--- Stathis Papaioannou <[EMAIL PROTECTED]> wrote: > On 3/6/07, Mitchell Porter <[EMAIL PROTECTED]> wrote: > > > > You radically overstate the expected capabilities of quantum computers. > > They > > can't even do NP-complete problems in polynomial time. > > http://scottaaronson.com/blog/?p=208 > > > What about a computer (classical will do) granted an infinity of cycles > through, for example, a Freeman Dyson or Frank Tipler type mechanism? No > matter how many cycles it takes to compute a particular simulated world, any > delay will be transparent to observers in that world. It only matters that > the computation doesn't stop before it is completed.
The computation would also require infinite memory (a Turing machine), or else it would cycle. Although our universe might be the product of a Turing machine, the physics of our known universe will only allow finite memory. The number of possible quantum states of a closed system with finite size and mass is finite. For our universe (big bang model), the largest memory you could construct would be on the order of c^5 T^2/hG ~ 10^122 bits (where c is the speed of light, T is the age of the universe, h is Planck's constant and G is the gravitational constant. (Coincidentally, each bit would occupy about the volume of a proton or neutron). A quantum computer is weaker than a finite state machine. A quantum computer is restricted to time-reversible computation, so operations like bit assignment or copying are not allowed. And even if you had a Turing machine, you still could not compute a solution to AIXI. It is not computable, like the halting problem. -- Matt Mahoney, [EMAIL PROTECTED] ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?list_id=11983
