unreality

I added you guys the conversation, hopefully you will be able to see all 4 pages; if not I will give you a summary

once again I apologize, I hope nobody minds waiting so long for the T3 results. We've been trying to get Gmaster's program running without much like - if you guys want, in the meantime, I can run the results with all the other algos as partial results

yeah you'll find all number sequence puzzles in the Math/Logic section too

Please put your answers in spoilers!

I know this has been inactive for a little while but I hope you guys don't mind waiting; darth and I have both been pretty busy but we're getting kinks in his algo straightened out, then T3 will be ready to rumble with the following contestants: 34 (phillip!) 35 (plasmid!) 36 (unreality!) 39 (darthnoob!) 40 (dawh!) 41 (MrApple!) 42 (Framm!) 43 (SomeGuy!) 44 (jazzship!) 45 (jarze!) These 10 contestants will match up for a final battle unlike any other I'll also release the full & final code for all to see Actually jazzship's is incomplete cuz his had randomness and he was gong to redo it; I'll PM him about that. And I'll see if Izzy wants to join in too. BUt anyway... soon, soon

v like this? v phillip makes an interesting argument that says that defect is best for a single round but NOT for a bunch of rounds. I think we're not arguing over that... like I said a few pages back, via induction or just common sense (though that can be misleading here), what applies to one seems to apply to all (for perfect Masters of Logic only - NOT for normal people) so the whole question can be resolved by looking just at a single round

if you select COPY instead of INVITE in the drop-down menu, I think it could work. I sent a test to both of you

I'll think more on this…

Right here: http://brainden.com/forum/index.php?/forum/7-new-logicmath-puzzles/ An ongoing discussion is: But you should check out these classics: http://brainden.com/best-puzzles.htm One of my favorites is 'Hats on Death Row' - I think you'll really enjoy this one… There are a lot of good ones on this site. If it's more of math that you like, there are a lot of unsolved mathematical dilemmas http://mathworld.wolfram.com/UnsolvedProblems.html

if anyone is interested we could host a quick algorithm contest similar to the Rock Paper Scissors one (although it probably wouldn't be as interesting, but maybe I'm wrong) - I've already copied some of the code from the RPS program and can pretty easily change it to the Prisoner's Dilemma if anyone is interested

The recursion kicks in when you reason about the other person's reasoning. That's what I've been trying to avoid because it leads to infinite regress.

Noooo do not play WoW. I have a few friends who have gone off the deep end playing that game *cough*drug*cough*. Trust me, it's not worth it.

Are you more into math/logic problems or word-riddle/lateral-thinking puzzles?

Thanks for pointing that out. That seems to be the core of our debate so I'll get back to that in a second. First, regarding my inductive process from the first round up that octopuppy criticized, I included that I realized this was not valid against anyone other than a Master of Logic. Another proof is the back-to-front induction from plasmid that octopuppy gives in the above post, which is essentially the same as what I said. I think we are all in agreement that this problem condenses all rounds into one between the two Masters of Logic, and that is what's being debated: a single round. Does the MoL cooperate or does it defect? So going back to what I quoted from neida, and with what octopuppy has been saying, this is my attempt at summarizing: OCTOPUPPY: I will choose the logical choice, as will my opponent. Whatever they choose, I can do better by defecting than by cooperating. KEY LINE FROM PROOF: "Since I do not yet know, I will consider both possibilities" NEIDA: Saying that you don't know what the opponent will do is illogical because, being a Master of Logic, you know what they will do. They will do the same as you, so the logical choice is for both to cooperate. KEY LINE FROM PROOF: "He forgot to take into account the fact that his opponent would do exactly the same as him" I think that I would be on Neida's side if not for a flaw I see in his assumption of symmetry. It's that if the other MoL thinks that and decides to go with cooperate, you can one-up them by defecting. Then of course both will defect. etc. The only stable non-looping solution seems to be when both players defect, even though the optimal seems to be when both players cooperate.

I haven't posted in a while but I've been reading every post, and thinking. At first I was agreeing with neida, but then when I thought about that kind of stuff myself I always ran into Godel's Incompleteness Theorem, over and over again. I realized that shouldn't be happening. Then I figured out a logical solution that stays first-order and never once makes an assumption about what the other person will do. This allows anyone to emulate the "logical decision" without having to be a Master of Logic, and gets rid of that paradox. First we need to establish a lemma that each round is independent of all other rounds. I don't know how to formally prove this so I suppose this is the underlying assumption. We could use a proof of induction: * the very first round does not depend on previous rounds * if you made the logical decision last round, and last round did not depend on previous rounds, then this round you can make the logical decision without depending on previous rounds And via induction, all rounds become independent. Or you could show that whatever is done the last round will ricochet backwards. I have a few other inkling ideas of why each round of this game may be independent (FOR MASTERS OR LOGIC OR PEOPLE USING A STRATEGY THAT A MOL WOULD USE, obviously it's not independent in the general case). Let me know if you disagree with this assumption. From there we can consider the game by just considering a single, arbitrary round. Back to the basics: I defect, s/he cooperates: +2 I defect, s/he defects: 0 I cooperate, s/he defects: -1 I cooperate, s/he cooperates: +1 Either way the opponent's move is locked in as the opponent's move. They are going to do what they are going to do. Therefore I should defect and thus get 1 more point than I would have if I had cooperated. I realize that the "lemma" (that each round is independent) is probably under more scrutiny now since the "logical choice" follows so simply from that, but at the very least we can establish an if/then relationship: IF the logical decision does not require input from the previous rounds, THEN defect. However, if it can be shown that the logical decision requires the past moves to establish itself, then it would have to be proven in a different way... My gut tells me that symmetry means everyone should cooperate all the time, and that's probably what I would do. But logic tells me I should defect

darth said what I was trying to say. If they do indeed play the same game, 50 and 50 cooperation will get them the most points

yeah that's what I was referring to. All algos are deterministic in that their only decision input is the a[], b[] and i variables. We've established that randomness is sub-optimal anyway. I'm sure you can think of a new implimentation Maybe a version 2.0. There's no rush

yep, and speaking of that, just waiting to hear from jazzship and possibly izzy if she thinks of something I can't wait to see which algo comes out on top

Interesting!! I entered it (as algo #46) - do you want it tested in some away against T2 programs or similar-to-T2 programs or something? Obviously this is just a recreational exercise [cuz remember no electronically testing a T3 algo before the big tourney - which btw should be coming up soon, I'm just waiting to hear some more from jazzship, Izzy and maybe some others - we already have 10 algos entered into T3]

but if they both defect, they both get 49. 100 may be maximum, but 50 is optimal

nvm, Framm 18 is accounted for, I just haven't put his algo into the system yet So we have seven algos done and in, with 2-5 more or so in the near future ;D