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" <adichad.domain.name.hidden>
To: <everything-list.domain.name.hidden>
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
Received on Sun Jul 24 2005 - 20:40:15 PDT