I was looking into the time complexity of matrix inversion algorithms. There is a table on Wikipedia: http://en.wikipedia.org/wiki/Computational_complexity_of_mathematical_operations#Matrix_algebra
They list 4 complexities
Gauss-Jordan elimination: O(n^3)
Strassen algorithm: O(n^2.807)
Coppersmith-Winograd algorithm: O(n^2.376)
Williams algorithm: O(n^2.373)
I'm curious where these numbers are coming from.
I've come across weird numbers in the bounds of approximation algorithms. There is an [ \alpha ]-approximation to MAX-CUT. People usually write [ \alpha=.878567 ], but there is a readable expression for it:
[ \alpha = \frac{2}{\pi} min_{0 \leq \theta \leq \pi}(\frac{\theta}{1-cos(\theta)}) ]
Is there a similar "readable expression" for these algorithms? I took a quick peek at the Virginia Williams' paper, but I quickly found myself over my head.
I'm currently listening to Lost Enlightenment, by S. Frederick Starr, a really wide ranging and accessible history of medieval central Asia, for anyone who's interested. I highly recommend it. I found the biography of Yaqub ibn-Layth al-Saffar particularly interesting. He seems like a fascinating man of the people and an exceptional military leader.
On realizing that his Saffarid dynasty was founded around 865, I figured he must be a playable character in the popular historical sim, Crusader Kings III. Indeed, he is. The game, which I also highly recommend, of course, starts in 867 just as Yaqub's Saffarid kingdom is at war with the Tahirid emirate to the north. I just started at the time of this writing but it should be a very fun campaign.
But shortly after starting the game, I noticed a curious little detail. For some reason, the developers at Paradox, had made me homosexual. In a game that focuses on dynastic inheritance and the siring of ever more and better offspring, that can add a bit of a fun challenge, but, I can't find out at all if it's historically accurate. It seems most sources make no mention of wives or children of al-Saffar, including Starr, who led me down this rabbit hole in the first place. I don't think that's very good evidence here, though. I'm left with several questions:
First, are there any known sources, friendly, hostile, or otherwise alleging that al-Saffar was gay?
More generally, what do we know about sexuality in medieval Afghanistan? Would the first question even be answerable in that context?
Most generally, does anyone have any thoughts on the running joke among some history enthusiasts (possibly including our friends at Paradox Interactive) that, "if a figure was never known to be in a heterosexual relationship, ipso facto homo?" It's obviously bad history, and bad critical thinking, but has it ever proved "accurate"? Or even just "useful"?
https://preview.redd.it/3no63yhhfpw71.jpg?width=1600&format=pjpg&auto=webp&s=66729c8030ef823fae3318e2f0f2cee96e2fae8e
The ERROR:
In 2014 and 2016, The Bureau of Engraving and Printing (BEP), printed series 2013 $1 Federal Reserve New York star notes from two facilities, Washington DC and Fort Worth. This, in itself is not unusual. The unusual part is they duplicated some serial numbers. There are dollar bills out there circulating with the same exact serial number as another dollar bill! The only difference is one bill has an indicator showing it was printed in Fort Worth, while the DC note does not. When the government does it it's legal, when WE do it it's called counterfeiting... LOL.
The PROJECT (prior and NEW)
In an attempt to help currency collectors find a matching pair of notes, Mr. Ed Zegers of Maryland and Mr. Karol Winograd of Florida started a project (known as the Zegers/Winograd project) of recording all the serial numbers submitted to them by fellow collectors. To date, there have been 9 matching pairs confirmed. The Zegers/Winograd project *ceased* maintaining the list in September 2021, but I have stepped in and carried on where they left off. For lack of a better name, I called it "Project 2013B".
https://project2013b.blogspot.com/2021/10/welcome.html
Let's get matched!
Please let fellow collectors know that the Zegers/Winograd project lives on under Project 2013B. There have been reports of collectors spending their 2013B star notes after hearing that Zegers/Winograd had stopped updating their list. A matched pair could be worth thousands of dolalrs, with one matched pair recently selling at auction for $7200! The new 'Project 2013B' website has an online form that allows you to submit the serial numbers of any 2013B star notes that you might have. When a match is found in the database, the two owners will be contacted, and they can then decide if they want to get the notes together to be auctioned off (or simply kept as part of a collection). It's worth at shot at $7200+ !
๐ต_(^ ฬฎ ^)/
Those who knew him best will remember him as a caregiver and friend.
Much of today's world hasn't reached the sleepy Texas shanty town where lifelong carpenter and 'Mr. Fixit' Coppersmith Dickinson spent his many years.
He is known perhaps just as well for his unusual name, which is said to have been attributed to a mislabeled hospital transfer form while being triaged as a infant. "S'was like a callin'" Coppersmith, or 'Big Smithy', said of the mistake. "Pa wrote his name where his profession 'spose to go and the best coppersmith aint gon lie"
Compounded by yet another unusual labeling mistake by local Texas pediatrics, and he was born to the world officially as 'Coppersmith Dickinson' and never let it bother him. In fact, he leaned into the unusual moniker and became a smiths apprentice at age 16.
"Smithin' coppers what a Coppersmith does. But it's not who I am. It may be my name and it may be my profession, but it aint who I am or what I do."
Sol Badguy, Gears, and modern magical contrivances have barely touched the rural farms of the Texas fringes where Coppersmith grew up. "Nothin' in that hill a' spice for me and mine. Bullets and a triggers' all I need for any of thems come a' callin. Think I take unintelligible and sip it back, I says."
A gifted soul with an equally blessed appetite, Coppersmith is survived by his two sons Ironron Dickinson, a sheriff in the 12th district of Neo New York, and Goldlewis Dickinson current Secretary of Absolute Defense of the United States.
Secretary Dickinson was on Capitol Hill this morning and glibly replied "It's not a big deal" when asked to comment on his father's death.
Be at peace Big Smithy. Hero of might and beef.
Helping currency collectors find a matching pair of series 2013B star notes with duplicate serial numbers. One matched pair was recently auctioned off for $7200
https://preview.redd.it/pffj6aanjpw71.jpg?width=500&format=pjpg&auto=webp&s=ef7327605987230d0c8014d084521e9f25445956
Project2013B: a project to connect people with matching 2013B star notes; potentially enriching them by up to an estimated $7,000 to $15,000!
" In 2014 & 2016 the Bureau of Engraving and Printing, the governmental body responsible for printing US currency, mistakenly printed two identical 6.4 million-note print runs of $1 bills. These bills were printed in two difference facilities located in Washington DC and Fort Worth, Texas. That means that there are 6.65 million pairs of bills with matching serial numbers, but are still legal tender.ย "
Check out the new project website at: https://project2013b.blogspot.com/2021/10/welcome.html
