Intel supercomputer market share from 1993 to 2020
. Source. This graph is shocking, they just took over the entire market! Some good pre-Intel context at The Supermen: The Story of Seymour Cray by Charles J. Murray (1997), e.g. in those earlier days, custom architectures like Cray's and many others dominated. Steve Jobs customers don't know what they want quote by 
Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01
Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01TODO clear attribution source:
Some people say, "Give the customers what they want." But that's not my approach. Our job is to figure out what they're going to want before they do. I think Henry Ford once said, "If I'd asked customers what they wanted, they would have told me, 'A faster horse!'" People don't know what they want until you show it to them. That's why I never rely on market research. Our task is to read things that are not yet on the page.
Has as a double cover.
Maxwell's equations with pointlike particles by Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01
Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01In the standard formulation of Maxwell's equations, the electric current is a convient but magic input.
Would it be possible to use Maxwell's equations to solve a system of pointlike particles such as electrons instead?
The following suggest no, or only for certain subcases less general than Maxwell's equations:
This is the type of thing where the probability aspect of quantum mechanics seems it could "help".
This is a good approach. The downside is that while you are developing the implementation and testing interactively you might notice that the requirements are wrong, and then the tests have to change.
One intermediate approach Ciro Santilli likes is to do the implementation and be happy with interactive usage, then create the test, make it pass, then remove the code that would make it pass, and see it fail. This does have a risk that you will forget to test something, but Ciro finds it is a worth it generally. Unless it really is one of those features that you are unable to develop without an automated test, generally more "logical/mathematical" stuff. This is a sort of laziness Driven Development.
Author of gwern.net.
Accounts:He posts insanely much on these websites. It's a bit like Ciro Santilli on Stack Overflow.
- news.ycombinator.com/user?id=gwern
- www.lesswrong.com/users/gwern LessWrong
- twitter.com/gwern locked 2021: www.reddit.com/r/slatestarcodex/comments/kp2fek/does_anybody_know_what_happened_to_gwern/
- www.reddit.com/user/gwern/
- en.wikipedia.org/wiki/User:Gwern on Wikipedia. Self summary: gwern.net/wikipedia-resume. Also he is a critic of deletionism on Wikipedia like Ciro Santilli
Ciro Santilli envies this guy a bit. He dumps his brain more or less full time on his highly customized static website partly due to early Bitcoin investments gwern.net/me says:
Also unsurprisingly he likes Haskell:
I mostly contribute to projects in Haskell, my favorite language
Ciro Santilli considers Gwern Ciro Santilli's e-soulmates due to his interest in "dark web things" like Bitcoin and Silk Road, his immense writing output in encyclopedic book-sized articles on a static website, and his desire to live frugally and just research and write all day. Ah, if only Ciro had some old coins!!!
This is likely a pseudonym, his real name not being publicly unknown, e.g. at news.ycombinator.com/item?id=5659278:
Why do you choose relative anonymity?For the reasons I've said in the past. To which I can add personal safety: my Silk Road page is a bit questionable legally, and we all know that there are ways to exploit knowledge of one's True Name and address (even if, as far as I know, I have no enemies willing to resort to, say, 'swatting' me) - one group of stalkers called up a college they thought I worked at to see if they could get me fired or otherwise ruin my day.
Company with a semiconductor fabrication plant by Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01
Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01A list of fabs can be seen at: en.wikipedia.org/wiki/List_of_semiconductor_fabrication_plants and basically summarizes all the companies that have fabs.
Basically the opposite of security through obscurity, though slightly more focused on cryptography.
Open source scientific computing consultancies by Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01
Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01Huge respect to this companies.
Time-independent Schrödinger equation by Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01
Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01The time-independent Schrödinger equation is a variant of the Schrödinger equation defined as:
Equation 1.
Time-independent Schrodinger equation
. So we see that for any Schrödinger equation, which is fully defined by the Hamiltonian , there is a corresponding time-independent Schrödinger equation, which is also uniquely defined by the same Hamiltonian.
The cool thing about the Time-independent Schrödinger equation is that we can always reduce solving the full Schrödinger equation to solving this slightly simpler time-independent version, as described at: Section "Solving the Schrodinger equation with the time-independent Schrödinger equation".
Because this method is fully general, and it simplifies the initial time-dependent problem to a time independent one, it is the approach that we will always take when solving the Schrodinger equation, see e.g. quantum harmonic oscillator.
The wave equation contains the entire state of a particle.
From mathematical formulation of quantum mechanics remember that the wave equation is a vector in Hilbert space.
And a single vector can be represented in many different ways in different basis, and two of those ways happen to be the position and the momentum representations.
More importantly, position and momentum are first and foremost operators associated with observables: the position operator and the momentum operator. And both of their eigenvalue sets form a basis of the Hilbert space according to the spectral theorem.
When you represent a wave equation as a function, you have to say what the variable of the function means. And depending on weather you say "it means position" or "it means momentum", the position and momentum operators will be written differently.
This is well shown at: Video "Visualization of Quantum Physics (Quantum Mechanics) by udiprod (2017)".
Furthermore, the position and momentum representations are equivalent: one is the Fourier transform of the other: position and momentum space. Remember that notably we can always take the Fourier transform of a function in due to Carleson's theorem.
Then the uncertainty principle follows immediately from a general property of the Fourier transform: en.wikipedia.org/w/index.php?title=Fourier_transform&oldid=961707157#Uncertainty_principle
In precise terms, the uncertainty principle talks about the standard deviation of two measures.
We can visualize the uncertainty principle more intuitively by thinking of a wave function that is a real flat top bump function with a flat top in 1D. We can then change the width of the support, but when we do that, the top goes higher to keep probability equal to 1. The momentum is 0 everywhere, except in the edges of the support. Then:
- to localize the wave in space at position 0 to reduce the space uncertainty, we have to reduce the support. However, doing so makes the momentum variation on the edges more and more important, as the slope will go up and down faster (higher top, and less x space for descent), leading to a larger variance (note that average momentum is still 0, due to to symmetry of the bump function)
- to localize the momentum as much as possible at 0, we can make the support wider and wider. This makes the bumps at the edges smaller and smaller. However, this also obviously delocalises the wave function more and more, increasing the variance of x
Bibliography:
- www.youtube.com/watch?v=bIIjIZBKgtI&list=PL54DF0652B30D99A4&index=59 "K2. Heisenberg Uncertainty Relation" by doctorphys (2011)
- physics.stackexchange.com/questions/132111/uncertainty-principle-intuition Uncertainty Principle Intuition on Physics Stack Exchange
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