[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]