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Science

1,604 cards. Each one is a 40-second story with a five-minute read behind it. Page 8 of 27.

421. Leibniz used the chain rule first, and fumbled a sign doing itIf a car is twice as fast as a bicycle and the bicycle four times faster than a walker, the car beats the walker eightfold. That multiplication of rates is the chain rule of calcu…
422. Christoffel symbols track how coordinates twist across a curved spaceOn a curved surface, the directions you call north and east quietly rotate as you move. Christoffel symbols are the bookkeeping for that drift, a three-dimensional grid of numbers…
423. Before microchips, computers stored bits as sound waves in mercuryEarly computers remembered things in some strange ways. One design sent pulses of sound rippling through tubes of mercury; another painted dots of charge on a cathode ray screen. …
424. Solving the cubic sparked secret formulas, betrayal and a maths duelRenaissance Italy settled mathematical rivalries with public contests, money on the table. The prize problem was the cubic equation. A method guarded as a secret, a broken promise…
425. Curl measures how much a flowing field spins at each pointDrop a tiny paddle wheel into moving water and it may start to turn. The curl of a vector field captures that spin as an arrow: its length gives the strength of the swirl, its dir…
426. Two vertical bars around a number trace back to Weierstrass in 1841The absolute value strips a number of its sign, so both 3 and minus 3 become 3. Think of it as distance from zero. That simple idea, written with the twin bars Karl Weierstrass in…
427. Some infinities are bigger than others, and Cantor labelled them with alephGeorg Cantor realised that infinite sets come in different sizes and named those sizes after the Hebrew letter aleph. The smallest, aleph-null, counts the natural numbers. Whether…
428. Every crystal fits one of just 14 repeating point patternsSalt, diamond and quartz look nothing alike, yet the scaffolding beneath every crystal belongs to one of only 14 point arrangements in three dimensions. Auguste Bravais catalogued…
429. The Cauchy–Schwarz inequality caps how much two vectors can agreeMultiply two vectors together with a dot product and the result can never exceed the product of their lengths. That modest-sounding cap, the Cauchy–Schwarz inequality, took three …
430. The charity behind Wikipedia writes none of its articlesThe Wikimedia Foundation keeps Wikipedia and 14 sister projects online, yet it neither writes nor edits their content; volunteers do all of that. The foundation was created in 200…
431. A total order means any two things can be ranked against each otherPick any two real numbers and one is always less than or equal to the other. Pick any two letters and the dictionary settles which comes first. Mathematicians call an arrangement …
432. Almost every number is transcendental, yet proving any single one is hardPi and e are the celebrities, but transcendental numbers, those that are not the root of any polynomial with integer coefficients, make up almost all real numbers. The strange par…
433. Triangular numbers, the stacked dots behind a famous schoolboy legendArrange dots in rows of one, two, three and so on until they form a neat equilateral triangle, and the total is a triangular number. A popular tale says young Gauss found their sh…
434. U and V were once the same letter, split apart by medieval scribesFor centuries printers wrote upon as vpon and have as haue. U and V were a single letter with two shapes, pointed at the start of a word and rounded elsewhere, whatever sound it m…
435. Surreal numbers grew out of Go endgames and contain infinity itselfWhile studying endgames in the board game Go, John Horton Conway stumbled onto a number system that holds every real number plus infinite and infinitesimal ones. Donald Knuth gave…
436. Aristotle's syllogism dominated logic for many centuries until Frege came alongAll men are mortal; Socrates is a man; so Socrates is mortal. Aristotle set out this pattern of reasoning around 350 BC, and it proved so durable that Immanuel Kant declared logic…
437. The symmetric group: every way of shuffling a set, treated as algebraTake a handful of objects and list every possible rearrangement. Treat each rearrangement as an action you can perform one after another, and you have the symmetric group. It soun…
438. Why a set of linear equations has one answer, none, or infinitely manyTwo straight lines on a page can cross once, run parallel forever, or lie exactly on top of each other. That picture explains every system of linear equations: any such system has…
439. In logic, a tautology is a statement that simply cannot be falseEither it is raining right now or it is not. Whatever the weather, the sentence holds. Logicians call such statements tautologies: formulas true under every possible assignment of…
440. Tetration stacks exponents into towers that explode almost immediatelyMultiplication is repeated addition and exponentiation is repeated multiplication. Repeat exponentiation and you get tetration, where a number is raised to itself again and again.…
441. A Babylonian clay tablet pinned down the square root of 2 almost perfectlyDraw a square with sides of one unit and its diagonal measures the square root of 2, roughly 1.4142. Scribes pressed a remarkably good value into a clay tablet now called YBC 7289…
442. The Dow and the Nikkei weigh their stocks by share price, a famously odd choiceTwo indices quoted on the news every day, the Dow Jones Industrial Average and Japan's Nikkei 225, give more weight to companies simply because each share costs more. That means a…
443. The integral sign began as Leibniz's stretched-out S for sumIn a 1675 letter, Gottfried Wilhelm Leibniz proposed a tall, elongated S to mark a sum of differentials, from the Latin for summing calculus. That symbol later became the integral…
444. Rorschach built his inkblots to diagnose schizophrenia, not to read personalitiesHermann Rorschach drew several hundred inkblots himself and kept just ten. He meant them as a tool for spotting schizophrenia and was sceptical about using them as a general windo…
445. A rounding habit quietly halved the Vancouver Stock Exchange indexIn 1982 the Vancouver Stock Exchange launched a new index at 1000. Twenty-two months later it stood near 520, even though the market seemed to be climbing. The culprit was not a c…
446. Pounds, shillings and pence were Charlemagne's idea and lasted over a thousand yearsBritain's old money, with 12 pence to the shilling and 20 shillings to the pound, was not a quirky island invention. It came from the Frankish emperor Charlemagne around the 780s,…
447. Every glance at a clock uses a Sumerian counting system around 5,000 years oldSixty minutes to the hour and 360 degrees to the circle are leftovers from base 60, a way of counting that began with the Sumerians in the 3rd millennium BC. Its appeal is simple:…
448. Why 1.0 and 1 are not quite the same number to a scientistWrite 1 and you are claiming one digit of certainty; write 1.0 and you are claiming two. Significant figures are the digits in a measurement that genuinely carry information, and …
449. The humble slash once did the job of the full stop and the commaMedieval scribes used a slanting stroke called the virgule, Latin for little twig, to end sentences, mark pauses and break lines of verse. Over the centuries those duties drifted …
450. From digging start holes with shovels to 9.58 seconds in under a centuryIn 1924 sprinters carried little shovels to dig footholds at the start line, and the 100-metre world record stood at 10.4 seconds. Starting blocks arrived by 1948, then synthetic …
451. Finding a square root means guessing, then improving the guess until it stops changingUnless a whole number is a perfect square, its square root is irrational and its digits never end. So no algorithm finds it exactly. Instead, most methods start with a sensible gu…
452. Principia Mathematica tried to build mathematics from pure logicAlfred North Whitehead and Bertrand Russell meant to write a sequel to a single book. Instead the subject swelled into three dense volumes, published between 1910 and 1913, attemp…
453. Problem solving is studied everywhere from Tower of Hanoi to theorem proversGetting across town and debugging a program are both problem solving, one simple and one complex. Psychologists, computer scientists, engineers and military planners all study how…
454. One formula solves every quadratic, and its inside-out twin is called citardauqAny equation with a squared unknown, a plain unknown and a constant can be cracked with a single expression: negative b, plus or minus the square root of b squared minus four a c,…
455. A matrix's rank counts its truly independent directionsLine up the columns of a matrix and ask how many genuinely point in new directions rather than being combinations of the others. That count is the rank. Surprisingly, asking the s…
456. Ratios began as Greek logos and now shape your TV screenEight oranges and six lemons give a ratio of 8 to 6, which reduces to 4 to 3. That same 4:3 once described television screens, before widescreen sets moved to 16:9. Behind the hum…
457. Root mean square tells you how hard a changing current really worksHousehold alternating current keeps reversing direction, so its simple average is useless for judging power. Engineers instead square every value, average the squares and take the…
458. Roots of unity sit evenly spaced around a circleSome complex numbers return exactly 1 when raised to a whole-number power. The nth such roots mark n evenly spaced points on the unit circle, one of them always 1 itself. Named oc…
459. Polymaths faded as knowledge exploded, yet may matter more than everAncient and medieval scholars could roam freely across disciplines. From the 17th century, as discoveries poured in, mastering many fields grew nearly impossible. Cambridge histor…
460. Power series treat functions as polynomials that never endAdd 1, then x, then x squared, then x cubed, forever, and for small enough x you get exactly 1 divided by 1 minus x. Power series like this let mathematicians rebuild sine, the ex…
461. Primary school's name was borrowed from French in 1802The English phrase primary school is a calque of the French école primaire, first appearing in the London Times in April 1802. Whatever it is called, from elementary school in the…
462. Your body deliberately kills billions of its own cells every single dayAn average adult loses somewhere between 50 and 70 billion cells a day to apoptosis, a tidy, genetically controlled form of self-destruction. It is not damage. Your fingers exist …
463. After 2,000 years, nobody knows if an odd perfect number existsAdd up the divisors of 6, leaving out 6 itself, and you get 1, 2 and 3, which total exactly 6. Numbers with that neat property have fascinated thinkers since Euclid, yet only 52 a…
464. Darren Aronofsky funded his debut film Pi with hundred-dollar donationsTo pay for his first feature, Darren Aronofsky and producer Eric Watson asked every friend, relative and acquaintance they could think of for $100. The whip-round raised about $60…
465. The plus sign is probably a squashed version of the Latin word etPlus and minus feel as ancient as counting, yet they are fairly recent inventions. Medieval scribes wrote P and M instead, a German arithmetic book used the signs for surplus and …
466. A straight border line stranded Point Roberts as a piece of America inside CanadaIn 1846 diplomats made the 49th parallel the dividing line between American and British land in the Pacific Northwest, without checking where it fell. The line clipped the tip of …
467. Numbers whose digits run forever to the left, not the rightOrdinary decimals trail off endlessly after the point. The p-adic numbers flip that picture: pick a prime p, write in base p, and let the digits stretch infinitely leftwards inste…
468. Paul Erdős lived out of a suitcase and co-wrote with 500 mathematiciansFor most of his adult life Paul Erdős had no fixed home. He travelled from one colleague to the next, expecting hosts to feed him, house him and wash his clothes, and in return pr…
469. Rome's famous two centuries of peace were quieter than before, not peacefulThe Pax Romana is usually dated from Augustus in 27 BC to the death of Marcus Aurelius in AD 180, one of history's longest stretches of relative calm. Yet it included revolts and …
470. The set-membership symbol in every maths textbook began as Peano's Greek epsilonCounting feels too obvious to need rules, yet in 1889 Giuseppe Peano set down a short list of axioms from which the arithmetic of whole numbers could be rebuilt using just zero an…
471. Cold sores come from a virus that hides for life in a facial nerveOnce the herpes simplex virus gets in, it never leaves. After the first infection it retreats up a nerve to a cluster of cells beside the brain called the trigeminal ganglion and …
472. Six elements make up almost all of your body's weightOxygen, carbon, hydrogen, nitrogen, calcium and phosphorus account for about 99 per cent of a human body's mass. Five more, potassium, sulfur, sodium, chlorine and magnesium, supp…
473. A broken gene's inactive twin causes most congenital adrenal hyperplasiaRight beside the working gene for the enzyme 21-hydroxylase sits a nearly identical copy that does nothing. When the two swap stretches of DNA, the working copy can inherit the du…
474. Your downward-pointing nostrils mark you as an Old World monkeyLook at a spider monkey's nose and then at your own. Its nostrils open sideways; yours point down. That small difference splits the simians into two great branches, and it places …
475. Your body splits cells about 10 quadrillion times in a lifetimeOver a single human life, cells divide roughly 10 quadrillion times. Each split has one overriding job: copy the full set of genetic instructions and hand an exact duplicate to ea…
476. Robert Hooke named cells after monks' rooms while staring at corkIn 1665 Robert Hooke peered at a paper-thin slice of bottle cork and saw a mass of tiny pores. He called them cells, after the Latin for a small room like a monk's lodging. What h…
477. Francis Crick admitted he never knew what the word dogma meantFrancis Crick called his big idea about genetic information the central dogma, and it haunted him. Years later Jacques Monod told him a dogma is a belief beyond doubt. Crick, who …
478. The tiny cell antenna biologists dismissed as useless for a centuryAlmost every animal cell sprouts a single hair-thin projection called a primary cilium. Found in 1898, it was written off for about a hundred years as a leftover with no real purp…
479. Your collarbone is first to harden and among the last to finishThe collarbone starts turning to bone in the fifth and sixth weeks after conception, before any other bone in the body. Yet it is one of the last to finish, not completing the pro…
480. C. difficile wears chain-mail armour and poisons its gut rivalsClostridioides difficile survives by a mix of armour and chemical warfare. A mesh-like protein coat shields it from saliva enzymes and some antibiotics, it releases a compound tha…

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