Hi Dick,
1. *****Paul: I think I understand what you mean by "so "explained"". It means that every collection of numbers must obey the constraints expressed by your fundamental equation. Dick: I think that right here you have missed a very subtle fundamental step. Not that you haven't seen it but rather that you have overlooked the real impact of a very large "IF" central to all that follows. *****
2. You are probably right. If so, I am eager to have you explain more clearly what it is that I am missing.
3. *****This concerns the mental machinations which constitute the creation of hypothetical "facts" (what I have called "unknowable" data: creations of my mind, the truth of which explain everything).*****
4. I am aware that your introduction of "unknowable" data is an important and innovative part of your discovery. But, you are right; I not only am not comfortable with exactly how this trick should be formally described (this is the point at which I am stuck in my attempts to write up your Chapter 1 as a theorem), but I am also vaguely aware that I am missing the significance of this trick, or, as you said, I am missing the "real impact" of it. Let me begin making up this deficit by analyzing what you wrote, and we can proceed from there. Since I know you to be very careful in thinking through what you write, and since you have many times advised me to pay very careful attention to exactly what you wrote, I will analyze what you wrote as carefully as I can.
5. *****If all of this can be represented by a set of numbers ...*****
6. First of all, I assume that the "If" quoted in 5. is the one you referred to in 1. as the "very large "IF"" whose impact I have overlooked. With that assumption, I will try to understand that impact from what you wrote.
7. I am trying to be clear about what you mean by "all of this". I think you mean everything mentioned in 3. Making that assumption, let me list individually the nouns, etc., that you used in 3. and then give you my understanding of the implications of each one in the context of 5.:
8. Here is the list:
a) "the mental machinations"
b) "the creation of hypothetical "facts""
c) the "hypothetical "facts"" themselves
d) the ""unknowable" data"
e) the "creations of [your] mind"
f) "[your] mind" itself"
g) "the truth of which"
h) "which"
i) "everything"
9. Rather than take these in order, I will take them in the order from easiest to hardest.
10. As I understand it, c), d), and e) all refer to the same thing, and it is easy to see how each of them can be represented by a set of numbers. As you have described them, they are numbers.
11. I am sure that the antecedent of h), "which", is e), the "creations of [your] mind", so, again, it is easy to see that h) can be represented by a set of numbers.
12. This leaves us with the hard ones: a), b), f), g) and i). Since a) and b) are the same thing, we are left with four concepts that I wonder about. I wonder whether you meant that each of them was to be interpreted as part of the "all of this" in 5. I'll list these four concepts, make a guess as to whether or not each of them can be represented by a set of numbers, and then leave it to you to correct my guesses where they are wrong.
13. The four "hard" concepts, are a-b) your mental process, f) your mind, g) the truth, and i) everything.
14. a-b) It has been formally proved that if your mental process could be represented by a set of numbers, then it would be equivalent to a Turing Machine. Roger Penrose, in "The Emperor's New Mind" and "Shadows of the Mind", has convinced me with arguments along the lines of Goedel's Proof, that the capabilities of the mind surpass those of a Turing Machine. This means that the mental process cannot be represented as a set of numbers. And he only talked about the conscious mind. Since you seem to acknowledge that the subconscious mind is in many ways superior to the conscious mind, that would mean that the case against representing the whole mental process as a set of numbers is even stronger. So my guess is that a-b) cannot be represented as a set of numbers.
15. f) I think you have agreed with me in prior discussions that your mind is part of the Great Original Dilemma. As such, I think it is not part of what can be represented by a set of numbers. That was the whole point of my long conversation with you in the General Interest forum quite a while ago. Let me know if I completely misunderstood the implications and conclusions of that discussion. My guess is that f) cannot be represented as a set of numbers.
16. g) I don't know that I have seen any definition of 'truth' that would allow me to speculate on whether or not it could be represented as a set of numbers or not. But I doubt that truth was included in your phrase "all of this" in 5., so my guess is that g) cannot be represented as a set of numbers. Let me know if I am wrong.
17. i) I am pretty sure that by "everything", you mean everything. That means that "everything" not only includes all of a) through h), but everything else conceivable or inconceivable that exists. So if any of the candidates a-b), f) or g) above cannot be represented as a set of numbers, then neither can i). At least, that's my guess.
18. Now, proceeding on the assumption that my analysis and guesswork above is correct, I am ready to take a crack at explaining my understanding of the "big IF" that you said I had overlooked. First, I will quote your statement of that "IF" and then I will follow it with my interpretation based on my assumptions in 6. through 18. above.
19.*****If all of this can be represented by a set of numbers (which I hold communicability requires) then, what I show is that if, the "Law" of the Universe is taken to be a very specific function (defined in my paper), then I can prove two very specific things: first, I can prove that I can create a set of hypothetical "facts" (what I have called "unknowable" data: creations of my mind, the truth of which explain everything) for absolutely any set of numbers (any set of "real" facts) conceivable; and second, I can prove that the "complete" set of facts so conceived (the totality of those numbers representing both "real" and imagined concepts) must obey my "fundamental" equation. *****
20. My interpretation of your assertion is as follows: If all known facts, as well as any set of hypothetical facts which make up a true explanation of those known facts, can be represented as a set of numbers then, you have shown a method of creating such a set of hypothetical facts, and moreover, you have proved that the complete set of facts comprising the known facts and any such set of hypothetical facts must obey your "fundamental" equation. Just so there's no misunderstanding, by "any such set of hypothetical facts" I mean those facts comprising any true explanation of the known facts, and it is possible that there may be many such sets for any given set of known facts.
21. I will stop at this point since I think this is enough to chew on for a while. We can discuss Chris Langan and possible interpretations of what Alan has been saying at a later time.
22. It's always good talking to you and learning from you, Dick. I am only sorry I can't find more time to devote to this fun.
Warm regards,
Paul |