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100 explainers so far, 3 more already read. Four fields — Science, Technology, Engineering, Math. Filter or search; nothing here leaves the page.

№ExplainerField SourceRead
№ 01 Why adding noise can create imagesDenoising diffusion Technology · Machine learning Ho, Jain & Abbeel 2:28
№ 13 Why there is no largest primeInfinitude of primes Math · Number theory Mevstrović 1:34
№ 14 Hilbert's hotel: infinities of different sizesHilbert's hotel Math · Logic & foundations Salehi 1:58
№ 15 Euler's identity: e^(iπ) + 1 = 0Euler's identity Math · Analysis Inoué 1:58
№ 16 Chaos: the butterfly effect in a deterministic equationThe butterfly effect Science · Physics Maiocchi, Lucarini & Gritsun 1:57
№ 17 The Monty Hall problem Math · Probability & statistics Gill 1:48
№ 18 Why π turns up where there are no circlesBuffon's needle Math · Probability & statistics Bäsel 2:04
№ 19 Gödel: a true statement that cannot be provedGödel's incompleteness Math · Logic & foundations Gusfield 1:50
№ 20 Random walks: why you end up about √n awayRandom walks Math · Probability & statistics Kostinski & Amir 1:58
№ 21 The four-colour theorem Math · Graphs & combinatorics Robertson, Sanders, Seymour & Thomas 2:18
№ 22 Benford's law: why 1 leadsBenford's law Math · Probability & statistics Gauvrit & Delahaye 2:26
№ 23 Why the night sky is darkOlbers' paradox Science · Physics Arpino & Scardigli 2:59
№ 24 Why time runs one wayThe arrow of time Science · Physics Lebowitz 2:50
№ 25 Why the Sun needs quantum tunnelling to shineQuantum tunnelling in the Sun Science · Physics Adelberger et al. 3:01
№ 26 How we learned to hear spacetime rippleGravitational waves Science · Astronomy LIGO & Virgo Collaborations 3:01
№ 27 Why a magnet floats over a superconductorThe Meissner effect Science · Physics Osorio & Suderow 3:01
№ 28 One particle at a time, and still the stripesThe double-slit experiment Science · Physics Bach, Pope & Batelaan 2:59
№ 29 Why ice floatsWater's density anomaly Science · Chemistry Song et al. 3:02
№ 30 Why a spinning top does not fall overGyroscopic precession Science · Physics Bolina 2:58
№ 31 Hundreds of trillions of neutrinos a second, and you feel nothingSolar neutrinos Science · Astronomy Vitagliano, Tamborra & Raffelt 3:00
№ 32 Why hot things glowBlack-body radiation Science · Physics Passon & Grebe-Ellis 3:02
№ 33 Why a moving bicycle balances itselfBicycle self-stability Engineering · Mechanical Kooijman et al. 3:03
№ 34 Why no engine can turn all its heat into workCarnot efficiency Engineering · Mechanical Esposito et al. 3:06
№ 35 Why AC won: the transformerTransformers Engineering · Electrical Lotfifard 3:00
№ 36 Why power lines run at high voltageTransmission losses Engineering · Electrical EIA; OpenStax 2:56
№ 37 Why an arch standsMasonry arches Engineering · Civil & structural Block, DeJong & Ochsendorf 2:58
№ 38 Why the Tacoma Narrows bridge tore itself apartAeroelastic flutter Engineering · Civil & structural Billah & Scanlan 3:03
№ 39 How a wing makes liftLift Engineering · Aerospace Wild 3:00
№ 40 Why rockets drop stagesRocket equation Engineering · Aerospace Zimmerman (NASA) 3:10
№ 41 How cruise control holds a speed without knowing the car or the roadPID control Engineering · Control & signals Åström & Murray 3:00
№ 42 Why wagon wheels spin backwards on filmAliasing Engineering · Control & signals Shannon 3:02
№ 43 How attention lets a model look back at everythingAttention Technology · Machine learning Vaswani et al. 3:02
№ 44 Why adding the input back lets networks go deepResidual connections Technology · Machine learning He et al. 3:07
№ 45 Why switching neurons off makes a network learn betterDropout Technology · Machine learning Hinton et al. 3:01
№ 46 Why a noisy bottleneck can invent new dataVariational autoencoders Technology · Machine learning Kingma & Welling 3:03
№ 47 Why a small model learns more from a big model's wrong answersKnowledge distillation Technology · Machine learning Hinton, Vinyals & Dean 3:08
№ 48 Learning from preferencesLearning from human preferences Technology · Machine learning Christiano et al. 3:05
№ 49 Why bigger language models are predictably better, until they are notScaling laws Technology · Machine learning Kaplan et al. 3:07
№ 50 Why no comparison sort can beat n log nSorting's lower bound Technology · Computing MIT OpenCourseWare; Jeff Erickson 3:05
№ 51 Why a hash table finds things in constant timeHash tables Technology · Computing MIT OpenCourseWare 3:01
№ 52 Why 0.1 + 0.2 is not 0.3Floating point Technology · Computing Goldberg 3:10
№ 53 Why checking an answer can be easier than finding oneP versus NP Technology · Computing Scott Aaronson 3:05
№ 54 How compression shrinks a messageHuffman coding Technology · Computing Jeff Erickson 3:07
№ 55 Sharing a secret in publicDiffie-Hellman key exchange Technology · Cryptography Diffie & Hellman 3:03
№ 56 How RSA locks and unlocks a messageRSA Technology · Cryptography Rivest, Shamir & Adleman 3:10
№ 57 Why a hash can't be run backwardsCryptographic hash functions Technology · Cryptography NIST 3:04
№ 58 Trading speed for force: gears and leversGears and levers Engineering · Mechanical Urone & Hinrichs 2:58
№ 59 Storing energy in a spinning wheelFlywheel energy storage Engineering · Mechanical Amiryar & Pullen 2:57
№ 60 How an electric motor spinsElectric motor Engineering · Electrical Urone & Hinrichs 2:51
№ 61 Charging a phone without a wireInductive charging Engineering · Electrical Detka & Górecki 2:55
№ 62 Getting to Mars the cheap wayHohmann transfer Engineering · Aerospace Widnall & Peraire 2:56
№ 63 Why we have seasonsThe seasons Science · Earth science Fraknoi, Morrison & Wolff 2:56
№ 64 Why there are two tides a dayTides Science · Earth science Fraknoi, Morrison & Wolff 2:59
№ 65 Why the Moon shows us one faceSynchronous rotation Science · Astronomy Fraknoi, Morrison & Wolff 2:47
№ 66 Why hurricanes spinCoriolis and cyclones Science · Earth science NOAA/AOML Hurricane Research Division 3:01
№ 67 Why flames have coloursAtomic spectra Science · Chemistry Flowers, Theopold, Langley & Robinson 3:06
№ 68 Stealing speed from JupiterGravity assist Engineering · Aerospace H. Morales 3:12
№ 69 Trusting two liarsKalman filter Engineering · Control & signals Welch & Bishop 3:01
№ 70 The weight that fights the swayTuned mass damper Engineering · Civil & structural Mazzon, Frappa & Pauletta 3:06
№ 71 Why triangles hold a bridge upTrusses Engineering · Civil & structural D. W. Baker & W. Haynes 3:04
№ 72 Size buys hours, chemistry buys voltsCells and batteries Engineering · Electrical Flowers, Theopold, Langley & Robinson 3:05
№ 73 Cut the square, keep the areaPythagoras by dissection Math · Geometry & topology Rachel Morley 3:01
№ 74 A triangle with too many degreesSpherical triangles Math · Geometry & topology I. Todhunter 3:11
№ 75 You cannot comb a sphereHairy ball theorem Math · Geometry & topology Peter McGrath 3:01
№ 76 Every answer is rightCoastline paradox Math · Geometry & topology Husain, Reddy, Bisht & Sajid 3:04
№ 77 A strip with one sideMöbius strip Math · Geometry & topology Cartwright & González 3:05
№ 78 Seven bridges, no routeThe bridges of Königsberg Math · Graphs & combinatorics Donna Kirk 3:41
№ 79 Everyone is six steps awaySix degrees of separation Math · Graphs & combinatorics Lars Backstrom, Paolo Boldi, Marco Rosa, Johan Ugander & Sebastiano Vigna 4:11
№ 80 Who asks mattersStable matching Math · Graphs & combinatorics Eric Lehman, F Thomson Leighton & Albert R Meyer 3:32
№ 81 The number that can't be a fractionWhy √2 is irrational Math · Number theory Richard Hammack 4:06
№ 82 Arithmetic on a clockClock arithmetic and Fermat's little theorem Math · Number theory William Stein 3:31
№ 83 Primes never stop, but they thin outWhy the primes thin out Math · Number theory William Stein 3:27
№ 84 0.999… is 1Why 0.999… equals 1 Math · Analysis D. O. Tall & R. L. E. Schwarzenberger 3:33
№ 85 The sum that never stops growingWhy the harmonic series diverges Math · Analysis Steven J. Kifowit & Terra A. Stamps; Jeffrey C. Lagarias 2:52
№ 86 Any shape from sinesFourier series Math · Analysis Jeremy Orloff 3:36
№ 87 The program that cannot be writtenThe halting problem Math · Logic & foundations Boaz Barak 3:34
№ 88 Twenty-three people, even oddsThe birthday paradox Math · Probability & statistics Charles M. Grinstead & J. Laurie Snell 3:40
№ 89 Prove you know it without saying itZero-knowledge proofs Technology · Cryptography Jean-Jacques Quisquater & Louis Guillou; Boaz Barak 4:22
№ 90 How a packet finds its wayPacket routing Technology · Computing J. Moy; E. W. Dijkstra; G. Malkin 4:32
№ 91 Why the network asks senders to slow downTCP congestion control Technology · Computing Van Jacobson & Michael J. Karels 4:22
№ 92 Fixing a flipped bitHamming codes Technology · Computing R. W. Hamming 5:25
№ 93 How a random surfer ranks the webPageRank Technology · Computing Sergey Brin & Lawrence Page; Lawrence Page & Sergey Brin 4:24
№ 94 How a nerve firesThe nerve impulse Science · Biology OpenStax Anatomy and Physiology 2e; A. L. Hodgkin and A. F. Huxley 5:10
№ 95 How bacteria outrun antibioticsAntibiotic resistance Science · Biology Michael Baym et al.; Julian Davies and Dorothy Davies 4:13
№ 96 Why an elephant's heart beats slowlyMetabolic scaling Science · Biology Geoffrey B. West, James H. Brown and Brian J. Enquist; Van M. Savage et al.; Craig R. White and Roger S. Seymour 4:57
№ 97 Herd immunity Science · Biology Paul Fine, Ken Eames and David L. Heymann; Paul L. Delamater et al.; Haley E. Randolph and Luis B. Barreiro 4:46
№ 98 How spots and stripes can draw themselvesTuring patterns Science · Biology A. M. Turing; Shigeru Kondo and Takashi Miura; John E. Pearson 4:38
№ 99 Why the sky is blue and sunsets are redWhy the sky is blue Science · Earth science Lord Rayleigh (John William Strutt) 5:05
№ 100 How a catalyst speeds up a reactionCatalysis Science · Chemistry Paul Flowers, Klaus Theopold, Richard Langley and William R. Robinson; Derek Cheung 4:16
№ 101 A reaction that ticks like a clockThe Belousov-Zhabotinsky reaction Science · Chemistry A. T. Winfree; Alexander Pechenkin; Anatol M. Zhabotinsky; Andrew Adamatzky et al. 4:55
№ 102 How we find planets around other starsTransit photometry Science · Astronomy David Charbonneau, Timothy M. Brown, David W. Latham and Michel Mayor; Joshua N. Winn 4:02
№ 103 How a transistor switches: the gate voltage opens the channelThe MOSFET Technology · Computing Chenming Hu 4:35
№ 104 Why an LED is one colour: the bandgap sets the photon energyLED colour Technology · Computing Chenming Hu; Class for Physics of the Royal Swedish Academy of Sciences 4:20
№ 105 How a touchscreen feels your finger: a grid of tiny capacitorsCapacitive touch Technology · Computing Gary Barrett and Ryomei Omote; Feargal Cleary 4:36
№ 106 Why GPS needs relativity: 38 microseconds a dayRelativity in GPS Technology · Computing Neil Ashby 3:58
№ 107 Why a few turns of rope hold so muchThe capstan equation Engineering · Mechanical Vlado A. Lubarda; Stephen W. Attaway 4:36
№ 108 The shape of a hanging chainThe catenary Engineering · Civil & structural Robert Osserman; Philippe Block, Matt DeJong, John Ochsendorf 5:10
№ 109 The sound barrier and the Mach coneThe sound barrier Engineering · Aerospace John D. Anderson, Jr.; Ames Research Staff; Harry W. Carlson; Jerry M. Seitzman; Domenic J. Maglieri et al. 4:33
№ 110 Balancing a stick on a cartThe inverted pendulum Engineering · Control & signals Bidhayak Goswami and Anindya Chatterjee; Karl Johan Astrom, Richard M. Murray 6:38
№ 111 Recovering a signal from too few samplesCompressed sensing Engineering · Control & signals Emmanuel Candes, Justin Romberg, Terence Tao; Ahmad Mousavi, Mehdi Rezaee, Ramin Ayanzadeh 5:10