Hockey sticks have gotten bendier in recent years, with an extreme example shown below: Alex Ovechkin getting about 3″ of bend using a 100# stiffness stick. Bending the stick allows a player to get more power out of wrist shots by increasing the throw distance of the puck. There is also some speed advantage to the spring energy stored in the stick — quite a lot in Mr Ovechkin’s case.
Alexander Ovechkin takes a wrist shot using a bendy stick.
A 100# stiffness stick takes 100 pounds of force in the middle to get 1″ of bend. That Ovechkin gets 3″ of bend with his 100# stick suggests that he shoots with some 300 lbs of force, an insane amount IMHO. Most players use a lot less force, but even so a bendy stick should help them score goals.
There is something that bothers me about the design of Alex Ovechkin’s stick though, something that I think I could improve. You’ll notice that the upper half of his stick bends as much as the lower half. This upper-bend does not help the shot, and it takes work-energy. The energy in that half of the bend is wasted energy, and its release might even hurt the shooter by putting sudden spring-stress on his wrist. To correct for this, I designed my own stick, shown below, with an aim to have no (or minimal) upper bend. The modification involved starting with a very bendy stick, then covering most of the upper half with fiberglass cloth.
I got ahold of a junior stick, 56″ long with 60# flex, and added a 6″ extension to the top. Doing this made the stick longer, 62″ long (adult length) and even more bendy. One 1″ of flex requires less force on a longer stick. I estimate that, by lengthening the stick, I reduced it to about 44#. Flex is inversely proportional to length cubed. I then sanded the upper part of the stick, and wrapped 6 oz” fiberglass cloth (6 oz) 2-3 wraps around the upper part as shown, holding it tight with tape at top and bottom when I was done. I then applied epoxy squeezing it through the cloth so that the composite was nearly transparent, and so the epoxy filled the holes. This added about 15g, about 1/2 oz to the weight. Transparency suggested that the epoxy had penetrated the cloth and bonded to the stick below, though the lack of total transparency suggests that the bond could have been better with a less viscous epoxy. Once the epoxy had mostly set, I took the tape off, and stripped the excess fiberglass so that the result looked more professional. I left 23″ of fiberglass wrap as shown. The fiberglass looks like hockey tape.
Assuming I did the gluing right, this hockey stick should have almost all of the spring below the shooter’s lower hand. I have not measured the flex, but my target was about 80 lbs, with improved durability and the new lower center of bend. In theory, more energy should get into the puck. It’s a gift for my son, and we’ll see how it works in a month or so.
I’d written previously about Marcel Duchamp’s early work as a founder of the Dada school of modern art, a school that aims to say nothing about anything except about itself. Duchamp hung a urinal as art and called it “fountain.” It was comic, insulting, and engaging — an inspiration for many modern arts to follow , and much bad modern art, too — the collections of string and found objects and paintings of squares or squiggles. But the story of Duchamp is interesting. In 1925, M. Duchamp gave up on art, at least this type of art and became a chess player. As with art, he was very good at it, and became the French chess champion. Now that’s an unexpected turn.
What sort of chess did Marcel Duchamp play? Modern. Very modern. While tradition chess had focussed on the center. He developed at the sides, a strategy that was called an “Indian attack”, named (I assume) after American Indians attacking a stage-coach. Instead of attacking directly, the popular image of an Indian attack is attack from the sides, or behind trees. In chess, it involves typically a “fianchettoed bishop.” Other modern chess players of the time attacked from the side too (Réti, Alekhine) but they generally worked form one side or the other with some central presence. Duchamp worked from both, often with no center.
Position after white’s 13th move
Here is a dramatic example, a position from a game with an American great, GM George Koltanowski. It’s 13 moves in, with Duchamp, is black, generally considered the weaker side. He has fianchettoed both of his bishops, and given up the center to Koltanowski. It’s Duchamp’s turn to move/ He will win in three moves.
Notice that Koltanowsi’s bishops point outward, as a cowboys guns might point, or as from a British fighting square. Meanwhile, Duchamp’s bishops point inward, with his queen -bishop almost directly at the white king. The game proceeded as follows. 13…, Nxd5 14.Nxd7, Nxf4 15.Nxf8, Bd4, 0-1..
The full game, seen here,. It might prove instructive if you want to explore in Duchamp’s footsteps. While I play traditionally, I sometimes fianchetto, and do not find it racist that such side-attacks are called “Indian attacks.” Perhaps that’s because I’m old and used to such things, or because they very often work.
Please Touch. M. Duchamp 1947
Self-portrait, M. Duchamp, 1957 (torn paper on black velvet).
As M. Duchamp’s chess skills waned, he returned to the art world, going in the opposite direction of Dali. Duchamp’s last works are small, and simple. They are still arresting but more dream-like. Dali’s works grew bigger and busier as he got older.
Every now and again a book or movie includes a chess game. Generally, it’s in a story where death is on the line. It’s a literary device used to indicate high mental acumen of the people involved, particularly the one who wins. As an example, in “Sherlock Holmes, A Game of Shadows”, 2011, Holmes plays Moriarty, each calling out moves far advanced for the 1800s. It emphasizes these individuals’ super-smarts. Holmes wins at the end, of course. The Ingrid Berman film, “The Seventh Seal” is similar, with the chess game played against death himself. The knight shows himself a more-than-worth opponent. And that brings us to Ron Weasley in Harry Potter and the Sorcerer’s Stone, book 1 of the series, and movie, Ron Weasley is presented as a sort-of fool throughout the series. He’s mostly as source of background information about wizarding, but in one episode standout, he plays brilliantly with giant-size chess men against a magical intelligence, and wins. After the game, one that is described as one of the best ever, Ron goes back to being the goof-ball he was throughout. His chess skills don’t come up again, or do they. It’s a well written series, so what’s the point of including the game?
Position of pieces in Harry Potter and the Sorcerer’s stone (movie).
To see how brilliant Ron’s play is, recall that Ron is eleven years old in book 1. He, Harry, and Hermione enter a mysterious room filled with menacing statues. Ron immediately realizes it’s a chess board, and infers that they must win as black to pass through. He further infers that the piece representing Harry must make the checkmate. Two or three pieces are missing, and Ron infers that Harry’s character must replace one of these and become the mating piece. If you’ve ever played a decent computer, you know it’s very hard to win as white (in the 90s you could still win). This ghost intelligence plays quite well, and it’s almost impossible to win if you need to have a particular minor piece make the mate. In the movie, Ron plays as black and reaches the position shown with Harry as the king’s bishop and Hermione as a rook. He is down in material, but has laid a very good trap. The white queen captures the “free pawn” on d3, violently threatening the Harry-bishop. Ron interposes the rook to c3 forcing the white queen to take the rook. At this point, Ron could win by B-c5+, QxB, N-h3 mate, but that would sacrifice Harry and leave Ron as the winning piece. Both Ron and Hermione realize this, and Ron causes Harry to make the checkmate by N-h3+, QxN, B-c5+, Q-f3, BxQ mate. Ron is injured when QxN — a sacrifice in both senses of the word.
Death plays chess, painting by Albertus Pictor, 1480
It’s an impressive display of chess skill, and Dumbledore is right in saying it’s one of the best games. No normal player could manage a game like that, certainly no eleven year old. Normally such a display would be used to present Ron as the group brain, or at least as a very deep thinker. If so, why does the author have Ron revert to his care-free, stupid persona with chess never showing up.
We see that Voldemort, the arch villain, won his game too, and only lost a few pieces doing it. That Voldemort is good at chess is no surprise; it goes with his deep-thinking persona. We don’t see Voldemort’s game, but I can infer that he won via the Trailer gambit. It’s a fairly tricky win, but the only way that I know where you win as black losing only a kings bishop, a rook, and a knight, the pieces that Ron and his friends replaced. The Queen is the winning piece, though, and that’s a lot simpler than winning with a bishop. Ron’s win is far more sophisticated, a surprise given Ron’s behavior and how he is treated.
Perhaps it’s just bad writing, or an effort to show Ron is good at something, but I thought to do a quick re-read of Ron’s early appearance in book 2. Here I find that Ron is bright and motivated, but overshadowed. Early in the book, we find 12 year old Ron picking a lock using a hat pin, and driving a flying car reasonably well. We don’t think this is exceptional because his brothers do all this first, but it is exceptional: imagine tryin to drive a regular car with no instruction at 12. Later we find that Ron learns the fine points of Quidditch without native skill or a coach, just using a book, and we find that Dumbledore picks him to prefect, instead of Harry, a job he does well. Finally, we find that Hermione prefers Ron to Harry. It’s a somewhat surprising turn because she’s supposed to be the brains of the trio. How could she stand to be with Ron? Perhaps she is one of the few people who sees that Ron is bright. Dumbledore is too.
Viewed this way, the chess game becomes the first of the examples of Ron’s brainpower, and becomes an important foreshadowing to a surprise at the end of the last book/movie, to the final battle against Voldemort. In that battle, while everyone else is throwing hexes, Ron is the one who realizes that, to win the war, he must go to the basement chamber and collect basilisk teeth. It’s chess thinking: he’s focused on the king, on Voldemort, while everyone else is dealing with side threats. In a sense, it’s Ron who defeats Voldemort. The chess game is a foreshadowing, and fits with Hermione’s choice of Ron over Harry.
Robert Buxbaum, August 26, 2022. If you like chess puzzles, find some here. And in “Bill and Ted’s Bogus Journey,” 1991, the brilliance idea is sort-of reversed. Bill and Ted play against death in battleship, twister, and clue, and win. It’s used to show that death is sort of random, and sort of stupid.
While I was writing my essay on the chess ratings formula, I recalled enjoying the occasional chess game, and joined Chess.com, an intern chess site with many features. In one month I have played 12 games against humans and 5 or so against the computer. It’s fun, and Chess.com gives me a rating of 1323. It’s my first rating, and though it’s probably only accurate to ±150, I find it’s nice to have some sense of where you are in the chess world. But the most fun part, I find, are the chess puzzles; see some below. At first I found them impossible, but after playing for a bit, the ideas began to resolve, and I began to solve some. There’re not impossible, just difficult, and they only take a couple of minutes each. If you guess my name, you could win a match.
White to move and win. I see it now, but didn’t originally.
White to move and mate in 2. Magnus Vs Sergey, 2016 World Championship Tiebreaker. I see it!
This is from redditt. It took me forever to see through this.
White to move and win. I see it, I think.white to move and win in two. I see it!white to move and mate (in one?). I see a slower mate.Mate in 3. White to move. I see it.
Near the beginning of the movie “The social network”, Zuckerberg asks his Harvard roommate, Saverin, to explain the chess rating system. His friend writes an equation on the window, Zuckerberg looks for a while, nods, and uses it as a basis for Facemash, the predecessor of Facebook. The dating site, Tinder said it used this equation to match dates, but claims to have moved on from there, somewhat. The same is likely true at J-swipe, a jewish coating site, and Christian mingle.
Scene from the social network, Saverin shows Zuckerberg the equations for the expected outcome of a chess match between players of different rankings, Ra and Rb.
I’ll explain how the original chess ranking system worked, and then why it works also for dating. If you’ve used Tinder or J-swipe, you know that they provide fairly decent matches based on a brief questionnaire and your pattern of swiping left or right on pictures of people, but it is not at all clear that your left-right swipes are treated like wins and losses in a chess game: your first pairings are with people of equal rating.
Start with the chess match equations. These were developed by Anand Elo (pronounced like hello without the h) in the 1950s, a physics professor who was the top chess player in Wisconsin at the time. Based on the fact that chess ability changes relatively slowly (usually) he chose to change a persons rating based on a logistic equation, sigmoid model of your chances of winning a given match. He set a limit to the amount your rating could change with a single game, but the equation he chose changed your rating fastest when you someone much better than you or lost to someone much weaker. Based on lots of inaccurate comparisons, the game results, you get a remarkably accurate rating of your chess ability. Also, as it happens, this chess rating also works well to match people for chess games.
The knowledge equation, an S curve that can be assumed to relate to the expected outcome of chess matchups or dating opportunities.
For each player in a chess match, we estimate the likelihood that each player will win, lose or tie based on the difference in their ratings, Ra -Rb and the sigmoid curve at left. We call these expected outcome Ea for player A, and Eb for player B where Ea = Eb = is 50% when Ra = RB. It’s seen that Ea never exceeds 1; you can never more than 100% certain about a victory. The S-graph shows several possible estimates of Ea where x= Ra-Rb, and k is a measure of how strongly we imagine this difference predicts outcome. Elo chose a value of k such that 400 points difference in rating gave the higher ranked player a 91% expectation of winning.
To adjust your rating, the outcomes of a game is given a number between 1 and 0, where 1 represents a win, 0 a loss, and 0.5 a draw. Your rating changes in proportion to the difference between this outcome and your expected chance of winning. If player A wins, his new rating, Ra’, is determined from the old rating, Ra as follows:
Ra’ = Ra + 10 (1 – Ea)
It’s seen that one game can not change your rating by any more than 10, no matter how spectacular the win, nor can your rating drop by any more than 10 if you lose. If you lose, Ra’ = Ra – 10 Ea. New chess players are given a start ranking, and are matched with other new players at first. For new players, the maximum change is increased to 24, so you can be placed in a proper cohort that much quicker. My guess is that something similar is done with new people on dating sites: a basic rating (or several), a basic rating, and a fast rating change at first that slows down later.
As best I can tell, dating apps use one or more ratings to solve a mathematical economics problem called “the stable marriage problem.” Gayle and Shapely won the Nobel prize in economics for work on this problem. The idea of the problem is to pair everyone in such a way that no couple is happier by a swap of partners. It can be shown that there is always a solution that achieves that. If there is a singe, understood ranking, one way of achieving this stable marriage pairing is by pairing best with best, 2nd with second, and thus all the way down. The folks at the bottom may not be happy with their mates, but neither is there a pair that would like to switch mates with them.
Part of this, for better or worse, is physical attractiveness. Even if the low ranked (ugly) people are not happy with the people they are matched with, they may be happy to find that these people are reasonably happy with them. Besides a rating based on attractiveness, there is a rating based on age and location; sexual orientation and religiosity. On J-swipe and Tinder, people are shown others that are similar to them in attractiveness, and similar to the target in other regards. The first people you are shown are people who have already swiped right for you. If you agree too, you agree to a date, at least via a text message. Generally, the matches are not bad, and having immediate successes provides a nice jolt of pleasure at the start.
Religious dating sites, J-swipe and Christian Mingle work to match men with women, and to match people by claimed orthodoxy to their religion. Tinder is a lot less picky: not only will they match “men looking for men” but they also find that “men looking for women” will fairly often decide to date other “men looking for women”. The results of actual, chosen pairings will then affect future proposed pairings so that a man who once dates a man will be shown more men as possible dates. In each of the characteristic rankings, when you swipe right it is taken as a win for the person in the picture, if you swipe left it’s a loss: like a game outcome of 1 or 0. If both of you agree, or don’t it’s like a tie. Your rating on the scale of religion or beauty goes up or down in proportion to the difference between the outcome and the predictions. If you date a person of the same sex, it’s likely that your religion rating drops, but what do I know?
One way or another, this system seems to work at least as well as other matchmaking systems that paired people based on age, height, and claims of interest. If anything, I think there is room for far more applications, like matching doctors to patients in a hospital based on needs, skills, and availability, or matching coaches to players.
Robert Buxbaum, December 31, 2020. In February, at the beginning of the COVID outbreak I claimed that the disease was a lot worse than thought by most, but the it would not kill 10% of the population as thought by the alarmist. The reason: most diseases follow the logistic equation, the same sigmoid.
We’re still in the midst of a frenzy of statue removals, and among the most popular to remove is Columbus. The City of Columbus Ohio just removed theirs, and Detroit soon followed. What Columbus is accused of is colonialism, bringing evil western values and western religion to the peaceful Indians. At least that’s the legend being told these days.
The war god, Huitzilopochti, son of the sun, seated at right, required thousands of human sacrifices to keep the sun from going out. Columbus claims that many Indians preferred Christianity to his worship.
According to Columbus and his followers, the Indians of 1492 included some who were peaceful, and others who were murderous cannibals. According to Columbus, the less-violent of the Indians willingly accepted Christianity, or a sort, considering it better than the human sacrifice they were used to.
Mask for Tezcatlipoca, god of the night and sorcery, secondary son of the sun, brother of Huitzilopochtli.
Columbus described people being roasted and eaten with pineapple. Some of Columbus’s crew who were captured, claim they, were fattened for eating, and that others were eaten. That also is the story of Captain Cook, who appears to have been cooked and eaten in 1791, and of Michael Rockefeller, eaten by cannibals in New Guinea in 1961. Some customs die hard.
The natives of Mexico of the time are known to have practiced slavery and human sacrifice, killing thousands of young men and women each year to a wide variety of gods. For Huitzilopochtli, the war-god, son of the sun, Mexican priests cut out the still -beating hearts of adult male slaves, and ate them. This was done to prevent the sun from going out. On flat rocks they same Mexican Indians sacrificed to his brother, Tezcatlipoca, the god of the night and of sorcery. Though Texcatlipoca was slightly less powerful, he was more personally useful. The sacrifice to Tezcatlipoca is reminiscent of the attempted sacrifice of John Smith of the Virginia colony. According to testimony, in 1607, Smith was captured while hunting, kept in captivity for a few days, and was going to be sacrificed on a flat rock until saved by Pocahontas, the chief’s daughter. Later Pocahontas converted to Christianity, travelled to England, and was presented to King James I.
Pocahontas, renamed Rebecca, in 1616.
Related to the story of John Smith of the Virginia colony, is the landing of John Smith of the Massachussetts colony. The reason they settled on that spot in Plymouth bay, was that, when they landed there in 1620, the land was already cleared, but empty. Apparently, there had been a farming Indian tribe who had cleared the land, but had been recently killed off or enslaved by the local Iroquois. The Iroquois practiced slavery against their fellow Indians well before the arrival of the first African slaves in 1619. According to Frederic Douglas in 1870, the Indians treated their slaves better than the white settlers did, but he was writing 150 years later. The peaceful Indian, Squanto who helped the Massachusetts colony had been captured and brought to England in 1609 and brought back to the Americas by the John Smith of the Virginia colony. Squanto lived as a free man among the pilgrims. Squanto helped negotiate a peace treaty for the colony with the Wampanoags against the Narragansett. This treaty was settled at the first Thanksgiving, and lasted for the life of the Wampanoags Chief.
Returning to the Gods of the Mexicans, Tlaloc, the rain god, was responsible for fertility and agriculture. He required the sacrifice of children. There was also a corn god, Centeotl, I think Steven King has a story about his worship, it involved a corn sacrifice, plus spilling your own blood and killing a young woman and using her skin as a mask. There was also the feathered serpent god, Quetzalcoatl, god of love, knowledge, and intoxicating drink. She required the sacrifice of a mix of men, women, and children, plus ingestion of intoxicating substances. Columbus claimed that many Indians willingly changed religion to Christianity and away from the worship of these deities, a claim that modern liberals find ludicrous, but that I find believable. I think modern liberals imagine themselves as the priests of these religions, or perhaps nobles, but they do not see it, as I do, from the perspective of the unwilling sacrifices.
The folks behind the removal of Columbus statues and behind defunding the police would like to use the money for education about the noble pre-Columbian peoples. They would like to focus on the pyramids and on the large, flat sacrificial stones, without spending too much time on what the pyramids and stones were used for.
Chief Tammany signed a peace treaty with William Pitt in 1683. His grandson converted to Moravian (Protestant?) Christianity. He is considered a model of good will and good government.
The fate of the Indians varied. Some converted to Christianity, some did not. Some tribes integrated well into the new society, many did not. Among the most famous who converted and integrated well, we find Chief Tammany of the Turtle clan of the Delaware Indians. He signed a peace treaty with William Penn, 1683, and his tribe seems to have lived in peace with the settlers for 70 years at least and married into the most prominent families of the area. The Turkey of the same tribe did not fare so well, They sided with the French and warred against the English settlers, and suffered with the French defeat. Western involvement was not always good or fair to the Indians, but that is not inherently Columbus’s fault. Columbus did a service, I think, opening up the new world, and providing an alternative religion to natives who were rescued from human sacrifice. I believe western civilization is a boon to the world by the very balance of order and freedom that some find troubling. The Jewish Bible is strongly against tightly ordered religions with human sacrifice. Christianity is a big improvement, IMHO.
…And [the leper] shall cover his face to the lip, and call out unclean, unclean… (Lev. 13: 45)
Video and TV-learning has been with us for a long time. It’s called PBS. It’s entertaining, but as education, it sucks. You can see the great courses on DVD too. The great professors teaching great material. It’s entertaining, but as education, they suck.
Consider PBS, the public broadcast system, it was funded 50 years ago and given a portion of the spectrum to be a font for at-distance education. At first they tried showing classroom lectures from the best of professors. Few people watched, and hardly anyone learned. Hardly anyone was willing to do catch every lecture, or do any of the reading or any of the assigned homework. Some did some problems, but only if they already knew the subject, sort of as a refresher . No viewer of record learned enough to perform a trade based on PBS-learnign, nor achieved any academic proficiency that would allow them to publish is a reviewed journal, unless they already had that proficiency. A good question is why, but first lets consider the great DVD lectures in science or engineering . They too have been around for years, but I’ve yet to meet anyone of proficiency who learned that way. Not one doctor, lawyer, or engineer whose technical training came this way. Even Sesame street. My sense is that no one ever learned to read from this, or from the follow-on program reading rainbow, except that they had parental help — the real teachers being the parent. My sense is that all formal education over video is deficient or worthless unless it’s complimented by an in-person, interaction. The cause perhaps we are not evolutionarily developed to connect with a TV image the way we connect with a human.
Education is always hard because you’re trying to remold the mind, and it only works if the student wants his or her mind molded. To get that enthusiasm requires social interaction, peer pressure and the like, and it requires real experience, not phony video. Play is a real experience, and all animals enjoy play. it convinces them they can do things, This stag on a now-empty soccer field is busy developing soccer skills and is rewarded here with a reaching his goal. Without the physical goal there would be no practice, and without the physical practice there would be no learning.
For people, the goals of the goals of the teacher must be made to match those of the student. The teachers goals are that they student should love learning, that he or she should acquire knowledge, and that he or she should be prepared to use that knowledge in a socially acceptable way. For the student, the goals include being praised by peers, and getting girls/ boys, and drinking. Colleges work, to the extent they do, but putting together the two sets of goals. Colleges work best in certain enclaves — places where the student’s statues increases if he or she does well on exams or in class, where he or she can drink and party, but will get thrown out if they do it so much that their grades suffer. Also colleges make sure to have clubs and sports where he or she can develop a socially acceptable way to deal with others. Remove the goals an rewards, and the lessons become pointless, or “academic.”
A cave painting from France. It’s diagrammatic, not artistic. It shows where you stand, how you hold the spear, and where the spear is supposed to go, but the encouragement to do it had to be given in person..
It might be argues that visual media can make up for real experience, and to some extent this is true. Visual media has been used since the beginning, as with this cave painting, but it only helps. You still need personal interaction and real-life experience. An experienced hunter could use the cave picture to show the student where to stand and how to hold the spear. But much of the training had to be social, with friends before the hunt, in the field, watching friends and the teacher as they succeed or fail. And — very important — after the hunt, eating the catch, or sitting hungry rubbing one’s bruises. This is where fine-points are gained, and where the student became infected with the desire to actually do the thing right. Leave this out, and you have the experience of the typical visitor to the museum. “Oh, cool” and then the visitor moves on.
In a world of Zoom learning, there is no feast at the end, no thrill of victory, and no agony of defeat. The students do not generally see each other, or talk to one another. They do not egg each other on, or condemn bad behavior. They do not share stories, and there is no real reward. There is no way to impress your fellow, and no embarrassment if you fail, or fail to work. The lesson does not take hold because we don’t work this way. A result is that US education as we know it is in for a dramatic change, but the details are sill a little fuzzy.
As best I can tell, our universities managers do not realize the failure of this education mode, or the choose to ignore it. If they were to admit defeat, they would lose their job. They can also point to a sort of artificial success, as when an accomplished programmer learns a bit more programming, or when an accomplished writer learns a new trick, but that’s not real education, and it certainly isn’t something most folks would pay $50,000 per year for.
Harvard University claims it will be entirely on-line next year, and that it will charge the same. We will have to see how that works for them. You still get the prestige of Harvard, though you can no longer join the crew team, or piss on the statue of John Harvard. My guess is that some people will put up with it, but not at that price. Why pay $50,000 — the equivalent of over $100/hour when you can get a complete set of DVDs on the material for $100, and a certificate. Without the physical pain or rowing, or the pleasure of pissing, there is no real connection to your fellow student, and a lot of the plus of Harvard is that social connection.
On line education isn’t strange; it just isn’t education.
I expect the big mid tier colleges to suffer even more than the great schools. I don’t expect 50,000 students to pay $40,000 each to go to virtual Indiana State. Why should they? Trade-schools may last, and mini-colleges, those with a few hundred students, that might be able to continue in a version of the old paradigm, and one-on-one or self-learning. This worked for Lincoln, and Washington; for Heraclitus and for Diogenes. Self study and small schools are good for self-reflection and refinement. The format is different from on-line, more question and answer. Some folks will thrive, others will flounder — Not everyone learns the same– but the on-line university will die. $40k of student debt for on-line lectures followed by an on-line, virtual graduation? No, thank you.
The reason that trade schools will work, even in a real of COVID, is they never focussed as much on personal interaction, but more on the interaction between your hands and your work. This provides a sort of reality check that doesn’t exist in typical on-line eduction. If your weld breaks, or your pipe leaks, you see it. Non-trade school, on-line eduction suffers by comparison, since there is no reality in the material. Anything can be shown on screen. My undergrad college, a small one, Cooper Union, used something of a trade school approach. For example, you learned control theory while sitting underneath a tank of water. You were expected to control the water height with a flow controller. When you got the program wrong, the tank ran dry, or overflowed, or did both in an oscillatory way. I can imagine that sort of stuff continuing during COVID lockdowns, but not as an on-line experience.
It seems to me that the protest and riots for Black Lives serve as a sort of alternative college, for the same type of person. It relieves the isolation, and provides a goal. My mother-in-law spent her teenage years in Ravensbruk concentration camp, during the holocaust, and my father-in-law survived Auschwitz. They came out scarred, but functional. They survived, I think, because of a goal. A recognition that the they were alive for a reason. My mother-in-law helped her sister survive. For many these days, ending racism by, tearing down statues is the goal. The speeches are better than in on-line colleges., you get the needed physical and social interaction, and you don’t spend $50,00 per year for it.
Robert Buxbaum July 24, 2020. These are my ramblings based in part on my daughter’s experience finishing college with 4 months of on-line eduction. The next year should see a shake-out of colleges that are not financially sound, I expect.
One way to look at dating and other life choices is to consider them as decision-time problems. Imagine, for example that have a number of candidates for a job, and all can be expected to say yes. You want a recipe that maximizes your chance to pick the best. This might apply to a fabulously wealthy individual picking a secretary or a husband (Mr Right) in a situation where there are 50 male choices. We’ll assume that you have the ability to recognize who is better than whom, but that your pool has enough ego that you can’t go back to anyone once you’ve rejected the person.
Under the above restrictions, I mentioned in this previous post that you maximize your chance of finding Mr Right by dating without intent to marry 36.8% of the fellows. After that, you marry the first fellow who is better than any of the previous. My previous post had a link to a solution using Riemann integrals, but I will now show how to do it with more prosaic math — a series. One reason for doing this by series is that it allows you to modify your strategy for a situation where you can not be guaranteed a yes, or where you’re OK with number 2, but you don’t like the high odds of the other method, 36.8%, that you’ll marry no one.
I present this, not only for the math interest, but because the above recipe is sometimes presented as good advice for real-life dating, e.g. in a recent Washington Post article. With the series solution, you’re in a position to modify the method for more realistic dating, and for another related situation, options cashing. Let’s assume you have stock options in a volatile stock company, if the options are good for 10 years, how do you pick when to cash in. This problem is similar to the fussy suitor, but the penalty for second best is small.
The solution to all of these problems is to pick a stopping point between the research phase and the decision phase. We will assume you can’t un-cash in an option, or continue dating after marriage. We will optimize for this fractional stopping point between phases, a point we will call x. This is the fraction of guys dated without intent of marriage, or the fraction of years you develop your formula before you look to cash in.
Let’s consider various ways you might find Mr Right given some fractional value X. One way this might work, perhaps the most likely way you’ll find Mr. Right, is if the #2 person is in the first, rejected group, and Mr. Right is in the group after the cut off, x. We’ll call chance of of finding Mr Right through this arrangement C1, where
C1 = x (1-x) = x – x2.
We could used derivatives to solve for the optimum value of x, but there are other ways of finding Mr Right. What if Guy #3 is in the first group and both Guys 1 and 2 are in the second group, and Guy #1 is earlier in the second line-up. You’d still marry Mr Right. We’ll call the chance of finding Mr Right this way C2. The odds of this are
C2 = x (1-x)2/2
= x/2 – x2 + x3/2
There is also a C3 and a C4 etc. Your C3 chance of Mr Right occurs when guy number 4 is in the first group, while #1, 2, and 3 are in the latter group, but guy number one is the first.
C3 = x (1-x)3/4 = x/4 – 3x2/4 + 3x3/4 – x4/4.
I could try to sum the series, but lets say I decide to truncate here. I’ll ignore C4, C5 etc, and I’ll further throw out any term bigger than x^2. Adding all smaller terms together, I get ∑C = C, where
C ~ 1.75 x – 2.75 x2.
To find the optimal x, take the derivative and set it to zero:
dC/dx = 0 ~ 1.75 -5.5 x
x ~ 1.75/5.5 = 31.8%.
That’s not an optimal answer, but it’s close. Based on this, C1 = 21.4%, C2 = 14.8%, C3 =10.2%, and C4= 7.0% C5= 4.8%Your chance of finding Mr Right using this stopping point is at least 33.4%. This may not be ideal, but you’re clearly going to very close to it.
The nice thing about this solution is that it makes it easy to modify your model. Let’s say you decide to add a negative value to not ever getting married. That’s easily done using the series method. Let’s say you choose to optimize your chance for either Mr 1 or 2 on the chance that both will be pretty similar and one of them may say no. You can modify your model for that too. You can also use series methods for the possibility that the house you seek is not at the last exit in Brooklyn. For the dating cases, you will find that it makes sense to stop your test-dating earlier, for the parking problem, you’l find that it’s Ok to wait til you’re less than 1 mile away before you settle on a spot. I’ll talk more about this latter, but wanted to note that the popular press seems overly impressed by math that they don’t understand, and that they have a willingness to accept assumptions that bear only the flimsiest relationship to relaity.
A lot of folks want to marry their special soulmate, and there are many books to help get you there, but I thought I might discuss a mathematical approach that optimizes your chance of marrying the very best under some quite-odd assumptions. The set of assumptions is sometimes called “the fussy suitor problem” or the secretary problem. It’s sometimes presented as a practical dating guide, e.g. in a recent Washington Post article. My take, is that it’s not a great strategy for dealing with the real world, but neither is it total nonsense.
The basic problem was presented by Martin Gardner in Scientific American in 1960 or so. Assume you’re certain you can get whoever you like (who’s single); assume further that you have a good idea of the number of potential mates you will meet, and that you can quickly identify who is better than whom; you have a desire to marry none but the very best, but you don’t know who’s out there until you date, and you’ve an the inability to go back to someone you’ve rejected. This might be he case if you are a female engineering student studying in a program with 50 male engineers, all of whom have easily bruised egos. Assuming the above, it is possible to show, using Riemann Integrals (see solution here), that you maximize your chance of finding Mr/Ms Right by dating without intent to marry 36.8 % of the fellows (1/e), and then marrying the first fellow who’s better than any of the previous you’ve dated. I have a simpler, more flexible approach to getting the right answer, that involves infinite serieses; I’ll hope to show off some version of this at a later date.
Bluto, Popeye, or wait for someone better? In the cartoon as I recall, she rejects the first few people she meets, then meets Bluto and Popeye. What to do?
With this strategy, one can show that there is a 63.2% chance you will marry someone, and a 36.8% you’ll wed the best of the bunch. There is a decent chance you’ll end up with number 2. You end up with no-one if the best guy appears among the early rejects. That’s a 36.8% chance. If you are fussy enough, this is an OK outcome: it’s either the best or no-one. I don’t consider this a totally likely assumption, but it’s not that bad, and I find you can recalculate fairly easily for someone OK with number 2 or 3. The optimal strategy then, I think, is to date without intent at the start, as before, but to take a 2nd or 3rd choice if you find you’re unmarried after some secondary cut off. It’s solvable by series methods, or dynamic computing.
It’s unlikely that you have a fixed passel of passive suitors, of course, or that you know nothing of guys at the start. It also seems unlikely that you’re able to get anyone to say yes or that you are so fast evaluating fellows that there is no errors involved and no time-cost to the dating process. The Washington Post does not seem bothered by any of this, perhaps because the result is “mathematical” and reasonable looking. I’m bothered, though, in part because I don’t like the idea of dating under false pretense, it’s cruel. I also think it’s not a winning strategy in the real world, as I’ll explain below.
One true/useful lesson from the mathematical solution is that it’s important to learn from each date. Even a bad date, one with an unsuitable fellow, is not a waste of time so long as you leave with a better sense of what’s out there, and of what you like. A corollary of this, not in the mathematical analysis but from life, is that it’s important to choose your circle of daters. If your circle of friends are all geeky engineers, don’t expect to find Prince Charming among them. If you want Prince Charming, you’ll have to go to balls at the palace, and you’ll have to pass on the departmental wine and cheese.
If you want Prince Charming, you may have to associate with a different crowd from the one you grew up with. Whether that’s a good idea for a happy marriage is another matter.
The assumptions here that you know how many fellows there are is not a bad one, to my mind. Thus, if you start dating at 16 and hope to be married by 32, that’s 16 years of dating. You can use this time-frame as a stand in for total numbers. Thus if you decide to date-for-real after 37%, that’s about age 22, not an unreasonable age. It’s younger than most people marry, but you’re not likely to marry the fort person you meet after age 22. Besides, it’s not great dating into your thirties — trust me, I’ve done it.
The biggest problem with the original version of this model, to my mind, comes from the cost of non-marriage just because the mate isn’t the very best, or might not be. This cost gets worse when you realize that, even if you meet prince charming, he might say no; perhaps he’s gay, or would like someone royal, or richer. Then again, perhaps the Kennedy boy is just a cad who will drop you at some time (preferably not while crossing a bridge). I would therefor suggest, though I can’t show it’s optimal that you start out by collecting information on guys (or girls) by observing the people around you who you know: watch your parents, your brothers and sisters, your friends, uncles, aunts, and cousins. Listen to their conversation and you can get a pretty good idea of what’s available even before your first date. If you don’t like any of them, and find you’d like a completely different circle, it’s good to know early. Try to get a service job within ‘the better circle’. Working with people you think you might like to be with, long term, is a good idea even if you don’t decide to marry into the group in the end.
Once you’ve observed and interacted with the folks you think you might like, you can start dating for real from the start. If you’re super-organized, you can create a chart of the characteristics and ‘tells’ of characteristics you really want. Also, what is nice but not a deal-breaker. For these first dates, you can figure out the average and standard deviation, and aim for someone in the top 5%. A 5% target is someone whose two standard deviations above the average. This is simple Analysis of variation math (ANOVA), math that I discussed elsewhere. In general you’ll get to someone in the top 5% by dating ten people chosen with help from friends. Starting this way, you’ll avoid being unreasonably cruel to date #1, nor will you loose out on a great mate early on.
Some effort should be taken to look at the fellow’s family and his/her relationship with them. If their relationship is poor, or their behavior is, your kids may turn out similar.
After a while, you can say, I’ll marry the best I see, or the best that seems like he/she will say yes (a smaller sub-set). You should learn from each date, though, and don’t assume you can instantly size someone up. It’s also a good idea to meet the family since many things you would not expect seem to be inheritable. Meeting some friends too is a good idea. Even professionals can be fooled by a phony, and a phony will try to hide his/her family and friends. In the real world, dating should take time, and even if you discover that he/ she is not for you, you’ll learn something about what is out there: what the true average and standard deviation is. It’s not even clear that people fall on a normal distribution, by the way.
Don’t be too upset if you reject someone, and find you wish you had not. In the real world you can go back to one of the earlier fellows, to one of the rejects, if one does not wait too long. If you date with honesty from the start you can call up and say, ‘when I dated you I didn’t realize what a catch you were’ or words to that effect. That’s a lot better than saying ‘I rejected you based on a mathematical strategy that involved lying to all the first 36.8%.’
Robert Buxbaum, December 9, 2019. This started out as an essay on the mathematics of the fussy suitor problem. I see it morphed into a father’s dating advice to his marriage-age daughters. Here’s the advice I’d given to one of them at 16. I hope to do more with the math in a later post.
Here is a classic math paradox for your amusement, and perhaps your edification: (edification is a fancy word for: beware, I’m trying to learn you something).
You are on a TV game show where you will be asked to choose between two, identical-looking envelopes. All you know about the envelopes is that one of them has twice as much money as the other. The envelopes are shuffled, and you pick one. You peak in and see that your envelope contains $400, and you feel pretty good. But then you are given a choice: you can switch your envelope with the other one; the one you didn’t take. You reason that the other envelope either has $800 or $200 with equal probability. That is, a switch will either net you a $400 gain, or loose you $200. Since $400 is bigger than $200, you switch. Did that decision make sense. It seems that, at this game, every contestant should switch envelopes. Hmm.
The solution follows: The problem with this analysis is an error common in children and politicians — the confusion between your lack of knowledge of a thing, and actual variability in the system. In this case, the contestant is confusing his (or her) lack of knowledge of whether he/she has the big envelope or the smaller, with the fixed fact that the total between the two envelopes has already been set. It is some known total, in this case it is either $600 or $1200. Lets call this unknown sum y. There is a 50% chance that you now are holding 2/3 y and a 50% chance you are holding only 1/3y. therefore, the value of your current envelope is 1/3 y + 1/6y = 1/2 y. Similarly, the other envelope has a value 1/2y; there is no advantage is switching once it is accepted that the total, y had already been set before you got to choose an envelope.
And here, unfortunately is the lesson:The same issue applies in reverse when it comes to government taxation. If you assume that the total amount of goods produced by the economy is always fixed to some amount, then there is no fundamental problem with high taxes. You can print money, or redistribute it to anyone you think is worthy — more worthy than the person who has it now – and you won’t affect the usable wealth of the society. Some will gain others will lose, and likely you’ll find you have more friends than before. On the other hand, if you assume that government redistribution will affect the total: that there is some relationship between reward and the amount produced, then to the extent that you diminish the relation between work and income, or savings and wealth, you diminish the total output and wealth of your society. While some balance is needed, a redistribution that aims at identical outcomes will result in total poverty.
This is a variant of the “two-envelopes problem,” originally posed in 1912 by German, Jewish mathematician, Edmund Landau. It is described, with related problems, by Prakash Gorroochurn, Classic Problems of Probability. Wiley, 314pp. ISBN: 978-1-118-06325-5. Wikipedia article: Two Envelopes Problem.
