4 ms·

If your emulator requires substantially different space to encode the raw description of the program than the original, then the emulator sucks. I can't try to

by dasht 16y ago

If your emulator requires substantially different space to encode the raw description of the program than the original, then the emulator sucks. I can't try to help you any further. You have a conceptual bug in your understanding of the relevant math / CS. Last I'll say is that your emulator doesn't necessarily "suck" - it may be that it is the best that is theoretically possible and still result in exponential growth in emulated program size. And, you also don't seem to be following a relatively simple argument about Omega. It's interesting stuff and we started down this thread on an interesting foot... I only mean here to explicitly sign off and note that, in my opinion, you're just not getting a few basic things I'm not too sure how better to present to you (which is not to say I'm normally particularly good at explaining such things -- only that for whatever reason, in this case, it ain't working).

btilly 16y ago
I suggest that you come back and re-read the thread tomorrow. Hopefully you'll come to a different opinion. About the emulator, the length of the emulated program is the length of the emulator plus the length of the representation of the program. On standard machine architectures you can represent binary data directly with little overhead. (Somewhere you have to declare the length of the binary data, so there is some overhead.) If you're encoding binary data within a programming language you may have a constant factor of encoding overhead because of your need to avoid reserved characters, etc. This is typically a small constant factor. I'm aware of no practical examples where that overhead is exponential, or even super-linear. About Omega, I understand the argument that you're trying to make. Your argument is that if Omega_A and Omega_B are to vary, then some programs from A have to go to much longer programs on B. My point is that this is not true, all that is necessary is that the programs from A have to be lost in a much larger sea of valid programs in B. Given that the number of programs of length n varies exponentially in the size of n, there are enough programs that this will happen even if all programs in A go to programs that are just a fixed number of bytes larger in B. Therefore Omega_A tells you very little about Omega_B.
- dasht 16y ago
  On standard machine architectures Yes, right there you are demonstrating a deep misunderstanding of what you are replying to or how it relates to Kurzweil's arguments. On Omega, you say: all that is necessary is that the programs from A have to be lost in a much larger sea of valid programs in B You left out that we're comparing sets of A and B programs of similar length -- the "sea" is not so large. Actually you kind of acknowledge this but then say bogus things about what it implies. You are confused or else just b.s.'ing on purpose. It's been fun. We're done, please.
  - btilly 16y ago
    You know, your response is basically content free insults. We know that you think I have a deep misunderstanding, but you haven't specified what said misunderstanding is. You say I'm saying bogus things, but you haven't said what was bogus. And you really haven't tried to explain your reasoning. You left out that we're comparing sets of A and B programs of similar length -- the "sea" is not so large. Actually you kind of acknowledge this but then say bogus things about what it implies. In this case "similar" was "differs by a constant". Thanks to exponential growth, even if said constant is something small like 50 bytes, the pool of programs on machine B would be 2^400 times as big as the pool of programs on machine A. That's about a factor of 10^120. If you think that a factor 2582249878086908589655919172003011874329705792829223512830659356540647622016841194629645353280137831435903171972747493376 difference is "not so large", then you've got a very different impression of what "large" means than most people do. Anyways now I think we're going around in circles. Unless you make a point of some substance in your next reply, I'm not going to bother replying. And no, insults do not count as points.

by dasht 16y ago

btilly 16y ago

I suggest that you come back and re-read the thread tomorrow. Hopefully you'll come to a different opinion. About the emulator, the length of the emulated program is the length of the emulator plus the length of the representation of the program. On standard machine architectures you can represent binary data directly with little overhead. (Somewhere you have to declare the length of the binary data, so there is some overhead.) If you're encoding binary data within a programming language you may have a constant factor of encoding overhead because of your need to avoid reserved characters, etc. This is typically a small constant factor. I'm aware of no practical examples where that overhead is exponential, or even super-linear. About Omega, I understand the argument that you're trying to make. Your argument is that if Omega_A and Omega_B are to vary, then some programs from A have to go to much longer programs on B. My point is that this is not true, all that is necessary is that the programs from A have to be lost in a much larger sea of valid programs in B. Given that the number of programs of length n varies exponentially in the size of n, there are enough programs that this will happen even if all programs in A go to programs that are just a fixed number of bytes larger in B. Therefore Omega_A tells you very little about Omega_B.

dasht 16y ago
On standard machine architectures Yes, right there you are demonstrating a deep misunderstanding of what you are replying to or how it relates to Kurzweil's arguments. On Omega, you say: all that is necessary is that the programs from A have to be lost in a much larger sea of valid programs in B You left out that we're comparing sets of A and B programs of similar length -- the "sea" is not so large. Actually you kind of acknowledge this but then say bogus things about what it implies. You are confused or else just b.s.'ing on purpose. It's been fun. We're done, please.
- btilly 16y ago
  You know, your response is basically content free insults. We know that you think I have a deep misunderstanding, but you haven't specified what said misunderstanding is. You say I'm saying bogus things, but you haven't said what was bogus. And you really haven't tried to explain your reasoning. You left out that we're comparing sets of A and B programs of similar length -- the "sea" is not so large. Actually you kind of acknowledge this but then say bogus things about what it implies. In this case "similar" was "differs by a constant". Thanks to exponential growth, even if said constant is something small like 50 bytes, the pool of programs on machine B would be 2^400 times as big as the pool of programs on machine A. That's about a factor of 10^120. If you think that a factor 2582249878086908589655919172003011874329705792829223512830659356540647622016841194629645353280137831435903171972747493376 difference is "not so large", then you've got a very different impression of what "large" means than most people do. Anyways now I think we're going around in circles. Unless you make a point of some substance in your next reply, I'm not going to bother replying. And no, insults do not count as points.