Highly recommend looking at Jacob Barandes’ formulation of quantum mechanics as non-Markovian stochastic processes. It was the first introduction to quantum mechanics I could actually follow.
I never said LLMs will not be able to do X. I gave my summary of the article and my anecdotal experiences with LLMs. I have no LLM ideology. We will see what tomorrow brings.
For example, ever since the first GPT 4 I’ve tried to get LLM’s to build me a specific type of heart simulation that to my knowledge does not exist anywhere on the public internet (otherwise I wouldn’t try to build it myself) and even up to GPT 5.3 it still cannot do it.
But I’ve successfully made it build me a great Poker training app, a specific form that also didn’t exist, but the ingredients are well represented on the internet.
And I’m not trying to imply AI is inherently incapable, it’s just an empirical (and anecdotal) observation for me. Maybe tomorrow it’ll figure it out. I have no dogmatic ideology on the matter.
The headline may make it seem like AI just discovered some new result in physics all on its own, but reading the post, humans started off trying to solve some problem, it got complex, GPT simplified it and found a solution with the simpler representation. It took 12 hours for GPT pro to do this. In my experience LLM’s can make new things when they are some linear combination of existing things but I haven’t been to get them to do something totally out of distribution yet from first principles.
Well one could make the argument that Musk is a short or medium term problem and that in 4 years when Trump is gone everyone will forget about hating on Tesla and it will be a great car company again. Musk is in his 50s and won’t be CEO forever. So if your investment horizon is 10+ years and you don’t predict total company collapse then it might be a bargain time to buy.
That's not how it works for Tesla. Totally different buying experience. You order online, get a notification some days or weeks later that it's ready, go to the store sign a couple of documents and drive off with the car. Maybe 10 minutes total. (Source: bought a Tesla a few years ago). I just recently got a Kia EV9 and it was a 3-4 hour marathon of paperwork, talking, more paperwork. Really terrible buying experience. Nice car though.
I would argue that the main benefit of democracy is not electing "the right people" by a free and fair election, but by having a mechanism to remove bad leaders without violence. So a propaganda machine influencing elections is not ideal, but if it results in bad leaders, then that will become obvious to people at some point and they will vote them out. Elections will always have some random factors. Not everyone is going to vote. There will be fads. So election isn't the important part, UN-election is.
This is not medical advice, but I have used rapamycin for an as of yet undiagnosed autoimmune condition (likely psoriatic arthritis vs rheumatoid arthritis) and it almost completely cures the condition while taking it, at the cost of mild-moderate hair loss and acne (which recovers on cessation of the drug). I cycle on and off rapamycin every few weeks to minimize side effects and whatever unknown long-term risks.
I was obsessed with topological data analysis which is basically applied algebraic topology, so I read every paper I could find on TDA. All of them were mostly incomprehensible to me at first, but by working backward, e.g. "What's a homology group?" Oh I need to learn some basic group theory first. Oh what's a Cayley graph? I kept working backward and forward until I could piece it all together. Working backward from a specific goal was very motivating compared to just working through a textbook aimlessly.
Try finding a cool research paper that contains a lot of math you don’t understand. Then spend a few months learning the math in that one paper until you get it. That is a highly motivating and enjoyable way to learn. Far better than textbooks. I did this to learn algebraic topology.
https://www.jacobbarandes.com/