In its simplest form, the 2nd law of thermodynamics... You imagine... a glass of wine sitting on a table... it falls off and wine splashes out onto t… - Roger Penrose

The idea of having an ambient space-time of some specific dimension seems to play less of a role of string theory than in conventional physics, and certainly less than the kind of role that I would myself feel comfortable with. It is particularly difficult to assess the functional freedom that is involved in a physical theory unless one has a clear idea of its actual space-time dimensionality.

[S]ome of these regions may be... indistinguishable, for example the air in the room. We might have molecules in some other places. You might like to say we don't care where the individual molecules are. We just care about overall parameters, and so we lump together the systems which look very much the same. ...[L]et's say with regard to macroscopic parameters we lump them together, and so we have these things called course graining cells in the phase space... [Y]ou then say, well let's measure the volume of these regions... <math>V</math>... and the logarithm of that volume is the entropy. This is a marvelous formula due to Boltzmann. This [<math>k</math>] is Boltzmann's constant, the only thing in the formula that wasn't due to Boltzmann... This was named afterwards. I don't think he was particularly interested in constants...

...the entire physical world is depicted as being governed according to mathematical laws. We shall be seeing in later chapters that there is powerful (but incomplete) evidence in support of this contention. On this view, everything in the physical universe is indeed governed in completely precise detail by mathematical principles — perhaps by equations, such as those we shall be learning about in chapters to follow, or perhaps by some future mathematical notions fundamentally different from those which we would today label by the term ‘equations’. If this is right, then even our own physical actions would be entirely subject to such ultimate mathematical control, where ‘control’ might still allow for some random behaviour governed by strict probabilistic principles.