Why does entropy invariably increase?

It's simple really. The Universe runs on BigNum rational arithmetic. As small perturbations are accumulated, ever larger rationals are required to represent state without destroying information or losing accuracy.

That proves the Universe has no GC.

>>1
http://pespmc1.vub.ac.be/macroscope/chap3.html

>>3
That explains what entropy is and states the observed laws of entropy, but doesn't explain fundamentaly where it comes from. It's also using very outdated models of the Universe.

Try something more modern like: http://en.wikipedia.org/wiki/Holographic_principle

From a computational Universe standpoint, BigNum rational arithmetic makes a lot of sense.

>>4
Is not 'that' outdated

One can generalise further. Thanks to the mathematical relation between disorder and probability, it is possible to speak of evolution toward an increase in entropy by using one or the other of two statements: "left to itself, an isolated system tends toward a state of maximum disorder" or "left to itself, an isolated system tends toward a state of higher probability." These equivalent expressions can be summarized:
Potential energy -> entropy
Ordered energy -> disorganized energy (heat)
High-quality energy -> heat (low-grade energy)
Order -> disorder
Improbability -> probability

The concepts of entropy and irreversibility, (...), have had a tremendous impact on our view of the universe. In breaking the vicious circle of repetitiveness in which the ancients were trapped, and in being confronted with biological evolution generating order and organization, the concept of entropy indirectly opens the way to a philosophy of progress and development.

I like how the text implies (at least in my point of view) later that, when we know something, or order something, the universe dies a little.

>>2
There's no need for a GC. Relations between states are representable in timeless (finite, as in the standard model of) arithmetic. If you don't like arithmetic, you can choose combinators or lambda calculus or the turing machine, they are all provably equivalent as far as computability power is concerned (although slightly more powerful than our finite state machines, if we don't allow for increasing memory - contrary to popular belief, all these models of computation allow for unbounded numbers (or in >>1's case, what he calls BigNums), but they're always finite).
>>1
It might be possible, at least if one doesn't stick to 'plank units' as being the ultimate unit and doesn't want quantization errors (there doesn't seem to be too much evidence for them). At least, IMO, using non-computable reals in physics can be seen as somewhat treacherous given that almost all of them are uncomputable concretely infinite non-enumerable beasts.

>>6
No, planck units are still the smallest units. Thus, there is such a thing as maximum entropy, or maximum information content, within a volume of space, namely the boundary of the event horizon of a black hole.

>>7
Possibly, but there were some experimental results that suggested smaller granularity than that. It would be nice if they were actually the smallest units since it would fit nicely with all the other physics we know so far, but it doesn't seem implausible to me that there could be some fractions of the planck unit or that merely in the wide majority of cases anything under that granularity isn't likely to have any easily discernable physical effects about the planck unit scale (measuring anything at that scale would obviously be a tremendous challenge, if not impossible).

*above the plank unit scale

>>8
At the energy levels required and at that scale, it's difficult to disceren between smaller microscopic degrees of freedom, hidden variables, or residual artifacts of the underlying computational machinery.

Store my BigDubs <<<<<<

>>11
DUBS FUCKEN SAVED