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The "Dust Theory", by Greg Egan, states that...

... there is no difference, even in principle, between physics and mathematics, and that all mathematically possible structures exist, among them our physics and therefore our spacetime. These structures are being computed, in the manner of a program on a universal Turing machine, using something referred to as "dust" which is a generic, vague term describing anything which can be interpreted to represent information; and therefore, that the only thing that matters is that a mathematical structure be self-consistent and, as such, computable. As long as a mathematical structure is possibly computable, then it is being computed on some dust, though it does not matter how much, only that there can be a possible interpretation where such a computation is taking place. [wikipedia]

There's a similar theory advanced by Max Tegmark [The Mathematical Universe, 2008]:

All structures that exist mathematically also exist physically. That is, in the sense that "in those [worlds] complex enough to contain self-aware substructures [they] will subjectively perceive themselves as existing in a physically 'real' world".

Most of the arguments against this kind of rationale base themselves on the impossibility of asserting claims in a kind-of-MUH [Stoeger et al.]:

... in a true multiverse theory, "the universes are then completely disjoint and nothing that happens in any one of them is causally linked to what happens in any other one. This lack of any causal connection in such multiverses really places them beyond any scientific support".

Despite epistemological concerns, the most plausible argument against the dust theory is given by Greg himself:

However, I think the universe we live in provides strong empirical evidence against the “pure” Dust Theory, because it is far too orderly and obeys far simpler and more homogeneous physical laws than it would need to, merely in order to contain observers with an enduring sense of their own existence. If every arrangement of the dust that contained such observers was realised, then there would be billions of times more arrangements in which the observers were surrounded by chaotic events, than arrangements in which there were uniform physical laws. [Permutation City FAQ]

Which is a kind of distorted anthropomorphic principle; since we are observers, it would be much more probable that the laws of physics would be less strict than those we observe, just to support us as conscious observers.

Suppose the dust theory is testable (Egan may already be drafting something along this line, by arguing that a kind of statistical reasoning may point to its own improbability). What would one expect to see in a dust-theory consistent (multi-)verse that we don't observe in our own, and thus render it invalid?

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You cannot just "suppose" that the dust theory is testable. You have to actually come up with a test as an existence proof of that claim, or show a contradiction if no such tests exist.

Leaving aside the Occam's razor style objections (why have it "being computed"; why not just pick our universe and all its time history out of some gigantic set of possible universes?), you (or Greg, actually) have already nailed it: for every program that produces our physics, there are many that produce our physics locally but have junk or bugs that affect distant processes, yielding something radically different. The universe seems to operate under the same physical laws (e.g. we can predict what absorption bands we'll see in light from distant galaxies) everywhere.

  • Computing the multiverse is just an example, not a requirement of the Dust Theory. The strong hypothesis points that any observer inside a system would observe the system as self-consistent, should a specific arrangement of information occur, without any need of time/space causality. – Hugo Sereno Ferreira Aug 5 '11 at 17:05
  • @Hugo S Ferriera - But there's no reason for it to be universally self-coherent. You can always just say, "the dust computes something indistiguishable from our universe" as a premise, and then it cannot be distinguished. – Rex Kerr Aug 7 '11 at 1:17
  • Although we can always apply a kind of anthropomorphic principles. Why is our universe self-coherent? Why does our universe have rules? Why does it have the rules it has? Because, otherwise, we wouldn't be here asking those questions. Is self-consistency is required for consciousness, then maybe we observe a dust-based universe because it is required. Still, you're right: it cannot be distinguished, so, by Occam's razor, it's the same thing. – Hugo Sereno Ferreira Aug 7 '11 at 22:22
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    @Hugo S Ferreiera - There are many vastly less regular universes that would support our existence. Thus, the anthropomorphic principle (or dust) only gets you partway there. – Rex Kerr Aug 8 '11 at 1:23
  • I have to agree with you. I was still looking for a stronger counter-argument, but it seems the consistency of the rules is enough. – Hugo Sereno Ferreira Aug 8 '11 at 20:55
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Let me just clarify the strong hypothesis of the dust theory (in my own words):

  1. In order for a system to be observable, it needs to be "expressive" enough to represent a conscious observer with its own symbols.
  2. A conscious observer is thus the mere arrangement of the symbols inside the system he/she/it exists.
  3. Consciousness requires a "sequence" of arrangements.
  4. The sequence of arrangements may be due to the rules of the system (e.g., it is being computed), but it's not required (e.g., may happen by chance).
  5. From the point of view of the observer, the specific order of a sequence of arrangements do not matter, as long as a consistent interpretation of any "specific" arrangement is enough to provide a self-consistent history.

Because the last point can be confusing, let me give an example... Suppose that a sub-structure of my consciousness has the following sequence of states:

  1. Birth
  2. {... 1, 2, 3, 4, 5 ...}
  3. {... 2, 3, 4, 5, 6 ...}
  4. {... 3, 4, 5, 6, 7 ...}
  5. {... 4, 5, 6, 7, 8 ...}
  6. Death

Premise: I would argue that any universe that produces (either by computation or by chance) the above sub-structure would be producing my own conscience. At point 3, I would be remembering my childhood. At point 5, I would be dead.

Now imagine that a specific universe produces the following:

  1. Birth
  2. LONG PAUSE
  3. {... 1, 2, 3, 4, 5 ...}
  4. LONG PAUSE
  5. {... 2, 3, 4, 5, 6 ...}
  6. LONG PAUSE
  7. {... 3, 4, 5, 6, 7 ...}
  8. LONG PAUSE
  9. {... 4, 5, 6, 7, 8 ...}
  10. Death

If every state produces exactly the same sub-structure, then no matter how fast or slow these sub-structures are being produced, my conscience would still be "experiencing" the same as before. Now imagine the following:

  1. Birth
  2. {... 4, 5, 6, 7, 8 ...}
  3. {... 3, 4, 5, 6, 7 ...}
  4. {... 2, 3, 4, 5, 6 ...}
  5. {... 1, 2, 3, 4, 5 ...}
  6. Death

Despite the reversed order, if my conscience only relies in any particular "state", I would still remember my childhood at point 3. Now, I can even mix all these states, and produce them out-of-order, but I would still be experiencing the same, from my point of view.

Therefore, we have just excluded "time" as a requirement for an universe that sustains consciousness. We may still require "time" to explain the "computation" of states (i.e., why a state follows from a previous one), but, from the point of view of the observer, it doesn't matter.

A similar exercise can be applied to space...

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    1 implies 2 only if said observer is required to be observable. – Evpok Aug 13 '11 at 9:47
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If I understand correctly, Egan statement that

all mathematically possible structures exist

it already gives you an argumentation against itself. If "mathematically possible" means "deduced from a set of axioms via first order logic", since it is possible to deduce mutually exclusive theories with this method (with, or without the axiom of choice, the continuum hypothesis, etc.), "all mathematically possible structures" can't exist at the same time.

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    As a mathematician, I would love to see some of the structures I have dealt with. If only they were all possible! – davidlowryduda Aug 13 '11 at 1:28
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    @mixedmath As a mathematician, I'd love to be able to imagine some of the structure I have dealt with, even if they are impossible. :) – Evpok Aug 13 '11 at 9:43
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    I have to disagree with that. I can easily build a system (concrete or abstract), expressible enough to represent other systems which are self-consistent, but inconsistent among themselves... I'm writing this message in one of those. – Hugo Sereno Ferreira Aug 13 '11 at 11:48

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