The Digital Sand Reckoner

To see a World in a Grain of Sand

And a Heaven in a Wild Flower
Hold Infinity in the palm of your hand
And Eternity in an hour

— William Blake

dave_grad_schoolarchimedes
New scientific ideas never spring from a communal body, however organized,
but rather from the head of an individually inspired researcher
who struggles with his problems in lonely thought and unites all his thought
on one single point which is his whole world for the moment.
Max Planck

elkies_power_five_formula

Connecting precise physical relationships between the finites and the infinites.

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One Ring that Binds Them All

rings_that_bind

They were her boys.

And she revolutionized the way to they thought about things.

And she proved it.

No, not a physical proof, for there is no such thing.  But a Mathematical proof.  Ironclad, never changing — Well almost.

To imitate, but not too much, if our discipline is not to become a marsh, a large one to be sure, but stagnant, with neither life nor movement. First imitate to learn, and then renew ourselves. … I love, at least when I am able, to regard science from a personal point of view, and always, again when possible, go beyond current opinions and look at the problem from a new perspective. I have the impression that some ways must be left behind, some mental habits must be abandoned, if we are not to clip the wings of progress. Even to science we must sometimes repeat Charon’s cry: By another way, by other ports, not here, you will find passage across the shore. In my role as teacher I hope to be able to show you other ways, if not other ports. — Giuseppe Vitali

Emmy was a teacher too.  And she fabricated some mathematics that binds them all, as they sought their own passages and ports of call. The Rings that Bind.

For she had had obstacles and a vast ocean to cross in her own passage in life — she was able to reach another shore and dwell for only a short while.  But her perspective and rings will live on forever.

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Within the Edge of …

October 27, 1992

His voice was bubbly and full of enthusiasm: “You know it’s tantalizing.  — I feel I’m on the edge of something.”

That was last thing he said to his wife.

“In considering the relationship between the finite and the infinite, we are led to observe that the whole field of the finite is inherently limited, in that it has no independent existence. It has the appearance of  independent existence, but that appearance is merely the result of an abstraction of our thought.  We can see this dependent nature of the finite from the fact that every finite thing is transient…”

He had developed his own interpretation — a non-local hidden variable deterministic theory, the predictions of which agree perfectly with the nondeterministic quantum theory. His work and the EPR argument became the major factor motivating John Bell‘s inequality, the consequences of which are still being investigated. [Wikipedia, revised]

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