Hitoshi Kitada (hitoshi@kitada.com)
Thu, 4 Nov 1999 22:42:29 +0900
Dear Bill,
I saw your new version of Nov. 4. I still have a question on section 2:
The second equation for f_n:
df_n/dt = h f_n (2)
is equivalent to
f_n = c exp(th) with c an arbitrary but fixed constant. (2)'
Namely this gives the general solution for (2).
But unlike you say there, f_{n+1} = f_n exp(th) is not the solution of (2)
because by (2)' we have
f_{n+1} = f_n exp(th) = c exp(2th),
which satisfies
df_{n+1}/dt = 2h f_{n+1}.
I wonder why you need subscript n, which, I assume, takes integral values 1, 2,
3, ...
I think you need just two quantities, say f_0 and f_1 that satisfy, e.g.,
f_1/f_0 = 1/(1-x)
in the case of relativistic/objective notion of change at the bottom of page 4.
In the case of exponential function case, this would become
f_1/f_0 = a constant,
if f_1 should satisfy the same equation (2) as for f_0. Namely the exponential
case is the extremal case where there is no substantial change between
subjective and objective values. And you seem to attempt to find some
non-extremal but more moderate case/view to the subjective change in your
present paper...
Best wishes,
Hitoshi
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