[Pen-l] Re: GMUonomics [was: behavioral (experimental) economics]

["Julio Huato" <juliohuato@xxxxxxxxx>]

Les wrote:

> i haven't seen anyone yet locate your fixed points in actual existing
> processes.

Les,

Consider a much simpler example, from anybody's world: A can with some
liquid.  Let the state of the system at $t$ be $x_t$.  Now shake the
can.  At $t+1$, after the shaking, the system is $x_{t+1}$.  Fixed
point theorems say that there'll be at least one point along the
mapping from $x_t$ to $x_{t+1}$ that will be fixed.

Now, you say.  But Julio, what do you mean a point in a physical
liquid?  Points are dimensionless.  Do you mean that a dimensionless
entity has an "objective" existence outside of our minds?  And even if
a dimensionless object existed, what if the world is discontinuous at
its most elementary micro-cosmic level, don't theorems predicated on
continuity collapse then?

I'll say, okay Les, I concede: A perfectly dimensionless point can't
exist but in our minds.  If the world is not continuous in any
meaningful sense at some level, then there may be a hole right about
where the hypothetical fixed point would be.  Etc. But -- but, if the
point of mathematical analysis is *approximation* (Gerretsen & Rau),
and approximation is a *practical human endeavor*, then for certain
*practical* purposes (e.g. inspect the quality of the liquid in a can,
etc.), a molecule can be thought of as a point.  They are small
enough.  So, for at least one molecule $x_t=x_{t+1}$ will pin a fixed
point.

But Julio, for *other* conceivable practical purposes (something
involving processes at a subatomic level), molecules are very complex
things.  Sure.  Then let the molecule be a sub-system or element $x^i$
of $x$ and replicate the argument.  The state of the molecule at $t$
is $x^i_t$.  Shake the molecule every which way.  At $t+1$, after the
shaking, there'll be a point defined by $x^i_t=x^i_{t+1}$.  Fixed
point.

This is still the early 21st century, how much further would you want to go?
_______________________________________________
pen-l mailing list
pen-l@xxxxxxxxxxxxxxxxxx
https://lists.csuchico.edu/mailman/listinfo/pen-l