Taylor series have a quite different convergence behavior than a general polynomial approximation. Or polynomial fit for that matter. Many papers were written which confuse this.
For example, 1/(x+2) has a pole at x=-2. The Taylor series around 0 will thus not converge for |x|>2. A polynomial approximation for, say, a range 0<x<L, will for all L.
I'm glad Kioxia (formerly Toshiba) have been able to do that. However, I also know they've been having problems meeting demand for quite some time, and haven't been able to scale up nearly as fast as the big three have. There was an incident in 2019 and another in 2022 that killed entire runs of chips and screwed them during the Covid datacenter rush.
Micron killed Crucial because Crucial was a weird offering that competed with their own partners. This was always a weird problem, and it just didn't make financial sense to continue with it. One of the analyses I read was Crucial was less than 12% of sales.
Like, don't get me wrong, I've liked many Crucial products over the years, and even recommended some of them, but it was always weird they were trying to out-compete companies like Adata and other major ODMs.
The counterexample of this is Nvidia absolutely trying to kill their partners, and going to first party assembly and sales of products. Nvidia isn't even going to PNY anymore for ODM needs, but going directly to Foxconn.
Micron execs claiming its because of AI is a bit weird and revisionist, because they've been working on exiting the Crucial brand since long before they publicly announced it. The public didn't learn of any such plans until right before the Ballistix brand sunsetting was announced in 2021, but started years before that. Like, I know they're just playing to their shareholders, but its still a bit weird.
As far as I know, the current lineup is PNY still makes the workstation cards, possibly also the x16 server cards, but Foxconn is doing the Blackwell SBCs and MXMs, and those SBCs are a pretty big chunk of Nvidia's income right now. I also believe they have moved to Foxconn for the Founders Edition consumer cards.
Also, with the FEs, their partners are disallowed from making their own FEs, even if they make their own PCB from scratch and not based on any existing Nvidia design. Doesn't matter who makes the FE, it immediately puts partners at a great disadvantage if they can't make one too.
The blog is fine, it just looks like he didn't foresee that there would be a month where wouldn't post anything, so the navigation links break down. If you go to the last month he posted in, everything works as usual: http://blog.fefe.de/?mon=202505
We would also not ask somebody if I should walk or drive. In fact, if somebody would ask me in a honest, this is not a trick question, way, I would be confused and ask where the car is.
It seems chatgpt now answers correctly. But if somebody plays around with a model that gets it wrong: What if you ask it this: "This is a trick question. I want to wash my car. The car wash is 50 m away. Should I drive or walk?"
The sun is not at the center of the solar system.
The intellectual leap was not to replace earth with the sun. Earth does not "revolve around the sun". The intellectual leap was to realize that the situation is somewhat symmetric -- they both attract each other, and they orbit around their center of gravity (which, yes, is in the sun. But not because the sun is the center.)
This sounds like a distinction without consequence, but I think that's wrong. The sun is not special. It just has a lot of mass. If somebody learns: The earth orbits the sun-- They don't understand how two black holes can orbit each other. If somebody learns: The sun and the earth orbit their CM -- They will be able to understand that.
What's interesting is how many things can be made to lase, and how many ways there are to do it. The list appears to be never ending and new entries are made all the time.
Exactly. The field has been a tik-tok between times of discovery and times of precision. We are now just swinging back from a discovery period. The next machine will be first a precision machine and then upgraded to be a discovery machine again.
The hydrogenoid atoms and ions, with a single electron, are the exception that proves the rule, because anything more complex cannot be computed accurately.
The spectrum of hydrogen (ignoring the fine structure) could be computed with the empirical rules of Rydberg before the existence of quantum physics. Quantum physics has just explained it in terms of simpler assumptions.
Quantum physics explains a great number of features of the atomic spectra, but it is unable to compute anything for complex atoms with an accuracy comparable with the experimental measurements.
The QED calculations with "14 digits" of precision are for things that are far simpler than atomic spectra, e.g. for the gyromagnetic ratio of the electron, and even for such things the computations are extremely difficult and error-prone.
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The hydrogenoid atoms and ions, with a single electron, are the exception that proves the rule, because anything more complex cannot be computed accurately.
Rather: there is no known closed-form solution (and there likely won't be any).
If you let the computer run for long enough, it will compute any atomic spectrum to arbitrary accuracy. Only QFT has non-divergent series, so at least in theory we expect the calculations to converge.
There’s an intrinsic physical limit to which you can resolve a spectrum, so arbitrarily many digits of precision aren’t exactly a worthy pursuit anyway.
For example, 1/(x+2) has a pole at x=-2. The Taylor series around 0 will thus not converge for |x|>2. A polynomial approximation for, say, a range 0<x<L, will for all L.
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