Multiverse—Too Much or Not Enough?
Round 1
Reviewer 1 Report
1. It is unfortubnate that the Penrose cyclic model is taken as a good predictive example of a multiverse scenario as the author (and coauthors) failed to appreciate the significant likelihood of the same effects being found in random data sets. I suggest excluding this.
2. Multiverse models don't offer much hope for verificationists but they do (in principle) allow falsification. Suppose that a multiverse theory predicted that every member of the ensemble of possible universes should share a feature (for example, a negative cosmological constant) then if this was not observed in our universe it suffices to falsify that multiverse model. We cannot of course ever confirm or refute the whole multiverse scenario -- only particular examples of it.
3. It always seems to be implicit that multiverses are infinite. A finite multiverse seems strange because there would have to be a 'reason' perhaps for the particular number of different universes it contained. But then is this any different to having a finite universe and having to provide an explanation for the number of particles it contains?
Author Response
All answers in the attached file.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The comment about a conical singularity needs clarification. Does the 'smoothness' refer to the space of solutions, or is the 'space' there the space of all smooth manifolds? Likewise, is the conical singularity in one of the manifolds, or in the space of solutions? And can the author give a hint as to why a conical singularity 'intervenes'?
Line 121. Is 'structural stability' the same as a set of measure zero? If so, it might be worth commenting that such solutions are not realistic because they would require a infinitely precise initial conditions.
Section 4, line 142: 'the observer permitting such a combination' seems odd. Is 'permitting' the right word? Surely, the observer consistent with such an observation would be more accurate. Or the observer 'permitted by such a combination' is the intended meaning here.
Line 207: 'no law of nature says anything about any of [the] multiverses.' Is this correct? The string theory Lagrangian is a law of nature that determines the multiverse landscape, for example. And the eternal inflation theory incorporates both general relativity and quantum mechanics. One can certainly envisage a wide class of multiverses in which meta-laws apply to all universes within the multiverse. However, it is true that one could postulate a multiverse devoid of laws. But the use of the word 'any' is not correct given the classes of multiverse listed in Section 4.
I am puzzled that collisions of baby universes, or Penrose's postulated CMB effects, are described as examples of acausal 'marks' and not causal in the usual sense, since if two baby universe collide there is a brief period of causal connection?
Line 256: the acronym SET is used without spelling it out. A few more words of explanation here would be welcome. In general, I found the passing comments there about topos theory and intuitionist logic impenetrable. Readers unfamiliar with these topics would not take away much from this paragraph.
A definition of 'functors' would help.
Line 270: 'not-quite-classical' is I think intended.
The comment that logic could be a physical variable is a major and thought-provoking claim I have not come across before. A few more lines about this would be welcome. For example, is it possible that the logical architecture of living things might differ from non-living things, permitting a type of 'top-down' causation?
Author Response
All answers in the attached file.
Author Response File: Author Response.pdf
