Crumpled Manifolds

"The whole process of applying this complex geometric transformation to the input data can be visualized in 3D by imagining a person trying to uncrumple a paper ball: the crumpled paper ball is the manifold of the input data that the model starts with. Each movement operated by the person on the paper ball is similar to a simple geometric transformation operated by one layer. The full uncrumpling gesture sequence is the complex transformation of the entire model. Deep learning models are mathematical machines for uncrumpling complicated manifolds of high-dimensional data. [...] Our own understanding of images, sounds, and language, is grounded in our sensorimotor experience as humans -as embodied earthly creatures. Machine learning models have no access to such experiences and thus cannot 'understand' their inputs in any human-relatable way [...] this mapping is just a simplistic sketch of the original model in our minds, the one developed from our experience as embodied agents—it is like a dim image in a mirror."

- François Chollet (1989 - )

Seed Unfolding

"The One, perfect in seeking nothing, possessing nothing and needing nothing, overflows and creates a new reality by its superabundance. [...] The process is like the unfolding of a seed, moving from simple origin to termination in the world of sense, the prior always remaining in its place, while begetting its successor from a store of indescribable power - power that must not halt within the higher realm [...] but continue to expand until the universe of things reaches the limit of its possibility, lavishing its vast resources on all its creatures, intolerant that any one should have no share in it. Nothing is debarred from participation in the Good, to the extent of its receptivity. "

- Plotinus (c. 204/5 – 270 CE)
The Enneads

Tennyson's Flower

"Tennyson said that if we could understand a single flower we would know who we are and what the world is. Perhaps he meant that there is no deed, however so humble, which does not implicate universal history and the infinite concatenation of causes and effects. Perhaps he meant that the visible world is implicit, in its entirety, in each manifestation, just as, in the same way, will, according to Schopenhauer, is implicit, in its entirety, in each individual."

- Jorge Luis Borges (1899 - 1986)

Cosmic Observer

"In quantum mechanics...

an observation here and now changes in

 general the ‘state’ of the observed system...

I consider the unpredictable change
 of the state by a single observation...
to be an abandonment of the idea of
 the isolation of the observer from the
 course of physical events outside himself."

- Niels Bohr (1885 - 1962)

"The cosmos is within us.
We are made of star-stuff.
We are a way for the
universe to know itself."

- Carl Sagan (1934 - 1996)

To See Takes Time

"I made you take time to look at what I saw and when you took time to really notice my flower you hung all your associations with flowers on my flower and you write about my flower as if I think and see what you think and see--and I don't.

...

You paint from your subject, not what you see…I rarely paint anything I don’t know very well. It was surprising to me to see how many people separate the objective from the abstract. Objective painting is not good painting unless it is good in the abstract sense. A hill or tree cannot make a good painting just because it is a hill or a tree. It is lines and colors put together so that they say something. For me that is the very basis of painting. The abstraction is often the most definite form for the intangible thing in myself that I can only clarify in paint.

...

To see takes time, like to have a friend takes time."

-  Georgia O'Keeffe (1887 - 1986)

Enfolded Energy Fields

 "In all ages even among scientific men,
there can be discerned the urge to
apprehend the living form as such,
to grasp the connections of
their external visible parts; to
take them as intimations of inner
activity, and so to master, to some
degree, the whole in an intuition."

- Johann Wolfgang von Goethe (1749 - 1832)

Postscript. This image is of the garden peony that adorns the ground beneath our mail-box; more precisely, and paraphrasing Minor White, I should say that the image is what else the garden peony is. What you are "really" looking at is a digital-negative (i.e., wherein the white-to-black tonalities are reversed) of a zoomed-in portion of what started out being 1:1 macro shot of the folds-within-folds of petals inside a single peony flower. The distance from left to right is no more than about two inches. In my physicist's mind's eye, I see an undulating play of interpenetrating enfolded forms of some mysterious energy field; the same impression I get when gazing at Bruce Barnbaum's mesmerizing slit canyon abstracts. Images such as this also remind us that magical otherworldly realms are always near us, just waiting for our eye to discover.