In the video below, I tell a few more personal stories related to games. It could have started earlier about group games. As kids we were playing the 15 puzzle a lot. The 15 puzzle is remarkable as the god number 80 has only been computed a couple of years ago. I remember having played it when we were sitting in the back of our Citroen 2CV car, the “deux cheveaux” (a cool car by the way which could be cranked by hand if necessary, the picture to the left is closest what I could find to what we had). The 15 puzzle looked exactly as can be see to the right. Plastic red and white, sometimes the pieces were a bit hard to move. Of course, the algorithm we played was extremely cumbersome. I would just go line by line and order the pieces, increasing the stabilizer groups. By the way, also the car our family had, when I was a kid, then was cool. One could take off the roof for example. One could also take out the seats, which was handy for transportation or to take the seats out for a pick-nick. In winter, one would put snow chains on it. We would attach ropes and my father would drive us up the hill for skiing. I think you could also hand crank the window wishers if necessary. I love simplicity in anything, in technology, in computing, in mathematics, in life. Simplicity, Clarity, Generality. In military, we would have these small jeeps, which I could drive (as I was a tank driver), where it was also usually without rooftop (also that picture is closest to what I had in memory, it is a 1969 Swiss army jeep (I was in military in the 80ies). There is something nice about simplicity. Things are robust. You can fix it. you can improvise. We do not need a car here in Boston and I do everything by bike, also there I buy the simplest bikes, single gear, where I can replace any piece by myself. Having everything generic makes things affordable and predictable.
Here are some more personal stories and some liniks.: 1) Here is a note which emerged, while I had been a course assistant at the ETHZ. We were at that time a bit too ambitious for writing problem sets and asked the class to author a program which finds an algorithm of the Rubik using the Schreier-Sims algorithm. It would have been wiser to run that on a smaller group. I think it would be a great exercise for example for the floppy 3x3x1 Rubik, which is a group with only 192 elements. By the way, Roman Maeder had been important for me: he was a professor at ETH and also a member of the military cryptology group which met yearly for 3 weeks in some beautiful place in witzerland. Maeder would bring his Next computer which had Mathematica on it. I was still stuck with Atari computers at home or small pocket DOS machines (of course at ETH we had access to Sun workstations), which however could already use a modem and compile C programs. But the Next blew me away and I needed one for home. As we earned quite well as graduate students, I could shell out the 6000 dollars for the Next with Laser printer. The next survived not only my grad school but also Postdoc times. I had to toss it while still being intact while we were here in Arlington, around 2006. It had come with Mathematica installed. I have never again in my life been more excited about a computer than the Next. It was perfect. Only in recent years, OS X would become as reliable as the Next.
2) Here is a video from November 2021 in which Rubik appears. Earlier that morning , I had a bike accident (I had tried to push simplicity further and kicked in the “fixie” version on my bike. But while biking downhill and not being used to it, the pedals were spinning so fast that I could no more stop and fell. Broke 3 ribs: number 2,3,7, Prime ribs (as I would later find out. See the note from MtAuburn). I had a really painful fall semester. During the recording, I had already quite a bit of pain, as one can see. Here is the doctor note which explains the prime rib story.
3) My website about the Chinese Remainder Theorem from 2014. There would have been an other rather funny story about that project. I had written that paper in 2005 and still after more than 20 years, I think it is nice. At one point, I had to referee a paper with a similar proof for the mathematical monthly and pointed out my ArXiv version from 2012. The author then submitted it to an other journal, of course without mentioning my work. But I’m flattered that the topic at least could convince some other referee.Here are some notes [PDF] I wrote in high school, handwritten. I tells about my personal solution to the cube. I also discuss the 2x2x2x2 (hypercube case). My personal solution was very inefficient and I needed typically a minute. We tried to make things faster by oiling the cubes but this would only destroy the plastic. As I reported, my solution needed typically about a hundred turns which allowed to do it under a minute.
4) I could dig out some photo which features one of our Citroen cars during a bicycle race event “tour d’Uhwiesen”. Standing in front of the car is Matthias Ackeret (who organized this Tour d’Uhwiesen) and my father Marcus Knill, who drove the media car. Matthias Ackeret reported while standing in the car. The picture to the left (still on the same page) shows me in the middle. I was second rank. The race was 20 miles long. I tried to trace the route here. To the left is a newspaper clip. The winner had 58 minutes. I was close but still under an hour. This is not bad for a 1000 feet height difference, 20 miles route on traditional regular road bikes.
