The basic workings of inflationary models are summarized, along with the arguments that strongly suggest that our universe is the product of inflation. The mechanisms that lead to eternal inflation in both new and chaotic models are described. Although the infinity of pocket universes produced by eternal inflation are unobservable, it is argued that eternal inflation has real consequences in te...

How do temporal and eternal beliefs interact? I argue that acquiring a temporal belief should have no effect on eternal beliefs for an important range of cases. Thus, I oppose the popular view that new norms of belief change must be introduced for cases where the only change is the passing of time. I defend this position from the purported counter-examples of the Prisoner and Sleeping Beauty. I...

The basic workings of inflationary models are summarized, along with the arguments that strongly suggest that our universe is the product of inflation. I describe the quantum origin of density perturbations, giving a heuristic derivation of the scale invariance of the spectrum and the leading corrections to scale invariance. The mechanisms that lead to eternal inflation in both new and chaotic ...

We prove that if V ⊆ V[h] is a generic extension by Prikry forcing then every transitive intermediate model M of ZFC , where V $ M ⊆ V[h] , is again a Prikry generic extension of V . Moreover the family of intermediate models is parametrised by P(ω)/finite. The result is proved by studying V-constructibility degrees of sets in V[h] using parameters in V .

We relate the Eternal Symmetree model of Harlow, Shenker, Stanford, and Susskind to constructions of stochastic processes related to quantum statistical mechanical systems on Cuntz– Krieger algebras. We extend the eternal inflation model from the Bruhat–Tits tree to quotients by p-adic Schottky groups, again using quantum statistical mechanics on graph algebras.

Cosmological inflation, if it occurred, radically alters the picture of the ‘big bang’, which would merely point to reheating at the end of inflation. Moreover, this reheating may be only local so that inflation continues elsewhere and forever, continually spawning big-bang-like regions. This chapter reviews this idea of ‘eternal inflation’, then focuses on what this may mean for the ultimate b...

We thank all of the discussants for their valuable insights and elaborations. In particular, we thank Prof. Clarke and Dr. Severinski for their conjectured extension to Theorem 3, the product of many personal discussions both in Austin and in Spain (and probably many more hours of work in Miami). The conjecture seems quite likely to be true, and strikes us as a nice way of understanding adaptiv...

We present communication efficient secure protocols for a variety of linear algebra problems. Our main building block is a protocol for computing Gaussian Elimination on encrypted data. As input for this protocol, Bob holds a k×k matrix M , encrypted with Alice’s key. At the end of the protocol run, Bob holds an encryption of an upper-triangular matrix M ′ such that the number of nonzero elemen...

Accents are local events that attract a listener’s attention and are either evident from the score (immanent) or added by the performer (performed). Immanent accents are associated with grouping, meter, melody, and harmony. In piano music, performed accents involve changes in timing, dynamics, articulation, and pedaling; they vary in amplitude, form, and duration. Performers tend to “bring out”...