Marxism and Mathematics
schatterjee2001 at SPAMyahoo.com
Tue Feb 13 12:36:32 MST 2001
> So what is 0/0? IIRC the tangent of a function
> (under certain conditions) at x is the limit of
> (f(x) - f(y)) / (y - x) as y -> x, evaluating
> this at x makes no sense.
This is how Marx looked at it. Let us say f(x) = x**2.
Then f(y) = y**2. So
[f(y) - f(x)]/(y - x) = x + y
The derivative at x, df/dx, is defined as the value of
the above ratio at y = x (note y exactly equals x, not
tends to x). Then
df/dx = 2x
But df/dx is actually a symbolic representation of 0/0
since if we put y = x on the right hand side (rhs),
then we should also put y = x on the left hand side
(lhs) and so
[f(y) - f(x)]/(y - x) = 0/0 = df/dx.
But in the 'mystical' calculus of Newton, on the left
hand side, it was said that y tends to x but never
reaches x, and this is commonly taught even today.
This causes confusion since on the rhs we put y = x
but on the lhs we say y -> x, which is not consistent.
To be consistent, y has to equal x on both sides of
the equation. So the derivative is a symbolic
representation of 0/0.
The derivative, according to Marx, is actually a
reflection of the principle of 'negation of the
negation'. In the first instance, we move away from x
towards y and form the ratio [f(y) - f(x)]/(y - x),
i.e., we negate x by y. In the second instance, we
again move back towards x from y, i.e., negate y by x.
But we reach a higher development, df/dx.
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