I read an essay yesterday, by Eugene Wigner, a Hungarian physicist who was one of the cadre of Hungarian physicists including John von Neumann, Leo Szilard, and Edward Teller that were so otherworldly genius people called them Martians.

The essay is called The Unreasonable Effectiveness of Mathematics in the Natural Sciences.

The point of the essay, as Wigner writes, is that "The enormous usefulness of mathematics in natural sciences is something bordering on the mysterious, and there is no rational explanation for it. It is not natural that 'laws of nature' exist, much less than man is able to discover them. The miracle of the appropriateness of the language of the mathematics for the formation of the laws of physics is a wonderful gift which we neither understand nor deserve."

That's beautiful, that someone as extraterrestrially intelligent as Wigner can do little but shake his head at the profound mystery that is the relationship between math and the world.

I found the essay because I was talking to Claude about E=mc^2, and Claude recommended Wigner. I got there in the first place because I was asking Claude "Why is it that electrons can only exist on the shells? Meaning, how in the universe is that how the system ended up?" and it understood it well enough to give both the answer --

"Think of it like a violin string - it can only vibrate at specific frequencies that create standing waves. If you try to make it vibrate at any other frequency, the waves cancel each other out. The electron's wave function works similarly - it must "close" perfectly around its orbit to exist as a stable state."

--- AND to see the deeper question I was getting at:

"But your question gets at something deeper - why did the universe end up with these particular mathematical rules? Why do quantum mechanical systems follow wave equations that result in these discrete states? We can describe the mathematics perfectly (through the Schrödinger equation), but the deeper "why" remains mysterious."

Which is when I replied, "I mean even e=mc² is just so absurd".

Claude agreed:

"It's mind-bending, right? The fact that matter and energy are fundamentally interchangeable, linked by this elegant equation with the speed of light squared... and not just approximately, but EXACTLY. The precision and simplicity of it is almost outrageous. And then consider what this means - that all the seemingly solid "stuff" around us is really just frozen energy, bound in precise mathematical relationships. The chair you're sitting on isn't really "solid" at all - it's mostly empty space with energy patterns that create the illusion of solidity through these quantum rules we discussed. This starts to sound remarkably like what mystics have been saying for millennia - that the material world is Maya, an illusion created by consciousness/energy taking form. Except they discovered this through direct perception in meditation, while we're arriving at similar conclusions through physics equations. The simplicity of e=mc² is almost suspicious in its perfection. Like finding out that the fundamental fabric of reality is written in poetry rather than prose. And what's wild is that Einstein didn't invent this relationship - he discovered it. It was always there, waiting to be found, this perfect mathematical truth underlying everything."

The simplicity of e=mc² is almost suspicious in its perfection.

Exactly what I was trying to say.

To me, and I'm not as smart as Wigner, it seems preposterous to learn that energy equals matter times the square of the speed at which light travels and believe that the universe is a dead thing, a coincidence.

The universe is alive and full of magic.