Recently in another topic I mentioned the "two bishops against two knights" chess endgame problem. I claimed it was investigated over two decades ago by a computer program and established that it is a win situation for the two bishops' side. Then I was unable to Google a solid reference for my claim.
I believe that subject to the ambiguity in what is meant by "a win situation for the two bishops", your recollection is correct.
The 6-piece pawnless endgames were were first analyzed systematically by Lewis Stiller starting in the late 1980s and reported in his papers in 1991 and 1992. The storage technologies available at this time meant that only summarized results could be saved, such as the longest win, and the total number of wins, draws and losses. I can't find these papers online, but the results also appear in Stiller (1995) and there's a summary of the state of the art in Thompson (1996).
For the KBBKNN ending Stiller only analyzed positions with the two bishops on opposite coloured squares (and I think with white to move), and reported that the longest win for white was 37 moves and the percentage of wins for white was 63%.You probably also want to note Stiller's caveat:
The percent-win can be misleading because of the advantage of the first move in a random position—White can often capture a piece in one move—and because it includes positions in which Black is in check.
So I think if you said "mostly a win for the two bishops from a random position with bishops on opposite-coloured squares, with the player with the bishops to move" that would be a fair summary of the facts.
Modern tablebases usually also include positions with the two bishops on the same colour square, so that analyses of these databases will give different results to Stiller. For example, according to Kirill Kryukov, the KBBKNN positions split like this:
With white (bishops) to move: 28429 losses, 885809752 draws (76%), 282912378 wins (24%)
With black (knights) to move: 54327970 losses (4%), 1247006005 draws (96%), 154105 wins
How could you have found this using Google? Well, it always helps to know of specialized databases to search (because the results tend to be of higher quality). I used Google Scholar to search for academic papers relevant to the keywords "6-piece chess endgame" and that returned Thompson (1996) as the first hit, and reading Thompson's summary of the state of the art led me to the Stiller papers. Of course, domain expertise is a big help too: I realised after discovering Stiller (1995) in the course of this search that I have a copy of this on my bookshelves.
References
What can I say - that this is the answer one can only wish. Bravo!
The information about this KBBKNN situation I've read around 1987, must have been a little deformed by that magazine. I've took them too seriously.
Now, I am going to investigate another piece I recall and I couldn't find it online until now. This time from the Science magazine sometimes during 1980's. The title I remember was "Never Out of Sorts".
The tables of contents for Science magazine are online. Looking through these might jog your memory. But there are quite a lot of issues.
Inside Google Scholar it is easy to find:
Baryon number conservation law ended
We suggest that baryon-number conservation may not be absolute ...
Off-topic from the post, but it fits with the title. SymbolHound is a new search engine for non-Google-able symbols, it was discussed on HackerNews a while back.
Would that be Hans Hermes, author of "Enumerability, Decidability, Computability", "Einführung in die Verbandstheorie", and others? It only took a few stabs to find that and many other references. Getting hold of the original books and papers (he wrote in German) may be more challenging, but of course he wrote before the internet, and despite Google's efforts, the day when every old book, journal, and newspaper has been scanned, OCR'd, indexed, and translated into all languages is not yet here. Some things are just not on the net.
Searching for "baryon conservation" yields 2910 results. You can't have been trying very hard. From a quick glance, baryon number is, so far, found to be conserved. Proton decay would violate it, has been theorised about and looked for, but has not been observed.
Here's another exercise for those wishing to test their search-fu: what can you find out about the Ion Brezoianu for whom a street in Bucharest is named? And how would you conduct the search? (I had a very boring and trivial reason for wanting to know this once; I found the dates of birth and death of someone I'm guessing to be the same person, but little more.)
what can you find out about the Ion Brezoianu for whom a street in Bucharest is named?
Apparently one of the men whose fame is ultimately based almost exclusively on a street named after them. Ion Brezoianu, 1817-1883, probably a moderately important figure in Romanian national revival. A pedagogue and author of a book called "Manualul mumelor". I was unable to quickly find what mumelor (or mume, which is the guessed singular nominative indefinite form) means. I am also a bit confused, because the street is called Strada actor Ion Brezoianu, but what I have found doesn't indicate he was an actor.
As for the method, I have searched for "Ion Brezoianu" -strada -nr -str to eliminate the overwhelming number of links to the street name, and after I have found the years of birth and death, I have included them into the search.
Skill and persistence are sometimes required for a successful Google search, so an unsuccessful search should necessarily not be taken as evidence of absence of online discussion of the topic.
You can restrict your google search to one site (e.g., I got this thread on the first page by googling hermes site:lesswrong.com).
For the first one, you may want to google "chess endgame database". First hit (using Ixquick, for me) is an online database where you can quickly confirm that 2 bishops vs. 2 knights is a draw (whereas K+B+B vs. K+N is won for the bishops).
I can't help you about the other two, but I think that searching more general terms might be better if you aren't certain how the professionals talk about the topic in question (e.g. "quantum number conversation").
that 2 bishops vs. 2 knights is a draw
There:
english.turkcebilgi.com/Bishop+(chess)
I found this:
Bishops generally gain in relative strength towards the endgame as more pieces are captured and more open lines are available for them to operate. When the board is empty, a bishop can influence both wings simultaneously, whereas a knight would need a few moves to do so. In an open endgame, a pair of bishops is decidedly superior to either a bishop and a knight, or to two knights. A player possessing a pair of bishops has a strategic weapon in the form of a long-term threat to trade down to an advantageous endgame.
If it's not Googleable, it's bingable.
Still not good enough.
Well, I was assuming you were talking about the pawnless endgame. For endgames with pawns, I guess there are far too much of them.
The late reverse engineer +Fravia has a site dedicated to the art of searching for things on the Internet. It started in the bad old days, before Google; but there's plenty there written in modern times. It includes tips like TrE's on finding a database dedicated to the niche you're interested in, and much more. The essay section is here.
Hermes set theory: Google gives me this for "hermes set theory" without any quotes, it looks relevant but I haven't read the PDF.
Googling "Baryon number conservation" gives me lots of relevant-looking results, including the wikipedia page for "baryon number" which has a section about conservation that includes a note and a link to another page about how they're not conserved due to "chiral anomalies"
Hermes is some other Hermes and the theory also.
For the "Baryon number conservation" I want to find "the law" which was probable for some time.
If you want to reference a solution to a chess problem, there are completely solved endgames online, e.g. http://chessok.com/?page_id=361
On this link of yours, for the KBB vs. KN the applet says - No data.
It also says "No data" for the K(A2) & N(D5) vs. K(G8) & B(G7) & B(F7). The latest is obviously wrong, since the N is just doomed no matter who moves first. And then we have the classic K vs. KBB situation.
I find TED talks are really hard to find, if you don't remember its exact title and/or speaker. The difficulty is that often you remember the basic idea, but not the keywords (since it might not be in a field you necessarily study).
So for example, you could think "Oh that one with the headband where they controlled the computer by thinking about it", but not know to search for BCI, or Brain-Computer Interfacing, if that's not your field. Searching for "controlling computer with thoughts" probably isn't going to get you anywhere either.
Besides that, I don't think their tags are all that comprehensive.
I don't think two bishops win vs two knights. Would be very surprised if they do. I think its a tie (except for relatively small number of special cases) It is the case though that king with 2 bishops vs king can always win, while king with 2 knights vs king can not (except rare special cases)
Recently in another topic I mentioned the "two bishops against two knights" chess endgame problem. I claimed it was investigated over two decades ago by a computer program and established that it is a win situation for the two bishops' side. Then I was unable to Google a solid reference for my claim.
I also remember a "Hermes Set Theory". It was something like ZFC, regarded as a valid Set Theory axiom system for 40 years, until a paradox was found inside. Now, I can't Google it out.
And then it was the so called "Baryon number conservation law", which was postulated for a short while in physics. Until it was found that a subatomic decay may in fact in/decrease the number of baryons in the process. I can't Google that one either.
Is that just me, or what?