YouTube lecture on this by the discoverer, Ryan Williams
Ryan Willaims's paper, "Simulating Time With Square-Root Space
This appears to be based partly but largely on Tree Evaluation is in Space O(log n * log log n)" by James Cook and Ian Mertz (2023 colloqium, STOC 2024 conference).

I'm just a programmer who has spent an hour or so looking at this, so please take the rest of this post with a grain of salt.

I get the impression that Professor Williams's result so far, already a tool for making progress about which computational complexity classes are the same and different, has the limitation of relying on how slow Turing machines are at accessing memory, based on the mention at 18min:50sec into that YouTube Video of how the space savings degrades for a Turing machine with tapes of more than one dimension. If I understand correctly, for such Turing machines, an algorithm with running time bounded above by time T(n) for any input of length n, the space used by this potentially much slower space-saving simulation is bounded by O( ( T(n) + log T(n) ) ** ( 1 - (1/(D+1))) ). I'm using "**" as exponentiation, so the exponent means square root (that is, exponent 0.5) for a one dimensional (linear) tape, two thirds power (exponent 0.66...) for a tape that is a two dimensional surface, 0.75th power for a three dimensional tape, and, so far, no known savings for a tree shaped tape, although I suppose that that three dimensional limit does ultimately apply to real world data storage systems.

They're (weak) access control features. Secure at the transport level.

"and then had them write a safe landing program in FORTRAN."

Sigh

More seriously, I wonder if subways currently store some of that kinetic energy by putting the passenger platforms at a slightly higher elevation (not as deep in the ground) in comparison to the other portions of the track. If I have my math right, the kinetic energy of moving at 30 meters per second ( ~67 miles/hour) is approximately the potential energy of an elevation of 45 meters in 1 Earth gravity (0.5mv^2 = mgh --> 0.5v^2 = gh --> h=0.5v^2/g --> h = 0.5(30m/sec)^2/(10m/sec^2) = 45 m/sec). I imagine that that would be much too rollercoastery for a local train, and you wouldn't want to have the train fly off the track so easily for arriving a little too fast, but it wouldn't surprise me if a dip of a meter or two is engineered into subway lines for a bit of energy savings.

There is nothing about being a Republic that prevents a country from also being a Democracy. I'm sick of that false distinction. A Republic is a state whose head of state is not a monarch. A Democracy is a state whose government's authority derives from the people. A state can be one, both, or neither.

for computers that deliberately offer a server to the public. Do what you want to do with network topology, instead. If your computer offers a web server, why is it listening for anything other than HTTP requests on its public-facing interface? If its not listening for anything other than HTTP requests on its public-facing interface, what does the firewall do?

Not sure if that counts as a "tool", but I really don't think anyone uses them anymore. The Blue Pill and the Corrosive Sublimate are pretty much gone.

Some of the data itself is from the public record, but compiling all of it yourself would be prohibitively expensive. It would take many trips to various libraries, churches, courthouses, etc. in lots of far-flung places in different cities, states, and countries. And that's all before you start indexing, searching, copying, or scanning any records.

Then consider they're hosting all those billions of records, have developed decent software for both building family trees and documenting them with their database of sources, and continually improve their software and increase their database holdings. The only reason they can charge so little is the economy of scale based on their huge userbase.

For me it's mostly just a hobby. I love history to begin with, and my family history is specifically interesting to me personally. Finding out where my ancestors lived, what their lives would have been like, and why they immigrated to America is fascinating to me.

I've read that genealogy is the second most common hobby in America, after gardening. Of course, that depends on how a hobby is defined. I consider reading my favorite hobby. However, for some people, i.e. Mormons, genealogy has religious significance. That's why Salt Lake City, Utah is the biggest destination for many people doing genealogical research.

I've also read that, which really interests me. Don't you find it fascinating that your (or at least some modern Turks) ancestors possibly spoke Hittite or another Indo-European or even Semitic language? I recently paid for a genealogical DNA test, which will tell me more specifically where my ancestors came from. My paternal ancestors immigrated to America from Germany in the 1880s (then Prussia), but there are several clues which point to them actually being ethnically Lithuanian. The area where they lived has been part of Lithuania, Poland, Russia, and Germany in just the last few hundred years.

Actually, every person on the planet is descended from immigrants if you go back far enough.

Census records are released 72 years later, to be exact. Also, although the US Census isn't available until then, many state listings of much more recent births, marriages, divorces, and deaths are available.

Too much data is far more preferable than too little. Back in the old days, before many sources were available online, most searching had to be done by hand, paging through entire paper records until you found a possible match. The earliest online sources were often just indexes to paper records. It made it much easier to find the records, but then you still had to travel to a library, courthouse, church, etc. that might be in another state or even country.

The reason the algorithm is so promiscuous is that it's probably using Soundex to match names. That's a good thing though, as I've found some of my ancestors names spelled in lots of different ways.

Definitely agree, the anonymous reader didn't try very hard. And records for living people are necessarily scarce because of privacy issues.

Actually, just creating and editing your family tree on Ancestry is completely free. And there's no limit to the number of people, AFAIK. The paid service is just for accessing their database of sources and connecting with other users who might have overlapping family trees.

I pay for ancestry.com because they have a huge database of sources online, and probably the largest number of users out of any other family tree websites. It's much more convenient for me to search and view their literally billions of records from the comfort of my own home than going to my local library or LDS center. If I did that, I'd have to copy their records and scan them myself. Ancestry's already done the legwork for me. Also, since they have so many users, I've connected to several other people doing research along the same family lines, which saved my quite a bit of time.