SymbolsPangaea

The story of Time and Symbols

[SymbolsPangaea @SymbolsPangaea]

The path followed by a "primes-observer" through space and time. Flower structure with 8 mirrored γ curves to show auto-correlation graphically. Fan fiction math series

[denis tremblay @denistremb34957]

I trust Bengio. I dont trust many people in the A.I. world.

[Martin Bauer @martinmbauer]

Almost as if they’re part of a single underlying field

In QFT, electrons are like notes played on the same guitar string. Pluck it twice and you might hear the same note louder, but you can’t tell which part of the vibration came from which pluck. They lost their individual identities

[Steven Strogatz @stevenstrogatz]

Why should we care whether humans still understand mathematics if AI can solve the problems for us? Fair question. But we can say this at least: Historically, understanding has been a route to predictive power — with enormous benefits for our lives.

https://t.co/44cUXi8sce

[SymbolsPangaea @SymbolsPangaea]

@stevenstrogatz Thank you! I remember when you posted this lecture as a video and it was a real treat!

[Steven Strogatz @stevenstrogatz]

Always a treat to go though the proof of Cauchy's integral formula!

[Steven Strogatz @stevenstrogatz]

Things are heating up on Terry Tao’s blog. In “If Math Is More Than Proof, We Need to Better Celebrate the Rest of It,” Grant Sanderson of @3blue1brown proposes “open exposition problems” -- rewarding the work of making math genuinely understandable.

https://t.co/zBOhhDNuNU

[Cliff Pickover @pickover]

“I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our ‘creations,’ are simply the notes of our observations.”

- G. H. Hardy,Mathematician’s Apology

[Mathelirium @mathelirium]

A coherent wave passes through two finite slits and the downstream field is rebuilt by a Huygens sum.

The filaments trace the probability current j = Im(ψ*∇ψ). The interference bands on detector grow from individual impacts sampled from |ψ|².

[Grant Sanderson @3blue1brown]

The last IMO problem AI could not solve.

For when you want to sit down for a longer problem-solving saga, here's the full video: https://t.co/bGlOv4YzVF

[Martin Bauer @martinmbauer]

Great choices!

[SymbolsPangaea @SymbolsPangaea]

@spacexfan_paul @Shaun_Fosmark @pickover Photon is a name we give to a modelled particle of light. They don't exist as conscious entities so talking about what they perceive seems odd. They traverse us, we perceive them as a mental model.

[SymbolsPangaea @SymbolsPangaea]

@pickover Mr Photon has the energy supply of the Big Drum

[Steven Strogatz @stevenstrogatz]

Marvelously instructive, for anyone who wants a visual, physical understanding of the recent Navier-Stokes (Millennium) singular solution.

[Mathelirium @mathelirium]

This is a Rubidium Rydberg wavepacket reshaped by an external electric field.

The electron is not shown as a particle. The surface represents regions of high probability density, |Ψ|², while the colours show the quantum phase, arg(Ψ).

[SymbolsPangaea @SymbolsPangaea]

Time creates atlases

[denis tremblay @denistremb34957]

Intelligence need only a finite physical body: be it LLM transformers CPU or a biological one. Consciousness need another kind of body. Consciousness imply a finite physical body linked to an infinite body. One die the other not.

[Emad @EMostaque]

Surely the most important question in alignment is aligned with who 🤔

[Joonas Nättilä @joonas_nattila]

Navier-Stokes Millennium saga continues. Here are my slides and a summary from a recent talk. Disclaimer: this is a physicists view of the problem & solution! 🧵

[Emad @EMostaque]

Day 3 dilemma

Another 3-5,000 word blog on something interesting or should I strip it back to 800-1,000 words for wider readership?

Should I discuss the equations of AI and get a bit technical or keep it high level and save equations for papers?