[OPE-L:1462] Re: Math and numbers

Alan Freeman (100042.617@compuserve.com)
Tue, 12 Mar 1996 08:48:58 -0800

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Paul writes [1419 of 11/03]

"The reason that I find these numerical examples rather
uninformative, is that they too have all sorts of hidden
assumptions: discrete time, synchronised production, no fixed
capital, no output stocks etc. At least in a formal model you
can explicitly analyse the effects of taking these into
account, and state what you are assuming about them."

You can't just refuse to confront a contradiction because you
find it uninformative! If a formal model doesn't work with even
one set of numbers, then the formal model is wrong.

The catholic church found Galileo's observations 'uninformative'.
The uninformative Galileo was right and they were wrong.

Why don't I just say I have a wonderful theory that tells me
all numbers in the world add up to three? Then when someone
tells me they found two numbers that add up to four, I can
presumably dismiss it as 'uninformative' and explain that their
error is their failure to use my model. Fantastic logic.

How can a *number* have an assumption? What is the 'assumption'
behind the number 2? *Theories* have assumptions.

The only assumptions in my numbers are that a definite quantity
of product is made in a definite period, a definite number of
workers work on it in this period, a definite amount of money
is paid for it, a definite amount of it exists at any time and
it has a definite price at a definite time. This aren't
assumptions, they are observations.

Discrete time, synchronised production, no fixed capital, no
stocks: these are all assumptions of the standard simultaneous

I applied these assumptions to definite numbers because the
authors of the simultaneous model make these assumptions. It
could not be more completely upside down to say that the
*numbers* are responsible for the assumptions.

I wholeheartedly support every single objection you raise to
these assumptions. Every one of them is made by the authors
of this model.

A is a *flow* matrix. Where is fixed capital in the *flow*
relation v = vA+L?

Which variable represents stocks in v = vA+L?

Which variable represents stocks of output in v = vA + L?

Where is the equation telling us the relation between stocks
and flows in v = vA+L?

Where is time, and where is nonsynchronous production in
v = vA + L? Indeed *everything* is synchronous in these
equations. There *is* no time in them. That's why they are
called simultaneous. We might as well call them synchronous

So why not throw out the model?

You want output stocks, add output stocks. You want fixed capital,
add fixed capital. You want desynchronised production, desynchronise
production. You want etcetera, add etcetera. You want it, you got it.

If these same numbers can be interpreted differently without
contradiction, then do it. Any way you like. But when you've
done it, you won't have anything recognisable as simultaneous.

The only reason the 'informative' assumptions of the simultaneous
interpretation can be maintained is because of a blanket refusal
to confront them with any data that doesn't suit them. In this
way astronomy spent one and a half millenia happily 'informing'
itself the sun went round the earth.