años rompiendo los huevos con que a la gente no hay que darle el pescado sino enseñarles a pescar y ahora te dicen que no necesitas saber que es un pez porque podés preguntarle a chatgpt
I want to talk about this Navier Stokes result for a minute because I see alot of people sharing it and not nearly enough people explaining it. A share for this one would be appreciated.
The Navier-Stokes equations are just Newton's second law of motion, F=ma, adapted for liquids and gases. Instead of tracking the acceleration of a solid object, the equations track how a bit of fluid moves, deforms, and flows as different forces push and pull on it. The reason these equations are so notorious, and the subject of a million dollar mathematics prize, is because of turbulence. Smooth, layered flow, or laminar flow, is relatively straightforward to calculate. But once the fluid speeds up and turns into a chaotic turbulence mess, the mathematics become incredibly non linear. The fluid's movement feeds back into itself, creating unpredictable, swirling eddies that become so complex you baisically need a super computer to simulate it.
Ok so what the hell is the millennium prize then?
The millennium prize is for proof that the equations can result in a singularity or what you see referred to as a "blow up". This is where the equations essentially go to infinity.
Ok so why doesnt your cup of tea blow up or turn into a singularity that swallows your house? The Navier Stokes prize isnt about proving that nature makes blow ups or singularities possible, its about proving the limitations of the model's mathematics.
Ok so why can a model allow for things we dont observe? This is THE SAME type of mathmatical allowance that general relativity gives when the model breaks down around black holes. The chance that a black hole is an actual singularity where everything goes to infinity is basically zero. Thats not how the universe actually works.
Ok so WHY is this possible in the model? The Navier Stokes equations assumes fluid is an infinitely divisible, perfectly smooth substance. In the math, you can zoom in forever, and it remains a continuous fluid. But that's NOT how a real fluid in reality is structured. Real fluids are made of discrete, individual molecules bumping into each other. Theres a real limit to how far you can zoom in. In the proof and the model it means that as a vortex shrinks and speeds up, it eventually gets smaller than the distance between individual water molecules. This cant happen in reality.
So the millennium prize isnt about finding if nature allows for infinite turbulence or eddies until a singularity forms, its about FINDING THE LIMITATION OF THE NAVIER STOKES EQUATIONS, proving global regularity false.
Ok so why all the drama with the Open AI solution? It used a method called "forcing". In the simulation they essentially used a continuous force to keep the vortex spinning faster and faster until it blows up, the vortex is smaller than the actual molecules that the fluid is made of. It goes to infinity in a time period that ISNT infinity. While the millennium prize doesnt specifically PROHIBIT forcing, most mathematicians would agree that they are specifically interested in the unforced proof, the spontaneous blow up. But that doesnt mean the result isnt legitimate.
I hope this clears up some of the misunderstanding.
NEVER FORGET THAT Charlie Kirk once said that “black people were better off in slavery and subjugation before the 1940’s” but right wing media love to say he just had opinions that liberals didn’t like
@ChrisMurphyCT From nukes to carbon emissions, any product that threatens human safety at a mass level can and should be regulated by a democratic body. Anyone who tells you that *their* dangerous product is exempt from this process is looking to gamble your safety for their profit
Science folk:
"First the intellectual property theft people came for the artists, and I cheered them on because I'm not an artist.
"Then they came for the scientists. I was livid, but was too late because I'd already cheered on the people committing intellectual property theft"
Terry Tao is probably the most measured, pro-AI mathematician on the planet - which makes this quote especially concerning to read. 😟
If sharing your hunches means getting scooped ~immediately without acknowledgement, then we're going to see not just math but all other science / engineering disciplines go dark.
No usen la IA para que les corrija sus textos, para que le dé "opiniones" sobre sus creaciones. No lo necesitan. Expongan sus textos, tus dibujos, muéstrenlos a alguien, hay humanización en esa retroalimentación. La IA no solo roba, te achata.
Hey, Mathematicians and Scientists:
This is exactly what happened to writers, artists and all creative professions.
Except we weren’t using any GenAj products. Our work was just stolen from us to power the machines.
GenAi Companies will exploit your labor too. Remember that.