> While playing solitaire to while away the time during rest, Ulam asked himself a straightforward question: what are the chances that a hand laid out with 52 cards will come out successfully? It is a deceptively challenging problem—there are around 8 × 10^67 ways to sort a deck of cards (a number approaching the estimated number of atoms in the observable universe). He wondered if instead of applying pure combinatorial calculations, which would be monstrously difficult, he could simply lay out the cards one hundred times and count the number of successful plays. Implicit was the assumption that each play started with randomized conditions.
Indeed, the best “results”, to this day, are still approximations based on brute-forcing a huge number of deals (aka, using Monte-Carlo.)
“The probability of being able to win a game of Klondike [Solitaire] with best-possible play is not known, and the inability of theoreticians to precisely calculate these odds has been referred to by mathematician Persi Diaconis as "one of the embarrassments of applied probability"” — https://en.wikipedia.org/wiki/Klondike_(solitaire)#Probabili...
“Here we show that a single general purpose Artificial Intelligence program, called “Solvitaire”, can be used to determine the winnability percentage of 45 different single-player card games with a 95% confidence interval of ± 0.1% or better. For example, we report the winnability of Klondike as 81.956% ± 0.096%” — https://arxiv.org/pdf/1906.12314v3 (2019)
More on HN here: https://news.ycombinator.com/item?id=42372083
I always completely forget that the metropolis-hastings algorithm is named after someone whose last name is actually Metropolis.
It never ceases to amaze me what an environment Los Alamos was for producing so much foundational research.
All/most of the US National labs are still incredibly productive at making big discoveries. I attribute it largely to the culture and organization system Ernest Lawrence set up during the Manhattan Project, which persists to this day- and of course generous funding.
Absolutely! I’ve gotten to work on some projects with folks from the labs - pretty much meaningless projects in the grand scheme of research going on there, but still feel proud to have done it and lucky to have worked with them.
They had some of the brightest minds in the world, thanks in part to the Nazi's rejection of "Jewish science".
> They had some of the brightest minds in the world, thanks in part to the Nazi's rejection of "Jewish science".
Indeed.
https://ahf.nuclearmuseum.org/scientist-refugees-and-manhatt...
However, the US didn't accept "Nazi science" when they accepted actual Nazis, because there's no such thing as Nazi science, any more than there is Jewish science; there is just science performed by individuals and groups, who may share a heritage, country, or culture, or may not.
https://en.wikipedia.org/wiki/Operation_Paperclip
Furthermore, it's unclear but some Nazis or Nazi sympathizers may have been leaking nuclear secrets from Los Alamos to Germany:
https://blog.nuclearsecrecy.com/2013/09/13/what-did-the-nazi...
Speaking of Jews involved in the project, Ethel Rosenberg's brother was working at Los Alamos on the Manhattan Project, and she and her husband were already working on behalf of the USSR as early as 1942.
https://en.wikipedia.org/wiki/Julius_and_Ethel_Rosenberg
> Rosenberg had been introduced to Semyonov by Bernard Schuster, a high-ranking member of the Communist Party USA and NKVD liaison for Earl Browder. After Semyonov was recalled to Moscow in 1944 his duties were taken over by Feklisov.
> Feklisov learned through Rosenberg that Ethel's brother David was working on the top-secret Manhattan Project at the Los Alamos National Laboratory; he directed Julius to recruit Greenglass.
> In February 1944, Rosenberg succeeded in recruiting a second source of Manhattan Project information, engineer Russell McNutt, who worked on designs for the plants at Oak Ridge National Laboratory. For this success Rosenberg received a $100 bonus. McNutt's employment provided access to secrets about processes for manufacturing weapons-grade uranium.
All of this is not to say that being Jewish or Gentile is a sign of scientific rigor or moral uprightness or lack thereof, but rather to say that "misery acquaints a man with strange bed-fellows," and that Nazis and Jews were both miserable, but in entirely different senses of the word, and that misery led to both astonishing atrocities and roses growing from concrete.
Almost all atomic spies were Jewish.
For example 13/15 on this list (exceptions are Klaus Fuchs, Alan Nunn May):
https://en.wikipedia.org/wiki/Atomic_spies#Notable_spies
Plus others, such as Ursula Kuczynski, Fuchs's handler:
I'm currently going through the Statistical Rethinking [0] class on Bayesian statistics, and it reminded me that Bayesian statistics' renaissance was basically thanks to Monte Carlo methods. Such methods can approximate posterior distributions that are often extremely difficult to calculate analytically.
I think we are on the cusp of another renaissance in Bayesian / MC methods - specifically, I think in some relatively short timespan (5 yrs? 10 yrs?), it’s reasonable to think that some new algorithms that are massively parallel at their core will break through. Whether it’s on the VI side or MCMC side or BO/GP side something totally new I don’t know, but it just feels like it is bound to happen eventually.
Big +1 for that textbook!
Also giving a +1 to the Bayesian Optimization/Gaussian Processes textbook [1] that came out last year - I mean 2 years ago - beautiful graphics and full PDF officially hosted.
[1] Garnett 2023, https://bayesoptbook.com/book/bayesoptbook.pdf
You seem to know quite a bit about Bayesian statistics; anywhere recommendations of reading material specifically about Bayesian inference applied on time series?
It has been a while since I read memoir, but as I recall he came to the US in 1939 to take up an appointment, not as fleeing anything.
"He would not even agree to being classified as a mathematician." That's a weird thing to write about someone who wrote an autobiography called "Adventures of a Mathematician".
Used widely in a nuclear engineering reactor simulator that was essentially a quadruple integral finite-element analysis program based on MC.
Particle physics experiments, such as the LHC, are simulated using an MC program call Geant (Giant). Various modules can be tweaked for new physics, and the signal/background statistics established for new decay signatures.
Yes, open source code and installers, so you too can simulate the LHC :)
Are most of the images on that page missing or is it just me?
They are missing (for me too). Unfortunately, they are also missing on the Internet Archive (https://web.archive.org/web/*/https://www.lanl.gov/media/pub...) :-(
The content.lanl.gov server is hanging indefinitely and never serving the images. So it seems the images should be there on the server, the server is just dead in a weird way.
I have emailed the journal and told them about the bug.
In the mean time, you can read it in the PDF version with images intact at https://cdn.lanl.gov/files/arq-2023-1_14f30.pdf#page=37 (mirrored: https://gwern.net/doc/statistics/probability/2023-summerscal... ).
Try searching for the captions. I think you can find all/most of them.