[FRIAM] Metaphor [POSSIBLE DISTRACTON FROM]: privacy games

[Jon Zingale]

Steve,

you write:
*I might instead say that the source domain of the metaphorical description
of "bent" or "curved" space IS the formal mathematical construction of "a
manifold"? *

What about Eddington's measurement or gravitational lensing? These both
appear situated in a phenomenological domain, and so we seem to have
another candidate domain for talking meaningfully about *bent* or *curved*
 space.
My preference is to grant that the metaphor maker has a domain in mind,
but one that I will only come to understand through investigation†. It is
perfectly acceptable to me that the metaphor maker intends a domain which
includes, but is not limited to, both phenomenological and mathematically
formal domains (say). Still, I suspect I am missing something important in
your emphasis on *apprehension.* Can you say a bit more about what you mean?

you write:
*Which I think is analogous or at least similar to Guerin's "least action
paths"?*

Yeah, I suspect so too. MacLane's book intentionally focuses on developing
Lagrangian and Hamiltonian mechanics. Mechanics, as far as I am concerned,
is the prototypical home for these ideas.

You write:
*feels a bit more to me like an "algebra of cliche's"?*

Thanks for that. Upon further reflection, I completely agree with you.

Jon

†) At the unintended risk of moving the conversation into the *meta*††,
I am including a link here to a page motivating the development of sheaves
<https://ncatlab.org/nlab/show/motivation+for+sheaves%2C+cohomology+and+higher+stacks#TheBasicIdeaOfSheaves>
.
In section 2 the author invents a game where he thinks up a space and the
player can query the author about how other spaces map into it.

†† *Meta* in that sheaves themselves offer a more flexible paradigm for
reasoning about generalized spaces than we get from manifold theory.
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