Later On

A blog written for those whose interests more or less match mine.

Archive for the ‘Games’ Category

A Game Designer’s Analysis Of QAnon

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In watching the videos of the attack on the Capitol it struck me that it seemed somewhat like a multplayer online game acted out in real life (especially given that such games usually seem to involve combat — as if we are doing simulation training to make people adopt violence as the standard way of solving problems). The parallels — and the effects of learning behaviors from online games — are discussed in a very interesting article on Medium.

Friedrich Nietzche’s famously wrote, “He who fights with monsters should look to it that he himself does not become a monster. And if you gaze long into an abyss, the abyss also gazes into you.” First I’ll observe that the QAnon worldview does indeed have its converts fighting monsters (cannibalistic pedophile Satan-worshiping liberals), and as we saw on Wednesday, some of the QAnon faithful have indeed become monsters. Moreover, as the following article points out, those playing the game QAnon are being played by the game.

One thing I gleaned from the article is why teaching by the Socratic method is so effective

Reed Berkowitz writes:

I am a game designer with experience in a very small niche. I create and research games designed to be played in reality. I’ve worked in Alternate Reality Games (ARGs), LARPsexperience fictioninteractive theater, and “serious games”. Stories and games that can start on a computer, and finish in the real world. Fictions designed to feel as real as possible. Games that teach you. Puzzles that come to life all around the players. Games where the deeper you dig, the more you find. Games with rabbit holes that invite you into wonderland and entice you through the looking glass.

When I saw QAnon, I knew exactly what it was and what it was doing. I had seen it before. I had almost built it before. It was gaming’s evil twin. A game that plays people. (cue ominous music)

QAnon has often been compared to ARGs and LARPs and rightly so. It uses many of the same gaming mechanisms and rewards. It has a game-like feel to it that is evident to anyone who has ever played an ARG, online role-play (RP) or LARP before. The similarities are so striking that it has often been referred to as a LARP or ARG. However this beast is very very different from a game.

It is the differences that shed the light on how QAnon works and many of them are hard to see if you’re not involved in game development. QAnon is like the reflection of a game in a mirror, it looks just like one, but it is inverted.

Guided Apophenia

In one of the very first experience fictions (XF) I ever designed, the players had to explore a creepy basement looking for clues. The object they were looking for was barely hidden and the clue was easy. It was Scooby Doo easy. I definitely expected no trouble in this part of the game.

But there was trouble. I didn’t know it then, but its name was APOPHENIA.

Apophenia is “the tendency to perceive a connection or meaningful pattern between unrelated or random things (such as objects or ideas)

As the participants started searching for the hidden object, on the dirt floor, were little random scraps of wood.

How could that be a problem!?

It was a problem because three of the pieces made the shape of a perfect arrow pointing right at a blank wall. It was uncanny. It had to be a clue. The investigators stopped and stared at the wall and were determined to figure out what the clue meant and they were not going one step further until they did. The whole game was derailed. Then, it got worse. Since there obviously was no clue there, the group decided the clue they were looking for was IN the wall. The collection of ordinary tools they found conveniently laying around seemed to enforce their conclusion that this was the correct direction. The arrow was pointing to the clue and the tools were how they would get to it. How obvious could it be?

I stared in horror because it all fit so well. It was better and more obvious than the clue I had hidden. I could see it. It was all random chance but I could see the connections that had been made were all completely logical. I had a crude backup plan and I used it quickly before these well-meaning players started tearing apart the basement wall with crowbars looking for clues that did not exist.

These were normal people and their assumptions were normal and logical and completely wrong.

In most ARG-like games apophenia is the plague of designers and players, sometimes leading participants to wander further and further away from the plot and causing designers to scramble to get them back or (better yet) incorporate their ideas. In role-playing games, ARGs, video games, and really anything where the players have agency, apophenia is going to be an issue.

This happens because in real games there are actual solutions to actual puzzles and a real plot created by the designers. It’s easy to get off track because there is a track. A great game runner (often called a puppet-master) can use one or two of these speculations to create an even better game, but only as much as the plot can be adjusted for in real time or planned out before-hand. It can create amazing moments in a game, but it’s not easy. For instance, I wish I could have instantly entombed something into that wall in the basement because it would have worked so well, but I was out of luck!

If you are a designer, and have puzzles, and have a plot, then apophenia is a wild card you always have to be concerned about.

QAnon is a mirror reflection of this dynamic. Here apophenia is the point of everything. There are no scripted plots. There are no puzzles to solve created by game designers. There are no solutions.

QAnon grows on the wild misinterpretation of random data, presented in a suggestive fashion in a milieu designed to help the users come to the intended misunderstanding. Maybe “guided apophenia” is a better phrase. Guided because the puppet masters are directly involved in hinting about the desired conclusions. They have pre-seeded the conclusions. They are constantly getting the player lost by pointing out unrelated random events and creating a meaning for them that fits the propaganda message Q is delivering.

There is no reality here. No actual solution in the real world. Instead, this is a breadcrumb trail AWAY from reality. Away from actual solutions and towards a dangerous psychological rush. It works very well because when you “figure it out yourself” you own it. You experience the thrill of discovery, the excitement of the rabbit hole, the acceptance of a community that loves and respects you. Because you were convinced to “connect the dots yourself” you can see the absolute logic of it. This is the conclusion you arrived at. More about this later.

Everyone on the board agrees with you because it’s highly likely they were the ones that pointed it out to you just for that purpose. (more on this later)

“Hey, what’s that?!”

“It looks like an arrow, pointing at the wall.”

“Why do you think it’s there? Do people just leave arrows pointing to things randomly? What does your common sense say about that?”

“It says there must be something there.”

“Yes. You are right. Maybe you should look at it more closely?”

Every cloud has a shape that can look like something else. Everything that flickers is also a jumble of Morse code. The more information that is out there, the easier it is to allow apophenia to guide us into anything. This is about looking up at the sky and someone pointing out constellations.

The difference is that these manufactured connections lead to the desired conclusions Q’s handlers have created. When players arrive at the “correct” answers they are showered with adoration, respect, and social credit. Like a teenage RP, the “correct” answer is the one that the group respects the most and makes the story the most enjoyable. The idea that bolsters the theory. The correct answer is the one that provides the poster with the most credit.

It’s like a Darwinian fiction lab, where the best stories and the most engaging and satisfying misinterpretations rise to the top and are then elaborated upon for the next version.

Even Q-Anon was only one of several “anons” including FBIanon and CIAanon, etc, etc. Q rose to the top, so it got its own YouTube channels. That tested, so it moved to Reddit. The theories that didn’t work, disappeared while others got up-voted. It’s ingenious. It’s AI with a group-think engine. The group, led by the puppet masters, decide what is the most entertaining and gripping explanation, and that is amplified. It’s a Slenderman board gone amok.

Let’s go back to the arrow on the ground again.

It was not an arrow on the ground, pointing to a clue in a wall. It was just some random bits of wood. They did not discover an arrow. They created it. They saw random pieces of wood and applied their intelligence to it, and this is everything.

It’s easy for people to forget that they are not discovering the story, but creating it from random data.

Propaganda and Manipulation

Another major difference between QAnon and an actual game, is that Q is almost pure propaganda. That IS the sole purpose of this. It’s not advertising a product, it’s not for fun, and it’s not an art project. There is no doubt about the political nature of the propaganda either. From ancient tropes about Jews and Democrats eating babies (blood-libel re-booted) to anti-science hysteria, this is all the solid reliable stuff of authoritarianism. This is the internet’s re-purposing of hatred’s oldest hits. The messaging is spot on. The “drops” implanted in an aspic of anti-Semitic, misogynist, and grotesque posts on posting boards that, indeed, have been implicated in many of the things the fake conspiracy is supposed to be guilty of!

Q is also operating in conjunction with  . . .

Written by LeisureGuy

11 January 2021 at 12:30 pm

Learning concentration through playing chess

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Jonathan Rowson, the co-founder and director of Perspectiva, a research institute in London, and the author of The Moves that Matter: A Chess Grandmaster on the Game of Life (2019), writes in Aeon:

Arriving at the chess board is like entering an eagerly anticipated party. All my old friends are there: the royal couple, their associates, the reassuringly straight lines of noble infantry. I adjust them, ensuring that they are optimally located in the centre of their starting squares, an anxious fidgeting and tactile caress. I know these pieces, and care about them. They are my responsibility. And I’m grateful to my opponent for obliging me to treat them well on pain of death.

In many ways, I owe chess everything. Since the age of five, the game has been a source of friendship, refuge and growth, and I have been a grandmaster for 20 years. The lifelong title is the highest awarded to chess players, and it is based on achieving three qualifying norms in international events that are often peak performances, combined with an international rating reflecting a consistently high level of play – all validated by FIDE, the world chess federation. There are about 1,500 grandmasters in the world. At my peak, I was just outside the world top 100, and I feel some gentle regret at not climbing even higher, but I knew there were limits. Even in the absence of a plan A for my life, chess always felt like plan B, mostly because I couldn’t imagine surrendering myself to competitive ambition. I have not trained or played with serious professional intent for more than a decade, and while my mind remains charmed by the game, my soul feels free of it.

In recent years, I have worked in academic and public policy contexts, attempting to integrate our understanding of complex societal challenges with our inner lives, while also looking after my two sons. I miss many things about not being an active player. I miss the feeling of strength, power and dignity that comes with making good decisions under pressure. I miss the clarity of purpose experienced at each moment of each game, the lucky escapes from defeat, and the thrill of the chase towards victory. But, most of all, I miss the experience of concentration.

I can still concentrate, of course, but not with the same reliability and intensity that a life of professional chess affords. In fact, from a distance, chess looks to me suspiciously like a socially permissible pretext to concentrate for several hours at a time. In The Island from the Day Before (1994), Umberto Eco composes a love letter that includes the line: ‘[O]nly in your prison does [my heart] enjoy the most sublime of freedoms’ – that could be said of chess, too, and the experience of concentration is what makes it possible. I believe concentration is a defining feature of a fulfilling life, a necessary habit of mind for a viable civilisation, and that chess can teach us more about what concentration really means.

Any skilled endeavour entails concentration, but chess is unusual in requiring that we concentrate not for a few minutes at a time, but for several hours at a time, within tournaments, for days at a time, and within careers, for years at a time. Concentration is the sine qua non of the chess experience.

In chess, concentration usually unfolds in quick succession through perceiving, desiring and searching. But it’s recursive, so I often find something I didn’t expect in a way that leads me to see my position differently and want something else from it. My perception is pre-patterned through years of experience, so I don’t see one square or piece at a time. Instead, I see the whole position as a situation featuring relationships between pieces in familiar strategic contexts; a castled king, a fianchettoed bishop, a misplaced knight, an isolated pawn; it’s a kind of conceptual grammar. The meaning of the position is embedded in those patterns, partly revealed and partly concealed, and my search to do the right thing feels fundamentally aesthetic in nature.

I could describe the feeling as a kind of evaluative hunting  not so much for a particular target, but for trails of ideas that look right and feel right. I am drawn towards some transfigurations of the patterns that make me look deeper, and repelled by others. Good moves have the qualities of truth and beauty. They are discoveries of how things are, and should be.

However, chess invites me to deepen my concentration a few centimetres away from another being who is also trying to concentrate; someone I can smell, sense moving, and hear breathing. I often know, even like, these people, but they loom within my psyche in a relatively impersonal sense – a familiar energy, not friends as such. I sometimes think of chess opponents as psychopathic flatmates with whom I have to share a living space. They look harmless, but I know we signed the same contract that says they need to try to get inside my room, steal my possessions and hunt me down, before killing me; naturally, I am obliged to do the same to them. Together we create a story, and narrative themes such as attack and defence are both reduced and reified into particular moves with particular pieces on particular squares, which we record like stenographers, into our own arcana of algebraic notation. The climax of a game’s story might be ‘Brutal counter-attack!’ but the record merely reflects the logical power of a short sequence of moves, for instance: ‘…34. Bf3 Nh3+ 35.Kh1 Qg4!! Resigns.’

The forces on the board are always . . .

Continue reading.

Written by LeisureGuy

27 December 2020 at 7:32 am

Posted in Chess, Daily life, Fitness, Games

Blob Opera: Watch, Listen, and Experiment

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Google engineers having fun. Go to this page, then click on everything to see what happens and click-and-drag the blobs. More entertaining than you might expect.

More experiments here.

Written by LeisureGuy

21 December 2020 at 10:32 am

10 fun chess games for beginners to enjoy

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Written by LeisureGuy

13 December 2020 at 6:41 am

Posted in Chess, Games, Video

If you liked “The Queen’s Gambit,” then watch “Searching for Bobby Fischer”

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The movie (from 1993) is on Netflix and is based on the true story of Joshua Waitzkin. It’s a feel-good movie with an amazing cast: Joe Mantegna, Joan Allen, Ben Kingsley, Laurence Fishburne, David Paymer, William H. Macy, Dan Hedaya, Laura Linney, Tony Shalhoub. No drug use in this one.

It’s listed now with the title “Innocent Moves,” but you can search for it under that title or the original and find it. (Netflix no longer enables direct links to titles.)

Written by LeisureGuy

13 December 2020 at 4:51 am

Posted in Chess, Movies & TV

Learn How to Play Chess Online: Free Chess Lessons for Beginners, Intermediate Players & Beyond

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When I first learned to play chess I knew no chessplayers, so I tried to figure it out with the instructions that came with the little plastic set I received. I only knew checkers, and from that got the (mistaken) idea that knights captured pieces by jumping over them (rather than as they do: by landing on them).

Nowadays the resources available are manifold. For those who already know the game, I have at the right a link to a excellent on-line book providing instruction in tactics: Predator at the Chessboard. But that assumes you know the game and have some experience in playing it. What if you have never played?

Open Culture has an excellent round-up of free on-line resources available to those who want to learn the game from scratch. And I’ll note that there are many opportunities to play on-line so that your opponent need not be physically present or even close.

Written by LeisureGuy

1 December 2020 at 10:24 am

Esperanto Scrabble tiles

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At last. They also have sign language tiles (Australian, British, and US) and Aurebesh.

Written by LeisureGuy

28 November 2020 at 9:08 pm

Posted in Esperanto, Games

Ward Farnsworth’s “Predator at the Chessboard: A Field Guide to Chess Tactics” — very good and totally free

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With the (excellent) Netflix series “The Queen’s Gambit,” based on the novel by Walter Tevis (who also wrote The Hustler, The Color of Money, and The Man Who Fell to Earth), being popular and with pandemic isolation, chess is enjoying a resurgence of popularity, particularly since (like Go) online play is easy to find.

Ward Farnsworth has made his guide to tactics freely available. He writes:

Chess tactics explained.

This site teaches chess in words. It has two parts.

1. The first part is a book that explains chess tactics (that is, how to make winning moves). It assumes no prior knowledge of the subject. Everything is explained progressively and in plain English. You can read it by clicking anyplace in the table of contents below. The headings can be expanded one at a time by clicking on the [+] signs, or click here to expand all of them at once. (And then you can click here to collapse them all at once.) There are 20 chapters, about 200 topics within them, and over 1,000 positions discussed.

2. The second part is a trainer: a set of puzzles shown without solutions that you can use to practice. Click here  to use it. You can try a random position from the book or one that involves a particular topic. The trainer allows you to ask for a hint if you’re stuck, and to see the answer when you are done.

You can always come back here by clicking the “contents” button in the upper right corner of every page. If you arrived by a different route, the best address for returning is http://www.chesstactics.org. This whole site has now been made much friendlier for mobile devices thanks to the help of a kind and ingenious reader.

Book versions of this site are available: over 700 pages in total in a two-volume set. Here are links to book one and book two. You can check out other books by the author about philosophy here, language here, metaphor here, and law here and here.

1.Introductory Matters.
[+]1.1.A Short Guide to the Site.
[+]1.2.Rationale for the Project.
[+]1.3.The Elements of Tactics: A Primer.
[+]1.4.Notation; Jargon; the Look of the Site; Hard Copies.
[+]1.5.Acknowledgments and Bibliography.
[+]1.6.Chess in Literature.

2.The Double Attack.
[+]2.1.The Knight Fork.
[+]2.2.The Queen Fork.
[+]2.3.The Bishop Fork.
[+]2.4.The Rook Fork.
[+]2.5.The Pawn Fork.

3.The Discovered Attack.
[+]3.1.Bishop Discoveries.
[+]3.2.Rook Discoveries.
[+]3.3.Knight Discoveries.
[+]3.4.Pawn Discoveries.

4.The Pin and the Skewer.
[+]4.1.Arranging a Pin.
[+]4.2.Exploiting a Pin.
[+]4.3.Other Patterns and Applications.
[+]4.4.The Relative Pin.
[+]4.5.The Skewer.

5.Removing the Guard.
[+]5.1.Capturing the Guard.
[+]5.2.Distracting the Guard (The Overworked Piece).
[+]5.3.Attacking the Guard.
[+]5.4.Blocking the Guard (Interference).

6.Mating Patterns.
[+]6.1.The Back Rank Mate.
[+]6.2.Other Classic Mating Ideas.

At the link, the TOC shown above consists of links to the pages of the book. Clicking a [+] displays the relevant pages for the heading. For example, clicking the [+] for “5.3 Attacking the Guard” displays:

5.3.1.Introduction.
5.3.2.Checks to Drive the King Away from Guard Duty.
5.3.3.Flush Checks (the Decoy).
5.3.4.Decoys on the Diagonal: Bishop Check Sacrifices.
5.3.5.Driving Off the Queen with a Threat.
5.3.6.Using the Priority of Check.
5.3.7.Attacks on the Queen to Loosen a Mating Square.
5.3.8.Flush Attacks Against the Queen.
5.3.9.Threats Against Rooks and Minor Pieces.
5.3.10.Forking the Guard and Another Piece.
5.3.11.Using Pawns to Threaten the Guard.

Each of those is also a link to the study page.

Written by LeisureGuy

27 November 2020 at 9:47 am

Posted in Books, Chess

Good example of a Plachutta in the wild

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A Plachutta is most often encountered in a problem, but here it occurs in a (famous) game:

Written by LeisureGuy

24 November 2020 at 10:45 am

Posted in Chess, Games

The peril of pursuing perfection

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I have written about the difficulty faced by adult beginners in playing piano: they are hyperconscious of the mistakes they make, and they don’t want to play until they can play without making such mistakes. But studying our mistakes is how we learn.

I just came across this story from Art and Fear, by David Bayles and Ted Orland:

The ceramics teacher announced on opening day that he was dividing the class into two groups. All those on the left side of the studio, he said, would be graded solely on the quantity of work they produced, all those on the right solely on its quality. His procedure was simple: on the final day of class he would bring in his bathroom scales and weigh the work of the “quantity” group: fifty pounds of pots rated an “A”, forty pounds a “B”, and so on. Those being graded on “quality”, however, needed to produce only one pot – albeit a perfect one – to get an “A”. Well, came grading time and a curious fact emerged: the works of highest quality were all produced by the group being graded for quantity. It seems that while the “quantity” group was busily churning out piles of work – and learning from their mistakes – the “quality” group had sat theorizing about perfection, and in the end had little more to show for their efforts than grandiose theories and a pile of dead clay.

Written by LeisureGuy

16 November 2020 at 3:42 pm

How to get good at chess

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Stephen Moss, author of The Rookie: An Odyssey through Chess (and Life), writes in the Guardian:

The first thing to say about chess is that we are not all natural geniuses like Beth Harmon, the star of The Queen’s Gambit, who is taught the game by grumpy but lovable janitor Mr Shaibel at the age of nine and is very soon beating him.

The daughter of a maths PhD, she sees the patterns and movement in chess immediately, can visualise effortlessly – being able to memorise moves and play without a board is the sign of chess mastery – and sees whole games on the ceiling of her orphanage dormitory. She is a prodigy, just like world champion Bobby Fischer, on whom Walter Tevis based the novel from which the TV series is drawn. We are mere mortals. So how do we get good?

  • First, by loving chess. “You can only get good at chess if you love the game,” Fischer said. You need to be endlessly fascinated by it and see its infinite potential. Be willing to embrace the complexity; enjoy the adventure. Every game should be an education and teach us something. Losing doesn’t matter. Garry Kasparov, another former world champion, likes to say you learn far more from your defeats than your victories. Eventually you will start winning, but there will be a lot of losses on the way. Play people who are better than you, and be prepared to lose. Then you will learn.
  • If you are a beginner, don’t feel the need to set out all the pieces at once. Start with the pawns, and then add the pieces. Understand the potential of each piece – the way a pair of bishops can dominate the board, how the rooks can sweep up pawns in an endgame, why the queen and a knight can work together so harmoniously. Find a good teacher – your own Mr Shaibel, but without the communication issues.
  • Once you have established the basics, start using computers and online resources to play and to help you analyse games. lichess.orgchess.com and chess24.com are great sites for playing and learning. chessbomb.com is a brilliant resource for watching top tournaments. chessgames.com is a wonderful database of games. chesspuzzle.net is a great practice program. decodechess.com attempts to explain chess moves in layperson’s language. There are also plenty of sophisticated, all-purpose programs, usually called chess engines, such as Fritz and HIARCs that, for around £50, help you deconstruct your games and take you deeply into positions. But don’t let the computer do all the work. You need to engage your own brain on the analysis. And don’t endlessly play against the computer. Find human opponents, either online or, when the pandemic is over, in person.
  • Study the games of great masters of the past. Find a player you like and follow their careers. Fischer is a great starting point – his play is clear and comprehensible, and beautifully described in his famous book My 60 Memorable Games. Morphy (Harmon’s favourite), Alekhine, Capablanca, Tal, Korchnoi and Shirov are other legendary figures with whom the aspiring player might identify. They also have fascinating life stories, and chess is about hot human emotions as well as cold calculation. Modern grandmaster chess, which is based heavily on a deep knowledge of opening theory, is more abstruse and may be best avoided until you have acquired deep expertise. The current crop of leading grandmasters are also, if we are brutally honest, a bit lacking in personality compared with the giants of the past.
  • Children will often find . . .

Continue reading.

Written by LeisureGuy

15 November 2020 at 11:39 am

Posted in Chess, Games

A close-fought frame: Ronnie O’Sullivan vs. Stuart Bingham, 2016 Masters

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Twelve minutes.

Written by LeisureGuy

13 November 2020 at 10:46 am

Posted in Daily life, Games, Snooker, Video

Match-winning break from Ronnie O’Sullivan, 2017 World Championship

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It’s amazing how Sullivan develops this break.

Written by LeisureGuy

7 November 2020 at 7:47 pm

Posted in Snooker, Video

Elizabeth Harmon v. Harry Beltnik with commentary.

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I’ve been enjoying The Queen’s Gambit on Netflix, a limited series based on a Walter Tevis novel of the same name. (Tevis also wrote The Hustler and The Color of Money, about “Fast Eddie” Felson (made into movies), and The Man Who Fell to Earth (also made into a movie).)

This game occurs early in the series, in Elizabeth Harmon’s first tournament in her home town in Kentucky. She enters as an unrated player. The YouTube chess commentaries by agadmator are all excellent. Below he comments on this game and also provides a link to the original, played in 1955, so in keeping with the era of the series.

A Vulture article explains why the chess in the series is so good. From the article:

Two key figures in putting together those sequences were Bruce Pandolfini, a longtime chess author and coach who also consulted on the original novel, and Michelle Tesoro, The Queen’s Gambit’s editor, who also worked with Frank on Godless. The two of them talked to Vulture about mapping out the series’ many chess matches, finding innovative ways to cut them together, and the useful advice they got from grandmaster Garry Kasparov.

If you’ve watched the series, that article is very interesting. And see also this Vulture article on the series.

Written by LeisureGuy

30 October 2020 at 11:24 am

Posted in Chess, Games, Movies & TV

Barry Hawkins ahead 64 to 0, and then misses a shot

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6 minutes that Hawkins will long remember.

Written by LeisureGuy

29 October 2020 at 8:01 am

Posted in Games, Snooker, Video

Tense semifindal decider between Ronnie O’Sullivan and Judd Trump in 2019

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Written by LeisureGuy

28 October 2020 at 9:39 pm

Posted in Games, Snooker, Video

Chess on the iPhone

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There’s a chess app for the iPhone, called simply “Chess,” by Vintolo Ltd. At the highest level, it’s a sucker for the Evans Gambit. I don’t always win with that opening (me playing white), but about 80% of the time I do.

I’m just sayin’.

Written by LeisureGuy

20 October 2020 at 8:03 pm

Posted in Chess

Celebrating the Playful Magic of John Horton Conway

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Pradeep Mutalik writes in Quanta:

The legendary mathematician John Horton Conway, who died in April of COVID-19, took a childlike delight in inventing puzzles and games. He performed detailed analyses of many puzzles, such as the Soma cubepeg solitaire and Conway’s soldiers. He invented the “Doomsday algorithm” (a fast method of calculating the day of the week in your head — Conway could do it in under two seconds) and countless games, including Sprouts and the famous Game of Life, which launched the study of cellular automata.

A great deal of Conway’s serious mathematical work also arose from his penchant for playing mathematical games. He made original contributions to group theory (the Leech latticemonstrous moonshine), higher-dimensional geometry, tessellations, knot theory, number theory (surreal numbers), algebra, mathematical logic and analysis.

This month, we celebrate the playful genius of the famous British mathematician with two puzzles and an exploratory game. First, we’ll play around with a numerical puzzle Conway invented that is perfection itself. Then we’ll enjoy a geometric puzzle that relates to some of his most visually pleasing work. Finally, we’ll immerse ourselves in an open-ended game contributed by a Quanta reader that resembles Conway’s iconic Game of Life.

Puzzle 1: Digital Perfection

There is a mysterious 10-digit decimal number, abcdefghij. Each of the digits is different, and they have the following properties:

a is divisible by 1
ab is divisible by 2
abc is divisible by 3
abcd is divisible by 4
abcde is divisible by 5
abcdef is divisible by 6
abcdefg is divisible by 7
abcdefgh is divisible by 8
abcdefghi is divisible by 9
abcdefghij is divisible by 10

What’s the number?

Before you begin this puzzle, take a minute to admire the absolute perfection of its form. It flows completely naturally, without an iota of arbitrariness or artifice. Once you read the first two conditions, you know exactly what the rest of puzzle is going to be. And then to have this natural set of conditions yield a unique answer is amazing. For me as a puzzle maker, this digit substitution puzzle inspires the same feeling that Mozart inspired in Einstein, who said that Mozart’s music “was so pure that it seemed to have been ever-present in the universe, waiting to be discovered by the master.” Only someone as numerically gifted as Conway could have plucked such a perfect Platonic form from puzzle heaven!

You can solve this puzzle by performing a brute-force search with a computer, of course, but you don’t need to. I urge you to do it using pencil and paper. All digit substitution puzzles of this type can be solved with a two-step process familiar to those who’ve solved a sudoku puzzle — first you deduce relationships between the digits, which narrows the possibilities, and then you do a systematic trial-and-error search for the unknown digits. In this case, you can use the tricks you learned in school for determining if a number is divisible by a given digit. If you squeeze the last drop of deduction from the puzzle conditions, you won’t have too many trial-and–error candidates to search through.

In fact, if you want a stiffer challenge, try doing this puzzle entirely in your head. After all, Conway was known for solving math problems “with his bare hands.” It requires a lot of focus and patience, but I assure you it can be done.

Puzzle 2: The Ambiguous Triangles

There is an isosceles triangle that contains an angle of x degrees. The ratio of the two different lengths of its sides is y.

It turns out that not one but two different triangles have the exact same values of x and y!

What are the values of x and for these two isosceles triangles? What’s special about the triangles, and how do they relate to Conway’s work?

For our final offering, . . .

Continue reading.

Written by LeisureGuy

15 October 2020 at 3:21 pm

Posted in Games, Math

Nice game of me (white) against SparkChess

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Written by LeisureGuy

9 October 2020 at 7:44 pm

Posted in Chess, Games

Stunning decider in World Snooker Championship Semifinal 2020, Ronnie O’Sullivan vs. Mark Selby

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O’Sullivan and Selby tied at 16 frames each in this match. Here’s the 33rd and deciding frame. It’s a nail-biter.

Written by LeisureGuy

3 October 2020 at 10:00 am

Posted in Games, Video

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