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.


> 
> [SPK]
> 
>     Ok, I would agree completely with you if we are using Kant's definition
> of *reality*- Dasein: existence in itself, but I was trying to be point out
> that we must have some kind of connection between the abstract and the
> concrete.
>     One thing that I hope we all can agree upon about *reality* is that what
> ever it is, its properties are invariant with respect to transformations
> from one point of view to any other. It is this trait that makes it
> "independent", but the problems with realism seem to arise when we consider
> whether or not this *reality* has some set of properties to the exclusion of
> any others independent of some observational context.
>     QM demands that we not treat objects as having some sharp set of
> properties independent of context and thus the main source of
> counterintuitive aspects that make QM so difficult to deal with when we
> approach the subject of Realism. OTOH, 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.
> Everett and others gave us the solution to this conundrum with the MWI. Any
> given object has eigenstates (?) that have eigenvalues (?) that are sharp
> and definite relative to some other set of eigenstates, but as a whole a
> state/wave function is a superposition of all possible.
>     So, what does this mean? We are to take the a priori and context
> independent aspect of *reality* as not having any one set of sharp and
> definite properties, it has a superposition of all possible. The trick is to
> figure out a reason why we have one basis and not some other, one
> partitioning of the eigenstates and not some other.
> 
>     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*.
> 
> Stephen
> 
> 


-- 
Aditya Varun Chadha
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