On 1/25/07, Don Dailey <[EMAIL PROTECTED]> wrote:
On Thu, 2007-01-25 at 20:16 -0600, Matt Gokey wrote: > Don Dailey wrote: > > You are still missing the point. > I can say the same of you. > > I merely am raising a question about the assertion that doubling of > _human_ thinking time results in _linear_ improvements. I am not > claiming that there is no improvement - never have. I am not claiming > that every turn must produce better results to improve overall play - > never have. However I am trying to explain a rationale for the > possibility that improvements may not be linear based on the nature of Go. It's possible, but I think my curve (it is a curve, it gradually tapers off as you get closer to perfection which is an obvious limit) holds in all non-trivial games of perfect information. The curve may have a different shape or slope but it's there. It's already easy to produce in computer go despite a reluctance by many (not you of course) to admit it. My sense is that many on this group want to believe that we just happen to be at the top of the curve but that it immediately falls off. There is no rational reason to believe that other than superstition.
I am not trying to say that you don't know what you are talking about, but how are you so sure that we must be on the linear part of the curve? Based on what you said, I estimate your ideal (non empirical) formula to be something like the following: S = P * (1 - e^-kt) where S is skill level and P is perfect play and k is some constant specific to the game. In fact this is an ideal formula that should apply given the reasonable assumption that the chance of reading one unit of skill is proportional to the amount of time taken and the amount left to be seen. This makes sense assuming a very specific distribution of the difficulties of different items that can be seen. That distrobution would have to have all units capable of being seen as equally likely to be seen. I think this could be a good theoretical model. Anyway, I would like to see you make more specific claims with formula and justifications for them. Vague statements about linear relationships that taper off and how we are clearly not anywhere near the top help nobody. You seem to know a lot about this. I would appreciate it if you would share your reasoning. You seem pretty skeptical of intuition. So, what is the reason you believe these things about go?
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