Hi Aditya,
I do not see anything in your reasoning that I would disagree with. ;-)
It seems that you subscribe to a concrete interpretation of mathematics,
which is one that I take on occasion. I merely wish to comprehend the ideas
of those that take a Pythagorean approach to mathematics; e.g. that
Mathematics is "more real" than the physical world - "All is number".
One thing that I have learned in my study of philosophy is that no
single finite model of reality can be complete. Perhaps that asymptotic
optimum involves the comprehension of how such a disparate set of models can
obtain in the first place.
Kindest regards,
Stephen
----- Original Message -----
From: "Aditya Varun Chadha" <[EMAIL PROTECTED]>
To: <everything-list@eskimo.com>
Sent: Sunday, July 24, 2005 2:20 AM
Subject: Re: what relation do mathematical models have with reality?
Greetings,
Here's my Rupee 1 on the connection between "abstract models" and
"reality";
Although it is ofcourse debatable, I hold that what we call reality is
our minds' "understanding" of our sensory perceptions. Thus the notion
of (our) reality depends on:
1. The nature of mind
Let's assume that the mind is simply the brain + the processes the
brain is capable of + the information it stores/processes. Then the
nature of the mind is the (sub)set of data-structures and computations
that the brain is capable of.
2. The process of "understanding"
Using the above informal definition of the mind, understanding is
simply the following process:
a. organize incoming data into data-structures that the brain is
capable of storing and processing (itself a brain-process),
b. process these data structures (computation) to make
"predictions" (just more data),
c. compare these predictions with more incoming feeds from our
senses (experiment/testing),
d. and finally re-adjust the organization of data in our brain
(data-structures) to accommodate the differences in prediction data
and sensory data.
The above process continues iteratively, thus the iterative
refinements in our theories of reality, aka physics.
3. Our sensory perceptions
The data that comes in to the brain. This clearly depends on the
instruments of perception (senses) themselves. For example a person
born with a microscope attached to his eyes will transfer very
different data to the brain than most of us, and thus may have a very
different "understanding of reality".
In other words, our understanding of reality depends on brains and our
senses. It can never be any more "real" or "imaginary".
[SPK]
we have to come up with an
explanation of how it is that our individual experiences of a world seem
to
be confined to sharp valuations and the appearance of property
definiteness.
response:
This is simply because of the similar constitution of our sensory
organs and brains (closeness in genotype and therefore phenotype if
you may). A fly's understanding of reality is probably very very
different (may or may not be sharp)
[SPK]
What does this have to do with mathematics and models? If we are
going
to create/discover models of what we can all agree is sharp and definite-
our physical world, we must be sure that our models agree with each
other.
This, of course, assumes that there is some connection between abstract
and
concrete aspect of *reality*.
response:
If we presume to take my above description of the nature of mental
models (mathematical/physical/etc.) as physical reality, then physical
reality itself guarantees that our models will always depend on not
only "objective reality" but also the "nature of our mind" and our
"sensory perceptions", which themselves form a subset of reality.
It is much easier to make other humans "understand" (have their brains
recalibrated to) a new model or theory than to attempt the same with a
fly (unless the fly is given a human brain and human sensory organs).
Thus this "agreement" is NOT a certificate of validity for our models.
But this does NOT imply that there is no connection between abstract
and physical "reality".
Abstract reality is a "parallel universe" created by extrapolation on
a very limited (finite?) subset of "concrete reality", namely our
brain, sensory perceptions and the computations therein. The purpose
of creating and refining this "abstract reality" (aka
mathematical/physical models) is to recalibrate the brain and senses
so that the abstract models it can hold predict incoming data
(concrete reality) with increasing accuracy.
Yet this accuracy itself is limited by laws like those given by QM
(that limits the power of our senses). This suggests that we are close
to the best we can do, although we may continue coming monotonically
closer to the asymptotic optimum that we are limited to.
snip
