From Osher Doctorow
Now let's use T3, which is time as causation, in the Knowledge
Equation. Recall that PI postulates 3 dimensions of time: T1 (time as
duration), T2 (time as causation, since causes precede effects in
time), T3 (time as transfer of causation, for example transmission of
causation through messages or channels).
The Knowledge Equation is:
1) K^(a+b+c) V^a V^(a+b) PI = L^a T^b M^c F^(a+b)
Since "causal Knowledge" is arguably the most important type of
Knowledge, it follows that if Knowledge exerts any real causation in
the real (physical) world, it would do so via T3. The question is what
function to assume relating K and T (where T now refers to T3). For
simplicity, let both K and M be relevant to the problem, so that K^c
cancels with M^c and K = k1M for some constant k1 as before
(incorporating k1 into PI), and this yields:
2) K^(a+b)V^(a+b)F^(-(a+b))(V/L)^a PI = T^b
So the simplest solution is:
3) K^(a+b) = T^b
from which we get:
4) T = K^((a+b)/b) = K^(1 + a/b)
With a, b positive, T increases more than linearly with K from (4).
For example, if a = b = 1, then:
5) T = K^2
Since "everything" is up to a multiplicative constant in view of PI but
also in view of T and K being dimensions as well as variables in a
formal sense (technically dimensions and general variables are
distinct, but it's briefer to use the same symbols), (5) is actually:
6) T = k K^2, k real constant (presumably k > 0)
As an amusing or not-so-amusing aside, people who remember E = mc^2
might notice that T = kK^2 looks like a Knowledge-based time-bomb
formally at least. But it could also be a Knowledge-based peace gift,
so we shouldn't jump the gun on this.
Recall in my recent threads that I emphasized that probability is a
function of Knowledge rather than vice versa, or more explicitly that
Knowledge is causal rather than probability by itself. Equation (6)
says a similar thing about time as causation - it's essentially the
square of Knowledge.
Of course, a = b = 1 is only one scenario with a, b, c variable
exponents, but it represents a very interesting phase indeed!
Notice, by the way, that M = k1K and T = kK^2 in this phase.
Osher Doctorow
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