[FRIAM] privacy games

[Frank Wimberly]

As with the physical entities described by the math in Baez's book, I feel
that I have a leg up on understanding the math but not so much on the
relationship to the described entities.  It must be my aversion to the real
world.

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Tue, May 26, 2020, 8:21 PM Jon Zingale <jonzingale at gmail.com> wrote:

> Glen,
>
> I am really enjoying steelmaning and getting steel-mansplained,
> so thank you for the discussion up to this point. For me the
> images are that of the constructions for free modules
> <https://en.wikipedia.org/wiki/Free_module> over a ring,
> dependent types, and algebraic varieties
> <https://en.wikipedia.org/wiki/Algebraic_variety>. In the first case,
> there
> is a natural interplay between the category of sets and the category
> of modules, equipped with a map describing *inclusions* of bases into
> the collection of vectors they span, and a map describing how to
> *evaluate* a vector in a context to return a single number. The thing
> I find relevant here is that while the evaluation function does
> much to *found* the module (a vector space say), the *evaluation* is
> not what is interesting about the module. What is interesting is that
> we have a playground to talk about *dimension*, to make metaphors about
> phenomenological experiences of space, and most importantly to play and
> entertain one another. The whole game comes to an end the minute we
> finally concatenate the *evaluation* function onto the end of our
> compositions.
> The entire notion of space collapses and we are left with a single number.
> To your comments on free/bound variables, I can interpret these bases as
> bindings for the underlying ring and the coefficients as representing free
> variables (do I have that right?).
>
> I don't have much to write that is specific to dependent types
> that would be all that different from the algebraic variety image,
> so let me jump next to there. Varieties are often described in terms
> of comprehension or inverse images. For instance in pseudo-Haskell
> I can write:
>
> conicVariety = [ (x,y,z) | (x,y,z) <- R3, x² + y² + z² == 1]
>
> Varieties as you can image get pretty nasty (singularities, cusps, etc..)
> This no doubt made the development of algebraic geometry much more
> treacherous than the study of manifolds, its tamer sibling. What is
> novel about the varieties like conicVariety above is that it can be
> understood in terms of sections. We can interpret the function above
> as asking for the collection of all triples which all map to 1, and
> when we do we have a fiber in hand. What is relevant here is the image
> that as we collapse states-of-affairs onto objects of designation,
> we get variety-like objects in the space of affairs. As conversants
> collaboratively build fibers over designations, they are constructing
> eidetic variations of concepts. Somehow in the sense of EricS, the
> collection of these variety-like concepts are personal and irreducible
> complexes of meaning.
>
> Jon
>
> ps. I will look up 'Dies the Fire'
> -- --- .-. . .-.. --- -.-. -.- ... -..-. .- .-. . -..-. - .... . -..-. .
> ... ... . -. - .. .- .-.. -..-. .-- --- .-. -.- . .-. ...
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