Recall that Susskind says that even with the no-boundary proposal, it is much more likely that we find ourselves to be random fluctuations in de Sitter space. Don Page offers various new ways how to interpret and justify this conclusion. His proposed loophole to avoid Susskind's conclusion is to assume that the number of e-foldings during the inflation was not just more than 64: it was more than 1000, more than a googol, more than a googolplex, in fact! ;-)
I think that they ask very interesting questions but end up with incorrect answers.
The starting assumption is that we should be looking at a conditional probability "P(B/A)" where "A" are assumptions and "B" are the observations we see. This probability should not be too much smaller than one because we do see "B", after all, and the theory shouldn't be grossly incompatible with our observations, which means that it should predict reasonably high probabilities of seeing what we're seeing.
The critical example takes "A" to be conditions for the observations and "B" to be conditions for ordered observations - with a nice arrow of time. The physicists conclude that the conditional probability "P(B/A)" is much smaller than one. In other words, such an approach implies that whatever observation - described e.g. by the projection operators that capture the state of your brain and senses - you choose, it is most likely that you experience these observations when the entropy is close to its peak.
The conditional probability could be a good object to study but even if it is physically interesting, one must be very careful what we mean by "A" and "B". I don't think that the right way to define a physical question is to ask why I am thinking why I am thinking why I am thinking, or to play similar philosophers' games.
The goal of science is to explain why the Universe is what it is. And by the Universe, I mean the most objective or inter-subjective description of reality that we can think about. The more you insert your own identity and your own features into the definition of the questions and into the definition of the quantities we should calculate, the less natural science - and more social science and/or research of subjective feelings - you will be pursuing.
If we're doing natural science, we don't want to upgrade the quantum projection operators on Don Page's brain or Lenny Susskind's brain in the multi-body Hilbert space to be the main physical observables whose expectation values would decide whether inflation is a good idea or not, or whether the no-boundary proposal is consistent with observations or not.
Quite on the contrary. We want to be calculating things that are as independent of our idiosyncracies as possible. After all, it would be nice if we could agree about the final theories once all the subtleties are taken into account. Building the scientific opinion on one's personal projection operators is a form of solipsism which is not the best starting point for universal and objective arguments.
In this sense, our arguments should be independent of the question whether the entropy of Don Page's brain is higher than the entropy of Lenny Susskind's brain: note that the entropy determine the rank of the corresponding projection operators that are used to determine the conditions "A".
Of course, I want to go much further. Our arguments about the origin of the Universe should be independent not only of our personal idiosyncracies: they should also be independent of other details that define our species, our civilization, or the environment where it was born. I personally want the ultimate scientific conclusions about the inflationary and pre-inflationary cosmology to be valid not only for my brain or Lenny Susskind's brain, but also for other people.
In fact, it would be nice if we could agree about the conclusions even with other civilizations where the intelligent observers are made out of sillicon and they will live billions of light years away from us and billions of years after our time. We want the conclusions of physics to have a permanent value. At least I want it.
I am convinced that many people will find my comments obvious but they do disagree with the assumptions of the papers: see page 4 of Page's paper to verify that his conclusions indeed depend on the mass of his brain. Nevertheless, the question how the Universe began is a question about physics near the fundamental physics - and physics of the early Universe when it was younger than a tiny fraction of a second. The questions about the origin of the Universe are not questions about the properties of the projection operators on the states describable as the brains of the famous physicists.
How many people still agree with me that the biology of the brain of a founder of string theory is a different piece of science than inflationary and pre-inflationary cosmology? ;-)
Regardless of the history how we found the answer, we know that the Universe evolved according to the Big Bang cosmology for 13.7 billion years - throughout its existence except for a (probably) very short era at the beginning. What the Universe has evolved into since the Big Bang cosmology started is a part of well-established physics and biology and the details of this physics and biology should simply have no effects on our opinions about the most ancient eras of cosmology!
So I am convinced that the task of the new and future portions of cosmology is to explain what made the Universe evolve into the initial conditions for the standard Big Bang cosmology or, if you believe in inflation, what has created the right initial conditions for inflation that was close to a realistic vacuum - what was the process that has led to the right outcomes.
Also, I think that all arguments leading to the conclusion that "now" should maximize the entropy are logically flawed. In a static Universe, such a conclusion disagrees with the time-translational symmetry because according to this symmetry, a similar argument should also exist that would imply that the peak of entropy will appear next year instead of today which is a contradiction.
More generally, the arrow of time is simply a part of the Universe's design that has also been tested in trillions of experiments. The arrow of time may be the thermodynamic one or the decoherence arrow of time - these two arrows probably always have to agree. At any rate, the existence of the arrow of time is a well-established and experimentally proven principle that is also extremely natural from a theoretical viewpoint. From this perspective, I view every theory and every approach to calculate the probabilities that grossly violates the second law of thermodynamics to be an experimentally falsified theory or an experimentally falsified approach. And I believe that such a theory is based on wrong theoretical ideas, too.
In other words, you can interpret this paradigm as the assumption that the conditions "A" also include the requirement that the Universe satisfies the second law of thermodynamics at the macroscopic scale. I do believe that this is true. I do believe that almost every sane person believes it is true. No one can prevent us from believing this principle and from including it among the conditions required from a theory.
Some people might think that the existence of multi-pound brains is more fundamental a principle of physics than the arrow of time and the second law of thermodynamics but I am confident that the intelligent mice from other galaxies who have already solved these questions will agree with me that the existence of multi-pound brains is neither a necessary consequence of the laws of physics nor a correct assumption for any justifiable physical arguments.
More generally, I would find a theory that demands the number of e-foldings to exceed a googolplex to be extremely unsatisfactory because such a huge but finite number of e-foldings amounts to a huge fine-tuning.
How much lucky do you have to be - how unlikely good things have to happen to you - in order to accept a religious explanation? It depends on the kind of religion we talk about. If your religion is the anthropic principle, you must accept the existence of good luck that is as unlikely as 10^{-120} - the selection of a vacuum with a reasonable cosmological constant and/or other quantities, as N.A-H. would say.
If you believe that God has created the world, you implicitly assume that events as unlikely as 10^{-10^{120}} are parts of the cosmic design. Page's loophole to avoid Susskind's argument seems to rely on a comparably unlikely event: note that with such a huge number (more than a googolplex) of e-foldings, the Universe will expand to 10^{10^{10^{120}}} Megaparsecs or so. It's a lot. The higher numbers with uncertain meaning we insert into our ideas about reality, the more inaccurate physics would become. I just feel that the scenarios that require these increasingly unlikely things based on increasingly large numbers are not justified by any observations. They are not natural and eventually we will see that they are not needed.
When we talk about the very early cosmology and the initial conditions, we should assume that the goal of this reasoning is to explain the very early events in our Universe only and not the mass of our brains.
And that's the memo.
