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If the universe is eternal and determinism is true, then...

...in that case it would be possible in principle to retrodict the past ad infinitum.  The present would either contain an infinite amount of information or the universe would be cyclical, albeit (methinks) in a manner analogous to the plot of the Lorenz attractor.

Comments

Eternitatis said…
The universe is eternal according to some string theorists. The universe is also deterministic because of the astonishing equivalence between a completely deterministic control problem (looking at the universe as a dynamic system) and a random process associated with observation. At the micro-level there is finite limit to how space-time and mater-energy can be divided - called the Planck limits. (i.e. Planck length, Planck mass, Planck time, Planck energy, etc.) One then might conclude that for a closed and bounded universe, there could only be a finite number of particles. This would be true whether or not determinism existed because you are dealing with finite sets, and even with all possible combinations and permutations there could only be 2^N states for N particles. So if the universe is compact - closed and bounded, and if the Ergodic Hypothesis of thermodynamics and physics holds, then Nietzsche's eternal recurrence follows naturally. However, whereas the number of observed particles is finite, the number of states co-existing to bring about any given finite universe is infinite! Why? Because all possible pathways are realized by the wave function. This requires the Everett Multi-worlds interpretation of QM rather than the Copenhagen interpretation. The space in which the wave function lives is an infinite dimensional normed inner product space called Hilbert space. There is plenty of room in Hilbert space. For the lay person, think of a Hilbert space as a continuous Probability space. So even for a closed bounded universe, one could describe a chaotic infinite path through multiverses as time evolves. You are absolutely correct about the path through phase space being a Lorentz attractor. Why? Because, all systems in nature are mathematically chaotic - non-linear and sensitive to initial conditions. So all chaotic systems follow orbits on a strange attractor for long term stability. It only makes sense to talk about stable universes, not ones that blow up. The Lorentz group describes all transformations of Minkowski space (Special relativity), but you actually need the Poincare group which contains the Lorentz group to describe General relativity. The strange attractor must include the dynamics and orbit diagrams seen in the Lorentz (butterfly ) attractor but would also include other strange attractors described by Poincare maps and bifurcations such as the Rossler attractor. Ironically, even with an open universe with infinite energy, determinism still exists because of the duality I mentioned earlier. Oh, and one other final point that would bury the retrodiction possibility is this. If there are a countably infinite number of states in a time-section of the universe, it’s evolution in the multiverse would be 2^alephnull. But 2^aleph*null is aleph*one. But aleph one is the power of the continuum, in which case an orbit through the phase space of the multiverse would be uncountably infinite. There would really be no realistic possibility of periodicity under these circumstances. One could always come up with a new orbit never seen before. In fact in your mind’s eye you can actually construct one by way of Georg Cantor’s 1874 diagonalization procedure.

So in summary:
The universe is determinist.
The universe evolves chaotically (in the mathematical sense.)
The universe is compact - closed and bounded.
Under the Ergodic Hypothesis, it is also periodic (as in Nietzsche's eternal recurrence.) This is because the Lorentz,/Rossler or other Poincare-driven strange attractor includes periodic orbits as well.
If the universe is open, the law of Conservation of Energy and the 2nd law of Thermodynamics no longer exist globally.
More likely the number of states of a compact universe would be deterministic and uncountably infinite and rarely, although possibly, a countably infinite number of periodic or quasi-periodic orbits. But, of course, the uncountably infinite “swamps out” the countably infinite.
8:36 PM
Eternitatis said…
The universe is eternal according to some string theorists. The universe is also deterministic because of the astonishing equivalence between a completely deterministic control problem (looking at the universe as a dynamic system) and a random process associated with observation. At the micro-level there is finite limit to how space-time and mater-energy can be divided - called the Planck limits. (i.e. Planck length, Planck mass, Planck time, Planck energy, etc.) One then might conclude that for a closed and bounded universe, there could only be a finite number of particles. This would be true whether or not determinism existed because you are dealing with finite sets, and even with all possible combinations and permutations there could only be 2^N states for N particles. So if the universe is compact - closed and bounded, and if the Ergodic Hypothesis of thermodynamics and physics holds, then Nietzsche's eternal recurrence follows naturally. However, whereas the number of observed particles is finite, the number of states co-existing to bring about any given finite universe is infinite! Why? Because all possible pathways are realized by the wave function. This requires the Everett Multi-worlds interpretation of QM rather than the Copenhagen interpretation. The space in which the wave function lives is an infinite dimensional normed inner product space called Hilbert space. There is plenty of room in Hilbert space. For the lay person, think of a Hilbert space as a continuous Probability space. So even for a closed bounded universe, one could describe a chaotic infinite path through multiverses as time evolves. You are absolutely correct about the path through phase space being a Lorentz attractor. Why? Because, all systems in nature are mathematically chaotic - non-linear and sensitive to initial conditions. So all chaotic systems follow orbits on a strange attractor for long term stability. It only makes sense to talk about stable universes, not ones that blow up. The Lorentz group describes all transformations of Minkowski space (Special relativity), but you actually need the Poincare group which contains the Lorentz group to describe General relativity. The strange attractor must include the dynamics and orbit diagrams seen in the Lorentz (butterfly ) attractor but would also include other strange attractors described by Poincare maps and bifurcations such as the Rossler attractor. Ironically, even with an open universe with infinite energy, determinism still exists because of the duality I mentioned earlier. Oh, and one other final point that would bury the retrodiction possibility is this. If there are a countably infinite number of states in a time-section of the universe, it’s evolution in the multiverse would be 2^alephnull. But 2^aleph*null is aleph*one. But aleph one is the power of the continuum, in which case an orbit through the phase space of the multiverse would be uncountably infinite. There would really be no realistic possibility of periodicity under these circumstances. One could always come up with a new orbit never seen before. In fact in your mind’s eye you can actually construct one by way of Georg Cantor’s 1874 diagonalization procedure.

So in summary:
The universe is determinist.
The universe evolves chaotically (in the mathematical sense.)
The universe is compact - closed and bounded.
Under the Ergodic Hypothesis, it is also periodic (as in Nietzsche's eternal recurrence.) This is because the Lorentz,/Rossler or other Poincare-driven strange attractor includes periodic orbits as well.
If the universe is open, the law of Conservation of Energy and the 2nd law of Thermodynamics no longer exist globally.
More likely the number of states of a compact universe would be deterministic and uncountably infinite and rarely, although possibly, a countably infinite number of periodic or quasi-periodic orbits. But, of course, the uncountably infinite “swamps out” the countably infinite.
8:37 PM
Leo White said…
I am afraid that this sounds like hand-waving to me. Call it my ignorance, if you wish.

If you'd like to have a conversation, that's great, but you'll have to speak in layman's terms. Very smart people, very smart scientists included, are capable of doing that. Why Einstein himself wrote a book, which, if I opened a page, I would be able to understand. You can do the same.

Again, if you really want to have a conversation, I'm game. But if you want to talk essentially to yourself (no one but you, me and my buddy Tim knows of the existence of this blog), well continue in the same manner that you are doing here.

Let me break down one sentence: "The universe is also deterministic because of the astonishing equivalence between a completely deterministic control problem (looking at the universe as a dynamic system) and a random process associated with observation":

No, I can't break it down. Can you?
12:08 AM
Leo White said…
Eternitatis,
Try addressing the argument that I provided, rather than reeling off your own, new argument.
7:38 AM
Leo White said…
What you need to address is the question of whether a finite amount of matter could contain an infinite amount of information... or whether there is nothing new under the sun... not even the sun.
7:44 AM
Eternitatis said…
You can't have your cake and eat it too. On the one hand you ask a very profound question with certain specific predicates offered as a foundation, and then you blow off my answers because they technically address the very issues you raised. If you are going to raise issues about the infinite then you must be prepared to address these technical issues. There is no such thing as a layman's answer to the infinite. Which infinite? the countably infinite? the uncountably infinite? the completed infinite? the infinite as an incomplete cardinal set? There is a whole set theory devoted to transfinite arithmetic. I'm sorry, but I know no way around that. The answer you seek depends upon your choice of which infinite you are talking about. Please get rid of these type in characters to prove I'm not a robot. I can't even read most of them.
9:47 PM
Eternitatis said…
You can't have your cake and eat it too. On the one hand you ask a very profound question with certain specific predicates offered as a foundation, and then you blow off my answers because they technically address the very issues you raised. If you are going to raise issues about the infinite then you must be prepared to address these technical issues. There is no such thing as a layman's answer to the infinite. Which infinite? the countably infinite? the uncountably infinite? the completed infinite? the infinite as an incomplete cardinal set? There is a whole set theory devoted to transfinite arithmetic. I'm sorry, but I know no way around that. The answer you seek depends upon your choice of which infinite you are talking about.
9:52 PM
Leo White said…
I think your argument about determinism is question-begging. So let me ask the question. Is there a scientific experiment that proves that any law of nature operates necessarily?

Let me propose an answer to the question: no.

Think Hume's problem of induction.

So I don't think talking about the results of this or that scientific experiment to prove nature operates with necessity is anything other than circular.

I think you need to read chapter 2 of Chesterton's ORTHODOXY.
8:21 AM
Eternitatis said…
Science never proves anything, it only disproves things. Therefore I cannot prove that there is a law of nature that is necessary. The two don't mix as Hume and Kant pointed out - synthetic/analytic aprior vs aposteriori. What I think you are getting at is the isomorphism between a random process associated with observation and a completely deterministic control system. It is astonishing that that is true, but I think it lends itself to the fact that random processes possess a symmetry which is effectively cancelled when they are transformed. (e.g. the bell shaped curve is symmetric, not skewed). I think that explanation only works if there is no "biased-noise," but if there is bias, then you are no longer talking about randomness are you? Also, implicit in using that 1:1 onto correspondence is that time is reversed in the other system. One you are given an input and causality flows from input to output. In the time-reversed situation you are given the output and asked to compute (the earlier) input. It is still an astonishing duality: that a noisy uncertain system could be completely deterministic! Hence, no free will either because of the same duality. You need to get over this exalted viewpoint of man being something special under the sun, when the evidence demonstrates clearly that he is not - just another insignificant speck of dust in the scheme of things.
10:40 PM
Leo White said…
You said in an earlier post that the universe is determinist. You said in your most recent post that science never proves anything.
Your most recent post undermines your earlier post.

Next!
6:54 AM
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