Ah, good morning. Glad you're completely back from the Sabbath and your day of rest!!
I knew I can count on you for an interesting problem. It isn't very difficult mathematically, but it does require math.
[Deep breath]
If for ALL probabilities between 1 (metaphysical certitude) and 0 (metaphysical impossibility), I state without proof
X*Y = Pr(X and Y)
then I will demonstrate how to calculate your answer.
First, you must assign a value to the relative certainty of X. I doubt that you can assign it 1 to infinite precision. There is some, albeit small chance, that the substance you start with is not beer. You could be holding a keg of Jim Hoffa's laundry water, or whatever. The nature of the Universe prevents that and other silly unlikely things, but there are a lot of silly, impossible things that could happen at a very low probability. So, it is
Pr(A) = 0.999999999999999
that the substance you have is beer.
Then you have to decide the threshold function where you consider the adulterated beer to be wholly not beer due to the principle of equivalence, maybe
Pr(B) = 0.000000000000001
or
B = 1 - A;
You now have a formula for determining how much dilution changes beer into something that is not beer. This is a gradual process and related to the number of dilutions. Let's say we do a 0.99 dilution per titer. We call this
D = 0.99
To figure out when BEER becomes (NOT BEER) you set up your equation:
Pr( B ) = (A * D)^N
log( Pr(B) ) = N * log( A * D )
N = log( Pr(B) ) / log( A * D )
You now know when beer becomes not beer and how many times you can dilute it.
Where the whole school of Logic when wrong was the assumption that abstract types could approach 1.0000000 to such a close degree that any number, N, evaluations of
Pr(A and B) = (A*B)
AND
Pr(A and B), N = (A*B)
Further, I would assert that
Pr( A and A ) = (A*A) = (A and A)
in all cases is only relatively true based upon the times it is evaluated. The reason propositional logic fails, IMO, is that the relatively true form of the equation is:
Pr(X and Y) = (X*Y*D)
where D is a reality dilution constant whose properties are related to X and Y. Frequently D is very close to 1.
so
If I keep asking if I have a block of cheese,
A=it is cheese
B=I have it
Pr(A and B), N = (A*B*D)^N
after MILLENIA that I have cheese will no longer be true, but something else will be true. Either I or the cheese will spontaneously change state. This is analogous to proton decay. I think that everything has decay. Red shift of starlight could be interpreted as "tired photons" who are decaying from cosmic ray down through light, infrared, radio, then eventually dying into 1/f field fluctuations.
I've managed to avoid the rigorous math and calculus, but using calculus I can demonstrate that the term 1/f arises naturally from the equations from which make my calculations. Given a Planck time quantum field fluctuation limit, this means that a numerically very large value of N exists. This suggests that all reality is like a Markov chain that started from the beginning of time, but with only a relative probability of the upstream events producing the expected outcome, instead of the value using "classical" methods. Markov chains are fine for things of low orders of complexity. Higher orders of N produce measurable deviations from "classical" P(A and B) = (A * B) behavior due to the presence of "D" and the exponential order of the equation.
[exhale, pant, pant] |
