[FRIAM] A/R theory

[Russ Abbott]

You may be interested in my Minds and Machines
<https://drive.google.com/file/d/1dKv7Dt_2pO1OlUL7BesB31FyjpCsO_2E/view?usp=sharing>
(also
Springer) paper on the same subject.

*The Bit (and Three Other Abstractions) Defne the Borderline Between
Hardware and Software *

*Abstract *Modern computing is generally taken to consist primarily of
symbol manipulation. But symbols are abstract, and computers are physical.
How can a physical device manipulate abstract symbols? Neither Church nor
Turing considered this question. My answer is that the bit, as a
hardware-implemented abstract data type, serves as a bridge between
materiality and abstraction. Computing also relies on three other
primitive—but more straightforward—abstractions: Sequentiality, State, and
Transition. These physically-implemented abstractions define the borderline
between hardware and software and between physicality and abstraction. At a
deeper level, asking how a physical device can interact with abstract
symbols is the wrong question. The relationship between symbols and
physical devices begins with the realization that human beings already know
what it means to manipulate symbols. We build and program computers to do
what we understand to be symbol manipulation. To understand what that
means, consider a light switch. A light switch doesn’t turn a light on or
off. Those are abstractions. Light switches don’t operate with
abstractions. We build light switches (and their associated circuitry) so
that when flipped, the world is changed in such a way that we understand
the light to be on or of. Similarly, we build computers to perform
operations that we understand as manipulating symbols.


In other words, it's all in our minds.

-- Russ Abbott
Professor, Computer Science
California State University, Los Angeles


On Sat, Nov 7, 2020 at 9:35 AM jon zingale <jonzingale at gmail.com> wrote:

> This work does seem to be relevant, up to 𝜀-equivalence, to many of the
> fibers in recent threads :) As the authors point out, the question of
> deciding which diagrams 𝜀-commute is the business of experimental science
> à
> la EricC's commentary on the history of chemistry. Also, the ideas
> expressed
> in this paper appear to point in a similar direction to the
> (model-theoretic) ideas I was attempting to land in the
> *downward-causation*
> discussion from last week. Lastly, the thesis is related to questions of
> how
> extensional (or purely-functional) computation arises from the intentional
> (maximally-stateful) variations of a substrate. So, thanks.
>
> 𝜀-equivalence itself is interesting because it comes with a *competence
> constraint* that prevents it from being a transitive relation, that in
> general a =𝜀 b ^ b =𝜀 c ⊬ a =𝜀 c is crucial to the theory. In other
> words, while there may be a wide range of arm shapes that can be used as
> bludgeons, one can evolve themselves out of the sweet spot. Dually, the
> 𝜀-equivalence condition provides a route to modeling *exaptation*, via
> modal possibility. As p's belonging to the Physical domain vary, images in
> the abstract theory vary into or out of 𝜀-equivalence with values
> belonging
> to other problem domains. In particular, if we imagine that the R-map in
> the
> paper is *actually* a structural functor as it seems to imply, we can
> imagine another functor R' which specifies yet another problem space.
> Natural transformations then, up to 𝜀-equivalence, provide a model of
> exaptation. Because of the experimental nature of 𝜀-equivalence, I suspect
> we would slowly discover an underlying Heyting algebra which would extend
> to
> a topos via studying relations on sieves of 𝜀-equivalent structures. This
> approach would formalize *how far from competent* a structure is wrt
> *proving* a particular computation.
>
>
>
> --
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