Posts Tagged ‘games’
“This was not that the subject was simple enough to be explained without mathematics, but rather that it was much too involved to be fully accessible to mathematics.”*…
The idea of ‘biological agency’ — that life devises its own goals and behaves accordingly — complicates our understanding of what it means to be alive. But, Philip Ball asks, does it serve a scientific purpose?…
In 1993, a team led by the planetary scientist Carl Sagan tentatively concluded that there is life on Earth. Not much of a deduction, you might think — except that the researchers confined their evidence to observations made by the Galileo spacecraft, which had flown past our planet three years earlier on a looping journey to Jupiter. So great is the transformative power of life that its presence can be detected just from the light and radio waves our planet emits or reflects into space. Today we scan the cosmos for some of these telltale signatures light-years away.
Life leaves a mark, yet even now there’s no scientific consensus about what makes living things so different from inorganic substances like the rocks, gases, and oceans that are the sole components of dead worlds. Many scientists cite properties such as replication or metabolism. Others speak in more abstract terms about the way life is out of thermodynamic equilibrium with its surroundings. But some give another kind of answer. Living organisms are different because they do stuff for reasons.
It’s not enough to say that life is a nonequilibrium organized state through which there’s a constant flux of matter and energy. That description applies to hurricanes, too. But hurricanes just are. Only living entities have goals: to find food, to reproduce, to survive, sometimes simply to experience good things. (Dog owners will recognize that this is not just a human attribute.)
One way to express this idea is to say that living organisms have “agency.” It’s a hotly contested term. Some biologists reject it outright, at least for any organisms except humans, because we decide on our actions with conscious deliberation. (Whether we’re truly the only species to do so is another issue.) Others think that agency is a fundamental attribute of all life. Since there’s no agreed-upon definition of the term, to some extent it can mean whatever you want it to mean. But the debate about biological agency touches on fundamental issues in our understanding of what it means to be alive, because agency evokes a notion that biologists and philosophers have always wrestled with: teleology, the apparent purposiveness of life. If we admit agency into biology, do we open the floodgates to ideas about design, vitalism, or cosmic meaning? Or is it just a recognition of what makes life such a special state of matter?
To me, the notion of agency indeed speaks to our intuitive sense of what makes living things so special: not mere machines pushed around by environment and circumstance. I suspect that aversion to agency betrays a queasiness about confronting life as something more than some kind of genetic program. But there’s danger in the idea, too: It could so easily derail the work of studying the mechanistic explanations of how life works. I’m not looking to either bury or praise agency, but to explore whether it can be a scientifically productive idea…
[Ball unpacks the idea of agency, then reviews both scientific observations and the theories that they have provoked. He concludes…]
… I’m cautiously optimistic about the prospects of uniting such theoretical ideas with biological mechanisms. It seems unlikely to be coincidental, for example, that organisms that seem to show more agency also have molecular pathways that permit more openness to the influence of context and external information.
If we can get a clearer idea of what makes an agent, this could help us to understand how collective goals arise — as they did when multicellular organisms first arose long ago — and how they can break down, as in cancer. What’s more, a proper theory of agency might give us a clearer idea of what’s needed to make genuine artificial agents, not just computers and machines programmed with our own goals, but ones that can formulate their own. We might then also get a clearer idea of the potential benefits and dangers such truly agential machines might bring. But perhaps the most compelling argument for recognizing agency is that it might help us understand what makes life so different — not just humans, but life — that it is able to shape an entire planet in a manner visible from outer space.
Purpose? Goals? On the idea of “biological agency”: “Is Life Just Different?” from @philipcball.bsky.social in @quantamagazine.bsky.social.
* Erwin Schrödinger in What Is Life? (in which he wrestled, in his way, with Ball’s question, contending that life feeds on negative entropy) Full text here.
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As we wonder why, we might send frustrated birthday greetings to Ernő Rubik; he was born on this date in 1944. An architect and inventor, he created the Rubik’s Cube (in 1974), which has become the world’s best-selling puzzle game, with over half a billion sold.
A Rubik’s Cube consists of 26 small cubes that rotate on a central axis; nine colored cube faces, in three rows of three each, form each side of the cube. After the cube arrangement is randomized (the highest level of entropy), the player must restore order (that’s to say, practice “negative entropy”), returning it to the original condition of faces with matching colors on each side — which is one among 43 quintillion possible configurations.
“Chess pieces are the block alphabet which shapes thoughts”*…
In Amritsar, at India’s oldest and largest chess manufacturing company, artisans have hand-carved the most complicated pieces in the game for generations. Roxanne Hoorn reports…
In the bustling streets of Amritsar, India, the markets are lined with shops full of colorful tapestries and sweet treats like warm local chai served in clay mugs. But the real treasures are kept behind closed doors. Beyond stacks of gnarled logs, inside unsuspecting brick buildings off the main streets, generations of master craftsmen carefully carve, sand, and polish intricate chess pieces, carrying on a long legacy in the country where the earliest versions of chess were played over 1,500 years ago.
These are no basic sets. The pieces make up elaborate professional and collector’s chess sets that sell for up to $4,000 U.S. dollars on the international market. That price is well deserved. Each set is a collective labor of love, with every component handcrafted by a man who specializes in one type of chess piece. (Traditionally, women are not chess carvers.) There are pawn makers, queen craftsmen, and the most coveted—the knight carvers.
“The knight carvers are only knight carvers,” says Rishi Sharma, CEO of the Chess Empire, India’s oldest and largest chess manufacturing company, which was founded in 1962. “The person who is making the queen, we don’t give him the pawn. Otherwise, he’s going to ruin it.”
Of all the chessmen, knights are considered the most difficult and require the most skill to carve. While pawns and other pieces can be shaped under lathes, the knights—resembling horse heads usually with wild flowing manes—are carved completely by hand. A chess carver won’t graduate from pawn to knight or any easier piece to harder ones, but instead will learn his craft from the start of his career, usually from their father or a mentor from one of the well-established chess companies. Surinder Pal, a knight carver at the Chess Empire, learned from his father at 18 years old. Now, he has been working on the craft for over 35 years. With his advanced and highly specialized skill, he can make up to 30 simple knights a day, or spend up to three days on a single ornate knight.
Today, chess pieces are carved from local species like boxwood or imported trees like rose and dogwood. But they were once made of a far more elusive and illicit material. Amritsar was originally known for its ivory carvers, who produced everything from hair combs and jewelry to furniture and sculptures. And of course, chess sets. After the international trade of ivory was banned in the 1990s, the craftsman turned to the similarly smooth but far more accessible medium.
With raw materials readily available, it’s the demand for these fine chess sets that determines how many are produced. And demand has fluctuated in recent years. The COVID-19 pandemic left many people secluded in their homes, leading to a boost in demand for many indoor games, says Sharma. In October 2020, that enthusiasm for chess was compounded by the release of The Queen’s Gambit, a series about a fictional American chess prodigy. “The Queen’s Gambit had a very big role in spreading awareness of chess,” Sharma says. “And after that, we see a big boom.” Despite the show’s creator stating they have no plans for a second season, Sharma stays hopeful. “We hope the next season comes as soon as possible.”…
Equipping the Royal Game: “Masters of the Knight: The Art of Chess Carving in India,” from @atlasobscura.com.
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As we prize the pieces, we might recall thatt it was on this date in 1996 that then-world chess champion Garry Kasparov and an IBM supercomputer called Deep Blue played game four the first of their two six-game chess matches. They played to a draw. Kasparov won the match– but by a margin of only 4-2 (two draws and a loss to the computer). They met for a rematch the following year, and Big Blue beat Kasparov (3 1/2- 2 1/2).
“Mathematics, rightly viewed, possesses not only truth, but supreme beauty”*…
Mark Frauenfelder at Boing Boing with a glorious memory…
This cover from the July 1965 issue of Scientific American illustrates the “Four Bugs Problem” featured in Martin Gardner’s “Mathematical Games” column about op art [see here].
The setup: Four bugs are placed at the corners of a square. They start crawling clockwise (or counterclockwise) at a constant rate, with each bug moving directly toward its neighbor. As the bugs move, they always form the corners of a square that both diminishes in size and rotates. Each bug’s path forms a logarithmic spiral.
Gardner said this can be generalized to any number of bugs starting at the corners of a regular polygon with n sides. In these cases, the bugs will always form the corners of a similar polygon that shrinks and rotates as they move.
Here’s an animated version of the Four Bugs Problem you can try out. If you want to try it with a different number of bugs, go here.
Your correspondent still has his copy of that issue. “The beautiful ‘Four Bugs Problem’” from @Frauenfelder in @BoingBoing.
* Bertrand Russell, A History of Western Philosophy
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As we marvel, we might send carefully-calculated birthday greetings to Ian Stewart; he was born on this date in 1945. As a teenager, he was an avid reader of Gardner’s “Mathematical Games,” from which he developed a love of the subject that led him to become a mathematician who has gone on to make important contributions to the field, especially in catastrophe theory.
But Stewart is more widely known as a popularizer of math– who credits Gardner with modeling the skills needed to be an entertaining communicator. Indeed, from 1991 to 2001 Stewart took over the Scientific American column (which had been renamed “Mathematical Recreations”).
For a list of his (remarkable) books on math and science, see here.
“Man’s most serious activity is play”*…
Until the mid-20th century, the “playing fields” on board games tended to be composed of squares; then hexagons emerged. Jon-Paul Dyson explains why…
A board game begins with the board. But how is that board divided up? Often the simplest unit of division is a square. Consider the 64 squares of a chess board, or the 92 squares on a Stratego board. In each case, players take control of a square which exists in relation to other spaces around it, especially if they share adjoining borders. The design of these game boards affords or encourages certain types of movement, usually horizontally or vertically (in four directions) or in some cases diagonally in eight directions (as with the bishop in chess).
And yet there exists a problem with this sort of layout in any game that allows freedom of movement, because the connection between these squares is uneven. Although squares share a long border horizontally and vertically, they do not share such a border on the diagonal connections. In a game like chess, where you physically pick up a piece to move it, this is not much of an issue. But as simulation board games began to develop after World War II, this proved more problematic. Many of these games involved sliding pieces (or cardboard tiles that were frustrating to pick up) from square to square, like army units occupying territory. For these situations, hexagonal spaces that provided equal movement in six directions, produced a better solution.
As is true throughout the history of innovation, whenever there is a problem, it usually turns out that multiple people arrive at similar inventive solutions. That was the case with the development of the hex as a basic unit of division in board games.
Piet Hein [see here], a Danish polymath, who was a quantum physicist as well as a designer, poet, and puzzle and game inventor, came up with the idea in 1942 for a game in which players competed to create connected lines across a game board made up of hexagonal spaces. Thus he might be credited as the father of hex. Yet in the late 1940s, American mathematician John Nash (the subject of the movie A Beautiful Mind) independently invented a similar game at Princeton that also used hex tiles [though we should note that it was a variation on the Shannon switching game, created by Claude Shannon sometime before 1951]. In 1952, Parker Brothers released a version of the game which they called Hex.
This was a time of post-war prosperity when people increasingly had the discretionary income to buy board games, but it was also a period when the United States and the Soviet Union, allies during the war, had become bitter rivals locked in a Cold War. Rather than downsizing after the victory over Germany and Japan, the American military complex shifted from fighting the Axis powers to planning for a major conflict with the Soviet Union and engaging in a series of smaller wars such as that fought in Korea. To help plan American strategy, the Army Air Force and the Douglas Aircraft Company created the Rand Corporation, a think tank that made significant contributions to American policy and computing.
One of the projects the Rand Corporation focused on was modeling conflict through the use of war games. To that end Alexander Mood, a staff member at the Rand Corporation, introduced a honeycombed, hex-shaped board that allowed pieces to move in six directions rather than just four. John Nash was at the Rand Corporation and, in a 1952 paper he coauthored entitled “Some War Games,” he and coauthor R. M. Thrall described using this hex-based system for ground and air games.
It was another game creator, however, who took this development and made the most significant contribution to the development of hex-based games: Charles S. Roberts. Roberts was an army veteran who in 1954 published Tactics, a military simulation board game that is often credited as the first modern wargame. Roberts then founded the game company Avalon Hill, and his games and their innovative simulation of battlefield odds drew the attention of the Rand Corporation because his Combat Results Table for determining the outcome of battles mirrored systems they had developed. The Rand Corporation invited Roberts to visit, and supposedly while he was there he noticed their use of hex-based boards.
Recognizing the superiority of a hex-based system for simulating movement, Roberts began using it in game design in 1961. That year was the centennial of the American Civil War, and so there was a demand for historical simulations. Roberts redesigned his recently released game Gettysburg with the new hex pattern. The Strong owns copies of Gettysburg belonging to Roberts, both in the older square format and in the revised hex version. He also used it for the Avalon Hill game Chancellorsville, another Civil War simulation. Soon the hex system became commonplace in a high proportion of wargames, as well as in more mainstream games such as the 1969 release Psyche-Paths.
Since then, hex board layouts have been used in a wide variety of games. Settlers of Catan is perhaps the most famous example, but plenty of others exist including the spaces in the game Hero Scape. Even video games will often use the hex layout, not only in wargames but in titles such as in Sid Meier’s Civilization V…
“Hex Marks the Spot,” from @jpdysonplay and @museumofplay.
* George Santayana
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As we make our moves, we might send playful birthday greetings to Seymour Papert; he was born on this date in 1928. Trained as a mathematician, Papert was a pioneer of computer science, and in particular, artificial intelligence. He created the Epistemology and Learning Research Group at the MIT Architecture Machine Group (which later became the MIT Media Lab); he directed MIT’s Artificial Intelligence Laboratory; he authored the hugely-influential LOGO computer language; and he was a principal of the One Laptop Per Child Program. Called by Marvin Minsky “the greatest living mathematics educator,” Papert won a Guggenheim fellowship (1980), a Marconi International fellowship (1981), the Software Publishers Association Lifetime Achievement Award (1994), and the Smithsonian Award (1997).
A champion of fun and games in learning, Papert was the brain behind Lego Mindstorms.
“The only reason for time is so that everything doesn’t happen at once”*…
Our lives are spread across range of ways that we spend our time. A newly-published study tracks time-use around the world…
How do you spend each day? Researchers sought answers to that basic question from people of various ages living around the world. They report that on an average day, people spend more than a third of their time focused on matters of health, happiness and keeping up appearances.
“We found that the single largest chunk of time is really focused on humans ourselves, a little more than 9 hours,” explained study author Eric Galbraith, of McGill University in Montreal, Canada. “Most of this—about 6.5 hours—is doing things that we enjoy, like hanging out, watching TV, socializing and doing sports,” he said. Reading and gaming also fall within this rubric.
The other 2.5 hours (out of the 9) are spent on hygiene, grooming and taking care of our own health and that of our kids, said Galbraith, a professor in the department of earth and planetary sciences.
Sleep and bedrest occupy the next largest chunk of time: more than 9 hours on average. That sounds like a lot of shut-eye, but Galbraith stressed this number reflects the average across the full age span, so it includes kids who might sleep up to 11 hours a day. “It also includes time in bed and not sleeping, which can be as much as one hour per day,” he said…
The remaining minutes? They seem to go toward getting organized, moving about or producing, creating and maintaining things and spaces…
For more findings and background on the methodology: “Sleep, cleaning, fun: Research reveals the average human’s day worldwide,” in @physorg_com.
* Albert Einstein
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As we contemplate chronology, we might recall that it was on this date in 2011 that the Swedish game design house Mojang Studios released the first full version of Minecraft. A sandbox game created by Markus “Notch” Persson, it has become the best-selling video game in history, with over 300 million copies sold– and countless hours consumed…
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