= 27d567bc2d48d9f40e9ccc20ea370b15)
Michaelos comments on Higher than the most high - Less Wrong Discussion
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (14)
Yes, I think that you and I are talking about the same thing.
Attempting to rephrase, In essence, my question is how specific do I have to make my number, function, terminating algorithm, or noncomputable algorithm.
Clearly 99999999 is valid as a number,
And presumably 3^^^^3 as a function,
But is a program "Hyper G" that generates a number using a terminating algorithm involving Graham's number being Knuth up arrowed to Graham's number, having the result stored in a variable, and then having the variable Knuth up arrowed to itself iteratively until the process has repeated Graham's number times valid as a terminating algorithm?
Is "The result of the Busy Beaver Function of a Turing Machine with Hyper G States and Hyper G symbols" valid? You might be able to say that names a large integer, but since it isn't even a computable function anymore. I don't know if Omega would accept that as an answer.
I'd say your Knuth up arrow is in, but the Busy Beaver number is out - you can't use Omega's (or anyone else's) hypercomputation to do the job for you, and you can't compute the Busy Beaver without hypercomputation.
Okay. As another question, to what extent should quantum effects be considered in the area?
1: If there are essentially no Quantum effects, then I don't have access to a source of true randomness, just pseudorandom numbers. This would influence my coding, because true randomness can be used to lengthen a program in ways that fake randomness cannot, so I would have to adjust my code to take that into account.
[My understanding may be off here, but I think that given a pseudorandom algorithm, there are events which can be defined as to never take place. Ergo, a bad pseudorandom algorithms might never generate "0.01" 4 times in a row. But given quantum randomness, any defined event will eventually happen with probabilities approaching 1 as runtime increases]
2: On the other hand, if there are quantum effects, I can attempt to make programs like the following:
X=0;
DountilHalt;
X=X+1;
Write "S" in Memory Register X;
If the Character in Memory Register X is "0" then halt.
Else goto DountilHalt;
Which would keep running until there is a Quantum bitflip of "S" into "0" at just the right moment (or some other bitflip in the program that also caused a halt.)
3: Alternatively, I could view it as "Your program can call Quantum Mechanical randomness, if you want it to, but neither your program, nor it's output, will be changed by Quantum Mechanical effects unless you program that in."
Which means that the Program in 2 would never halt because I did not call a Quantum function anywhere inside the program.
It seems sort of like the implicit scenario is 3, but I may be incorrect (or I may have cast 1,2 or 3 incorrectly.)
If I were Omega (feels good to think about the possibility), I would demand a program written in a specified high-level computer language which prints a string in the form SSSS...S0 (or something equivalent). This would exclude all sophistries from "the number my opponent chose plus one" to "the largest number you, Omega, can calculate [under specific conditions]".