On Thu, Mar 15, 2018 at 7:36 AM, Lawrence Crowell < goldenfieldquaterni...@gmail.com> wrote:
*> Eternal black holes with the inner horizon r_- continuous with I^+ means > in principle a Turing machine approaching r_- could receive an infinite > stream of bits or qubits so it could make a catalog of all Turing machines > that halt and do not halt.* Black holes are not eternal , the lifetime of a Black Hole in seconds can be found with the formula 10,240*PI^2 *(G^2*M^3)/(h*c^4) where G is the Gravitational constant, h is Planck's constant, c is the speed of light and M is the mass of the black Hole in kilograms. And Bekenstein's bound says Black Holes can't deal with infinite information, the number of bits they can deal with is 4 times the area of the event horizon in Planck Areas (1.6* 10^-69 square meters). The formula for the maximum number of bits that can be contained in a sphere of radius R is PI *R^2 *c/G*h*ln2 . So the maximum information that can be contained in any sphere is proportional to the square of the radius (the area) not the cube of the radius (volume) as you might expect. And if you really did somehow have such a complete list then you could use it to construct a device that could tell you if any Turing Machine will halt or not, it would input any Turing Machine and it would only have 2 possible outputs, YES it will halt or NO it will not halt. Now I can make a device of my own, it would consist of two parts, the first part would be IDENTICAL to your machine, the second half would take the output from your device and if it says YES it will halt then my device will go into a infinite loop and never halt, and if it says NO it will not stop then my device stops immediately. Now I feed my entire device into itself and then ask your device if my device will ever stop. If you device says YES it will stop then it will not stop and if it says NO it will not stop then it will stop. Therefore your claim to have a list of all Turing Machines that will stop and all Turing Machines that will not stop must be untrue. *> Quantum mechanics enters into the physics, such as Hawking radiation, > that separates r_- from I^+. However, this may adjust the Chaitan halting > probability. With NP-complete problems this would translate into the > existence of systems that approximate such solutions. [...] I suspect the > individual consciousness of a person or even animals is wrapped up in some > sort of code, that while it might be derived in some approximate way it is > tough to find from outside.* Scott Aaronson has this to say about the relationship between consciousness and uncomputable problems: *"I don’t see any compelling reason, at present, to admit the existence of any physical process that can solve uncomputable problems. And for me, it’s not just a matter of a dearth of evidence that our brains can efficiently solve, say, NP-hard problems, let alone uncomputable ones—or of the exotic physics that would presumably be required for such abilities. It’s that, even if I supposed we could solve uncomputable problems, I’ve never understood how that’s meant to enlighten us regarding consciousness. I mean, an oracle for the halting problem seems just as “robotic” and “unconscious” as a Turing machine. Does consciousness really become less mysterious if we outfit the brain with what amounts to a big hardware upgrade?"* Aaronson has more very interesting stuff to say about this at: https://www.scottaaronson.com/blog/?p=2756 > *> The thesis that all of consciousness is a manifestation of calculation > presumes the brain is primarily involved with computation. The problem is > that the brain computes little in the way of mathematical solutions* You can call it mathematical solutions or something else but it doesn't change the fact that the brain changes from one state to another state with the passage of time, and so does a Turing Machine. And given information about the present state of a brain a Turing Machine could figure out what a future state would be. *> I am not going to sign up for having my brain states downloaded any time > soon. You pretty much have to die for this to take place. * Obviously, if you never die then the entire procedure would be unnecessary. *> I am not sure how the brain is preserved this way in the few minutes > before redox reactions begin to demolish neurons once blood flow stops. * You use cold. There are cases where people have been trapped under ice covered lakes in near freezing water for over a hour and been revived with no brain damage, in one case a woman’s body temperature went all the way down to 56.7 °F and she lived. *> I will also prognosticate that the main use of this sort of technology > may end up being to support a complete reign of terror. Brain states > downloaded into computers could easily be subjected to endless torment, and > a reign of terror based on a sort of techno-eschatology might easily be > established.* Why? What on earth would be the point of a Jupiter Brain doing that ? John K Clark > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. 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