Posts Tagged ‘puzzles’
“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.
“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.
“Chance, too, which seems to rush along with slack reins, is bridled and governed by law”*…
… though that law can sometimes be less than obvious. Erica Klarreich reports on one creative mathematician’s efforts to help us learn…
In late January, Daniel Litt [pictured above] posed an innocent probability puzzle on the social media platform X (formerly known as Twitter) — and set a corner of the Twitterverse on fire.
Imagine, he wrote, that you have an urn filled with 100 balls, some red and some green. You can’t see inside; all you know is that someone determined the number of red balls by picking a number between zero and 100 from a hat. You reach into the urn and pull out a ball. It’s red. If you now pull out a second ball, is it more likely to be red or green (or are the two colors equally likely)?
Of the tens of thousands of people who voted on an answer to Litt’s problem, only about 22% chose correctly. (We’ll reveal the solution below, in case you want to think it over first.) In the months since, Litt, a mathematician at the University of Toronto, has continued to confound Twitter users with a series of probability puzzles about urns and coin tosses.
His posts have prompted lively online discussions among research mathematicians, computer scientists and economists — as well as philosophers, financiers, sports analysts and anonymous fans. Some joked that the puzzles were distracting them from their real work — “actively slowing down economic research,” as one economist put it. Others have posted papers exploring the puzzles’ mathematical ramifications.
Litt’s online project doesn’t just highlight the enduring allure of brainteasers. It also demonstrates the limits of our mathematical intuition, and the counterintuitive nature of probabilistic reasoning. As Litt wrote, there’s “nothing more exhilarating than posing a multiple-choice problem on which 50,000 people do substantially worse than random chance.”…
The answer to this puzzle, other puzzles, and Litt on what makes a great puzzle, and why simple probability questions can be so deceptively difficult: “Perplexing the Web, One Probability Puzzle at a Time,” from @EricaKlarreich in @QuantaMagazine.
Vaguely related (but also very interesting): “The Bookmaker,” via @annfriedman, who observes: “Leif Weatherby and Ben Recht on Nate Silver and the addiction to prediction: ‘Silver insists that viewing all decisions through this lens of gambling is the underappreciated characteristic of Very Successful People,’ they write. ‘But what Silver willfully ignores is that the successful players in this world aren’t the bettors. They are the bookies and casino owners—the house that never loses.'”
* Boethius, The Consolation of Philosophy
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As we contemplate chance, we might send confirmatory birthday greetings to Carl David Anderson; he was born on this date in 1905. An experimental physicist, he shared the 1936 Nobel Prize in Physics for his discovery (that’s to say, confirmation of the existence) of the positron, the first known particle of antimatter… which had been predicted by mathematician and physicist Paul Dirac, whose “Dirac Equation“– in part a product of its author’s application of probability theory– had predicted (among many other features of quantum theory as we know it) the existence of the particle (and antimatter).
“Advantage! What is advantage?”*…
Pradeep Mutalik unpacks the magic and math of how to win games when your opponent goes first…
Most games that pit two players or teams against each other require one of them to make the first play. This results in a built-in asymmetry, and the question arises: Should you go first or second?
Most people instinctively want to go first, and this intuition is usually borne out. In common two-player games, such as chess or tennis, it is a real, if modest, advantage to “win the toss” and go first. But sometimes it’s to your advantage to let your opponent make the first play.
In our February Insights puzzle, we presented four disparate situations in which, counterintuitively, the obligation to move is a serious and often decisive disadvantage. In chess, this is known as zugzwang — a German word meaning “move compulsion.”…
Four fascinating examples: “The Secrets of Zugzwang in Chess, Math and Pizzas,” from @PradeepMutalik.
* Fyodor Dostoyevsky, Notes from Underground
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As we play to win, we might recall that it was on this date in 2011 that scientists involved in the OPERA experiment (a collaboration between CERN and the Laboratori Nazionali del Gran Sasso) mistakenly observed neutrinos appearing to travel faster than light. OPERA scientists announced the results with the stated intent of promoting further inquiry and debate. Later the team reported two flaws in their equipment set-up that had caused errors far outside their original confidence interval: a fiber optic cable attached improperly, which caused the apparently faster-than-light measurements, and a clock oscillator ticking too fast; accounting for these two sources of error eliminated the faster-than-light results. But even before the sources of the error were discovered, the result was considered anomalous because speeds higher than that of light in a vacuum are generally thought to violate special relativity, a cornerstone of the modern understanding of physics for over a century.
“Do I rue a life wasted doing crosswords? Yes, but I do know the three-letter word for ‘regret'”*…
Efforts to diversify the crossword puzzle industry might be having the opposite effect. As Matt Hartmann explains, although puzzles are an increasingly important part of The New York Times’ and others’ business strategies, only a handful of people actually make a living from crosswords…
The conspiracy theory writes itself. Start looking, and you’ll notice how many New York Times crossword puzzles are co-constructed (the preferred term for what most people would refer to as co-written) by a professional crossword constructor and someone with a day job—it’s hard not to see all the artists, web developers, professors, and other titles that imply a degree of wealth and elite connections. As the pandemic handed the work-from-home class extra time for their hobbies, the number of first-timers published in the Times has skyrocketed. Obviously, rich people are paying others to get the glory of their name in ink.
But the theory is almost diametrically wrong. It turns out the crossword industry really does consist of earnest wordplay lovers donating their time to unpaid mentorships, generally as part of an industry-wide effort to bring new and underrepresented people into crosswords.
Unfortunately, the end result might be even more exclusive than a pay-to-play scheme. And a game that brings the Times at least one million monthly subscribers—at $1.25 a week or $40 for a year—provides a sustainable living wage for shockingly few people…
Learn why at “Inside the Elite, Underpaid, and Weird World of Crossword Writers,” from @themhartman in @newrepublic.
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As we fill in the blanks, we might recall that it was on this date in 1977 that South Park premiered on Comedy Central– where it runs to this day. The animated saga of Stan, Kyle, Eric, and Kenny and their exploits in their (titular) Colorado hometown has won five Emmys and a Peabody Award. A theatrical film, South Park: Bigger, Longer & Uncut, was released in June, 1999 to commercial and critical success, and scored an Academy Award nomination.
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