(I was saying:
<snipped > More shortly: if we are living in a massive computer then we are living > in arithmetic-platonia, and by the church thesis and other computer-science > theoretical constraints, this is testable.)
Actually this is the whole subject of my thesis. Let me try to explain briefly without technics. Let us suppose there is a physical universe. Let us suppose "we are living in a massive computer" belonging to that universe. This means comp is actually true, that is: there is a level of description of ourselves such that we could survive any functional substitution made at that level. I guess you will agree with the following propositions:
1) If the clock of that massive computer slows down, we cannot, from our first person perspective, be aware of that slowing down. In case the computer stops for one year, and then proceeds again, we cannot be aware of that stopping. OK?
2) If a description of the computer is made, at some stage, and then destroyed by "real inhabitants" of that universe, and then build again again we will not be aware of that destruction reconstruction. OK?
3) Suppose now that the computer is again "read" and destroyed, and then build, but now in two different places of the "universe", and in two slightly different states. I mean the inhabitant of the universe programs the computers in such a way that in the simulation 1 some event A will take place, and in the simulation 2 some event B (different from A) will take place. Then in case the simulated person would be aware of this (because the inhabitants of the universe would have tell us the truth, we would know that we are completely ignorant about which events A or B will take place. This is the first person indeterminacy.
4) This remains true even if the first copy is run quasi-immediately, and the second copy of the massive computer is run after a long delay, because the simulated people cannot be aware of any imposed "external delay" OK?
5) As a particular case, we can consider that the inhabitants just make a copy of the computer (in which A will be realized), and build from that copy a version of the computer in which B be realized. Again the first person probability of A and B remains the same (consider that the first computer has been destroyed and reconstituted with a null delay, so that this is a particular case of the preceding step).OK?
6) This shows that if we are in a massive computer running in a universe, then (supposing we know it or believe it) to predict the future of any experiment we decide to carry one (for example testing A or B) we need to take into account all reconstitutions at any time of the computer (in the relevant state) in that universe, and actually also in any other universes (from our first person perspective we could not be aware of the difference of universes from inside the computer).
7) Here is an admittedly more difficult point: from the first person point of view the simulated people in the computer cannot make the difference between a "real universe" or any "fictive universe" which belongs to Platonia. We can go back to this point later. This has been discovered by myself and independently Tim Maudlin gave a better (more informative) proof. See ref in my thesis.
8) So, if we are being simulated by a massive computer somewhere in a real universe, then to make any first person verifiable prediction we must take into account all the possible computations going through our actual state. So "the laws of physics", which we can temporarily define as the laws of whatever we can predict consistently, should be given by a measure on those 1-person computational histories.
9) Now, from computer science and logic, startlingly enough perhaps, we can isolate a measure on the 1-person comp histories, and this give us the laws of physics (this is too technical to be put here, and actually I have derived only the logical structure of the probability one, but I got something non trivial and very close to a quantum logic (which can be seen as the logic of the quantum probability one, as von Neumann has shown).
10) Having extracted the necessary (with comp) physical laws, let us compare it with the laws we can infer from our neighborhood (actually simulated by your massive computer). If it is the same, then we can conclude we are NOT simulated by a particular massive computer embedded in a universe (only apparently so for the inhabitant of the "universe"). More precisely we are no more simulated by it than by any of those emulated in Platonia. Or we discover some discrepancies between the inferred "physical" laws (from our experiences inside the massive computer) and the laws which comes from the measure on all comp histories, then, either comp is false and we are then obviously not executed by a massive computer, or we keep comp, and then, like in a lucid dream, we can correctly infer we are simulated by a computer. Put in another way, *either* the massive computer simulates the exact laws of physics (exact with comp = the laws extractible from the measure on all 1-computations) in which case we belong to it but in that case we belong also to all its "copy" in Platonia, and our prediction or physics relies on all those copies (so that to say we belong to the massive computer has no real meaning: if it stops, nothing can happen to "us" for example); *or* the massive computer simulates only an approximation of those laws (like a brain during the night), and then we can in principle make the comparison, and find the discrepancies, and conclude we inhabit a fake reality ... OK?
If you want we can discuss the more subtle point 7, but please let me know if you have followed the nine other steps. You can also look at my URL and at some of the everything-list explanations for some precisions, but don't hesitate to ask any question if I have been unclear (at any steps).