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[applause] matt parker: thank you. thank you. oh. wow. can you all hear me? ok. how's that for the correctlevel of disturbingly loud? is that about right?

excellent. so thank you all very muchfor coming along in your lunch break to hear metalk about things to see and hear inthe fourth dimension. my name, as allen verykindly said, is matt parker. and in terms of mybackground i used to be a high schoolmath teacher actually. so my original job wasteaching math to teenagers. and i'm originallyfrom australia.

so i taught inaustralia for a year. and then i realized not enoughpeople were throwing chairs at me. and so i moved to london,and that fixed that. and i taught in londonfor a few years, again in a couple ofdifferent high schools. and then i started to driftfrom normal math teaching to kind of education support. i started working for someuniversities in developing

resources and doingsessions for school kids. so schools would send theirkids along to the university and we'd do like summerschools and things with them. and so i did that for a while. actually, i didthat for 18 months, and then i started to getnostalgic for the classroom. so actually, at onepoint, i went back. i did six months in aninner city london school. and that just clearedthat right up.

right? and at the end of thati'm like, i'm out. so since 2009 was the last timei was a real teacher as such. and my career now has spreadacross several things. you can see i'm based at queenmary university of london, which is a universityin east london. i'm there one day a week. i'm their public engagementin maths fellow, which is what happens when you'reallowed to write your own job

title. so fun fact, fellow is themost academically sounding credential you can havewith no qualifications. and so i teach the academicsand the undergraduates to communicate mathsto other humans. and then the rest of my time isspent doing things like this. i do a lot ofwriting about maths. i do a lot ofspeaking about maths. i work as a stand-up.

so actually for awhile i was doing both. i was a math teacher andi was doing stand-up. so during the day, i wasteaching math to teenagers, and in the eveningi was telling jokes to drunk people incomedy clubs, which is a surprisinglysimilar skill set. and after awhile i realizedi enjoy doing both together. and so i do a lot ofvery nerdy comedy. and i do a lot of bitsand pieces for media

and youtube and the like. oh, i do a lot of, quitea bit of work on youtube. so if i look familiar but inhigher resolution than normal, i do the numberphilechannel on youtube. actually that wasin the first round of funded youtube channels. that was the only non-us onewas the numberphile channel. we started in the uk. so thanks, there youare, which is great fun,

and we still do it. and there was a weird crossoverpoint where the kids in school started recognizing me morefrom youtube than from tv work. and the teachers had no ideawhat they were talking about, which it's great that a lot ofnerdy kids if they get bored at school can turn to youtube towatch fascinating bits of math. you know? i think that'sabsolutely fantastic. and it's kind of fixed aproblem where bright kids would

get very bored atschool and they get switched off the subject. whereas now they can access thismuch wider community of people, and they can see theexciting side of mathematics. and that kind of keeps themgoing while they're at school. and so the book was an attemptto do a very similar thing as well where i wanted to kind ofpackage up some of the things i do with schoolkids. i thought there's no pointbringing you along here

and making you hear about metalk about the book themes "to make and do in the fourthdimension," which is why you're currently enjoying the talk,"things to see and hear in the fourth," awilding different talk, i must point out. i mean, completelydifferent content. but there are booksaround, and i'll be around to chat afterwards. and i may refer to a fewthings that are in the book.

and so that's pretty muchin terms of who i am. so what i'm going todo today is effectively just show you some of myfavorite bits of math. and i'll do that forapproximately the remaining 2/5 of an hour-- 24 minutes. if you didn't knowthat was 24 minutes, you're working forthe wrong company. and then i will be around. we'll do somequestion and answers,

and then i will loiter aroundafterwards to have a chat. and we are actually goingto do some math, by the way. that's not an idle threat. so can everyone whobought their calculator, could you take that out now? really? is that an actual calculator? no. it's a phone.

fine. what? you're going for a phone? phones are perfectly acceptable. some of you have alreadygot wolfram alpha open. that's brilliant. so if you could get out yourfavorite calculation device and switch into calculatemode-- you don't have to. this is purely optional.

we're going to do a fewwarm up calculations just to get us going. so once you've got it out, putin any two-digit number you fancy, and then calculate thecube of that two-digit number. and if i was doingthis with schoolkids-- i do a lot of thiswith high school kids-- i'd be very careful to saymultiply it by the same two digits, then hit multiply,same two digits again, then hit equal.

if you tell it to yourfriends, and you're not sufficiently specific,you'll get the fourth power by accident. but most of you shouldhave very happily cubed a two-digit number. and what you'redoing is the kind of boring part of math--the multiplying thing over and over. it's the reason whywe have calculators.

the fun part is what you cando with patterns in the answer. is there anyone who'sprepared to share the answer that they've got? not the number thatyou start with, but the answer on your screen. yes, sir. what have you got? audience: 357,911. matt parker: soyou put in 357,911?

so you put in 71 and cubed that. you're keeping your excitementat a manageable level. don't patronize me. right. so has anyone else got ananswer they're prepared? tell me, if i get it right,instead of just going, hm, if you could say, yes. the thumbs up is optionalbut highly recommended. if you could say yeswhen i get them right

that would help myself-esteem dramatically. has anyone got ananswer they're prepared? and if you give it in so manythousands and then the rest. what have you got atthe back, phone guy? audience: 804,357. matt parker: 804,000--you put it in 93. audience: yes! audience: sweet! audience: awesome.

matt parker: some of you areapplauding sarcastically. i would do threemore, and then you've go the correct amount of wild. so are there three people--don't call them out yet-- three people who are preparedto give me the answers. if i get all three rightin correct succession, then you can humor mewith some applause. so this is one. hang on a second.

remain calm. one. anyone else? two over there. and three over here. we'll make it likean exponential trick. so we'll start withyou over there, and then you, ma'am, andthen that guy on the end. around.

here we go. so what have you got over there? what's the answer? audience: 531,441. matt parker: 81. matt parker: remain calm. audience: 21,962. matt parker: 28. silent nod yes.

and? audience: 132,651. matt parker: 51. woo! matt parker: fine. now, by the way,because some of you are now working outhow that's done. some of you probablyknow how that's done. and so i'm not goingto explain it fully.

but first of all, i'venot just memorized every single two-digitnumber cubed. actually, i've beendoing it for a few years, so i'm dangerously closeto having done that. what i'm actually doing is thereare patterns in the answer. and so there are twopatterns in the answer. and one pattern givesyou the first digit, and the other patterngives you the second digit of the originaltwo-digit number.

so as you're calling outthe number, all i'm doing is i'm scanning it for thefirst pattern that comes up is the first digit-- yeah. the first digit andthe second pattern gives me the second digit. so i'm just scanning forthose as you call it out. and it's not analarmingly difficult thing to do in your headif you learn it. if you want to work out how todo that, if you come and see me

afterwards i'mhappy to explain it. or if you just try cubing sometwo-digit numbers, as some of you are doing right now,or you're texting a friend. you wouldn't believe what wasin the lunch time talk today. and so if you try somenumbers-- most of you have probably got aspreadsheet open right now. it's reasonably easy towork out how that's done. so i'm going to do amuch harder calculation. and a few of you, again,will know how this is done.

but if you haven't i willexplain this one at the end so you can all learn this. and this doesn'tinvolve a calculator. it involves somethingwith a barcode on it. could everyone have a look? i need someone inthe audience who's brought a productthey've purchased in a shop with a retail barcode. not technically a joke butthank you for joining in.

so, oh, my book. so not my book. has anyone got a--what have you got? what is that? chewing gum. can you have a look atthe barcode for me, sir? is there are tiny little digitto the left and a tiny digit to the right, and all theother digits are underneath? don't say what they are, butthere's a digit on each side.

what i'm going to get you todo in a second is to read out all the digits tothat barcode, starting with the one off tothe left, all the ones underneath, and do not tellme the one off to the right. i'm going to try andcalculate in my head what the one offto the right is. if i get it correct,you shout, yes. everyone goes bananas. and i already know some ofyou are very good at that.

and don't go too fast. i will say, yep, after eachdigit as we go along so i can-- people can oftenrace through them. audience: zero. matt parker: hang on. hang on. i'm getting in themath zone over here. all right? i'm ready.

first digit. matt parker: is it the samezero or a different zero? is this the one you said? that's the one onthe left is a zero. i'm sorry. well, give me a second. got that. yep. audience: one.

matt parker: one. got it. audience: two. matt parker: yep. audience: five. audience: four. audience: six. audience: seven. audience: eight.

the final digit. is there one more? it's a six. audience: yes. yes! audience: woo! yeah! matt parker: i like abrief moment of confusion before the climax to a stunt.

so now that-- some of youhave no idea what you just applauded. so that, those of you who knowabout check digits and error detection and errorcorrection, which is a vast majorityof you, will know that there is a patternin all barcodes. and all north americanbarcodes have the same pattern. it's a slightlydifferent pattern to what they have in europe.

so i had to learn a differentmethod to make it work here. if you want to learn how todo that-- this is the pattern. so as someone is reading outthe digits of the barcode, initially, all you haveto do is add together every odd positioned digit. so you add the first thingthey call out to the third to the fifth all the way up. and if you addevery second digit, starting in the firstposition, you get a subtotal.

you multiply thatsubtotal by three, and then you go back and add onthe other digits you skipped. and if you add every seconddigit, multiply by three, add the other digits,for all us barcodes, the grand total willbe a multiple of 10. and so if you keeptrack in your head and there's one of themissing at the end, it's whatever you need toget-- ok now some of you are mildly impressed--is what you

need to get up tothe next digit. so the total in myhead ended in a four. and so i knew it must be asix to get up to the next one. i'm a hoot atparties, by the way. and so i think it's amazing,because most people have no idea that these patterns arebuilt into barcodes and things around them. and so actually ifyou look on the book, it's got the barcode at thebottom and the isbn at the top.

and the isbn is a subtlydifferent pattern. but again, it's gotexactly the same thing. credit cards havethe same thing. i can do the same stuntwith credit cards. but very few people will readtheir entire 16 digit number out in public. but that's subtly different. you double everysecond position. and if you get atwo-digit number,

you add the digits togetherto get the digit root. and then once you addall of those together, you get a multiple. and most people go abouttheir daily lives completely oblivious that all thesemathematical patterns are in the background. if we didn't have thatpattern in barcodes, our modern shoppingcenters wouldn't work. because when you scansomething at the supermarket,

because the lasers aren'tvery accurate-- because lasers make a lot ofmistakes-- physics. but thankfully mathcomes to the rescue. because if it scans the barcodewrong, the pattern won't match. and so it knows it'smisscannned the barcode. and so it keepstrying to scan it until it gets one wherethe pattern matches. the vast majority of thetime that then means it scanned it correctly andit goes onto your bill.

and people get very emotionalif they scanned one product and had to pay for something. well, it depends on theprice difference, i guess. and so people don'tknow that this pattern is hidden in thebackground there. and the same thing happenswith text messages. so those of you whoknow reed-solomon and the types oferror and coding you can do with textmessages, there's

a fantastic way to look at whathappens with a text message. because when you'retyping in the text message and your phone is turningall the characters you're entering intonumbers, it effectively puts those numbersinto a giant grid. it goes through that grid andputs a mathematical pattern into every single row, andthen puts another pattern into every singlecolumn, and then puts a third pattern intosubsections within the grid.

and if that soundsvaguely familiar, it's because it turns your textmessage into a sudoku puzzle. and so people have a sensethat if you give them a soduku puzzle, even though hugesections are missing-- all these numbersare missing here, all these numbers aremissing down here-- if you know the threemathematical patterns, you can recreate allthose missing digits. and so people, for fun,do error correction

as kind of a leisurely activity,which i think is fantastic. and so you see, i pushpeople like on the train will be doing. i'm like, oh, you loveerror correction too. but this is absolute amazing. and if you give itto more than one person everyonegets the same answer because you're usingthe same pattern. so the differencewith text messages

is it's done more as a cube,and the its coefficients or polynomials are done inthree different directions across the cube toget the same pattern. but it's exactly thesame logic behind this. and people are quite happythat the can solve a soduku. but yet, they thinkit's astounding that if there's anerror or information is lost when they send a textmessage that the phone can recreate all themissing information.

the same thing with blu-raysand everything else. and there's suchgood error-correction to blu-ray discs, you canget a drill bit, which is about three or fourmillimeters across-- so that's some obscure fraction of aninch-- and if you get that, and if you get blu-ray disc--if you get someone else's blu-ray disk, youcan drill a hole straight through the middle. well, not straightthrough the middle.

there's already a whole there. you can just to the side,you can drill a hole. and if the laser--physics-- is good enough in the blu-ray, becausethe main issue is cheap blu-ray players will losetrack of where they're up to. if it can keep track, itcan recreate all the missing information that'sbeen drilled out. and again, without thesemaths, modern technology simply wouldn't be possible.

oh, and i made thisone myself, by the way. i'm quite proud of this. i wanted it to looklike and x, like an algebraic-- tough crowd. whoa. the top row are the digits inthe order they appear in pi. there you go. so if you want a copy ofthat, send me an email. and so i quite like that.

it's kind of usefulmaths-- like maths you can actuallydo something with. well, actually i've got anotherbit of fantastically useful maths i'm going to teachyou, because i thought i've got to show you somethingyou've not seen before. you've going to bevery disappointed. and you people work on encoding. you've been working on encodingall day, and you come in here and you're like, oh, great.

this is my lunch breakdoing error correction. so i'm going to showyou some useful maths to save time in yourday to day life. and to do that i broughtwith me down here-- actually, i'm going to go offmic and yell for a second. possibly even betternow that i've got-- ok. so i've got down here a camera. so this is on the floor here. i'm going to teach youthe mathematical way

to tie your shoes. and this will speed upyour life immensely. so can you all see? can you all see my shoe? you get four of them. that is-- oh wow. this is like the world'smost surreal chorus line. look at that. so if anyone comes inlate now just go with it.

ok? so here' what you do. so normally whenpeople tie their shoes, they get the laces in likea little foundation knot, and they get theseand they do all sorts of moving them around andmashing them together. what you can actually do, ifyou just hold the two places and passed themacross each other, they will tie themselves.

you again, keepingyour excitement at a nice, manageable level. what do you watch? actually, is there adelay on the camera? can i? i bet i can tie this andthen watch myself tie it. ready? read. so i'm just holdingthe laces, and tied.

close. i'll bet you never triedthis, because normally i do this for school kids,and normally they're sitting fire tosomething by now. would you like to try it? if you've got to shoe, chooseyour favorite, undo the laces, and i will actuallyteach you how to do this. so you do that littlefoundation knot there. so you've all got that.

take the shoelace onthe right and curve it so it goes up and forward,and you hold on the way down. so it goes up in aloop and then down. you're holding on thedescending part of the loop. the other side is the samething, but it curls back, and you hold it on thedescending part of the loop. and then all youhave to do is pass the bitch you're holdingunder the other loop, swap hands, and pull.

audience: whoa! matt parker: oh. that's-- we'vebeen through there. don't patronize me a bit. so if you practice that,you can save literally ones of seconds of yourlife on a daily basis. and it's exactly the sameknot that you end up with. so mathematically,that is the same knot. and a lot of peopledon't appreciate

that there's a whole areaof maths about knots. there's knot theory. best name of a theory ever. and so people areknow theorists. are you a theorist? i am knot theorist. so knot theorists look at themaths behind different knots. and as humans we knowdangerously little about knots. it's a reasonably newarea of mathematics.

well, it kickedoff in the 1800s. but today we still haven't gota great understanding of knots, in general. and, in fact, i put a pictureof one knot in my book. i've got a shot of it up here. we still do not know thebest way to undo this knot. this is called the1011 knot if you want to look it up afterwards. and when you do aknot diagram, you

leave a gap whenit goes underneath. these are not justjoint bits of string. this is where it goesunderneath there. and to undo a knotmathematically, you do sort of acrossing switch. so you would cut onebit of the string, move it around another one,and join it back up again. so you take it from one side tothe other side and rejoin it. and we know this not canbe undone in three crossing

switches, but no one'sfound a way to do it in two, and likewise, know one's managedto prove that there isn't a way to do it in two. this is an openquestion in mathematics. this is, in fact,the most simple knot for which we do not understand. at for the vast majority ofknots above it we have no idea. and so my theory is, if enoughpeople make this out of string and try it, sooneror later, if there's

a way to do it-- for a verygenerous definition of sooner or later possibly-- we will comeacross how it can be undone. and at that point fameand mathematical fortune is yours, for a very narrowdefinition of fame and fortune. so, dude if you can try andmake that out of string, you look it up online. it's the 1011 knot. if you do find a wayto do it let me know. photograph yourselfpointing at the bit

where you're going to makethe crossing switches first. then make them. if it untangles, we'llknow what you actually did. because if ithappens and you don't know how it was arranged--because in this arrangement it won't work. we've tried everythingin this arrangement. you have to make it that way,pick it up, jumble it around, put it down a different way,make two crossings switches,

see if it untangles itself. and actually, it'sreally important that we know how to do this,because at the moment bacteria is betterat undoing knots than humans, which isa little bit worrying. because when bacteriareproduces-- in fact, same thing happenswith most cells, and human included-- the dnagets tangled and knotted. and so some bacteriahave circular dna,

gets very knottedwhen they reproduce. and there are enzymeswhich go around and perform crossing switchesexactly like that. they will snip one bit of dna,move it around another one, and rejoin it. and they do thatvery efficiently to untangle the dna. and if they can't do that,the bacteria can't reproduce. and so knot theoristsfrom the maths department

are working with biologiststo try and work out what the bacteria is doing,why it's better than us, and if we get a betterunderstanding of both what it's doing and how to undoknots in general, that could be a new waveof antibiotics. if we have a way toimpede or stop bacteria from unknottingits dna, then we'll be able to stop itfrom reproducing. and so i thinkit's very exciting

that a future wave of newmedicine, the new therapies, can come about because knottheory, which was started initially by physiciststrying to understand a string theory of matter iswhat first kicked off, but then mathematicians took iton because it was kind of fun. and it could be savinglives in the future, which i think is absolutely fantastic. so i've got two--actually, you know what? let's do threethings, and then i'll

wrap up for questions, becausei've got a new toy that i'm going to show you very quickly. and i've put it in my bag here. i wasn't originallygoing to talk about this, but while i'm here, imade this two days ago, and i'm very excited about it. what i did was i bought abrass disk off the internet. i bought this. i'm sure i used a googleservice or another.

and so it definitelywasn't from amazon. and then what i've done is i'veput a small notch in the disk. and that notch is 14 and1/2 percent of the diameter. or it's 29% of the radius. or it's 2 minus root 2 on 2%of the radius to be specific. and the reason i've done thatis if you do it to two disks-- so a circle rollsbecause as it rotates the center of mass staysat exactly the same height. very, very handy.

but if you get twodisks and you intersect them like this atright angles-- and i made those notches so thecenters of the two disks are now root 2 apartcompared to the radius. so if you've got oneunit is the radius, that's root 2-- the distancebetween the two disks. so what it means is as thisrotates on a flat surface, the center of mass staysat exactly the same level. and i haven't got aflat surface here.

i'm going to try it over here. i checked. my cable's not long enoughto get the camera over there. but i'm going to try on thisbench, if you don't mind. so if i put it there, if i givethat a bump, the center of mass stays at exactlythe same height. and if you want to kick thatback in the opposite direction. it's optional. feel free to join in.

it's all right. so the center of massis going side to side. it's not even a sin wavegoing backwards and forwards. it's a quite complicated wave. it's a combinationof different curves. but in terms of itsheight above the surface, it stays perfectly flat. and you can prove that for twomain locations using nothing more complicatedthan pythagorean's

system of triangles. so i shall challenge forwhen you should be working, use some of your 10%time to calculate why the center of mass forthat one, because what you do is the shoe in the centerof mass is the same height, and it would drop out, andthe center of the disks has to be root 2 a part. that's the easiestway to go about it. and using the pythagorean'ssystem of triangles

you can show that. i will leave it up there. and if you want tohave a play with it afterwards you can rollit backwards and forwards on there. or you can makeyour own out of cds, which you might have insome of the display cases with technology from the past. or make your own circles.

you can get those toroll quite nicely. it's kind of fun. so the last two thingsi'm going to show you is a ridiculous project thati did a couple of years ago. and i'm going to finish byshowing you the christmas present that my mom gave me twoyears ago, which is relevant. it's not just like, hey,check out this jumper. it's a proper maths thing. but before i get that, thisis a ridiculous project

i did a couple ofyears ago where i was trying to explain theway that logic circuits work. and to try to explain circuitryto people in general i decide to use dominoes. because what i'vedone here is i've set up a chain of dominoes. and the great thing abouta set up of dominoes is you can send theinformation along dominoes, because if you puta signal in one end,

that signal willmove along the chain and come out the other end. and so you could use this. this could be practical. so if your doorbellhas broken, you could have a longchain of dominoes. so you've got atsign at the door that says please bump domino. and that goes all theway through your house

into the living room. and a few of the otherdominoes fall over. you go, oh, there'ssomeone at the door. and they're sending information. not hugely efficient,but it would work. and you can get farmore complicated. so instead of just sendingone little bit of information, you can have a networkthat interacts. so now i've got two inputsand a single output.

and this is step soyou have to bump over both inputs for theoutput to go over. if you bump overeither one separately it won't make it all theway through the circuit. and so if you wantmore information about who's at the door-- solet's say you order a pizza, and you've got one thing thatsays bump this domino if you're here, and anotherone that says bump this domino if you have a pizza.

and only if there's someonethere with a pizza will the signal get allthe way through. and i can show you thisworking, because what happens is this one by itself blocksitself from getting through. whereas if you'vebump that one as well, it would have stopped thisone from stopping itself and the signal wouldhave gone through. and for this, i like to considerknocking a domino over as a one and it standing up as a zero.

and so you can see i'vegot a table in the corner. i'll make it alittle bit bigger. so for completeness, thisis the complete setup for that circuit. we can still think ofthis in terms of pizza. so zero and zero. no one's at the door andthey haven't got a pizza, and so nothing will happen. this is there'ssomeone at the door

and they haven't got a pizza. that won't get through. for completeness, somehow apizza has arrived at the door and has managed to read thesign and bump the appropriate. so should there bea self-aware pizza, this is what will happen. the signal, thank god,won't get through. because that is ahorrifying experience. and then here we had theperson with the pizza

and the signal gets through. and this is an and gate. so if you've donelogic gates, this is an and gate madeout of dominoes. we can do even better. this is the exclusive orgate where the signal only gets through if you bumpover one and the other one, but not both. so that's the exclusivebit-- one or the other,

not both simultaneously. there it is madeout of dominoes. if you've got 100dominoes and you're bored, you can make these. it's about 100 dominoesto put these together. and what happens now isyou hit them both together, they collide in themiddle and stop. but if you hit eitherone separately, it will travel throughand out the other side.

so they stop and annihilate,where as one, by itself, would've carried on and out. now at this point, a fewof you are thinking, why? why would you do? you know where i'mgoing with this. and if you know wherei'm going with this, my only advice is fornow just remain calm. because we have a longway to go with this. because what you can donow is get to a circuit

where it shows bothsimultaneously. if you have two inputs and twooutputs and one's the and gate and one's the exclusiveor gate, you've got a circuit which countsthe number of inputs that have been bumped. so this is a verybasic calculator. so if you think of theoutputs as a binary number-- the exclusive order to theunits, the and as the twos-- and then it tellsyou how many inputs

were bumped as a binary readout. so this can count in binary. and to make one you need200 to 300 dominoes. it looks a little bit like this. and so this has twocircuits coming in. it's basically exclusiveor but with an extra block on the side. this is a delayed circuitto give this long enough to run, you slowdown this signal

so it doesn't getthere ahead of time. so there's a few timingissues with this circuit, but it can be made. and a few of youare thinking, well, if you've got thisfar, what you really want is-- this isthe full adder. right! so try not to skip ahead tothe punchline without me. so this is the full adder.

so you can do any arithmeticyou want with a full adder, because you've got thetwo numbers you're adding, you've got a carry fromany previous calculation, you've got the carry out thatflows on to the next column, and you've got theright out, which is the output you're doing. and so if you canmake a full adder, you're effectivelycounting any free inputs and getting the two digit out.

now unfortunately, at thispoint, i worked it out. to build one of these wouldtake about 1,000 dominoes, and it would look like that. [laughing] so this is me at themanchester university. this is the mathsfloor-- very flat. we managed to sneak in there. we have 1,000 dominoes, andwe built a working full adder out of dominoes.

and so again the problem wasslowing down the signals. you've got a lot ofsynchronization issues. but we got to slowingthe right ones and sending the other ones. slowly the whole thingworked really well. and then we were like,well, this is brilliant. and some of you know ifyou chain these in a row-- if you have adders in row, youcan add numbers of any size. so if you had threeof these in a row,

you could add twothree-digit binary numbers and get a four-digitbinary output. but that would take10,000 dominoes, and it would look like this. so i now own 10,000 dominoes. so this took us a whole day. it took 10 of us, or 12 people. we were rotating in shifts. oh my god.

this is nerve-wracking work. and so we managedto build a circuit with 10,000dominoes, which would add two three-digitbinary numbers and give you afour-digit output. so this is a workingcomputer circuit. this is an actual computer. i mean, the displayresolution is terrible. but it does actuallywork as a computer.

and we ran it and it worked. we were able to addtwo three-digit numbers and got a four-digit output. and we had the museum-- this ismuseum of science and industry in manchester. brilliantly-- you can'tsee it in this shot-- we are directly in front ofthe rebuild of the first baby computer that alanturing worked on. so it was behind us.

i could see the vacuum tubes andeverything of the original baby computer. and i was allowed onceto have a play on it. and it's so cool,because the memory-- the input for the memoryis a board of buttons. and literally each onecorresponds to a bit. and so you enterthe ones you want. that ones to be a one. that one's a one.

and so you enter the ones thatyou want to switch to ones and hit go. nominal piece of kit. and i got to meetalan turing last ever student who worked withhim on that machine. and so he told mestories about turing where the operating system thatran the version after that. absolutely incredible. happy to chat about that.

oh, and by the way. "theimitation game" film, not that bad. pretty good. the mass is-- i mean,it was very brave. the first half an houris cumberbatch describing how you prove the existenceof uncomputable numbers. so i was very impressed. it's not. he just lookshandsome and smolders.

but if you want to talkturing, see me after this. so anyway, so wegot to build this in manchester, whichi was so pleased. and we did it on thefirst day, and it worked. at we had a backup day. and we're like, well,let's not waste this, because we could havetwo four-digit inputs and get a five-digit readout. and we did that.

but it didn't work. two things went wrong. because we didn'thave any more space because we had the samesection of the museum kind of sectioned off. and we didn't haveanymore dominoes. so we had to make itmore dense, and we had to make it more efficient. so we have to cutback on the timing,

and we had to have therows closer together. and two things wenthorribly wrong. the first one is here. we had cross torque. we had signal bleed from onerow of dominoes onto another. so if you watch, this onehere should not fall over. that domino should stay up. but if you watch as the otherchain comes through-- here it comes-- as the other onecomes through, it-- here it

comes. look at that! and, in slow motion,here it comes. no! so that gave us an extraoutput we didn't want. so that ran through and trippedwhat should have been zero, and the answer became a one. and the other one was here. so let me should youwhat happens right here.

if you watch thatrow of dominoes, it is going to carryalong to this output here. but this one should get theirfirst and, bam, stop it. i've been watching alot of american football while i've been over. and so, bam, itshould stop it there. so this signal stops. it closes this gate beforethat signal gets there. unfortunately it didn't work.

if i show it toyou in slow motion, is this one so goingto get there first. so going to get there first. here it is. here it comes. coming in. it's going to closethat gate, and-- ah! two dominoes off. but at least it wentwrong in interesting ways.

if it had just beenbumped by accident that would havebeen very upsetting, but it went wrongin sightful ways as to what happensin actual circuits. because that was asynchronization issue. so i was so please withthe way that worked out. well, actuallythe last project i did was a collaborativeproject using different museums around the world, andwe use google hangouts.

we used a livefeature on hangouts to link between differentbuild sites around the world. so i was inmanchester, and i could talk to people whowere working in finland and canada and the us. and the fractal, we'rebuilding a mega menja, the one that is at moma, museumof science and industry, here. so if you want togo and look at it, it's an amazing fractalthing they've put together.

and it was great thatwe could use hangouts. people could watchat home, and we could cut between thedifferent builds sites. absolutely brilliant. anyway. the last thing i'mgoing to show you, and then we'll doquestions, is i brought the christmaspresent my mom made me. i've got it right here.

and so i'll bringup my-- is that my? it looks like-- ok. so you should have seenmy giddy face on christmas morning when unwrapped a knittedscarf made entirely out of ones and zeroes. i had no idea she wasdoing this behind my back. and she went and she made this. i was like that's amazing. and when i saw itinitially, i thought

they were just randomones and zeroes. and so then i went,well, hang on. every single rowstarts zero, one, zero. and so that meansevery single row is an upper caseletter in unicode, because my mom knits theway she text messages. old habits die hard. huh? and so i was like,well, i've got

to look work out what it says. this is christmas morning. i was like this is brilliant. so i got the back ofthe wrapping paper. i got my pen out. what a christmas morning. i get to sit around with thefamily and decode my present. and if you actually gothrough and work it out-- oh, i'm now fluent in binary,by the way, of course.

because when people get meto sign their book, i can say do you want that in normalcharacters or in ascii? and so i can do people'snames in binary. if you're boredafterwards, come up and i'll put yourname in in binary. and i suspect most of youwould then go and fact check that very quickly. and so anyway i wasable to work it out. my mom found a quote for me.

she found [inaudible]for a website. so it says, "maths is fun. keep doing maths." except it doesn't. when i actually decoded it,she swapped a one with a zero. there's a mistake part way down. and so it was right on the end. it turned a u into a v. a so itactually says, "maths is fvn. i was like, oh, mom.

i hate to ruin your fvn,but, you have swapped a one with a zero, andshe was very upset. because she is quitethe [inaudible]. and i was like,well, actually mom-- because she wanted totake it back and fix it. she wanted to undoand replace it. i said no, no, no. the thing is you don'thave to do that actually, because to make thescarf long enough

she knit the samemessage four times. so it repeats, front,back, front, back. and she only made amistake in one of those. so what is meansis all i have to do is calculate the average valueacross all four versions, and they gives you backthe original message without the mistake. and so today, ladies andgentlemen of google, i can present to you the world'sfirst error-correcting scarf.

if you would liketo meet the scarf, i will leave it at the front. it does also sign autographs. you have to hold itwith the pen yourself. so you're coming toget a photo of you wearing the scarf, that's fine. i will leave that here. you can come and check thecode to make sure it all works. otherwise, i will be loiteringuntil i get kicked out

or people have togo back to work. if you want me tocome and deface your book so itlowers resale value, i'm more than happy to do thator answer any other questions. if i've mentioned somethingand you've missed, or you want to copy of all thecircuit diagrams for the domino computer are in the book. and originally they were like,i put them in, in my head and looked at it and went, ok.

you're not having it. they're not going in. oh, ok. it happened to a few things. i said, tell you what,would i be allowed answers at the back of the book? and they were like sure. brilliant. so seriously a massivechunk of the book

is answers at the back. and so the circuit diagramsto the dominoes are in there. but if you could send me anemail of anything else you want a copy of or i'vementioned something and didn't go into enoughdetail, let me know. but on that note, i've finished. i'd like to thank allenvery much for organizing all of this. it has been fantastic coming in.

thank you all very muchfor listening so well. cheers. oh, we have to q and a. right. so-- he had that look ofyou're not finished yet. i know you got thefree lunch first but now you've got to earn it. so any questions peoplewould like to ask? if you can't get to themic, i will repeat them for the sake of the recordingsso the end up apparently

encoded. but if anyone wouldlike to come up, you can ask questionsfrom the center. if you're bringingyour laptop with you it's going to bequite the question. i simulated this and frankly. audience: while writingthe book, what's the most amazing thing that youlearned that you didn't already know, and that fascinated youas a problem and the solution.

that is a very good question. so writing the bookwhat was the thing i learned that wasthe most surprising? there's a few bitsin there where i found new examplesof types of numbers, because i've been learningpython as a hobby. so i had to programat university, and i hadn't done it for years. there was a few bitswhere i ran simulations

to find ridiculous numbers. some of those were kindof fun, but i kind of knew they would be out there. if i ran the code they wouldshow up sooner or later. what i really found amazingwas because the book, the conceit is it's aboutthe fourth dimension. there are huge sectionsabout 4d shapes. and in 3d-- i knew this before,but i've never actually looked into it-- in 3d you getwith the platonic solids.

if you've not comeacross these, they are very, veryregular 3d shapes. all the faces are the same,all the vertices are the same, edges are the same. and there's famouslyfive of them. so there's the tetrahedron,octahedron, cube, icosahedron, and dodecahedron, in arandom order i just made up. and in 4d there's another one. so you get the 4d equivalenceof the fine standard platonic

solids. there's another one thati call the hyper-diamond. it's the 4d equivalent ofa rhombic dodecahedron. but it is a platonic solidin 4d, and it's not in 3d, and it's not again in 5d. it breaks again in 5d. it only works infour dimensions. and so visualizing it-- i tryto find a way to visualize it. and in 3d a rhombicdodecahedron is

what happens if you get a solidcube and turn it inside out. so if you imagine sixsquare-based pyramids and flipped them allaround the other way, you get a rhombic dodecahedron. the same thing happensin four dimensions. if you get a 4d tessaract--a 4d cube and-- oh, if anyone's, i don't want toruin-- you know spoiler alert-- "interstellar" theymention tesseract. i was like, yes.

oh, and by theway, i can confirm, the fifth dimension is love. and so the same thing happens ifyou turn a 4d cube inside out, you get the hyper-diamond. and then, in caseyou're wondering, 5d is any three-point solids. and that's everydimension above that-- 60, 70, as long as you go,you'll only ever always get the cube, the tetrahedron,and the octahedron repeat

all the way up. and then the other onesyou never see them again. and so there's thisfantastic flare up of shapes in kind of threeand four dimensions that doesn't happen again. i think that was fascinating. further answers will be shorter. yes? audience: can youtell us some more

about the testingof the calculator? like did someone accidentallyhit a domino down? did you try it out? if something goes wrong, canyou reset the whole thing? how long did all that take? matt parker: ok. so the questionwas can you tell us more about testingthe domino calculator, and could you relive some ofthose horrifying experiences?

so to this day the sound ofdomino toppling on concrete breaks me out in a cold sweat. so originally i bought abox of about 100 domino. i'd seen a youtube videoof someone trying it. and they'd kind of cheated. they'd taped dominoes together. and they were doingthe and gate, i think. well, surely youcan do a half adder. so i bought a couple hundred.

and it kind of worked. and then i went, all right. and so i bought 2,000. and then we had the concretefloor at the university. and we wanted to know firstof all is it reliable enough? we were really worried aboutif it would be reliable enough. and can it be built fast enough? because if we couldn'tactually build that thing it wasn't going to work.

and the big problem was havingthe junctions work routinely. and a very goodmathematician sean, she came up with-- we calledit the juncsean, which was a reliable way of buildingthe junction, and it was very, very, if you did it exactly theright way, it works every time. it was very robust. and so we built astencil of that. and we chalked onall those junctions because we knew they would work.

and then you kind of freestylegetting between them. but we knew as long as we usedthose for the uncritical bits it would work. in terms of actually buildingit, you'd leave gaps. and the rule was,trust the gaps. that was our official rule. well, actually, onerule we had was, if you bumped dominoesover by accident, because occasionally you wouldknock them and they'd all go.

you're like, ah. the rule was you thenstand up and walk away. because someoneelse will come in, someone who's nowemotionally invested, because you're nowbalancing dominoes with a sense of revenge. and so someone else would thencome in and put them back up for you. and the rule was trustthe gaps, because we

knew we were going tobump them over by accident and they were going to run. but as long as there wasa gap they would stop. and i saw one volunteer,because i just asked on twitter, hey, people come andbalance dominoes. and one got bumped it,and it started to run. and he lunged totry and stop it. and he bumped theones after the gap. and so then they sayand he was like, oh.

i was like you idiot. and then he realized what hedid and tried to stop those and bumped the onesthere, at which point we were just wrestlinghim away from them. and if you watch the video--i've got a youtube video. it's about half an hourof me balancing dominoes. and i explain the binaryand everything else. you can see people walkingaround inside-- because we had to fill in the gapswhen we were done--

and we did like a fractal. we did every like middle bit. and then we went back and dida little bit and a little bit so trying to minimizethe possible damage. but to load it we left gapswhere the data would go in, and you filled in for oneand left it blank for zeroes. and we picked randomnumbers at the end, and then people had to walkout into the center of it and fill in where the ones were.

it was the most hair-raisingthing of my life. but in the end it worked. we had one spontaneous bit wherewe were just standing around and suddenly a dominofell over and a bit ran. but we hadn't doneall the gaps yet, and so we were able to fix that. very, very stressful. if anyone's everin the uk and you want to borrow 10,000dominoes, let me know.

i'm happy to lend them to you. i bring up a place because iwant to buy them wholesale. i ring them up and say i wantto buy dominoes wholesale. and they go, oh, no. we only send them to shops. and i said well, i want 10,000. they were like, we'llwork something out. and so i got themdelivered to the museum. it was brilliant.

so now actuallyschools use them now. so schools cantake them for free if they pay transportfrom the previous school. so they get sentaround between schools, and they try and build thecircuits, which is great fun. so i will do one morequestion, and then i will loiter around if youwant to have a chat with me afterwards. has anyone got?

it could just be-- i thinkthe pressure's on now. better be a good question. it could be-- no? is it the tech guy? start again, but havethe microphone closer. audience: could you potentiallybio-engineer the knot that you showedout of dna and set a bacteria that woulddestroy its own type. matt parker: oh, wow.

so a very goodquestion from matthew, the guy filming in the backthere, who said could you make the knot outof dna, and then use that to find the mostefficient way to undo it? and that's very good question. the answer is no idea. so i'm not sure actually,because what actually happens if you want to see theway you get knots in dna-- you can try this.

because if anyone'sever made a mobius loop and then cut itin half, you will find that you end upwith one longer loop. it's fascinating. if you have more twists,you get longer loops that are tangled together. and that's what'shappening with dna. it's and incrediblytwisted molecule. because it unzipsdown the middle,

but all those twistsmeans the two halves are all tangledaround each other. and so what the enzymes--they're called tropo something undabellabella monaseand so what they're doing is-- i'm not abiologist-- is working on a huge mass of this stuff. so i suspect theynever encounter knots that simple is my gut reaction. i think it's a bit like solvinglike the traveling salesman

problem. you've got goodstrategies, but you can't guarantee you'vedone the best way, but it's incrediblyefficient in general. but i don't know. i will contact some biologistsand say, look, put down all this curing cancer stuff. we've got a knotwe've got to solve. and i'll report back.

so on that note, iam going to wrap up, but i will be loiteringaround for as long as i can. i think i am going tohave to finish now. and so on that note, again,thank you all very much. yes.