Noesis 58 - February 1991
The first half of George Dicks's
NOESIS 49 REBUTTAL
ran in the previous issue. Here's the second half.
George W. Dicks, Jr.
198 Stunn St.
New Haven IN 46774
Rebuttal-Point 3 (CTMU solution unsatisfactory)
As any member of our society journal probably realizes, the only reason I felt compelled to write my paper was because I found the CTMU solution unsatisfying in some way or another. Let me explain my reasoning at this time.
You see, when I read Chris Langan's original paper I was actually quite impressed. Those of you who know me know that I am a computer person myself and can therefore figure out the rest on your own. I have spent tremendous time using the computer to simulate a wide variety of processes, physical, economic, and otherwise and can therefore appreciate the assertion that because we can model almost anything on a computer why not simply assume that the theory of computation is the dominant theory of the universe?
It is here that I met with my biggest obstacle. In modeling the universe in this fashion, we have simply replaced one formalism, Logic and Mathematics, for another one, CTMU. At this point we are led to ask what we have gained. In my estimation, there is nothing describable in the old formalism which is not describable in the new one. However, it also seems apparent that the new formalism really has nothing much new to add either. It does, however, serve to neatly render all previous results into one neat and tidy formalism. This benefit must not be discounted.
The problem, as I saw it, with the Noesis 44 solution was simply that it was like using a B2 for crop-dusting. This formalism is simply too general and too powerful to claim it as the solution to any specific problem. At the high level represented by the theory, the most which may be said is that the problem is computable which, given the fact that the theory can handle any conceivable situation, is not terribly helpful. The author of the Noesis 44 solution does attempt to focus on the problem somewhat but the end result is that without knowing many of the parameters to each of the presumed automata we simply cannot make any kind of prediction as to the particular dynamics of any particular instance of the Newcomb Problem.
Because we aren't given these parameters I felt it necessary to factor this computational process out of the problem in order to have any chance of solving the problem for a given Predictor in a given situation. I realized that such a factoring could be easily handled with probabilistic methods and I also realized that such a method does carry an attendant loss of ability to predict any particular trial. The result of the concerns is the Noesis 49 paper. As the editor of Noesis 49 correctly pointed out, the Noesis 49 solution can be tricked by playing games with the experimental data. However, the editor failed to mention two very important facts. First, we don't know the parameters to the automata so we cannot make a prediction from them. Also, the Noesis 49 solution admits that it may be fooled, but it also learns pretty quickly from its mistakes.
Rebuttal-Point 4 (It is reasonable to distinguish Predictor and Chooser)
I actually find this point kind of ridiculous but I will contain myself. The entire problem is presented from this standpoint. Namely, that the entire reward structure is determined by the actions of one of the players.
The editor argues from the standpoint that each of the two players is trying to ascertain the choice made by his opponent in order to maximize his own personal gain from the situation. This having been said, we must realize that within the context of the problem one of the two players must eventually dominate in order to avoid an infinite computational regression.
Also, please understand that the names chosen are purely arbitrary and that Fred and Barney, Tweedle-Dee and Tweedle-Dum, or any other pair would serve our purposes equally well. The whole purpose to using this type of name was to sterilize the problem. Names like Demon, God, Super-Being, and Alien tend to force possibly unwarranted assumptions about Predictor's ability. Also, names like Human, You, Guinea Pig might lead to similar unwarranted assumptions about the abilities of Chooser. This was the whole reason for changing the names, to rid the problem of superfluous intellectual baggage. I'm sorry. I didn't quite meet my objective in this regard because Predictor and Chooser also lead to unwarranted assumptions. I will try not to lead you astray like this in the future.
Better names would be Aleph and Alpha, Beth and Beta, or some similar pair of non-loaded, equally rooted pair of identifiers.
Rebuttal-Point 5 (Certainty theory is reasonable)
Let me preface my remarks by saying that I nearly omitted the entire section on certainty theory because the Noesis 49 solution basically doesn't require it because any type of empirical induction would suffice.
The basic premise of the Noesis 49 solution is quite simple. It isn't any different from the basic premise of all of science. Namely it is the assertion that given sufficient data about the past and given sufficient information about the present, we can predict the future.
The method which I developed to handle this type of situation I titled Certainty Theory. I have since learned that this isn't a completely original idea and in fact that it is the inverse of Sampling Theory. However, for me it was original. The only reason I included it in my paper is because I understood the audience who would receive my paper. I knew that if I had made a mistake that this audience could easily point it out and I could correct my thinking. That the only criticism I received was philosophical and not mathematical made me feel reasonably good.
The idea began in response to a question which one of Marilyn's readers posed about the lottery. I believe the question dealt with which numbers should the reader bet on or some related subject. Marilyn's response was correct as far as it went, being the classic probability response that the outcome of given game is in no way determined by the preceding games. I had read this explanation many times before, but each time it never felt right. That's when I realized that classic probability is based solely on the assumption that a randomizer is not biased in any way. Unfortunately, we live in a physical world and all of our randomizers are biased, just ask the dungeon master we caught playing with shaved dice!
I then set out to determine how these biases may be determined and how the attendant probabilities may be estimated. I realized that actual probabilities are the result of an infinite number of trials and also that each trial would slightly reduce the amount of doubt which we have about a given estimate. This is why I set out to produce a method which can learn from experience and therefore can correct itself. Also, I knew that the rashness of simply doing a certain number of trials and basing the probability upon the result is rife with peril and therefore I wanted some method of keeping track of how sure I was of my estimate of the probability. The result is certainty theory.
I understood quite well the problems which the review in Noesis 49 points out such as the blindness to bluffing, etc. However, I realized that even these problems could be reduced to a probability estimate. In other words, if the other player is bluffing, this will show up as erratic play which means that his probability of a correct play is determinable for his actual skill level and the odds of a bluff. Since we assume that any trial is like any other trial, this probability may be used to calculate the expected value of it.
The Noesis 49 review then proceed to indicate by means of several other paradoxes and problems to show that certainty theory is blind. However, the simple fact is that without complete knowledge about the situation, a certainty 1 estimate of the probabilities involved, we must infer from past data an estimate of the probability. This is what certainty theory attempts to do. In fact, to dispute the empirical basis for probabilistic methods such as this is to dispute the entire basis for science. This leaves us with nothing but a chaotic mess of unprovable hypotheses with completely convinced adherents. Consider the long, irrational history of religious struggles if you consider this tolerable. Let me close this tirade by saying if you can't prove your assertions to an open-minded critic, then you can't prove them to anyone. Faith isn't proof.
Let me say in closing that I appreciate your patience in allowing me to defend some of the points which were made in my paper published in Noesis 49.
I have attempted with varying degrees of success to make the following points:
1) That the Noesis 49 solution was more general to the presented Noesis 44 solution while the Noesis 44 solution is potentially more general.
2) That the Noesis 49 solution is complete as to all facets of the problem.
3) That the CTMU solution is too general for the problem.
4) That the Predictor and Chooser should be treated as separate entities.
5) That certainty theory is not essential to my paper but is reasonable.
Also, let me reiterate that the entire purpose of this rebuttal is simply to defend certain points and to clarify others. It was not intended to step on any toes and absolutely not intended to humiliate or criticize anyone.
Also, let me repeat my appreciation to all members involved in working on this problem. It's been interesting and I think I've learned a lot. I would especially encourage Chris to continue work on his CTMU and I would appreciate the opportunity to see the entire thing at some time in the future. As I told him in a letter, I Find it very interesting and believe there's quite a bit there for those who look.
Let me close by encouraging any and all of you to send me any correspondence you find appropriate on this or any other mailer. I truly enjoy hearing from each and every one of you. My phone is always on the hook and my mailbox is always open. It's up to you.
George W. Dicks, Jr
The Mega Society
Copyright © 1991 by the Mega Society. All rights reserved. Copyright for each individual contribution is retained by the author unless otherwise indicated.