[APPLAUSE] MATT PARKER: Thank you. Thank you. Oh. Wow. Can you all hear me? OK. How's that for the correct
level of disturbingly loud? Is that about right? OK. Excellent. So thank you all very much
for coming along in your lunch break to hear me
talk about things to see and hear in
the fourth dimension. My name, as Allen very
kindly said, is Matt Parker. And in terms of my
background I used to be a high school
math teacher actually. So my original job was
teaching math to teenagers. And I'm originally
from Australia. So I taught in
Australia for a year. And then I realized not enough
people were throwing chairs at me. And so I moved to London,
and that fixed that. And I taught in London
for a few years, again in a couple of
different high schools. And then I started to drift
from normal math teaching to kind of education support. I started working for some
universities in developing resources and doing
sessions for school kids. So schools would send their
kids along to the University and we'd do like summer
schools and things with them. And so I did that for a while. Actually, I did
that for 18 months, and then I started to get
nostalgic for the classroom. So actually, at one
point, I went back. I did six months in an
inner city London school. And that just cleared
that right up. Right? And at the end of that
I'm like, I'm out. So since 2009 was the last time
I was a real teacher as such. And my career now has spread
across several things. You can see I'm based at Queen
Mary University of London, which is a university
in East London. I'm there one day a week. I'm their Public Engagement
in Maths fellow, which is what happens when you're
allowed to write your own job title. So fun fact, fellow is the
most academically sounding credential you can have
with no qualifications. And so I teach the academics
and the undergraduates to communicate maths
to other humans. And then the rest of my time is
spent doing things like this. I do a lot of
writing about maths. I do a lot of
speaking about maths. I work as a stand-up. So actually for a
while I was doing both. I was a math teacher and
I was doing stand-up. So during the day, I was
teaching math to teenagers, and in the evening
I was telling jokes to drunk people in
comedy clubs, which is a surprisingly
similar skill set. And after awhile I realized
I enjoy doing both together. And so I do a lot of
very nerdy comedy. And I do a lot of bits
and pieces for media and YouTube and the like. Oh, I do a lot of, quite
a bit of work on YouTube. So if I look familiar but in
higher resolution than normal, I do the Numberphile
channel on YouTube. Actually that was
in the first round of funded YouTube channels. That was the only non-US one
was the Numberphile channel. We started in the UK. So thanks, there you
are, which is great fun, and we still do it. And there was a weird crossover
point where the kids in school started recognizing me more
from YouTube than from TV work. And the teachers had no idea
what they were talking about, which it's great that a lot of
nerdy kids if they get bored at school can turn to YouTube to
watch fascinating bits of math. You know? I think that's
absolutely fantastic. And it's kind of fixed a
problem where bright kids would get very bored at
school and they get switched off the subject. Whereas now they can access this
much wider community of people, and they can see the
exciting side of mathematics. And that kind of keeps them
going while they're at school. And so the book was an attempt
to do a very similar thing as well where I wanted to kind of
package up some of the things I do with schoolkids. I thought there's no point
bringing you along here and making you hear about me
talk about the book themes "To Make and Do in the Fourth
Dimension," which is why you're currently enjoying the talk,
"Things to See and Hear in the Fourth," a
wilding different talk, I must point out. I mean, completely
different content. But there are books
around, and I'll be around to chat afterwards. And I may refer to a few
things that are in the book. And so that's pretty much
in terms of who I am. So what I'm going to
do today is effectively just show you some of my
favorite bits of math. And I'll do that for
approximately the remaining 2/5 of an hour-- 24 minutes. If you didn't know
that was 24 minutes, you're working for
the wrong company. And then I will be around. We'll do some
question and answers, and then I will loiter around
afterwards to have a chat. And we are actually going
to do some math, by the way. That's not an idle threat. So can everyone who
bought 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 already
got Wolfram Alpha open. That's brilliant. So if you could get out your
favorite calculation device and switch into calculate
mode-- you don't have to. This is purely optional. We're going to do a few
warm up calculations just to get us going. So once you've got it out, put
in any two-digit number you fancy, and then calculate the
cube of that two-digit number. And if I was doing
this with schoolkids-- I do a lot of this
with high school kids-- I'd be very careful to say
multiply it by the same two digits, then hit multiply,
same two digits again, then hit equal. If you tell it to your
friends, and you're not sufficiently specific,
you'll get the fourth power by accident. But most of you should
have very happily cubed a two-digit number. And what you're
doing is the kind of boring part of math--
the multiplying thing over and over. It's the reason why
we have calculators. The fun part is what you can
do with patterns in the answer. Is there anyone who's
prepared to share the answer that they've got? Not the number that
you start with, but the answer on your screen. Yes, sir. What have you got? AUDIENCE: 357,911. MATT PARKER: So
you put in 357,911? So you put in 71 and cubed that. Thank you. OK. You're keeping your excitement
at a manageable level. Don't patronize me. Right. So has anyone else got an
answer they're prepared? Tell me, if I get it right,
instead of just going, hm, if you could say, yes. The thumbs up is optional
but highly recommended. If you could say yes
when I get them right that would help my
self-esteem dramatically. OK. Has anyone got an
answer they're prepared? And if you give it in so many
thousands and then the rest. What have you got at
the back, phone guy? AUDIENCE: 804,357. MATT PARKER: 804,000--
You put it in 93. Thank you. AUDIENCE: Yes! AUDIENCE: Sweet! AUDIENCE: Awesome. MATT PARKER: Some of you are
applauding sarcastically. I would do three
more, 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 prepared
to give me the answers. If I get all three right
in correct succession, then you can humor me
with some applause. OK. So this is one. Hang on a second. Remain calm. One. Anyone else? Two over there. And three over here. OK. We'll make it like
an exponential trick. Right? So we'll start with
you over there, and then you, ma'am, and
then that guy on the end. OK. Around. Here we go. So what have you got over there? What's the answer? AUDIENCE: 531,441. MATT PARKER: 81. AUDIENCE: Yes! MATT PARKER: Remain calm. Right. AUDIENCE: 21,962. MATT PARKER: 28. Silent nod yes. And? AUDIENCE: 132,651. MATT PARKER: 51. AUDIENCE: Yes! Woo! [APPLAUSE] MATT PARKER: Fine. Now, by the way,
because some of you are now working out
how that's done. Some of you probably
know how that's done. Right? And so I'm not going
to explain it fully. But first of all, I've
not just memorized every single two-digit
number cubed. Actually, I've been
doing it for a few years, so I'm dangerously close
to having done that. What I'm actually doing is there
are patterns in the answer. And so there are two
patterns in the answer. And one pattern gives
you the first digit, and the other pattern
gives you the second digit of the original
two-digit number. So as you're calling out
the number, all I'm doing is I'm scanning it for the
first pattern that comes up is the first digit-- yeah. The first digit and
the second pattern gives me the second digit. So I'm just scanning for
those as you call it out. And it's not an
alarmingly difficult thing to do in your head
if you learn it. If you want to work out how to
do that, if you come and see me afterwards I'm
happy to explain it. Or if you just try cubing some
two-digit numbers, as some of you are doing right now,
or you're texting a friend. You wouldn't believe what was
in the lunch time talk today. Right? And so if you try some
numbers-- most of you have probably got a
spreadsheet open right now. Right? It's reasonably easy to
work out how that's done. So I'm going to do a
much harder calculation. And a few of you, again,
will know how this is done. But if you haven't I will
explain this one at the end so you can all learn this. And this doesn't
involve a calculator. It involves something
with a barcode on it. Could everyone have a look? I need someone in
the audience who's brought a product
they've purchased in a shop with a retail barcode. Not technically a joke but
thank you for joining in. So, oh, my book. Right? So not my book. Has anyone got a--
What have you got? What is that? Chewing gum. OK. Can you have a look at
the barcode for me, sir? Is there are tiny little digit
to the left and a tiny digit to the right, and all the
other digits are underneath? Don't say what they are, but
there's a digit on each side. OK. What I'm going to get you to
do in a second is to read out all the digits to
that barcode, starting with the one off to
the left, all the ones underneath, and do not tell
me the one off to the right. I'm going to try and
calculate in my head what the one off
to the right is. If I get it correct,
you shout, yes. Everyone goes bananas. OK. And I already know some of
you are very good at that. And don't go too fast. I will say, yep, after each
digit as we go along so I can-- People can often
race through them. AUDIENCE: Zero. MATT PARKER: Hang on. Hang on. Hang on. I'm getting in the
math zone over here. All right? OK. I'm ready. OK. First digit. AUDIENCE: Zero. MATT PARKER: Is it the same
zero or a different zero? Is this the one you said? That's the one on
the left is a zero. OK. I'm sorry. OK. Well, give me a second. OK. Got that. Yep. AUDIENCE: One. MATT PARKER: One. Got it. Yep. AUDIENCE: Two. MATT PARKER: Yep. AUDIENCE: Five. MATT PARKER: Yep. AUDIENCE: Four. MATT PARKER: Yep. AUDIENCE: Six. MATT PARKER: Yep. AUDIENCE: Six. MATT PARKER: Yep. AUDIENCE: Seven. MATT PARKER: Yep. AUDIENCE: Zero. MATT PARKER: Yep. AUDIENCE: Zero. MATT PARKER: Yep. AUDIENCE: Eight. MATT PARKER: Yep. The final digit. Is there one more? It's a six. AUDIENCE: Yes. Yes! AUDIENCE: Woo! Yeah! [APPLAUSE] MATT PARKER: I like a
brief moment of confusion before the climax to a stunt. So now that-- some of you
have no idea what you just applauded. So that, those of you who know
about check digits and error detection and error
correction, which is a vast majority
of you, will know that there is a pattern
in all barcodes. And all North American
barcodes have the same pattern. It's a slightly
different pattern to what they have in Europe. So I had to learn a different
method to make it work here. If you want to learn how to
do that-- this is the pattern. Right? So as someone is reading out
the digits of the barcode, initially, all you have
to do is add together every odd positioned digit. So you add the first thing
they call out to the third to the fifth all the way up. And if you add
every second digit, starting in the first
position, you get a subtotal. You multiply that
subtotal by three, and then you go back and add on
the other digits you skipped. And if you add every second
digit, multiply by three, add the other digits,
for all US barcodes, the grand total will
be a multiple of 10. And so if you keep
track in your head and there's one of the
missing at the end, it's whatever you need to
get-- OK now some of you are mildly impressed--
is what you need to get up to
the next digit. So the total in my
head ended in a four. And so I knew it must be a
six to get up to the next one. I'm a hoot at
parties, by the way. And so I think it's amazing,
because most people have no idea that these patterns are
built into barcodes and things around them. And so actually if
you look on the book, it's got the barcode at the
bottom and the ISBN at the top. And the ISBN is a subtly
different pattern. But again, it's got
exactly the same thing. Credit cards have
the same thing. I can do the same stunt
with credit cards. But very few people will read
their entire 16 digit number out in public. But that's subtly different. You double every
second position. And if you get a
two-digit number, you add the digits together
to get the digit root. And then once you add
all of those together, you get a multiple. And most people go about
their daily lives completely oblivious that all these
mathematical patterns are in the background. If we didn't have that
pattern in barcodes, our modern shopping
centers wouldn't work. Right? Because when you scan
something at the supermarket, because the lasers aren't
very accurate-- because lasers make a lot of
mistakes-- physics. But thankfully math
comes to the rescue. Right? Because if it scans the barcode
wrong, the pattern won't match. And so it knows it's
misscannned the barcode. And so it keeps
trying to scan it until it gets one where
the pattern matches. The vast majority of the
time that then means it scanned it correctly and
it goes onto your bill. And people get very emotional
if they scanned one product and had to pay for something. Well, it depends on the
price difference, I guess. And so people don't
know that this pattern is hidden in the
background there. And the same thing happens
with text messages. So those of you who
know Reed-Solomon and the types of
error and coding you can do with text
messages, there's a fantastic way to look at what
happens with a text message. Because when you're
typing in the text message and your phone is turning
all the characters you're entering into
numbers, it effectively puts those numbers
into a giant grid. It goes through that grid and
puts a mathematical pattern into every single row, and
then puts another pattern into every single
column, and then puts a third pattern into
subsections within the grid. And if that sounds
vaguely familiar, it's because it turns your text
message into a Sudoku puzzle. And so people have a sense
that if you give them a Soduku puzzle, even though huge
sections are missing-- all these numbers
are missing here, all these numbers are
missing down here-- if you know the three
mathematical patterns, you can recreate all
those 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 push
people like on the train will be doing. I'm like, oh, you love
error correction too. What? But this is absolute amazing. And if you give it
to more than one person everyone
gets the same answer because you're using
the same pattern. So the difference
with text messages is it's done more as a cube,
and the its coefficients or polynomials are done in
three different directions across the cube to
get the same pattern. But it's exactly the
same logic behind this. And people are quite happy
that the can solve a Soduku. But yet, they think
it's astounding that if there's an
error or information is lost when they send a text
message that the phone can recreate all the
missing information. The same thing with Blu-rays
and everything else. And there's such
good error-correction to Blu-ray discs, you can
get a drill bit, which is about three or four
millimeters across-- so that's some obscure fraction of an
inch-- and if you get that, and if you get Blu-ray disc--
if you get someone else's Blu-ray disk, you
can drill a hole straight through the middle. Well, not straight
through the middle. There's already a whole there. Right? You can just to the side,
you can drill a hole. And if the laser--
physics-- is good enough in the Blu-ray, because
the main issue is cheap Blu-ray players will lose
track of where they're up to. Right? If it can keep track, it
can recreate all the missing information that's
been drilled out. And again, without these
maths, modern technology simply wouldn't be possible. Oh, and I made this
one myself, by the way. I'm quite proud of this. I wanted it to look
like and x, like an algebraic-- tough crowd. Whoa. The top row are the digits in
the order they appear in pi. There you go. So if you want a copy of
that, send me an email. And so I quite like that. It's kind of useful
maths-- like maths you can actually
do something with. Well, actually I've got another
bit of fantastically useful maths I'm going to teach
you, because I thought I've got to show you something
you've not seen before. You've going to be
very disappointed. And you people work on encoding. You've been working on encoding
all day, and you come in here and you're like, oh, great. This is my lunch break
doing error correction. Right? So I'm going to show
you some useful maths to save time in your
day to day life. And to do that I brought
with me down here-- Actually, I'm going to go off
mic and yell for a second. Can you all hear me? Possibly even better
now that I've got-- OK. Right. So I've got down here a camera. So this is on the floor here. I'm going to teach you
the mathematical way to tie your shoes. And this will speed up
your 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's
most surreal chorus line. Look at that. Yeah! So if anyone comes in
late now just go with it. OK? So here' what you do. So normally when
people tie their shoes, they get the laces in like
a little foundation knot, and they get these
and they do all sorts of moving them around and
mashing them together. What you can actually do, if
you just hold the two places and passed them
across each other, they will tie themselves. OK. You again, keeping
your excitement at a nice, manageable level. OK. What do you watch? Actually, is there a
delay on the camera? Can I? I bet I can tie this and
then watch myself tie it. Ready? Here we go. Ready? OK. Read. So I'm just holding
the laces, and tied. Close. [APPLAUSE] I'll bet you never tried
this, because normally I do this for school kids,
and normally they're sitting fire to
something by now. Would you like to try it? If you've got to shoe, choose
your favorite, undo the laces, and I will actually
teach you how to do this. So you do that little
foundation knot there. So you've all got that. Take the shoelace on
the right and curve it so it goes up and forward,
and you hold on the way down. So it goes up in a
loop and then down. You're holding on the
descending part of the loop. The other side is the same
thing, but it curls back, and you hold it on the
descending part of the loop. And then all you
have to do is pass the bitch you're holding
under the other loop, swap hands, and pull. AUDIENCE: Whoa! MATT PARKER: Oh. One. OK. That's-- We've
been through there. Don't patronize me a bit. So if you practice that,
you can save literally ones of seconds of your
life on a daily basis. Right? And it's exactly the same
knot that you end up with. So mathematically,
that is the same knot. And a lot of people
don't appreciate that there's a whole area
of maths about knots. There's knot theory. Best name of a theory ever. And so people are
know theorists. Are you a theorist? I am knot theorist. So knot theorists look at the
maths behind different knots. And as humans we know
dangerously little about knots. It's a reasonably new
area of mathematics. Well, it kicked
off in the 1800s. But today we still haven't got
a great understanding of knots, in general. And, in fact, I put a picture
of one knot in my book. I've got a shot of it up here. We still do not know the
best way to undo this knot. This is called the
1011 knot if you want to look it up afterwards. And when you do a
knot diagram, you leave a gap when
it goes underneath. These are not just
joint bits of string. This is where it goes
underneath there. And to undo a knot
mathematically, you do sort of a
crossing switch. So you would cut one
bit of the string, move it around another one,
and join it back up again. So you take it from one side to
the other side and rejoin it. And we know this not can
be undone in three crossing switches, but no one's
found a way to do it in two, and likewise, know one's managed
to prove that there isn't a way to do it in two. This is an open
question in mathematics. This is, in fact,
the most simple knot for which we do not understand. At for the vast majority of
knots above it we have no idea. And so my theory is, if enough
people make this out of string and try it, sooner
or later, if there's a way to do it-- for a very
generous definition of sooner or later possibly-- we will come
across how it can be undone. And at that point fame
and mathematical fortune is yours, for a very narrow
definition of fame and fortune. So, dude if you can try and
make that out of string, you look it up online. It's the 1011 knot. If you do find a way
to do it let me know. Photograph yourself
pointing at the bit where you're going to make
the crossing switches first. Then make them. If it untangles, we'll
know what you actually did. Because if it
happens and you don't know how it was arranged--
because in this arrangement it won't work. We've tried everything
in 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's
really important that we know how to do this,
because at the moment bacteria is better
at undoing knots than humans, which is
a little bit worrying. Because when bacteria
reproduces-- in fact, same thing happens
with most cells, and human included-- the DNA
gets tangled and knotted. And so some bacteria
have circular DNA, gets very knotted
when they reproduce. And there are enzymes
which go around and perform crossing switches
exactly like that. They will snip one bit of DNA,
move it around another one, and rejoin it. And they do that
very efficiently to untangle the DNA. And if they can't do that,
the bacteria can't reproduce. And so knot theorists
from the maths department are working with biologists
to try and work out what the bacteria is doing,
why it's better than us, and if we get a better
understanding of both what it's doing and how to undo
knots in general, that could be a new wave
of antibiotics. If we have a way to
impede or stop bacteria from unknotting
its DNA, then we'll be able to stop it
from reproducing. And so I think
it's very exciting that a future wave of new
medicine, the new therapies, can come about because knot
theory, which was started initially by physicists
trying to understand a string theory of matter is
what first kicked off, but then mathematicians took it
on because it was kind of fun. And it could be saving
lives in the future, which I think is absolutely fantastic. So I've got two--
actually, you know what? Let's do three
things, and then I'll wrap up for questions, because
I'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 originally
going to talk about this, but while I'm here, I
made this two days ago, and I'm very excited about it. What I did was I bought a
brass disk off the internet. I bought this. I'm sure I used a Google
service or another. And so it definitely
wasn't from Amazon. And then what I've done is I've
put a small notch in the disk. And that notch is 14 and
1/2 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 that
is if you do it to two disks-- So a circle rolls
because as it rotates the center of mass stays
at exactly the same height. Very, very handy. But if you get two
disks and you intersect them like this at
right angles-- and I made those notches so the
centers of the two disks are now root 2 apart
compared to the radius. So if you've got one
unit is the radius, that's root 2-- the distance
between the two disks. So what it means is as this
rotates on a flat surface, the center of mass stays
at exactly the same level. And I haven't got a
flat surface here. I'm going to try it over here. I checked. My cable's not long enough
to get the camera over there. But I'm going to try on this
bench, if you don't mind. So if I put it there, if I give
that a bump, the center of mass stays at exactly
the same height. And if you want to kick that
back in the opposite direction. It's optional. Feel free to join in. OK. Look at that. It's all right. So the center of mass
is going side to side. It's not even a sin wave
going backwards and forwards. It's a quite complicated wave. It's a combination
of different curves. But in terms of its
height above the surface, it stays perfectly flat. And you can prove that for two
main locations using nothing more complicated
than Pythagorean's System of Triangles. So I shall challenge for
when you should be working, use some of your 10%
time to calculate why the center of mass for
that one, because what you do is the shoe in the center
of mass is the same height, and it would drop out, and
the center of the disks has to be root 2 a part. That's the easiest
way to go about it. And using the Pythagorean's
System of Triangles you can show that. I will leave it up there. And if you want to
have a play with it afterwards you can roll
it backwards and forwards on there. Or you can make
your own out of CDs, which you might have in
some of the display cases with technology from the past. Or make your own circles. You can get those to
roll quite nicely. It's kind of fun. So the last two things
I'm going to show you is a ridiculous project that
I did a couple of years ago. And I'm going to finish by
showing you the Christmas present that my mom gave me two
years ago, which is relevant. It's not just like, hey,
check out this jumper. Right? It's a proper maths thing. But before I get that, this
is a ridiculous project I did a couple of
years ago where I was trying to explain the
way that logic circuits work. And to try to explain circuitry
to people in general I decide to use dominoes. Because what I've
done here is I've set up a chain of dominoes. And the great thing about
a set up of dominoes is you can send the
information along dominoes, because if you put
a signal in one end, that signal will
move along the chain and come out the other end. And so you could use this. This could be practical. So if your doorbell
has broken, you could have a long
chain of dominoes. So you've got at
sign at the door that says please bump domino. And that goes all the
way through your house into the living room. And a few of the other
dominoes fall over. You go, oh, there's
someone at the door. Right? And they're sending information. Not hugely efficient,
but it would work. And you can get far
more complicated. So instead of just sending
one little bit of information, you can have a network
that interacts. So now I've got two inputs
and a single output. And this is step so
you have to bump over both inputs for the
output to go over. If you bump over
either one separately it won't make it all the
way through the circuit. And so if you want
more information about who's at the door-- so
let's say you order a pizza, and you've got one thing that
says bump this domino if you're here, and another
one that says bump this domino if you have a pizza. And only if there's someone
there with a pizza will the signal get all
the way through. And I can show you this
working, because what happens is this one by itself blocks
itself from getting through. Whereas if you've
bump that one as well, it would have stopped this
one from stopping itself and the signal would
have gone through. And for this, I like to consider
knocking a domino over as a one and it standing up as a zero. And so you can see I've
got a table in the corner. I'll make it a
little bit bigger. So for completeness, this
is the complete setup for that circuit. Right? We can still think of
this in terms of pizza. So zero and zero. No one's at the door and
they haven't got a pizza, and so nothing will happen. This is there's
someone at the door and they haven't got a pizza. That won't get through. OK. For completeness, somehow a
pizza has arrived at the door and has managed to read the
sign and bump the appropriate. So should there be
a self-aware pizza, this is what will happen. The signal, thank god,
won't get through. All right? Because that is a
horrifying experience. And then here we had the
person with the pizza and the signal gets through. And this is an AND gate. So if you've done
logic gates, this is an AND gate made
out of dominoes. We can do even better. This is the exclusive OR
gate where the signal only gets through if you bump
over one and the other one, but not both. So that's the exclusive
bit-- one or the other, not both simultaneously. There it is made
out of dominoes. If you've got 100
dominoes and you're bored, you can make these. It's about 100 dominoes
to put these together. And what happens now is
you hit them both together, they collide in the
middle and stop. But if you hit either
one separately, it will travel through
and 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 few
of you are thinking, why? Why would you do? You know where I'm
going with this. Right? And if you know where
I'm going with this, my only advice is for
now just remain calm. Because we have a long
way to go with this. Right? Because what you can do
now is get to a circuit where it shows both
simultaneously. If you have two inputs and two
outputs and one's the AND gate and one's the exclusive
OR gate, you've got a circuit which counts
the number of inputs that have been bumped. So this is a very
basic calculator. So if you think of the
outputs as a binary number-- the exclusive order to the
units, the AND as the twos-- and then it tells
you how many inputs were bumped as a binary readout. So this can count in binary. And to make one you need
200 to 300 dominoes. It looks a little bit like this. And so this has two
circuits coming in. It's basically exclusive
OR but with an extra block on the side. This is a delayed circuit
to give this long enough to run, you slow
down this signal so it doesn't get
there ahead of time. So there's a few timing
issues with this circuit, but it can be made. And a few of you
are thinking, well, if you've got this
far, what you really want is-- this is
the full adder. Yes! Right! So try not to skip ahead to
the punchline without me. All right? So this is the full adder. So you can do any arithmetic
you want with a full adder, because you've got the
two numbers you're adding, you've got a carry from
any previous calculation, you've got the carry out that
flows on to the next column, and you've got the
right out, which is the output you're doing. And so if you can
make a full adder, you're effectively
counting any free inputs and getting the two digit out. Now unfortunately, at this
point, I worked it out. To build one of these would
take about 1,000 dominoes, and it would look like that. [LAUGHING] So this is me at the
Manchester University. This is the maths
floor-- very flat. We managed to sneak in there. We have 1,000 dominoes, and
we built a working full adder out of dominoes. And so again the problem was
slowing down the signals. You've got a lot of
synchronization issues. But we got to slowing
the right ones and sending the other ones. Slowly the whole thing
worked really well. And then we were like,
well, this is brilliant. And some of you know if
you chain these in a row-- if you have adders in row, you
can add numbers of any size. So if you had three
of these in a row, you could add two
three-digit binary numbers and get a four-digit
binary output. But that would take
10,000 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. Right? And so we managed
to build a circuit with 10,000
dominoes, which would add two three-digit
binary numbers and give you a
four-digit output. So this is a working
computer circuit. This is an actual computer. I mean, the display
resolution is terrible. But it does actually
work as a computer. And we ran it and it worked. We were able to add
two three-digit numbers and got a four-digit output. And we had the museum-- this is
Museum of Science and Industry in Manchester. Brilliantly-- you can't
see it in this shot-- we are directly in front of
the rebuild of the first baby computer that Alan
Turing worked on. So it was behind us. I could see the vacuum tubes and
everything of the original baby computer. And I was allowed once
to have a play on it. And it's so cool,
because the memory-- the input for the memory
is a board of buttons. And literally each one
corresponds to a bit. And so you enter
the ones you want. That ones to be a one. That one's a one. And so you enter the ones that
you want to switch to ones and hit go. Nominal piece of kit. And I got to meet
Alan Turing last ever student who worked with
him on that machine. And so he told me
stories about Turing where the operating system that
ran the version after that. Absolutely incredible. Happy to chat about that. Oh, and by the way. "The
Imitation Game" film, not that bad. Pretty good. Pretty good. The mass is-- I mean,
it was very brave. The first half an hour
is Cumberbatch describing how you prove the existence
of uncomputable numbers. So I was very impressed. It's not. He just looks
handsome and smolders. But if you want to talk
Turing, see me after this. So anyway, so we
got to build this in Manchester, which
I was so pleased. And we did it on the
first day, and it worked. At we had a backup day. And we're like, well,
let's not waste this, because we could have
two four-digit inputs and get a five-digit readout. Right? And we did that. But it didn't work. Two things went wrong. Because we didn't
have any more space because we had the same
section of the museum kind of sectioned off. And we didn't have
anymore dominoes. So we had to make it
more dense, and we had to make it more efficient. So we have to cut
back on the timing, and we had to have the
rows closer together. And two things went
horribly wrong. The first one is here. We had cross torque. We had signal bleed from one
row of dominoes onto another. So if you watch, this one
here should not fall over. That domino should stay up. But if you watch as the other
chain comes through-- here it comes-- as the other one
comes through, it-- here it comes. Here we go. Look at that! And, in slow motion,
here it comes. No! So that gave us an extra
output we didn't want. So that ran through and tripped
what should have been zero, and the answer became a one. And the other one was here. OK. So let me should you
what happens right here. If you watch that
row of dominoes, it is going to carry
along to this output here. But this one should get their
first and, bam, stop it. Right? I've been watching a
lot of American football while I've been over. And so, bam, it
should stop it there. So this signal stops. It closes this gate before
that signal gets there. Unfortunately it didn't work. If I show it to
you in slow motion, is this one so going
to get there first. So going to get there first. Look at that. Here it is. Here it comes. Coming in. It's going to close
that gate, and-- Ah! Two dominoes off. But at least it went
wrong in interesting ways. If it had just been
bumped by accident that would have
been very upsetting, but it went wrong
in sightful ways as to what happens
in actual circuits. Because that was a
synchronization issue. So I was so please with
the way that worked out. Well, actually
the last project I did was a collaborative
project using different museums around the world, and
we use Google Hangouts. We used a live
feature on Hangouts to link between different
build sites around the world. So I was in
Manchester, and I could talk to people who
were working in Finland and Canada and the US. And the fractal, we're
building a mega menja, the one that is at MoMA, Museum
of Science and Industry, here. So if you want to
go and look at it, it's an amazing fractal
thing they've put together. And it was great that
we could use Hangouts. People could watch
at home, and we could cut between the
different builds sites. Absolutely brilliant. Anyway. The last thing I'm
going to show you, and then we'll do
questions, is I brought the Christmas
present my mom made me. I've got it right here. And so I'll bring
up my-- is that my? It looks like-- OK. Here we go. So you should have seen
my giddy face on Christmas morning when unwrapped a knitted
scarf made entirely out of ones and zeroes. I had no idea she was
doing this behind my back. And she went and she made this. I was like that's amazing. And when I saw it
initially, I thought they were just random
ones and zeroes. And so then I went,
well, hang on. Hang on. Every single row
starts zero, one, zero. Right? And so that means
every single row is an upper case
letter in Unicode, because my mom knits the
way she text messages. Right? 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 of
the wrapping paper. I got my pen out. What a Christmas morning. I get to sit around with the
family and decode my present. Right? And if you actually go
through and work it out-- oh, I'm now fluent in binary,
by the way, of course. Because when people get me
to sign their book, I can say do you want that in normal
characters or in ASCII? And so I can do people's
names in binary. If you're bored
afterwards, come up and I'll put your
name in in binary. And I suspect most of you
would then go and fact check that very quickly. And so anyway I was
able 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 it
actually says, "Maths is fvn. Keep doing maths." I was like, oh, mom. I hate to ruin your fvn,
but, you have swapped a one with a zero, and
she was very upset. Because she is quite
the [INAUDIBLE]. And I was like,
well, actually mom-- because she wanted to
take it back and fix it. She wanted to undo
and replace it. I said no, no, no. The thing is you don't
have to do that actually, because to make the
scarf long enough she knit the same
message four times. So it repeats, front,
back, front, back. And she only made a
mistake in one of those. So what is means
is all I have to do is calculate the average value
across all four versions, and they gives you back
the original message without the mistake. And so today, ladies and
gentlemen of Google, I can present to you the world's
first error-correcting scarf. [APPLAUSE] If you would like
to meet the scarf, I will leave it at the front. It does also sign autographs. You have to hold it
with the pen yourself. So you're coming to
get a photo of you wearing the scarf, that's fine. I will leave that here. You can come and check the
code to make sure it all works. Otherwise, I will be loitering
until I get kicked out or people have to
go back to work. If you want me to
come and deface your book so it
lowers resale value, I'm more than happy to do that
or answer any other questions. If I've mentioned something
and you've missed, or you want to copy of all the
circuit 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. Right? So seriously a massive
chunk of the book is answers at the back. And so the circuit diagrams
to the dominoes are in there. But if you could send me an
email of anything else you want a copy of or I've
mentioned something and didn't go into enough
detail, let me know. But on that note, I've finished. I'd like to thank Allen
very much for organizing all of this. It has been fantastic coming in. Thank you all very much
for listening so well. Cheers. [APPLAUSE] Oh, we have to Q and A. Right. So-- He had that look of
you're not finished yet. I know you got the
free lunch first but now you've got to earn it. So any questions people
would like to ask? If you can't get to the
mic, I will repeat them for the sake of the recordings
so the end up apparently encoded. But if anyone would
like to come up, you can ask questions
from the center. If you're bringing
your laptop with you it's going to be
quite the question. I simulated this and frankly. AUDIENCE: While writing
the book, what's the most amazing thing that you
learned that you didn't already know, and that fascinated you
as a problem and the solution. MATT PARKER: Oh. That is a very good question. So writing the book
what was the thing I learned that was
the most surprising? There's a few bits
in there where I found new examples
of types of numbers, because I've been learning
Python as a hobby. So I had to program
at University, and I hadn't done it for years. There was a few bits
where I ran simulations to find ridiculous numbers. Some of those were kind
of fun, but I kind of knew they would be out there. If I ran the code they would
show up sooner or later. What I really found amazing
was because the book, the conceit is it's about
the fourth dimension. There are huge sections
about 4D shapes. And in 3D-- I knew this before,
but I've never actually looked into it-- in 3D you get
with the platonic solids. If you've not come
across these, they are very, very
regular 3D shapes. All the faces are the same,
all the vertices are the same, edges are the same. And there's famously
five of them. So there's the tetrahedron,
octahedron, cube, icosahedron, and dodecahedron, in a
random order I just made up. And in 4D there's another one. So you get the 4D equivalence
of the fine standard platonic solids. There's another one that
I call the hyper-diamond. It's the 4D equivalent of
a rhombic dodecahedron. But it is a platonic solid
in 4D, and it's not in 3D, and it's not again in 5D. It breaks again in 5D. It only works in
four dimensions. And so visualizing it-- I try
to find a way to visualize it. And in 3D a rhombic
dodecahedron is what happens if you get a solid
cube and turn it inside out. So if you imagine six
square-based pyramids and flipped them all
around the other way, you get a rhombic dodecahedron. The same thing happens
in four dimensions. If you get a 4D tessaract--
a 4D cube and-- Oh, if anyone's, I don't want to
ruin-- you know spoiler alert-- "Interstellar" they
mention tesseract. I was like, yes. Oh, and by the
way, I can confirm, the fifth dimension is love. And so the same thing happens if
you turn a 4D cube inside out, you get the hyper-diamond. Absolutely brilliant. And then, in case
you're wondering, 5D is any three-point solids. And that's every
dimension 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 ones
you never see them again. And so there's this
fantastic flare up of shapes in kind of three
and four dimensions that doesn't happen again. I think that was fascinating. Further answers will be shorter. Yes? AUDIENCE: Can you
tell us some more about the testing
of the calculator? Like did someone accidentally
hit a domino down? Did you try it out? If something goes wrong, can
you reset the whole thing? How long did all that take? MATT PARKER: OK. So the question
was can you tell us more about testing
the domino calculator, and could you relive some of
those horrifying experiences? So to this day the sound of
domino toppling on concrete breaks me out in a cold sweat. So originally I bought a
box of about 100 domino. I'd seen a YouTube video
of someone trying it. And they'd kind of cheated. They'd taped dominoes together. And they were doing
the AND gate, I think. Well, surely you
can 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 concrete
floor at the University. And we wanted to know first
of all is it reliable enough? We were really worried about
if it would be reliable enough. And can it be built fast enough? Because if we couldn't
actually build that thing it wasn't going to work. And the big problem was having
the junctions work routinely. And a very good
mathematician Sean, she came up with-- we called
it the Juncsean, which was a reliable way of building
the junction, and it was very, very, if you did it exactly the
right way, it works every time. It was very robust. And so we built a
stencil of that. And we chalked on
all those junctions because we knew they would work. And then you kind of freestyle
getting between them. But we knew as long as we used
those for the uncritical bits it would work. In terms of actually building
it, you'd leave gaps. And the rule was,
trust the gaps. That was our official rule. Well, actually, one
rule we had was, if you bumped dominoes
over by accident, because occasionally you would
knock them and they'd all go. You're like, ah. The rule was you then
stand up and walk away. Because someone
else will come in, someone who's now
emotionally invested, because you're now
balancing dominoes with a sense of revenge. Right? And so someone else would then
come in and put them back up for you. And the rule was trust
the gaps, because we knew we were going to
bump them over by accident and they were going to run. But as long as there was
a gap they would stop. And I saw one volunteer,
because I just asked on Twitter, hey, people come and
balance dominoes. And one got bumped it,
and it started to run. And he lunged to
try and stop it. And he bumped the
ones after the gap. And so then they say
and he was like, oh. I was like you idiot. And then he realized what he
did and tried to stop those and bumped the ones
there, at which point we were just wrestling
him away from them. And if you watch the video--
I've got a YouTube video. It's about half an hour
of me balancing dominoes. And I explain the binary
and everything else. You can see people walking
around inside-- because we had to fill in the gaps
when we were done-- and we did like a fractal. We did every like middle bit. And then we went back and did
a little bit and a little bit so trying to minimize
the possible damage. But to load it we left gaps
where the data would go in, and you filled in for one
and left it blank for zeroes. And we picked random
numbers at the end, and then people had to walk
out into the center of it and fill in where the ones were. It was the most hair-raising
thing of my life. But in the end it worked. We had one spontaneous bit where
we were just standing around and suddenly a domino
fell over and a bit ran. But we hadn't done
all the gaps yet, and so we were able to fix that. Very, very stressful. If anyone's ever
in the UK and you want to borrow 10,000
dominoes, let me know. I'm happy to lend them to you. I bring up a place because I
want to buy them wholesale. I ring them up and say I want
to 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'll
work something out. And so I got them
delivered to the Museum. It was brilliant. So now actually
schools use them now. So schools can
take them for free if they pay transport
from the previous school. So they get sent
around between schools, and they try and build the
circuits, which is great fun. So I will do one more
question, and then I will loiter around if you
want to have a chat with me afterwards. Has anyone got? It could just be-- I think
the pressure's on now. Better be a good question. It could be-- No? Is it the tech guy? Start again, but have
the microphone closer. AUDIENCE: Could you potentially
bio-engineer the knot that you showed
out of DNA and set a bacteria that would
destroy its own type. MATT PARKER: Oh, wow. OK. So a very good
question from Matthew, the guy filming in the back
there, who said could you make the knot out
of DNA, and then use that to find the most
efficient 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 the
way you get knots in DNA-- you can try this. Because if anyone's
ever made a Mobius loop and then cut it
in half, you will find that you end up
with one longer loop. It's fascinating. If you have more twists,
you get longer loops that are tangled together. And that's what's
happening with DNA. It's and incredibly
twisted molecule. Because it unzips
down the middle, but all those twists
means the two halves are all tangled
around each other. And so what the enzymes--
they're called tropo something undabellabella monase
and so what they're doing is-- I'm not a
biologist-- is working on a huge mass of this stuff. So I suspect they
never encounter knots that simple is my gut reaction. I think it's a bit like solving
like the traveling salesman problem. You've got good
strategies, but you can't guarantee you've
done the best way, but it's incredibly
efficient in general. But I don't know. I will contact some biologists
and say, look, put down all this curing cancer stuff. We've got a knot
we've got to solve. And I'll report back. So on that note, I
am going to wrap up, but I will be loitering
around for as long as I can. I think I am going to
have to finish now. And so on that note, again,
thank you all very much. Yes. [APPLAUSE]
