mechanics is most likely true between these two: the “single-history version” and the “many-worlds version”. According to the first view, whenever the collapse of the wave function of a particle is recorded, this particle goes in a certain direction and not in another, which it might also have followed. According to the second view, whenever indeterminacy is involved, the world multiplies and all the paths that the particle can follow are followed, each, however, in a different world.

The idea of Bostrom is as follows. Suppose we can (one day) prove that the appearance of observers in the physical universe is something infinitely unlikely, given the known laws of nature and the initial conditions of our universe. We, then, should probably not exist. If we exist, then the “many-worlds version” is probably true, where even the most unlikely outcomes occur. For the Bayes’ theorem, in fact, if something E has little initial probability (in our case: that observers appear), but it could happen with much greater probability if a certain hypothesis H was true (in our case: the “many-worlds version”), then, if this E occurs, it is likely that this hypothesis H is also true.

Before introducing the SSA, Bostrom had similarly argued discursively in favor of the theory that ours is one of many other universes: this should make the existence more likely, otherwise very unlikely, of our universe (characteristically fine-tuned and marked by the emergence of conscious observers).

The SSA also has the merit of making the appearance of so-called “Boltzmann brains” highly unlikely, if not impossible (Bostrom does not refers to them, but speaks, similarly, in chap. 3, of “freak observers”, e.g. human brains random emitted by black holes as offsping of Hawking radiation). The idea of Bostrom is this: it cannot be excluded that we live in an illusion (like the famous brain in the vat), as observers completely randomly sprung e.g. by the evaporation of black holes and marked by deceptive perceptions. However, within the “reference class” of all possible observers, it is much more likely that we are observers evolved by natural selection from other living organisms, as we seem to be. In fact, in a fine-tuned universe the number of “normal” observers is reasonably much higher than that of “freak observers”. Just as, when there is traffic, it is more likely to be in the slowest lane, because there are more vehicles, so, in the universe, it is more likely to belong to a species that has evolved over millions of years and that can count billions of individuals than to be “intelligent lives” arising by pure chance from the combination of quantum particles during the evaporation of a black hole. Although it cannot be excluded that some “observer” has this bizarre origin, it is very unlikely that “we” belong to this “exclusive club”, so to speak.

Summing up, applying Bostrom’s “anthropic” reasoning and adopting his “mathematics” (which in chap. 10 takes the form of a very Observation Equation), we should conclude that we exist by pure chance within a multiverse of which we observe an extremely limited portion, “our” universe, the only one that we can observe (for an obvious observation selection effect). There would be nothing wonderful or strange about this. The fact that the universe is fine-tuned would in turn be an observation selection effect: if it were not such, there would be no one to witness it and, above all, we would not be able to do.


Problems with Bostrom’s approach

Is that a convincing conclusion? In my opinion, no. One thing, in fact, is to argue that, if there are countless universes, it is likely that, sooner or later, or somewhere, observers will appear; which, if there was only one universe, would be unlikely. Another thing is to argue, on the same basis (that is, “if there are countless universes…”), that it is probable that we have appeared and, conversely, that, if there are us, there are likely to be countless universes.

“We” are not just any observers who have appeared somewhere. We have come here and now. We are also characterized by being conscious, which means something more than “observing” if by observing we mean an action that could be performed by something or someone who might not be “us” (as e.g. an extraterrestrial intelligence). Consciousness is something that we can only experience by being conscious in the first person.

Summing up: according to Bostrom it is the more probable the appearance of a fine-tuned universe that allows the emergence of observers, the more other universes we admit (multiverse hypothesis).  The objection (mine and of a certain Roger White, quoted by Bostrom himself in chap. 2) is that this does not apply if the fine-tuned universe is ours, that is, the observers are us.

Apparently this objection seems unjustified. Bostrom himself (again in chap. 2) points out to White (and implicitly to me too) that, if, in general, the appearance of a fine-tuned universe, which allows the emergence of observers, favors the hypothesis of an almost infinite succession of universes (the multiverse) it would be strange that what applies, in general, to the universes containing observers does not apply to this universe (meaning “this” as a rigid reference), that is, to the universe in which we are.

Bostrom states that White does not bring convincing arguments in favor of his thesis (according to which what generally applies to fine-tuned universes would not apply to ours).

But in my opinion there is a convincing argument. Ironically, Bostrom himself offers it to us on a silver platter (he mentions it in chap. 2). This is an argument drawn from the so-called inverse gambler’s fallacy.

Consider the direct fallacy, the most well-known. A gambler is wrong to think that the more he hasn’t been rolling a double 6, the more likely it is that he is going to roll a double 6 next time.

The inverse fallacy is: if a double 6 has now come out, that means (the gambler mistakenly believes) that there have been many rolls before in which this result has not come out.

But it is easy to understand that this is not necessary at all, because this series of previous rolls would not make the double 6 outcome any more likely.

Similarly – I maintain – the fact that our universe contains observers and is fine-tuned does not entail that there have been many other universes before.

Of course, if you roll two dice many times, the probability that sooner or later a double 6 comes out increases; not this double 6, but only a double 6. In fact, if we do not want to fall into the inverse gambler’s fallacy, we must recognize that, if a double 6 comes out now, this does not increase the likelihood that the dice have been rolled many times before rather than a few times or none.

Thus, if the “many-worlds version” of quantum mechanics were true (which Bostrom believes he can support on the basis of the SSA, provided that certain experimental conditions are given), the probability that sooner or later observers would appear, certainly, would increase.

But the fact is that these observers do not appear sooner or later from our point of view or from the point of view of other observers who can record (observe!) the event. These observers are us now.

If, therefore, we do not want to fall into the inverse gambler’s fallacy, we must grant the following: our (albeit very unlikely in itself) presence makes neither a multiverse more likely than a simple limited universe (like this we observe) nor the “many-worlds version” of quantum mechanics more likely than the “singole-history version”. In sum our presence not make that Nature has rolled countless times the dice more likely than a few or a single time.

In short, the fact that the observers we are talking about are ourselves, now, this short circuit, makes a huge and decisive difference.

So why does the SSA work with traffic and not quantum mechanics? Because I, who already exist and am aware that I exist, can certainly predict that, if I ever get stuck in traffic, it will be more likely that I find myself in the slowest lane rather than the fastest one. But how could the “lane”, whose probability should be calculated, be my own future existence as a conscious observer? There is no “place” where I can calculate the probability that I might be born, because “I myself”, in that place, would not be there yet.

Conversely, if and when there is me, there is me now, in a present (whose probability is equal to 1), which is not just any time when “someone” becomes conscious sooner or later.

It is only the moment whenever any observer emerges to suggest, provided that the emergence of an observer is rare and improbable, that Nature must have made many “vain attempts” to bring it out first. But the present moment, “my” moment, the moment when there is me, the moment only when consciousness emerges properly (a consciousness experienced at the first person) does not require at all to be preceded or joined by failed attempts (by other universes in a multiverse or by many words in the “many-words version” of quantum mechanics), unless you want to fall into the inverse gambler’s fallacy.

It is as if Bostrom calculated in abstract the probability that observers emerge in the universe, for example in the form of Homo sapiens. And this he did as if he were an alien or a computer unconscious and out of the picture. Then he noticed: “What a surprise, we are these observers and we are now!”. So what applied to Homo sapiens applies to us!

But here lies the “bias”. This is not an innocent passage, because there is a difference between

  1. saying that by rolling pairs of dice increases the probability of a double 6 (the appearance of intelligent life in the universe), which is certainly correct, and
  2. saying that the fact that there is now a double 6 (we are aware that we exist here) supports the fact that a lot of pairs of dice have been rolled, which is not at all correct.

In short, unless you want to fall into the inverse gambler’s fallacy, since at each roll a double 6 can come out with probability 1/36, when we record a double 6 it could be the only roll made. Of course, there may have been other rolls before, but not “so that” this double 6 came out (or so that it was more likely, here and now, a double 6). Indeed the result I am witnessing here and now is not made any more likely even by a million previous rolls (direct fallacy of a gambler, who bets on numbers that have not come out for some time).

The truth is that a roll made “here and now” makes this roll mysteriously different, whatever arguments Bostrom. In fact, Bostrom is right: the more you roll two dice, the more, in general, it is likely to come out a double 6 (like any other pair of numbers between 1 and 6). But not now! Now the probability is always damn 1/36 (regardless of the number of previous casts).

Similarly, the fact that intelligent life is given here and now in this universe does not tell us damn if there have been other universes before this or not. If the argument drawn from the inverse gamblerìs fallacy is valid, Bostrom is wrong to consider the probability of multiverse high.

The final refinement of the SSA (in chap. 10) in terms of the SSSA (Strong Self-Sampling Assumption) does not change anything and underlies the same bias. Turning “observers” into ” observer-moments” enhances the performance of the SSA, avoiding potential arguments against it, but the problem remains. How can we move from these “observer-moments “, described in third person, to first-person experience (i.e. your or my experience) of these moments? What is true for these moments described in the third person, no longer applies if we live them (estimates of the probability of the conditions that would have made our conscious existence possible or probable lose their value).


Another approach

How to explain, then, our existence as conscious observers, if Bostrom’s reasoning falls into this fallacy?

Let us also admit that the structure of the universe doesn’t favor the argument of intelligent design. An intelligent creator could have created man (a consciousness) in times and spaces much more limited than real, appropriately manipulating energy and matter (although in this way final and formal causes would have been exposed, as when you distinguish an artifact from a natural product). Also the creator could have made a even nicer universe than it is. The breadth of universe spacetime and the clear signs of imperfection that the universe contains suggest that everything happened randomly. Well, let’s say that’s what happened.

Now, if the hypothesis of intelligent design must be rejected and if I am right to find the hypothesis of the multiverse (which Bostrom argues probable, but which to me seems a flagrant violation of Ockham’s razor and an useless hypothesis, as the deceptive appearance of its usefulness is a mere effect of the inverse gambler’s fallacy) how to explain the origin of consciousness (that is, identically, of an observed universe)?

Consciousness seems to arise quite randomly (without anyone having designed it). Its emergence is only made a little more likely by the enormous dimensions of our universe (more precisely, as Barrow and Tipler argue in The Anthropic Cosmological Principle, Oxford, Oxford University Press, 1986: if our universe were not so big and old, intelligent life would in all likelihood be simply impossible). Yet we can certainly imagine countless universes of all possible dimensions in which consciousness never arose. The fine-tuning was therefore an incredible stroke of luck (the analogue of the double 6 above)?

If we eliminate the explanation of the multiverse and also of an intelligent design, what remains to think?

My hypothesis is that the fine-tuning of our universe was not a stroke of luck at all, but depends on the fact that, for a universe to exist, someone must be aware of it. My hypothesis is that a universe, like a quantum particle, in order to exist, must be simply observed. Otherwise it can exist at most only in a unfocused and contradictory way.

As seen in this perspective, the indexical (relative to the observer) aspect of what is observed is relevant. Bostrom also gives importance to this aspect. For example, in the case of traffic, it is because I am slower than others that I can infer that I am in the lane of more vehicles. However, this indexical aspect is treated by Bostrom in an overtly physicalistic way (as he argues in chap. 8). The information we get from our particular perspective is considered valuable, but is only used to enrich our objective knowledge with further information, as in the example of Bostrom: the fact that I have blue eyes (indexical) informs me of the fact that there are people with blue eyes (not indexical). In other words, the information we obtain because we exist in the first person is always translated as information that can be obtained from third parties.

My hypothesis is different: what is calculated (through the SSA) as probably real  (for example the multiverse) when we consider observers as third persons must be considered as only possible if we start from the first person experience (here and now): it is not necessary to suppose countless “real” worlds and universes before or beside us to account for the high improbability of our existence; it’s enough to recognize that only one of all the countless possible universes is the real one, the one in which there are we who can observe it and make it, therefore, real.

From this point of view the multiverse could be understood simply as the set of all possible universes, but rendered unreal by the fact that no one is conscious of it.

Similarly, all rolls of two dice (approx. 35 rolls) that give outcome other than the double 6, to which a gambler attends, can be “retrieved” not as material “antecedents” of the double 6, but as spectral “virtual” companions of it: all that could have happened but did not happen.

A final word on this. Also in chapter 2 Bostrom indirectly denies the relevance of the example of double 6 (and, therefore, of the inverse gambler’s fallacy) to the case of the observable universe.  He claims that the release of a double 6 has nothing to do with observation selection effects. “As pointed out by three authors […] there is no observation selection effect in his example—an essential ingredient in the purported anthropic explanation of fine-tuning”. It would have something to do with these observation selection effects if you imagined that “the gambler has to wait outside the room until a double 6 is rolled”. So watching a double 6 would be the effect of an observational selection (the gambler could watch “only” at double 6, by convention).

But the opposite is true! If the gambler had to wait outside the room, he would also exist whenever no double 6 is rolled in the room. He would exist and be aware that he exists. If he then had to wait hours and hours before being called in, he would also have good reasons to think that many other pairs of numbers came out before the double 6.

What is wrong in this analogy? Let’s consider: there is a consciousness, that of the gambler, waiting to watch a double 6. What is analogous to this situation? “There is a consciousness waiting to see if in this or that universe appears a… conscious being!” But it is clear that, if the analogy between the roll of the dice and the appearance of observers is to work, the double 6 must directly represent the appearance of observers (or consciousness), not the appearance of observers… of observers!.

My hypothesis, that this universe exists simply because it is the only one of which one is aware (and not as one among countless others, equally “existing”, but of which no one is aware), can also be reached by another way, in which the SSA returns to play a role.

A merit of the SSA consists in the fact that, as Bostrom shows (in chap. 5), it allows to dismantle the claim of Boltzmann, followed in this by many others, to justify the time’s arrow of “our” universe. According to Boltzmann, the irreversible increase of entropy that distinguishes our universe, breaking its symmetry with respect to time, was due to the fact that in a very large universe it would not be impossible to observe local fluctuations in the values of entropy, so in some regions (like the one we are in) entropy could be randomly very low and therefore destined to grow (as we actually observe it happening). This would be compatible, therefore, with the image of a universe globally symmetrical with respect to time.

Bostrom has a good game to prove that, if the SSA is valid, these fluctuations are certainly possible and “we” could certainly find ourselves in a region marked by an increase in entropy and, therefore, by a time’s arrow (unique condition compatible with the appearance and evolution of life). However, this region, probably, should be much smaller than our universe which is about 40 thousand light years wide and appears globally marked by irreversible increase in entropy. In fact, the fluctuations Boltzmann talks about should be both small and large. But the small ones should be much more frequent and numerous. Therefore, for the SSA, conscious observers should appear much more frequently and in larger number in much smaller regions of the universe than we do. For the SSA we should therefore inhabit a much smaller universe. Since this is not the case, Boltzmann’s explanation of why we experience an irreversible increase in entropy is probably wrong.

This criticism of Boltzmann’s argument remains valid even if the SSA, as I maintain, cannot be used to argue (as Bostrom does) that our universe appeared randomly within a much larger multiverse. In fact, used against Boltzmann’s argument, the SSA does not directly apply to the emergence of consciousness here and now (which, as I have already argued, unless you want to fall into the inverse gambler’s fallacy, is an event that does not allow you to estimate the probability of the multiverse), but to the problem of time’s arrow, determined by the direction of the increase in entropy (which is an objective datum, not related to “here and now”). The conclusion of Bostrom is, therefore, correct: the fluctuations conjectured by Boltzmann do not explain why a time’s arrow of time characterizes a universe as large as ours.

My explanation of this mystery goes in the same direction as my explanation of the origin of our observable universe: as there cannot exist but a universe of which one is conscious, so there cannot exist but a universe admitting living observers, that is a universe marked by an irreversible increase of entropy and a consequent time’s arrow (the unique condition to which living beings can exist). In short, it is the same consciousness to decide which universe (not only appears to us, for a “trivial” observation selection effect, but also simply) exists, both a) regarding its being, generically, fine-tuned, and b) regarding its being, specifically, characterized by irreversible increase in entropy.

And here I mention, finally, another limit of Bostrom’s approach. Bostrom thinks as if space and time could be real (existing) in the absence of observers. Expanding at will space and time Bostrom can then imagine multiverses, many worlds and other possible conditions capable of making the appearance of conscious observers less unlikely. Although in chap. 1 he refers to Kant as a precursor of the need to take into account observation selection effects, he seems to ignore the fundamental Kant’s lesson: the first (distorting) effect due to observation could be the belief that the universe is traversed by a system of spacetime axes, but a spacetime system may not exist at all in the absence of observers, because it is part of the perceptive system.

So, if, following Leibniz, Kant and many others, we suppose that space and time are “subjective”, that is, they depend on the fact that there are observers (they are in short only a way of observing reality), the “multiverse” that Bostrom posits as a plausible condition of the appearance of conscious observers can be conceived only as something “virtual” or purely “conceptual”, as the imaginary (“spectral”) set of rolls other than the double 6 that we ourselves are.

It must be said that Bostrom, beyond his specific theses, has the great merit of analytically discussing, using suitable mathematical tools, the different hypotheses formulated by him and by many other authors about anthropic reasoning, providing the reader with a vast and fascinating panorama.  He also motivates a reader who does not agree with his thesis to argue alternative points of view with the same rigour. And that’s exactly what I tried to do.