DragonPetter said:
If you write a computer program to find the roots of a solution to give you an answer that matches physical reality, the throw away roots are still processed. At some point we make a decision to stop finding roots or throw away roots, which costs energy and creates heat by the computer, and so I think it might be more than just an analogy.
Yes, all actual computation will generate entropy (putting aside
http://en.wikipedia.org/wiki/Landauer's_principle for the moment). But the central trick of computation is precisely that it minimises any interaction with the world - so as to put itself into a "Platonic" realm.
A sequential symbol processing computer - a Turing machine - executes any individual step with exactly the same heat dissipation. So as far as the world knows (as far as the second law cares), calculating nonsense looks the same as calulating mentally-significant results. Inside the machine, spitting out a positive or negative answer is still a symmetric situation as the entropic cost is precisely the same.
The real impact on the world only comes from the actions people take based on what they believe. Some further choice has to be made as to which answer is the correct one. Further energy is required to break the entropic symmetry of the computational result, even if some entropic effort was required to produce that result - get things to the stage of a choice between a positive and negative root in your example.
DragonPetter said:
I am taking the step to say that the universe's rules makes the choice automatically, but the universe's rules also allowed for the existence of the negative root solution as well, even if it has no other physical grounding to the world than its own existence.
But the laws of physics are a human invention. They may certainly encode some regularity, some generality, that describes nature. But it is falling back into the confusion of Platonism to mistake our models of reality with reality itself.
So here it is our model (expressed in mathematical statements) that allows for a symmetric pair of choices. The Universe just does what it does and if our model can't predict that, then this is just a sign of its incompleteness.
It is the model that has rules. And it is the rules themselves which create the appearance of choice. The Universe by contrast exists in time and has locked in its critical "choices". (See
http://en.wikipedia.org/wiki/Loschmidt's_paradox).
DragonPetter said:
But if what you suggested is the case, that the universe breaks symmetry from math, then the universe is not purely mathematical or does not include all math. If that is the case, I would guess that we should not even be aware of these abstract ideas.
No, my argument is that we create math (or rather, our mathematical descriptions of material reality) by stepping back from the current broken symmetry we see all around to recover the original symmetry that must have been the Universe's initial state.
We are modellers, so there is no problem with being aware of our own created abstractions.
DragonPetter said:
To the first question: Our brains are part of the universe, and so the interaction is with parts of the universe. The neurons exchange signals, consume energy, generate heat, organize synapses to form ideas, etc. This is all physically governed by the laws of the universe. If the laws of the universe don't allow our brains to do something, then there is no possibility for it to exist in our thoughts. Likewise, if our brains can process the information that generates abstract mathematical logic, then its only because it is built into the interaction of the universe's laws.
Humans cannot ultimately escape the second law of thermodynamics (the relevant law here). But again, the whole point about computation (and modelling in general) is that it allows for the kind of temporary escape available to life/mind as an order-creating dissipative structure - http://merkury.orconhosting.net.nz/lifeas.pdf
So computation must create heat in practice. But it is useful because it demands so little energy compared to the amount of energy it allows us to harness. And the energy consumption is the same regardless of whether we are computing sense or nonsense - which is what gives us free choice about what to compute, what results to generate.
So the second law can't effectively see what we are doing inside our heads, or computing inside our computers. We have created a private Platonic realm of pure thought and choice. On the larger scale of course, the second law does rule. We have to eat to think, plug in our computers to compute. But that still leaves us a fantastic amount of Platonic freedom to play around in.
DragonPetter said:
Also, I don't see the organization of those symbols as noise if there is no brain around to interpret them. That organization of symbols still exists, regardless of anyone to interpret it. I don't know for sure though :P
This is the symbol grounding problem. And quite clearly symbols require interpreters.
Information theory can be used to model an observerless reality. But that is just another of our useful modern abstractions that should not be mistaken as the deep truth of reality.
Bits are just entropy - countable states. To be "orderly", they have to also be placed within an interpretive context. Someone has to care enough to count.
