This post is a little bit different although not totally unrelated to my theme of “Russell’s Problem”. It has to do with some interesting arguments from the Australian born mathematical physicist Brandon Carter, known for his contributions to classical general relativity.
The issue here is “Carter’s Catastrophe” or the “Doomsday Argument”. This basic idea behind Carter’s Catastrophe was also discovered independently by the philosopher John Leslie, who has also presented a popular account, and the cosmologist J Richard Gott III. I remember reading a paper of his way back on cosmic strings, but that’s another story.
The idea behind Carter’s Catastrophe is easy to state. As Nic Bostrom states in his detailed literature review most discussion on the argument focuses on refutations and counter-refutations. Bostrom, taking his cue from Leslie, gives us a neat quick explanation of the reasoning behind Carter’s Catastrophe,
…Imagine that two big urns are put in front of you, and you know that one of them contains ten balls and the other a million, but you are ignorant as to which is which. You know the balls in each urn are numbered 1, 2, 3, 4 ... etc. Now you take a ball at random from the left urn, and it is number 7. Clearly, this is a strong indication that that urn contains only ten balls. If originally the odds were fifty-fifty, a swift application of Bayes' theorem gives you the posterior probability that the left urn is the one with only ten balls. (pposterior (L=10) = 0.999990). But now consider the case where instead of the urns you have two possible human races, and instead of balls you have individuals, ranked according to birth order. As a matter of fact, you happen to find that your rank is about sixty billion. Now, say Carter and Leslie, we should reason in the same way as we did with the urns. That you should have a rank of sixty billion or so is much more likely if only 100 billion persons will ever have lived than if there will be many trillion persons. Therefore, by Bayes' theorem, you should update your beliefs about humankind’s prospects and realize that an impending doomsday is much more probable than you have hitherto thought…
In other words Carter’s Catastrophe is an argument for a probability shift as to our future prospects for survival. Most people would adopt the intuitive position that our higher order intelligence compels us to adopt an optimistic view as to the future prospects of the species but Carter’s argument asks us to re-consider this position in the opposite direction?
What is the relation to superstring theory?
Well, Brandon Carter is also well known for introducing the Anthropic Principle. Paul Davies has just recently published an interesting popular discussion on the Anthropic Principle. The Anthropic Principle comes in a few forms of graduated strength with the “Final Anthropic Principle”, FAP, of Barrow and Tipler being the most notorious. Barrow and Tipler surmised that at the final singularity of a closed universe, what they called the “omega point”, intelligent life would necessarily become, basically eternal and God like. This prompted the mathematician Martin Gardner to propose his own Anthropic Principle, CRAP…Completely Ridiculous Anthropic Principle!
Of course Barrow and Tipler wrote before we discovered the accelerating expansion of the universe which puts closed universe models very much on the nose.
But back to the topic. The Anthropic Principle in its most plausible form comes to us
as the Weak Anthropic Principle which Barrow and Tipler informs us states,(p16)
…The observed values of all physical and cosmological quantities are not equally probable but they take on values restricted by the requirement that there exists sites where carbon-based life can evolve and by the requirement that the Universe be old enough for it to have already done so…
This seems reasonable and uncontroversial. The key issue here is the principle of the self-selection of observers. As Barrow and Tipler point out,(p3)
…we are a carbon-based intelligent life-form which spontaneously evolved on an earthlike planet around a star of G2 spectral type, and any observation we make is necessarily self-selected by this absolutely fundamental fact…
Now, what is of interest to us is that Carter’s Catastrophe, as Carter and Leslie point out, is a clear application of the Anthropic Principle because it is related to the principle of the self-selection of observers. In this case our probability shift occurs because we ourselves live in an epoch when 10% of all humans who have ever been born are alive today. We add the Copernican principle, to which we return, and then bang we have our probability shift!
The link is further drawn by Barrow and Tipler’s observation that (p17)
…Carter, and others, have pointed out that as a self-selection principle the WAP is a statement of Bayes’ theorem…
As Bostrom points out,
…The very difficulty of thinking of a way to settle these questions may even encourage us to doubt the validity of the DA itself, not just to be uncertain about exactly what it would show if it were right. For these are questions that it could seem that there ought to be an objectively right answer to if the DA is right. It would be strange if there was no fact of the matter about such crucial parameters as whether more intelligent minds should be given more weight (i.e. a higher sampling density in the set of all observers) than less intelligent minds. If there is no fact of the matter about such things then one would have an additional reason for suspecting that the whole DA, and perhaps many other forms of anthropic reasoning as well, were built of air and rested on some sort of confusion…
There lies the rub. The DA is very much tied in to the whole self-selection of observers principle. Leslie cites a letter from Carter, (p193)
…Carter describes this question as introducing ‘an application of the anthropic principle outstandingly free of the questionable technical assumptions involved in other applications’ and ‘obviously the most practically important application’…
Although you can see from Bostrom’s account that the DA as Gott presents it is a somewhat stronger application of anthropic reasoning than the WAP,
…The Copernican anthropic principle says that you are more likely to be where there are many observers that where there are few. This can be seen as a strengthening of the weak anthropic principle, which says that you will be where there are observers. The Copernican anthropic principle and the weak anthropic principle both assert that the prior probability that you should be find yourself as anything other than an observer is zero. But whereas the weak anthropic principle is silent as to the prior probability that you should find yourself as a particular observer, the Copernican anthropic principle makes an assertion about this too. It says that this prior probability should be 1/N, where N is the total number of observers that will ever have existed. In other words, the Copernican anthropic principle says that all (intelligent) observers should be assigned equal sample density…
But Carter’s observation still stands because you can clearly see that the Copernican principle follows as an application of the WAP. If you buy into the WAP it’s difficult to reject the Copernican principle.
String theory has been noted for some of its charming features like greater than 4 spacetime dimensions, shadow matter and the like that makes for selling popular books but which have little empirical support. After a surge of activity following the application of supersymmetry to string theory and the discovery that the resulting theory is both anomaly free and contains an account of gravity within itself things started to level off after too many versions of the purported theory of everything sprang up.
But up popped the string master Ed Witten and hey presto we had the second superstring revolution and a whiff that all the versions of string theories are in fact versions of an underlying theoretical structure that also included N=11 supergravity!!! The underlying structure is unknown but has been dubbed “M-theory”.
When I first learnt of this link with supergravity I thought wow that’s heavy!
However the weird implications of the theory got weirder still for now it appears we have to swallow many universes.
This is where the anthropic principle comes in. Even M-theory, whatever it is, apparently has many solutions hence the universes. It is here that anthropic reasoning comes into M-theory. This is controversial even amongst M-theorists but consider Michael Duff’s review of one of the advocates of anthropic reasoning in the context of M-theory (Leonard Susskind),
…Unfortunately, there are not one but five mathematically consistent superstring theories, each competing for the title of the theory of everything; clearly an embarrassment of riches. This problem is cured by M-theory, a unique, all-embracing theory that subsumes the five superstring theories by requiring 11 space-time dimensions and incorporating higher-dimensional extended objects called branes…
…The problem with M-theory is that although its equations may be unique, it has billions and billions of different solutions. (Susskind claims about 10500, but I would take issue with this: in 11D supergravity - the low-energy approximation to M-theory - the number of ways of curling up its extra dimensions is actually infinite.) Susskind's landscape is just this space of possibilities - a schematic representation of all the possible environments permitted by theory.
Each possible environment has its own laws of physics, its own elementary particles and its own constants of nature. Even the number of space-time dimensions might be different. So what singles out our particular universe? For many years, physicists hoped that some selection principle would be discovered that would pick one valley in the landscape - and that that valley would be our universe. But as Susskind notes, this selection principle has proved to be a lot like the Loch Ness monster:…
You can see the solution to all this…the principle of the self-selection of observers!
…An alternative answer to what makes our universe so special might be the anthropic principle. As its supporters note, all it takes is a small change in Newton’s laws, or to the rules of atomic physics, and life would either be instantly extinguished or would never have formed. In other words, the anthropic principle says that the world is fine-tuned so that we can be here to observe it…
Let us accept that to make sense of M-theory it follows that we need the anthropic principle and the principle of the self-selection of observers that lies at its core.
If Carter is correct, that the Doomsday Argument is a clear and uncontroversial application of the anthropic principle, then it follows that if superstring theory is correct then we may well be closer to extinction than we believe!
Could the future of the species Homo Sapiens sapiens be tied up with the experimental fortunes of superstring theory?
Many books have been written on string theory that has greatly aided its dissemination.
We are now starting to see a shift with Roger Penrose in his The Road to Reality who argued that string theory is an example of fashion in science. Lee Smolin has published two counter arguments in favour of loop quantum gravity, Alan Connes (perhaps the world’s leading mathematician) is offering an alternative to strings and the mathematician Peter Woit has offered a delightful book titled after Pauli’s famous statement Not Even Wrong.
Let me offer a version of Pascal’s Wager and state that we sincerely hope that Woit et al are right and string theory is CRAP!
For all those into global security who have stayed with me to the end let me conclude by stating this. Leslie argues that the Carter probability shift on our prospects for future survival means that any risk assessment for catastrophic population decline due to nuclear war or climate change must be revised upwards.
It is uncontroversial, or at least should be, that the risk on both fronts are non zero and increasing.
Recall Russell’s Problem and the epistemic argument that lies at its core. Carter’s Catastrophe means that we must take Russell’s Problem seriously. Epistemic considerations rather than weakening the probability shift tend to strengthen the case, as I will show later.