Hello, this is my first post on lesswrong, a community I deeply value. Feel free to tell me to RTFM, especially if you can point me there.
Yesterday I attended the weekly rationalist meetup at "The Territory" in Seattle for the first time. I attended for many reasons, but I was particularly excited to discuss Yudkowsky's new novel with others. His novel can be found here: https://www.glowfic.com/posts/4582
Only one of the eleven or so people there had heard about it, so this post is my attempt to market the book. Since all marketing should also add value, I will now move on to adding value by giving you a warm-up problem for some of the math and concepts you will encounter in this novel.
The problem is as such:
You are playing a game against ROB, the robber. In this game, ROB will choose two distinct arbitrary (real/computable) numbers, A and B. ROB will send both numbers to TABI the arbiter, who will secretly flip a fair coin and then hand you either A or B depending on the outcome of the flip. Your task is to come up with an algorithm which does better than 50% accuracy in determining if you were handed the larger number.
I will post the solution tomorrow, and then I will highlight specific ways I have applied the lessons from Yudkowsky's latest work in real/professional life.
Note that the book will not explicitly spoil this problem for you, and vice versa.
ROB selects A and B. First suppose A < B. Suppose A is revealed. Further Suppose that some deterministic Algorithm R exists which takes in A, and produces the probability that A is smaller.
In round one the only input to the algorithm can be A alone. Furthermore since we have supposed that R is "better than 50%", we must see have R yield us that P( A smaller ) > 0.5. We can then easily extrapolate P( A bigger ) < 0.5.
Now suppose we have the opposite case, that A > B. Again the only input to our algorithm can be A for the first round. However we must receive as output: P( A smaller ) < 0.5 and thus P( A bigger ) > 0 5
But consider that in both cases our only input was A, then it follows that R must not be deterministic since it produces two different results on the same input. This is a contradiction, hence there is no such deterministic algorithm R.
It is possible that there is a nondeterministic algorithm R', however I'm almost certain that no such algorithm can outperform a deterministic one in a case like this.
Hello, this is my first post on lesswrong, a community I deeply value. Feel free to tell me to RTFM, especially if you can point me there.
Yesterday I attended the weekly rationalist meetup at "The Territory" in Seattle for the first time. I attended for many reasons, but I was particularly excited to discuss Yudkowsky's new novel with others. His novel can be found here: https://www.glowfic.com/posts/4582
Only one of the eleven or so people there had heard about it, so this post is my attempt to market the book. Since all marketing should also add value, I will now move on to adding value by giving you a warm-up problem for some of the math and concepts you will encounter in this novel.
The problem is as such:
I will post the solution tomorrow, and then I will highlight specific ways I have applied the lessons from Yudkowsky's latest work in real/professional life.
Note that the book will not explicitly spoil this problem for you, and vice versa.
Edit: solution is here.