This is a followup on how I consider interest to be a function of
a different type from a price. Gil argues that:
I don't see how granting that the limit as t approaches infinity
of P(0)(1+r)**t is infinite implies that r cannot be expressed as a
ratio. Indeed it can be, as can be seen by anyone who lends money
for one period (or enters into a one-period futures contract, see
below).
Paul:
Firstly the distinction between functions of exponential order
and of order zero is quite fundamental and does not depend upon
the exponent (time in this case) tending to infinity.
Let q = Kp for some constant K
then
let f(t)= R^t for some R >1
Then there exists a finite x such that f(x)p > q for any arbitrily
chosen K.
If we express the function for the money due on a loan as
d(p,t,r) = p.r^t
then we can indeed derive the sort of ratios that Gil talks about
by partial application of the function if we
Let ratiogenerator = proc(real t,r->real) d(1,t,r)
then we can derive a ratio of the type that Gil refers to
by;
Let ratio = ratiogenerator( 4, 1.05)
in the case of a loan for 4 years at 5%. But the ratio is of type
real, whereas the ratio generator is of type (real x real -> real).
Thus on type theoretic grounds they are fundamentally different things.
This would be brought out immediately if you tried using an
automated theorem proving system like LCF to check your argument.
The fact that bank officers think that interest is a price paid
to purchase money tommorrow is testimony only to the false consciousness
of the agents of capital, and is of interest only in terms of how
capitalism appears to operate, rather than how it does operate.