Matt Parker: “The Greatest Maths Mistakes” | Talks at Google

Matt Parker: “The Greatest Maths Mistakes” | Talks at Google

[GOOGLE LOGO MUSIC PLAYING] [APPLAUSE] MATT PARKER: All right. Thank you very much. Thank you for the kind
introduction, Ian. It was very kind of you. It’s always nice to be
introduced by the organizer, saying I didn’t think this talk
was going to be well-attended. So my name is Matt Parker. And, oh, as appears
on the screen here. It’s an absolute pleasure
to be back at Google. I did a author’s
talk at Google– trying to make it out– it
was 2014, late 2014, I think. So it’s been over four
years since I was last here. And it’s pushing me back. I do a little work on YouTube,
as was kindly mentioned. And so I’ve been to the
building here before. Last time I was over
near Victoria Station. I’ve been to this
building previously. But it’s the first time
I’ve been allowed out of the basement, which is– it’s really nice, the
rest of the building. Anyway. So the idea is I’m going
to talk to you today a little bit about my
book, “Humble Pi,” which is kind of the whole
conceit of the talk. And so the book came
out a couple weeks ago. And it’s all about
mathematics mistakes. And so what I thought I
would do is– oh, there will be Q and A at the end, right? So that anything I
don’t cover or you’ve worn your favorite
Parker square t-shirt and you think I
won’t notice, then there’ll be a time for that
kind of interaction later on. I’ll take questions and I’ll
be around to chat afterwards. What I thought I would do in
the more straightforward part of this talk is initially
I’ll talk a bit about the book and why I wrote it and
what’s going on there. And then secondly,
well, I thought would be a bit different. Because it’s easy to go along. And you get asked to do a lot
of talks when you write a book, and so I try to make them
all a little bit different, particularly at Google, who
are very keen on digitizing just everything. And so this talk
will be recorded, and it will be online. Hello, everyone. I don’t even know where
they’ve hidden the cameras. They may be filming
the audience. That’s going to be quite
an immersive experience. You can watch it back
from my point of view. So I thought I’d mix it up and
do something a bit different, which is what really happened
on some of the greatest maths mistakes. And when I foolishly read
the reviews on Amazon for this book– and
I should have learned having been honed in
YouTube comments– and I read the reviews. And people say, oh, why
isn’t this story in there? This story should be in
there, or this story. And I’m, like, OK. A lot of them I fact checked
and turns out it wasn’t right. And a lot of them– what
the general consensus of that mistake was is correct
or they’re slightly off. So what I thought I would do is,
once I’ve introduced the book, I’m going to go through my
favorite stories that made it into the book and
what I actually found when I researched
those stories. Because a lot of
them I kind of knew this maths mistake
happened and there was an interesting result.
But I was surprised, when I dug into it, what
the true and slightly more accurate, if not more precise,
answer is to what happened. So we’ll start with
the book itself. So as was covered
very efficiently, my career is an unusual
mix of different types of mathematics communication. So I used to be a
secondary school teacher. So I used to teach maths
to teenagers, originally in Australia, where I’m from. I grew up in Perth
in Western Australia. I studied mathematics and
miscellaneous other bits and pieces when I
was at university. Then got my teaching
qualification, taught in Perth for a year, moved to the UK. I taught in a couple
of different schools in and around London. Fairly easy going to
difficult schools, because I enjoyed challenge. And I knew each time
I was just teaching at the school for a year. And you can tolerate a
lot for a single year. And I’ll take my hat off
to some of the teachers who do that day in, day out. Right? And they’re there
every single year, and they actually learn,
like, the students’ names. Whereas I was kind of in, boom,
maths out, which is great fun. And I gradually transitioned
from being a classroom teacher to what I do now, which
is doing a lot of work on YouTube, doing
bits of writing. I originally started
doing newspaper articles and doing little live shows. So actually, if anyone
does want to come along to “An Evening of
Unnecessary Detail”, it’s once a month
in East London. It’s exactly what it says. That is not an ironic title. We invite comedians
who like science. And scientists who
think they’re comedians. And we get them to come
and talk about something in an unnecessary
level of detail. It’s fantastic for me. Reviews in the audience vary. So it’s a weird mix of things. And I’ve gone to writing books. And my first book, which I
came and spoke about here previously, was all about
hands on mathematics. It was recreational maths. Here’s some interesting maths. Here is how you can actually
try a puzzle, build a thing, or somehow interact with it. Because so much of mass
is about the doing, and the experimenting,
and then having a go, of which I am a big fan. And when I went back to
Penguin to write a second book, they’re, like,
“Things to Make and Do in The Fourth
Dimension”– great book. It sold adequately. I’m paraphrasing. It sold– because it sold
good for a maths book. It sold adequate as a book. And that’s kind of what
Penguin care about. And they’re like why should
we publish another maths book from you? Again, they didn’t say this,
but it was in their eyes. Why should we publish
another maths book from you when we could do another
celebrity cookbook, which is the only other option? And I said, hey, what if I wrote
a book about maths mistakes, when maths goes wrong? And they’re like, oh,
that’s interesting. Because they thought there
would be a much wider appeal of a book about
mistakes and things going wrong than another
pure mathematics book. And I was, like, oh, brilliant! So I started collecting stories
of when maths had gone wrong. And my kind of ulterior
motive, and what I talk about quite a
bit in these talks, is that I wanted to show
how much maths are required in our modern society, how
much goes on behind the scenes, behind all types of technology
and finance and medicine, and things I don’t have to
labor in front of this audience. And I thought, oh, you
know, when it goes wrong, that’s a good excuse to have
to explain the maths about why that went wrong. And it means I can cover
all these interesting areas of technology and modern
life when maths goes wrong. But then as a teacher,
I was, like, yeah, but I don’t want to
have a whole book which is making fun of people who
get maths wrong or discouraging people from making mistakes. I’m a big fan of these things. And so partly I put
in a bunch of just– I’m always curious. How was that mistake made? Is it important? What was going on
behind the scenes? And so actually,
as a teacher, this was one of my absolute favorite
posters, which I managed– I saw this online. I got a copy of this. This is absolutely brilliant. And try not to skip
ahead to the punch lines. “Education works best when
all the parts are working.” Now just– if you would
tolerate me breaking this down into unnecessarily small steps– it’s students, the cog labeled
students is going clockwise. Anything that meshes with
it has to go the other way. So teachers are going to
be going anti-clockwise. But neither of them can move,
because parents are jamming up the whole system, which makes
this one of the more accurate educational posters out there. And I had a good
chuckle at this. Someone just hadn’t thought
through the geometry. And it’s not important. But it’s funny, right? So I thought this
poster was hilarious, which is why I went
and bought a copy. And now I started
spotting this everywhere. Is it the frequency illusion,
where you’re aware of something and suddenly you start
spotting it in loads of different places? And so this was in Manchester,
when they brought out a new public transport system– “making the city work together.” Brilliant, pretty accurate
for the trans in Manchester, in my experience. And then someone
did point out online that– well, hang
on, hang on– there’s a whole third dimension
available here. All right? You’ve only got one
perspective on it. You’ve got to broaden your mind. Look at that! If you think outside
the plane, look at that! It works a treat. That doesn’t work,
though, if you’ve already used the third
dimension in the cogs. So early on in the
Trump administration they were going to renegotiate
the North America Free Trade Agreement, right? And so “USA Today” illustrated
the incredible progress they were making– so good. And they were already 3D. So you’ve used up your
third dimension, right? So I paid good money. I paid more money than I should
have, out of my own pocket, to license this image so
I could put it in my book. So if you’ve got the book,
I believe in the fine Google tradition, they
will show up late. There will be copies around. Are they here? Or are they still– SPEAKER 1: They’re here, yeah. MATT PARKER: They are here. SPEAKER 1: [INAUDIBLE]. MATT PARKER: Wow, you guys
are more organized than ever. OK. Oh, that’s fine. [INAUDIBLE] you’ve got them. OK. If you flip through
the book, you’ll find I paid money to
put this in the book just because I’ve wanted
to have the caption Making Cogs Great Again. I took the rest of day
off after writing that. And my favorite
example, possibly, is the two pound coin. So these came out about 20
years ago, two decades past. And there’s different circles
that different ages of the UK. And there’s one in the
middle with lots of cogs. And there was a competition
to design the coin. It was won by a guy called Bruce
Russian, who lives in Norwich. He’s a art teacher and an
artist in his own right. And he had the winning
design for this. However, if you count
the number of cogs, you will see that there
are an odd number of cogs. And so if they’re
alternating clockwise, anti-clockwise, they will
not be able to move, right? So famously, in
particularly niche circles, the cogs in the two pound
coin don’t go anywhere. I will let you decide what
era of the UK that represents. And I thought about
contacting Bruce. Because online you can find
out who won the competition. That’s public knowledge. I figure I can
probably find this guy. And so I thought,
I will look them up and I will very politely
inquire if they had deliberately done this. Right? Or did they not
even think about it? What was the thought process? I was always curious to what
went on behind the scenes. Because obviously,
it’s not important if the cogs work in a coin. They can’t move anywhere. They’re made of
one piece of metal, which is a bigger flaw than just
the number of cogs that mesh. And so I went to their website
and found the original design. This is on Bruce’s website. And I had a close look at it. And that would have worked. That is an even number of cogs. But when it was turned
into the two pound coin, these three were removed. And that set it to an
odd number of cogs. And so the original
design would have worked. I was, like, wow. Now I’m extra curious. Was that deliberate? And it was broken by the mint? So I emailed him. I said, hey, really
sorry, just wondering– did you think this through? Did you know it
would have worked? Did you blah blah blah, all
this, yours sincerely, Matt. All right, send. I got a reply back. And it turns out he
did think about it. He replied and said,
yeah, I thought about it and I realized
that it would only work if there was an
even number of cogs. But I decided that’s
not important. And he said how
he was an artist. And as an artistic
expression, he doesn’t think it’s
important if it’s actually mechanically plausible or not. It’s just important that it gets
across the right impression, which to be fair, I kind of
agree with him on that right. I’m all for the
artistic impression of what’s going on here. So I’m not making fun of
people who get this wrong. I just think it’s interesting
the thought process behind it. But then he went on to say
that he decided in the end to make sure it would
work, because otherwise, he would get loads of annoying
emails from [INAUDIBLE].. Anyway, that bit was in bold. But hey. And then, yeah– and
then the mint broke it. So when they turned it into the
thing, that took the cogs out. And it no longer worked, right? And this one, for
me, this was the kind of fun trivial example. And I kind of use these as a way
of getting people just thinking about the geometry
and the logic, right? And hopefully I’ve done it in
a way that is nice and positive and engaging and everyone
can get involved. And so this one hobby
I picked up recently, which is trying to spot– I’ll show you the example first. See if you can work out why
I’m so upset with almost every iteration of “Sesame
Street’s” “I Don’t Want to Live on the Moon”, as sung by Ernie. This gets me really
outraged because you can see stars shining through the moon. The moon is still there. I also accept that is
not an accurate crescent, as if you were illuminating a
sphere from one side, right? But that’s just going too far. But I don’t like
the fact that you’ll see these crescent moons, and
you can see right through them. And there’s loads
of great examples. I’ve shown this in a
few talks, actually. People have emailed me. And they’ve realized a wallpaper
or something on their laptop is fake. It was meant to be a real photo. But you can see stars
shining through the moon. It’s obviously
been photoshopped. People have sent me
screen grabs of TV shows. And they’re, like, it
just totally took me out of the moment when I
realized you could see stars through the moon. And I found the license
plates in Texas, which were used– oh,
let’s just zoom in, in case it being 5% bigger helps. These are the license
plates from Texas. And to celebrate NASA’s
presence in the Lone Star state, they have this in the corner. And I saw these images online. I was, like, oh, hang on. That star looks
dangerously close. The only way I
could find out would be to actually buy some license
plates from Texas so that I could get a high quality scan. And you may notice that’s
quite a high quality scan. Because I bought the plates. These are mine now. I’ve got two of these. I put them on the scanner,
which is the image you’re looking at here. I zoomed right in on that moon. And if you fill in the circle,
sure enough, the plate’s undone by a lone star. There you go. And people have since argued
that– some people have argued it’s gravitational lensing. I’m not buying that. Number one, mass,
and number two, lensing doesn’t make
things appear in front. You just see them
around the sides, right? Anyway, as if I’d taken that
complaint way too seriously already. Although, someone said it might
be marking the first Apollo landing site. And it’s pretty much
in the right spot. So I’m prepared to give
them a pass on that and just assume it’s labeling
where NASA landed on the moon. The plate will be around. If you want to come and
check it for yourself and convince
yourself either way, I’ll have that
around afterwards. These were the kind
of ridiculous examples I was coming up with. And then I gradually
pieced them together with more and more serious ones. And so by focusing on ones
that weren’t so important, and looking at why it happens,
and a big focus in the book is the fact that humans
are not good at maths. And I go on and on about
this because people see people who are
good at mathematics and think, well, they
must be a genius. It must come naturally. And I’m, like, no,
for the vast majority of people who are into maths,
they don’t find it easy. They’re just people who
enjoy how difficult it is. And the public don’t know– this is particularly
true for everyone here who is a coder, right? It’s just– you’ve got a
thing for self-punishment. It’s insane, all right? Just what’s the most
frustrating task I can try and achieve, right? And it’s the fact that it’s
a challenge, and it’s hard. And you eventually notice
one semicolon, right? And it’s hard work. And it’s difficult. But
that’s why people do it. Not because it comes
naturally and it’s easy, but because it’s a challenge. And that was the kind of goal. And there’s obviously
a lot in there about why we make mistakes,
how we make mistakes, and systems we can put
in place to avoid them, and how mistakes end
up becoming disasters, and all these things. But now, now we’re going
to play the middle part of the show, the game of
guess what stories Matt put in the book. And I’ve got three, at
least, here that I’m prepared to talk about. But I’m just curious to
know, if those of you who have not flipped
through it or you haven’t already read the book
or listened to the audio one available on Does anyone know? What stories do you
think might be in there? What are the classic–
very hesitant person in the second row? AUDIENCE: Yeah. The Mars Lander getting
that [INAUDIBLE].. MATT PARKER: That’s great. You’re absolutely correct. In fact, you are so
correct, you even gave the correct
units that were wrong. So I’m going to break
with my normal tradition and say that you should have
a round of applause, well done for that. That’s– [APPLAUSE] Let me bring that up. That’s so good. So the Mars– it was the
Mars climate orbiter. And when it was launched in,
oh, goodness, over a decade ago and sent to Mars, there
was a famous understanding that there were– the
general understanding that there was a
spacecraft from NASA which crashed into a planet because
of a unit’s conversion error. And that’s the kind of
headline a lot of people– hands up, who’s aware
there was a spacecraft that crashed because of a unit? That’s everywhere, right? Now the most common
version of the story is it was a Lander going to
Mars, which is correct– which it was an orbiter. It wasn’t a Lander. And it was a unit’s conversion
between metric and imperial. And they were using
feet instead of meters. So it was too close or
something, and it hit. And often it’s a
length measurement. You were absolutely correct. It was actually the force on
the aircraft, on the spacecraft, on its way to Mars. So as it was flying
to Mars, you got this big gyroscopic,
big flywheel thing, which is used for controlling
the spacecraft in space. Because there’s
very, very little to push against in space. And so you got to bring your
own thing to push against. And so you bring a
big spinning wheel. But sometimes the
wheel goes too fast. And you’ve got to have these
angular momentum desaturation events, right, where
you slow it down. You adjust it. But that slightly alters the
trajectory of the spacecraft. And so over the course
of all these corrections, you have to keep track of
exactly what twists and force was applied to the spacecraft. And the contractor was
in charge of doing that. And then they had to give the
final results over to NASA so they knew exactly its
final approach towards Mars. And this is where it went wrong. The contractor– oh,
by the way, it’s often said that NASA got it wrong. No, NASA actually
specified very clearly in all their documentation
to the contractors that it had to be metric. NASA were totally metric. They wanted to be metric. They thought it was metric. It wasn’t the other way around. The contractor,
however, did it in– because normally you do it
in newtons or newton meters if you’re doing torque. And they did it, I
don’t know– in pounds per bushel or something. And they just fed the numbers
in and it all went wrong. And here’s a little– this is
my version of a famous graphic. This is the sort of AMDs, so the
Angular Momentum Desaturation events, where they’re
adjusting the flywheel. And this was the actual
path that it was coming in on, much bigger forces. Because they were
using, effectively, it was a pounds-kilograms,
ironically, kind of mistake. This is what they
thought was happening. And they thought they would
have 150 to 170 kilometers clearance from the surface. It actually came in about 57
kilometers off the surface. Mars hasn’t got a whole lot
in the way of atmosphere, but it’s a non-zero
amount of atmosphere. And it slowed it down
quite dramatically, and then it crashed. So it was, like, half a billion
US dollars’ worth of spacecraft slammed into Mars because
a units correction, that the contractor didn’t
follow the specification document given by NASA. Does anyone know the other
spacecraft rocket maths mistake? Right over on the wall, in fact. AUDIENCE: Ariane 501? MATT PARKER: The Ariane 5, yes– so the Ariane 5– I have got it. I’ve got the video of the
launch of the Ariane 5. This is the first ever
launch in French Guiana. Now I’ve taken the sound
off and everything. This is just the
launch of the rocket. And I’ve never been
to a rocket launch. But my wife does
physics research. She does space physics research. She looks at magnetic fields
in the atmosphere of the sun and all her observations
come from spacecraft. And her colleagues actually
had some of their spacecraft on the Ariane 5 when it
was first being launched. The Cluster mission– they
had four spacecraft on there. But then, very
unfortunately, it did this. No one’s on there. There’s no humans
on that, right? It’s just spacecraft,
which still– now I know a friend of mine– I didn’t realize
this until later on. A friend of mine had
just started her PhD. I know her because she’s
a friend of my wife’s. She just got her PhD
when this happened. And her PhD was going to
be on the Cluster data. And she was there watching
it with everyone else. And this happened. And the room went
about that happy. And the room just went
silent when it happened. And she was just thinking,
there goes my PhD, right? And the bits rained down
on the mangrove swamps in French Guiana. And they actually
posted it back to them. So more detail than normal,
but it’s that kind of crowd. So my wife works at UCLA in
the Mullard Space Science Laboratory. And so they actually
design the instruments that go on the spacecraft there. And it’s in an old,
Victorian era mansion, out halfway between
Guilford and [INAUDIBLE],, in the Surrey countryside. And they’ve converted
a bunch of it in to clean rooms and
engineering workshops. They literally make spacecraft
in the old potting sheds. And it’s phenomenal. So they make all this. And it takes so long
to design and make these instruments
and these detectors. And the cluster ones were
going to be orbiting the Earth, tracking the Earth’s
magnetic field and how it responds to
changes from the sun. And they spent ages on
this instrumentation. And they got it launched. And then they weren’t
expecting to get it back. And it came back in a box,
covered in bits of swamp. And there was, like, decades
of people’s lives were there. And what went wrong
was an operant error. So the way this
system worked was they had a bunch of
sensors which were dotted around the spacecraft. They were all feeding
into a thing called the inertial reference
system, or the SRI for System Reference– eh, it’s ESA. And then that took all the
raw data from the sensors, turned it into meaningful
navigation or location data, and then pushed that off
to the main processor. I know. For some of you, this is an
excruciating amount of data that you don’t need. You’re, like, Matt, we
know how sensors work. So the problem was they were
given quite strict budgets on how much power
and, effectively, computation they were allowed
for all the different bits of spacecraft. And people working
on the SRI were trying to keep their overheads
in terms of energy use down. And they looked at all the
sensors which were coming in. They had to turn them
into 16-bit values before they were then sent off. And looked at all the
instruments, and seven of them could give a 64-bit read out. OK. So we need to check everything
from these seven sensors. And they went, well, hang on. What values are we actually
going to get from them? And of the seven which
could give a 64-bit number, three of them would
never actually physically be able to record
a value that big. And so they actually
worked out they didn’t have to check
those before they put them into whatever the memory was. And so those three
didn’t have a check. The other four did have a check. And the whole system worked
great on the Ariane 4. Then, without
checking it properly, put the same stuff
on the Ariane 5. And because it had a
different flight trajectory and slightly
different sensors, I believe– don’t
quote me on that. I spent a long time reading
through ESA official reports. Because of this, the sensor
wasn’t being checked. It gave a 64-bit value. It was copied into
a 16-bit space. It caused an overflow error. And that crashed the SRI. Which, in and of itself,
would have been OK. There are backups. Except when it crashes, it
sends off an error message, like, the final– I always describe
error messages– it’s like the cliched, someone’s
oh, tell my spouse I love them. But it’s, like, tell my
debugger the following context relevant information. And so it did that. But no one had
noticed it was going to send that at the same
channel to the main processor or computer as it was
sending its navigation data. That the system got it,
thought it was navigation data. Thought the rocket had
veered off to one side and tried to correct. But it wasn’t veering, and
the correct ironically, was the veer. And then it rightfully decided
to self-destruct at that point, and rained down on the swamp. And so I get a little annoyed. Because everyone
goes, oh, it was just an overflow error or maths
error or programming thing. Actually, no– the original
code was very clever. It just hadn’t been
properly checked before it was put
into the new system. And actually, that sensor
didn’t have to be on. It was actually a pre-launch. I think it was location or
something or tilt sensor. And originally, the Ariane
4, they got really annoyed that, if they went to
launch and they turned off the pre-launch stuff, it took
a long time to reset everything if they didn’t end up launching
and they wanted to do it again. So they changed the code
so it would continue running for 50 seconds after
the initial launch in case it had to be restarted or
it wasn’t an actual launch that time. And it caused this error. It actually exploded 40
seconds into the launch. And so it didn’t even
have to be on, right? And so all these extra
layers and details are what I find fascinating
about what went wrong. And sure enough, in the common
room at the Mullard Space Science Laboratory, where
my wife and her colleagues have coffee, they have the
bits of the spacecraft. They dusted off most
of the bits of swamp. Apparently, you’re not
allowed to touch them because they’ve still got rocket
fuel on it, which is something something carcinogenic. And they had them in
a box as a reminder to future generations
of space scientists that decades, like, their
entire career, can go up. It could disappear in
the blink of an eye because someone didn’t
double check some code. And they weren’t insured. However, ESA decided to
rebuild them and relaunch them. And there was a bit of
discussion about should we? Because by then,
technology has moved on. They’re, like, should
we upgrade them, or should we just rebuild
them exactly the same? They decide to rebuild
them exactly the same. And they launched them. They’re working fine. They’ve been up
there for years now. So ultimately, it was
a successful mission. But all of that, wow, because
there’s a couple lines of code. OK. So Mars Orbitor, good guess–
the other answers maybe shorter. So any other guesses? What might have
gone in the book? I got one on the
side over there. We’re going to go with
person on the side. We got reluctant– Let’s get person on the side. Yeah? AUDIENCE: [INAUDIBLE]? MATT PARKER: Oh. OK. So I wasn’t able to find
out any details on this. There was a fly-by-wire aircraft
which, correct me if I’m wrong, is the kind of aircraft where
the controls are connected to what’s actually happening. It’s not like electronics. And they flipped at the equator. I don’t– that’s not in there. I can’t remember if I tried
to fact check that or not. Has anyone else heard of that? We’ll talk afterwards. What I have put in is the US– I think it was Air Force– had a bunch of F22s. And this is in the
early, mid-2000s. The first time they flew
from Hawaii to Japan that crossed the International
Date Line and their navigation systems turned off. Genuinely happened,
incredible– they tried to restart them in the air. It’s so good. But they couldn’t. And so they always have this
fueling aircraft with them– because they couldn’t navigate,
but they could still fly– they had to just
limp back, following the refueling aircraft all
the way back to Hawaii. That definitely happened. I found reports on that. I guess what I
couldn’t verify in that story is there were rumors
that they were in the aircraft, and they heard the Microsoft
Windows startup noise. Cannot verify that. That would be so good– no way. And I managed to verify
there was a US aircraft carrier, a massive
warship, which was cut adrift without any
power because one of its systems divided by zero. Mwah. Mwah. Any other guesses
what’s in the– OK, you, second row. AUDIENCE: I think it was the
Patriot missile [INAUDIBLE]?? MATT PARKER: Oh, yes. So the Patriot missile– this was a missile
defense system which was to stop SCUD missiles
in the first of n Iraq wars. And it had an issue where it
was keeping track of time. I forget the interval,
something like milliseconds in a certain space. And the longer it was on,
the less precise its time. Therefore, location
calculations [INAUDIBLE].. And that’s
particularly horrific, because people
died in that case. But they’d already told
them it was a problem. They just hadn’t done
the restart often enough. And there was already an
updated version of the software. It arrived days
later at the camp. So yes, that’s a tough one. Because in so many
of these stories, they end, and then
everybody died. Because in engineering
and medicine, and anything with a military
application, that is so. And because I’ve
promised Penguin a comedy book about
maths, I couldn’t have every second story– and then everybody died. This collapsed, everyone died. This happened. Guess what? So I’ve tried to be careful
and strategic with what I put– because it is important. Because if these maths things
go wrong, people do die. But I’ve tried to be careful
how and when I put them in and how many examples
I use like this. Actually, all the aviation
stories in my book, nobody dies. And that’s partly
because aviation is phenomenal in terms of
how they deal with mistakes and how they avoid disasters. Obviously, it does
still go wrong. I was really annoyed. The Ethiopian report
into the Boeing 737 was supposed to come out
on Monday, yesterday. And they’ve delayed its release. And everyone keeps asking. Because obviously I’ve got
a book about maths mistakes with a plane on the cover. And I’m doing media interviews. And I’m, like, I just
don’t know, right? There’s a lot of
rumors and reports and pilot’s testimony and
stuff about the autopilot, I think, in piloting speak,
that’s the up and down flapping movement of the plane. And something is
going wrong there. But I don’t know the details. I’m waiting for that report
to come out so I can read it. But I was very careful to only
put in ones where nobody died. And then likewise,
there was one, again, kind of roll over errors. I didn’t mean to do
entirely roll over errors, but I think they
were fascinating. And obviously, a
lot of people here are well aware of the
limitations of binary and coding and roll over errors. But to the general public,
it’s just fascinating that you’ve just not left
enough room to write down a big enough number. Right? And obviously, the millennium
bug is a great example. We only used two digits,
and then the year got bigger than that. And obviously, there’s a bit
about Unix time and the Y2K 38, crash harder, the
sequel is coming up. And I found– this is great. I did not know this. In Switzerland, trains are
not allowed to have 256 axles. How great is that? A train must not have an
effective total number of axles equal to 256. Because they use axle
counting detectors. And they roll over
once they hit 256. And so if a train has
exactly 256 axles, it would count it
as zero, and it would move around as a
phantom train on the network. And I mean, I’ve seen hardware
problems fixed in software. There’s that before. I’ve never seen a hardware
problem fixed in bureaucracy. That’s such– such a Switzerland
solution to the problem. And again, I found many
cool machines which had the same roll over error. One machine used
for radiation had a bunch of checks to make sure
it wasn’t going to overdose. Because it could do
electrons or x-rays. And if it had the
wrong setting, it could have a horrific
overdose of radiation. And the check– they
had a thing called check call to check if
the columnar was in place. And check call, if
it was non-zero, it wouldn’t run the machine. And every time it
does the check, if it wasn’t in the right place,
it would increment check call. Except that every
one in 256 times, it would over roll to zero. And if the person hit go right
then, and it wasn’t safe, and it happened to
be rolling over then, it would still turn
on despite the fact that checks hadn’t been done
and the things were in place and people died. Right? Because of this–
it’s just terrifying. So I tried to balance that with,
hey, funny story about trains, people die, and Pac-Man! So this– oh, I’ve got– I shouldn’t have converted
this to widescreen without looking at it closely. Fixed, I reckon I
could have done that, and if I hadn’t been
talking out loud, no one would have noticed. OK. So this is the final
level of Pac-Man. People are often vaguely aware
that the 256th level of Pac-Man crashes. This is what it looks like. This is actually me
playing the level, because I know how to
cheat using an emulator. And when you hit this level,
the left is what you expect. This is the classic
arcade version of Pac-Man. The left is what you expect,
and the right is just this mess. As it’s often said that
you hit the 256th level, and that number is too big to
fit in your 8-bit of memory. And so it overflows
and everything crashes. And that’s actually
not what happens. So I dug through this. People have gone through. And there has been a project
to comment the original– whatever it is, machine, I
don’t know, whatever code this was written in. People try and comment
it and look at it. And people, in fact,
have released a patch that fixes this problem now– oh, nerds! And if you dig through what
happened, it’s not the level. Right? Because 256– I
mean, programmers know how to index from zero. Please. Right? So the first level
1 is indexed as 0. Level 2 is indexed as 1. So when you get to level
256, it’s indexed as 255. It’s fine. That does not
cause any problems. The problem is when it tries
to draw the pieces of fruit at the bottom of the screen. And in Pac-Man, they’re
generally called fruit. But there’s keys that he eats
and all sorts of other objects. And the idea is there’s a
different one for each level. And for no reason
other than decoration, they decided to
display, at the bottom of the screen, the
pieces of fruit from the recent levels
the player had played. Few people play more than one
level, so no one really ever notices. But they show up
to, I think, it’s seven or eight of
the last levels that you’ve gone through. And the way that it prints
them is in the memory. They’ve stored the table
of fruits and the graphics for each one. And first of all, it checks
if there have been– actually, I’m going to bring
in my pseudocode. Oh, OK. So the first step is–
this is a paraphrase this– the first step is, is
it level 7 or lower? Because it is level 7
or lower, then it only needs to print as
many pieces of fruit as the current level number. If it’s greater
than 7, it’ll only go up to the most recent, 8. Let’s say 7 or 8. And so what happened was
it would take the index of the level, increment it by
one to get the actual level number– this is
where it went wrong– so 255. That becomes zero. It does a quick check to go, oh,
is that below or above seven? Zero is below seven. But then what it did
was to print anything from below seven. So instead of just doing
the most recent eight, what it would do is, first of
all, draw a piece of fruit. Then let’s not check now. Let’s first of all subtract
one from the level number, then let’s check if
it’s zero and stop, then otherwise keep on fruiting. And so it would
print a bit of fruit. Subtract one. Go back down to 255. That’s not 0. Keep on fruiting. And so it was this weird– it was just hovering
above and below zero at just the wrong times. It tries to print 255,
56, eh, off by one, one of the two pieces of
fruit and the rest of it. So it starts printing fruit. And because of the way
the coordinates work, it prints across a couple times. And then it starts top
left and just runs down until it thinks it’s
done enough fruit. And this is just the rest of
the stuff in the memory being interpreted. It looks like it
finds with where the characters are stored. It’s just whatever else
is in the memory, splashed onto the screen. And the levels don’t finish when
Pac-Man has eaten all the dots. The levels know how many
dots there should be, and they finish when
Pac-Man has eaten that many numbers of dots. And because it doesn’t
print them all, because they’ve been
obliterated by the fruit, it’s impossible to go
on to the next level. And that’s why it crashes. In the original version,
you would loop back to one. And you would just
continue playing forever. This is actually preferable,
in my humble opinion. And so that’s it. So you can check out the
online project to fix it, which I think is incredible. And I did play it myself once. I’ve been meaning to
learn to play it properly to get there legitimately. But I just used the
emulator and I got there. And it was kind of fun. So again, another fun
example of a roll over error. So you know what? Let’s do one more guess. And then I’ll go into
Q&A. So we’ll do– any other guesses
what I might have put in the book, any
other classic stories? Very hesitant person
in the middle here– AUDIENCE: I think I remember
a story about Royal Navy guns being inaccurate in
the Southern Hemisphere because they did the
Coriolis effect wrong. MATT PARKER: Oh. That’s a good one! That rings a tiny bell. That’s not in the book. And so if you missed it. It’s Royal Navy guns
being inaccurate in the Southern Hemisphere
because the Coriolis effect is going to bump them
off into the other direction. And too late–
the thing is now– because in the
book, I didn’t want to make the book just
be a bunch of stories people could find on Wikipedia. I liked the fact I got
the common, famous stories and properly fact checked
and researched them and put them in there. So now it’s on the public
record what actually happened in a bunch of these situations. And then some of them were
people I knew or had worked with or contacts or anonymous. I wanted to have
extra stuff that’s in there which were new stories
that weren’t out before. And so people I
know, friends of mine who were engineers and
developers and database people and occupations I’m
not allowed to reveal, would give me these stories. And I would put them in either
anonymously, or carefully, as the case may be. And so I was quite
happy to add new ones. But now the book is
out, loads of people are contacting me with
more great stories. And I’m, ah, I
should keep a list and just write a lazy sequel. No. But I haven’t come across that. The only thing I
have done is– you know there’s the
classic, the water goes the different way down the plug
on the toilet thing, right? And it’s not true. It’s not true. The best you can
do if you actually imagine a sink, which is,
like, a meter in radius, like, a two meter diameter sink. And you fill it with water. And you let the water
totally settle so there’s no movement whatsoever. And then you very
carefully release– you can’t just
pull the plug out, because that’s
too much movement. If you release some kind
of valve or something at the bottom, and let it
drain over the course of hours, you will get different
rotations in that situation in the different hemispheres. And people have done
that experiment. Smarter Every Day,
YouTube channel Destin did it with
Veritasium with Derek. And so they filmed the same set
up in different hemispheres, brilliant. And I was, like, wow, hang on. But what about in a sink? Will it work in an actual
working environment? And so I got a sink. I took it to London
so I could film me at the front of the
Houses of Parliament. So I’m definitely in London. And I fill the sink
with a bowl of water. And I drain it. And I had a plumbing thing
set up into a bucket. You know, I put a
lot of effort to make it look super suspicious. And no one told me to stop. There you go. And so I filled this thing
and emptied it loads of times, to where it was a mix
of both directions. It depends what
the water is doing. I even tried– I had a thing to try and pacify
the water, like dividers, to stop it from moving. But any movement, it
goes different ways. I then got the same sink,
put it in a suitcase, flew it to the
Southern Hemisphere, did the same thing in Sydney. And so I got a
split screen of me with the same sink
in both hemispheres. And it goes in different
directions all the time, right? There’s no consistency. But I imagine, yeah, it would
make a difference launching– firing something
like a trajectory of that kind of scale
would make a difference. OK. So I am going to take some
questions in a second. They don’t have to be
guessing what’s in the book. It’s not just me crowd
sourcing the sequel. They can be questions of
anything I do or bits of maths or other stories and the rest. I’m going to put my
slide back up here. So that’s kind of
what I covered. There’s the book. I think about people
already got it. I’ll be around and
defacing them afterwards. I am fluent in ASCII, so I’m
happy to encode your name. Most people get very
upset about the URL being People here are, like, yeah,
you’re jerking your subdomains. There you go. I thought I was so funny
when I got that working. Penguin less so, because
they noticed if you go to,
it doesn’t work. And I was, like, yes,
people have to earn it. Matt, you have
misunderstood marketing. So that’s that. If you’ve not come
across anything I’ve done, as I’ve
mentioned before, I do Numberphile channel,
which is great fun. I imagine a lot of people
have come across those videos. In fact, the most recent
video on Numberphile was filmed in this building,
the one that I did. So I always wanted to do–
channels do live coding, which I love on YouTube. And often, in videos, I will
say, I found this number by– I coded a thing up. And I found it. I did this, right? And I’m amateur to terrible
level Python coding. And so live, I wrote a
little bit of Python– still in version 2. That got a lot of comments. And so never code
live on the internet. It’s a terrible idea. People have opinions,
it turns out. And so the video went out. And it shows me doing
the live coding. Like, for people who’ve never
done it, and I keep saying, I wrote a program to do this–
what that actually entails. And so I quite enjoyed it. But we filmed that. Brady and I just happened to
have some time before a YouTube event. And so we’re in a dark
corner, literally, it’s the dark corner in the basement
somewhere that just went out. So check out Numberphile. Stand Up Maths is
my other channel. That’s just me. And I put Patreon on there,
as well, because why not? Because they’re all
crowdfunded, basically. So my stand up maths videos– what I’m saying is Aunty Adsense
doesn’t give me enough pocket money. And so on Patreon,
people contribute. And I do ridiculous things
filming mass videos with that. So if you want to
check out anything more about what I’m
doing, there are links. I will wrap up the official part
of today’s proceedings there. And we’ll move on to
any other business. Let’s punctuate this
with around of applause, and then we’ll do questions. That’s the end of my
talk, [INAUDIBLE].. [APPLAUSE] Oh! How genuine– so how– [INAUDIBLE] got the mic. How are we going
to do questions? SPEAKER 1: Yes. I just wanted to ask
you to go to the middle, to the microphone,
so we can hear you when you ask the questions. MATT PARKER: Oh, yeah, so we’ve
got a mic on the stand right in the middle. So if you wish to
ask me a question, to there’s a certain amount of
public awkwardness involved. So you have to walk
over to the mic there. If I was playing a game of
are they leaving, or are they asking a question? AUDIENCE: Yeah,
thanks for the talk. There was a story
of some scientists that tried to give
cocaine to elephants as a part of an experiment. And they messed up the scaling. They scaled it by the
mass instead of scaling by the radius. And turns out the volume grows
with a cube of the radius. But what they needed
for the dosage was the surface
area of the organs, which grows with the square. And so they massively– I mean, they killed an
elephant with cocaine. MATT PARKER: I mean, what I
love about your question– and there is a lot
to choose from– is that you said,
you know, there were scientists who were
giving an elephant cocaine. That’s not even it. That’s just the start
to my favorite bit. And they did it based on
the cube of the radius, as if we’re all, like,
well, we all know how to dose an elephant. Those amateurs! No. Thank you. It’s a great story
everyone can connect with in their normal lives. No. I hadn’t come across that. That’s amazing, right? So I don’t know. Drug dose– I guess
they don’t necessarily scale with body mass, do they? And so they did it with mass. And it’s actually area. That’s lovely. Ah. Can someone write these down? I hadn’t come across that. That’s great. I have nothing
more to add, other than I will be looking that
up afterwards from a browser in private settings. OK. Any other questions– one
elephant’s worth of cocaine, please. Oh, here we go. The individual in the
Parker Square t-shirts. That’s going to be– AUDIENCE: [INAUDIBLE]. MATT PARKER: Is that unrelated? It is what you
normally wear to work? Or is– AUDIENCE: Yeah. MATT PARKER: Oh, really. Just threw it? You didn’t even think. You just threw it
on this morning. AUDIENCE: Thank
you for the talk. My question would be,
have you ever considered making another channel with
maybe more advanced features? And another question
I have are you aware of Three Blue, One Brown? MATT PARKER: Yes. So great, great– two
questions for the price of one. You may sit down now. So OK. First of all, to deal with
the [INAUDIBLE] question, the t-shirt, which I’ve made
a couple references to– I did a video ages ago
about how no one has ever found a magic square, a
three-by-three magic square, so that’s nine numbers in a
three-by-three grid, where every single column and row
and both the main diagonals all add to the same
total, such that all the numbers in the magic square
are themselves square numbers. No one’s ever found that– with certain extra constraints,
like, all the numbers have to be different,
and a few other things. Right? So I found one which is
close, but not quite. I gave it a go. Same story– I gave it a go. I wrote some code. I did a bit of a search. I found the best one I could. And I knew people
have checked them up to some crazy threshold. So I knew I wasn’t going to
discover the whole solution. I wanted to see how
well I could do, as a fun thing to talk about. As I made the video, and I
showed this square in the video on Numberphile. And then the guy making it,
Brady, behind the camera, just went, it’s not
very good, is it? And I was, like, what? This is my best effort. He’s, like, nah. He’s, like, what’s it called? And I said I am not going to
call it the Parker Square. Because then you’ll be ha,
ha, ha, that classic Parker Square it’ll
become– and so he’s, like, OK, fine, fine, fine. I won’t make a big
deal out of it. And then he released
a range of t-shirts and named the video
the Parker Square. Now it’s become this
mascot for when your best is not just good enough, right? But I like it, because
I’ve tried to repurpose it to be give it a go, right? So much in maths is
you try something, and people think maths
are all about getting the correct answer. You try something,
and it’s important you get the right answer. But it’s not. You give it a go
and you’re wrong. You go, oh, OK. And you try again,
and you’re less wrong. Yeah? And you try again,
you’re more wrong. And then eventually,
hopefully, you converge in on getting it right. And so I like the fact that
it’s all about giving it a go. I’m going to answer your
second question simultaneously. So have I considered doing
more advanced mathematics? And am I aware of
Three Blue, One Brown? Which is– I do,
yes, great channel. And so it’s difficult how
you pitch a YouTube channel about particularly
technical subjects. And you’re going to get slightly
different audiences depending on what you do. Numberphile we pitched
higher than anyone else thought was smart. And it’s because it was the part
of the original– back in 2011, it was a part of the early
Google funded channels, when Google was, like, TV is dead. And so we had a little freedom
when we first set it up. And partly because
of the people Brady chose to work with and
partly deliberately, we pitched it higher than
most people would expect, and it worked. People liked seeing
mathematicians nerding out on their
favorite numbers and doing actual working out. But since then, now it seems
quite tame in comparison. And now, a lot of people
who were into it when they were younger have now gone
on to become mathematicians. I’ve met people now are,
like, oh, I finished my PhD. And I remember
watching your videos when I was in high school. And I’m like, oh. Now I feel old. And so it’s kind of
stayed around that level. Stand Up Maths– I like to do two things. I occasionally like to
have quite heavy content in the videos, but
not often, to be fair. In fact, I’m due one which is a
bit more pure, or interesting, or more advanced mathematics. I tend to go for
one of two things. I tend to go for accessible
things I think will– while being enjoyable
for nerds– will help draw in new people. I’m much more of an evangelical
channel than a teaching channel. And secondly, I
try and do things which people of a
nerdy persuasion will just find delightful. And that’s because I’m
largely making the videos to entertain myself. And a bit like we do on
Numberphile when we printed out over a mile of pi, and
we had the first million digits on one continuous
piece of paper on a runway at an airport,
it’s just ridiculous. But it was great. And recently,
someone– I did a video which was a little
bit more in depth, but we didn’t go into any
of the technical details, about things called
superpermutations. Which I won’t go into here. They’re a very long
list of symbols that contain all the possible
permutations of the symbols in there and every
single permutation’s in there somewhere. And how short can you
find the permutation is kind of the challenge. And there’s a lot of open
questions in superpermutations. And I did a video about it. And someone pasted
a new breakthrough, like a new, shorter
superpermutation for seven symbols. It’s like 5,907 symbols long. They just pasted it in
as a YouTube comment. Like, no fanfare,
just here it is, boom. And I’m, like, wow! So new mathematics happened
in the comment section of my video. But then, based on
those breakthroughs, because there were
people working on it, got in touch with the
person who did it. And they had a bit of a chat. And some other stuff they were
working on kind of meshed up. And they found one even shorter. They had another breakthrough. And we’re, like, well, how
are we going to announce this? And then we realized, basically,
this one was one shorter. So it was 5,706 symbols. But there’s only seven
different symbols. And we’re, like, well,
an octave on a piano has seven notes, right? Eh, music– and so we
hired a self-playing piano. And the first ever announcement
of this mathematical result was played on a grand piano. And I was, like,
that’s just fun. Like why? And if you support
me on Patreon, that’s how I waste your money. And so I’m just trying do fun
things to enrich nerd culture, I think, is the
shortest way to put it. Channels like Three Blue One
Brown I’m super envious of. Because they guy, Grant
runs Three Blue One Brown, he’s a fantastic individual
And maths YouTuber community is super friendly
and nice, right? And so I know Grant
reasonably well. He’s a great guy. And we chat and nerd
out on mathematics. And one day we’ll actually
both do a collaboration we keep talking about. But he’s incredible at animating
advanced mathematical causes. I’m super envious that he can
take these more advanced things I would like to do and he can
actually make them happen. And I struggle. His visualizations
are incredible, and my visuals are adequate. That’s my career. And I do so many
different things that I don’t have as much time. I can’t justify too
much time, because I make a loss on my
channel, as it stands. I can’t justify too much time. I throw a lot of time at
it, don’t get me wrong. Right? But doing difficult
advanced maths well, so it’s still
engaging– and there are other channels like Red
Pen, Black Pen, and obviously, Khan Academy, and
these other channels who are doing more
advanced maths in much more of a lecturing style. They’re great, and they kind
of already feel that niche. So I stay at the low
hanging, entertaining fruit– the most concise description
of my job I’ve ever made. We’ll do one more
question, and then I’ll loiter around afterwards
to say hi and deface books. Oh, we’re forming a queue. AUDIENCE: Sorry. Were you in the queue? MATT PARKER: No,
you got there first. AUDIENCE: OK. MATT PARKER: We’ll hear both
of them, and we’ll vote. AUDIENCE: So in this
company, as you may know, we have quite a strong
postmortem culture. So when stuff goes wrong,
we write postmortems with the main goal to learn from
them and not repeat mistakes. Entertainment value
is kind of secondary. And given that you’ve
spent quite a lot of time, apparently, to look into some
of these things that went wrong, did you find a commonality? What’s kind of the big learning
to take from those, other than don’t do this? MATT PARKER: That’s a
really good question. And do the postmortems done at
Google ever get made public, or are they entirely
internal, locks down? Sometimes? OK. It’s interesting. It’s interesting how
much things [INAUDIBLE].. So I’ve got two
answers, which are I’ll try and do pretty swiftly. One answer is it’s interesting
which industries do and don’t make their postmortems public. And so there’s a sampling
bias that I have of the ones I’m able to see. And I know of ones that have
happened in other industries. But I cannot put
them in the book, because I only know about
them because I know the people involved. And there is no way
they can release them. And I talk about
a friend of mine– let me think about how
vague I have to be. They worked on a project
which was a thing. And there was a trivial mistake,
which slightly changed it aesthetically. And I was, like, this
is such a good example. Because the maths
mistake is lovely. The result is lovely and
funny, but not important. And nothing is
actually compromised. And it’s a contemporary one, and
no one died, and all the things I look for in just my life. And I was like, hey, can I put
the story in that you told me that time in the pub? And they were, like, no way. They’re still under so many NDAs
that they cannot disclose what happened. And so it’ll often feel like,
when you’re reading my book, lots of the examples come from
the military or government or things that
were quite obvious. So actually, you have a
lot of engineering ones where either it was
an organization who have some duty to
the public to release a certain level of report
into what happened, or it was so big and so obvious
that a report had to come out. And so I’ve kind
of got a problem where I only get a lot of the
public ones I can talk about. In terms of what I’ve actually
learned, what I found amazing is the different attitude
between different industries to blaming the human. And in aviation, they
don’t blame the human. In medicine, they
blame the human. And there are loads of others
in both categories, right? But they’re just
my two favorites. And aviation are
great at looking at the system as a whole and why
the mistakes became disasters. And there’s the Swiss cheese
model of accident prevention. People have come
across this, which is where you imagine your
mistakes as being projectiles, and they’re going
through a bunch of layers of Swiss cheese. And each layer is like a
different part or component of the system. And each one is meant
to stop mistakes. And so ideally, the mistake
will hit one of these. But occasionally,
the holes line up, and a mistake will
make it all the way through the entire system
and become a disaster. And aviation is big on
and this [INAUDIBLE].. I don’t think that
came out of aviation. It was actually research from
the UK that came out with that. But it’s a big one for aviation,
the Swiss cheese model. And it’s the system as a whole. Whereas in medicine,
if you give someone the wrong dose of a certain
drug, if you’re, I think, as a pharmacist or something,
that’s actually illegal. And so that’s not
encouraging people to discuss when it’s gone
wrong if you make the mistake and you’re arrested, or
fired, or all these things. And so you get this false
sense of the only people left in medicine are the people
who never made mistakes. And that’s not good for
teaching the next generation. It’s not good for developing
systems that deal with it. And so I think that
is fascinating. And then there’s a
whole other category of when the safety features
you put in place cause a new type of mistake. And there’s some
great researchers, a group called
ChiMed, who are based at Queen Mary University of
London, where I used to work. It’s a great place. And they looked at
the hot cheese model, where they imagined horizontal
slices of cheese, which occasionally, the pieces
of cheese themselves might drip and cause extra mistakes. And in medicine, they
found if they bring in a new system of barcodes– so you’ve got to scan
the patient’s barcode and scan the medication
barcode to stop mistakes when they get the wrong medication. They discovered
when it was actually implemented staff would
just get duplicate barcodes and stick them on their
clipboard to scan patients, because it’s quicker. Or they’ll have a bunch
up in the storeroom. And so there were new ways of
giving the wrong medicine now, because of a system
to stop people from giving the wrong medicine. It’s just fascinating. So blaming the individual
versus looking at the system and also the intricacies of
the system I find fascinating. I don’t know how
much that meshes up with what happens here
at generic tech company, but that’s just how anonymous
I can make your stories if you see me afterwards. So we’ll wrap up there. I will be around. I would love to talk
and chat for a bit, if people want to come
and tell me stories. Or I’ll sign your
books, et cetera. Is there any more official
business to be done? We’re done. At which point, I thank you so
much for having me along, it’s always a treat, I’m done. [APPLAUSE]

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100 Replies to “Matt Parker: “The Greatest Maths Mistakes” | Talks at Google”

  1. I sometimes play Matt Parker's videos when I study maths.
    I like to hear him chatter in the background. =P

  2. Blah blah blah … the talk may be interesting live, but on YouTube, it can be shortened by 50%. Additionally, many of the so-called "mistakes" are either communication mistakes, engineering mistakes or other human errors. I can't see why those are "math mistakes".

  3. Maths?
    Is there a plural for math?
    Is it "when Maths gone wrong", or "when math has gone wrong", or "when math went wrong"?

  4. @57:21 The sunlight and shadow on that building in the upper right of the screen behind Matt looks like an Amiga mouse pointer.

  5. I edit TV commercials, mostly for car dealerships. One GM requested a commercial with a visual of a balance scale with a $ on one side and a car on the other. Naturally when I animated it I had the car going down and the $ going up to suggest that you get more car for less money. They told me to reverse it, as the visual of the $ going up meant that the price would be increasing. I tried to explain their error but I was overruled.

  6. 12:45 – The shape is better explained as a lunar eclipse …but the earth is then much too small. Perhaps Sesame Street occurs on another planet, one much more similar in size to its moon.

    Stars are still not supposed to be there. No getting around that one.

  7. Would be weird if matt parker collaborated with someone named trey stone. They'd be the bizarro version of the creators of south park, trey parker and matt stone.

  8. It seems a lot of the stories are more about "greatest programming mistakes" instead of "greatest maths mistakes"

  9. I don't know, maybe I am wrong, but seems the title of the talk is kind of misleading. Everything else goes wrong here except the Maths… wrong conversions, numerical computation limitations… etc…

  10. According to the NASA Hubble project manager that I met some years ago, Hubble had an incorrectly polished lens due to metric/imperial conversion and so when launched was out of focus and sent useless pictures back. Another lens had to be inserted to correct the problem at the first inspace upgrade.

  11. Apollo 11 didn't land near that location.

  12. Lake Peigneur Salt Mine drilling accident was just a point error. It was lucky accident and with colossal dimensions, resulting barges sunk under ground, river direction changed so that salty water fish species came in. Noone got hurt!

  13. First advertising audible and then complaining about Adsense not giving enough money. Absolute mad lad.

  14. Sometimes your probe will lithobreak. Unfortunately, unless it is a lander, your probe typically will not survive. But, hey, at least it made it to space.

  15. Re Q&A the elephant and cocaine. In recent years someplace in Science News, briefly mentioned within a larger article, there was an incident reported of early researchers involving an elephant and LSD. I wonder if the cocaine story is a folk tale morph. The story I read was some researchers…how loose that word is sometimes…were trying to see how the LSD affected an elephant. They did a linear calculation of animal mass vs dosage. The math was technically correct, but without any understanding of what they were doing. The elephant got a huge dose of LSD and after a delay, gave a very loud snort, and keeled over and died.

  16. Looking at all the cranes in the background, I'm thinking, "London will be a great city once they get it finished!"

  17. 30:45 – There's a more acute example than the 'millennium bug':

    Loudspeaker driver manufacturers would rubber-stamp each of their drivers with the year and month of manufacture. They encoded the year using ONE digit! One couldn't tell if a certain speaker was made in 1955 or 1965!

  18. Matt Parker has taken to the gesticulations of a clever market-trader and the prancings of a mediocre dancer

  19. 17:56 Matt finishes his intro and starts talking about the Fucking subject: when wrong "maths" causes a problem.

  20. Why didn't the mint stick to the WINNING design? Was the minter like one of those DJs who mangles good songs because he "has to express himself creatively".

  21. Stars shining through the moon. Yeah, have you seen the number of kids books where the illustrator just can NOT get a rainbow right? I can (just) understand if they miss indigo, but having a rainbow with only 5 colours, or colours out of order is just careless.

  22. Great talk however I would like to take issue with the title ‘maths mistakes’; most of these feel a lot more like software testing mistakes than maths mistakes. I speak as someone who studied maths and later became a test manager for a number of companies. In the past I also worked for the European Space Agency on the Meteosat project and have vivid memories of a live stream of a Meteosat launch when the satellite itself failed and wondering if I would still have a job. On leaving ESA I was also test manager on a project to provide a tracking system for Ariane 5 which would blow the rocket up if it went off course (it was a replacement system for the one that blew up the specific Ariane 5 rocket in your talk). Examples of testing failures I used to quote (although I can’t remember the original source now) were, the Hoover free flight offer where they hadn’t correctly assessed the value of their offer and were inundated with claims, a soft drink promotion with too many winning cans, and a Y2K problem (which actually triggered before 2000) where a stock control system read a date in 2000 as out of date, sent the supposedly out of date stock for destruction and reordered new stock ad infinitum.

  23. The content is interesting, but it's really difficult to follow the presentation due to all the interjected commentary on the presentation itself and the excessive wording in general. I think it would be better with about half the words.

  24. When he said you could see stars through the moon I zoomed in on the white portion and tried so hard to see stars through it like it was transparent LOL

  25. Just wanna say that the Audible version isn't available in the US till next year, clearly hugely maths mistake there.

  26. 12:41 there is also a star right next to Ernie's pyjamas, in front of a hill, dangerously close to Earth. Nobody noticed?

  27. 12:41 there is also a star right next to Ernie's pyjamas, in front of a hill, dangerously close to Earth. Nobody noticed?

  28. Its true that parents will often be the biggest factor in a students education. Not to ignore, the student and teacher. What many ignore is the students access to food, healthcare, extraciricular activities and a stable home.

  29. Shhht. Shut up and tell nobody about the end of Unix time. It's kind of my secret pension fund.
    You can hire me in 203x to fix your old C code.

  30. The title of this video should be “Six minutes of momologue about the life story of some guy and then you quit disappointed by not learning anything about math”.

  31. The improper use of "maths" is as bad as a street moron saying "X-cape." Or the more recent "X-tablishment."

  32. I kind of always knew I was too smart to hang out with everyone I met in school, and I just realized I spent an hour watching a programming and maths talk, completely enthralled. 🙂

  33. Paid money to license an image of three cogs meshed for the NAFTA image? Meshed gears is an image which shows synchronicity. The gears don't have to be shown in a viable configuration when they are clearly not being represented as mounted. Everyone who has worked with cogs has laid them on the table meshed.

  34. The Texas license plate…it is the "Lone Star" State…since there is one star in the moon circle…
    maybe it's an inside joke?

  35. I can't give a reference to it, but there was once a motor torpedo boat on exercise, probably 30 years ago, testing a new kind of torpedo. They got the torpedo armed and lined up, and at that moment, the test was called off, and the boat turned around to go home – then blew up. Lives were lost. In the final analysis, the torpedo had a fail-safe mechanism in it, that would cause the torpedo to self-destruct it went off course in the water and turned around to face a friendly boat. It was still armed, and the turn-around sensor had done its job.

  36. May I make a request for your next talk or video? Either pass the person speaking in the audience a mike, or perhaps you could repeat the person's answer, since your mike seemed to be working fine. Thank you.

  37. @10:20 Still wouldn't work if the teeth ratios aren't right. Hey, no less pedantic then the even/odd issue.                                    @22:57 A 64 bit word is not neccessarily a larger value then a 32 bit word. It could be the same value with a higher degree of resolution.

  38. 7:14 Morons forgot Administrators, the cog that allow funding & other support for the teaching process. (PTSA)

  39. It was the F-15 That flipped at the equator. Luckily the error was found in simulation, because it flipped back "wrong side up" so fast that it would have broken the pilot's neck had it been in a real aircraft.

  40. If there is anything that we need more of at schools, then it is light-hearted and enthusiastic math teachers.
    A lot of them just stand there and look all super-serious and never smile or laugh, which really triggers me sometimes.

  41. This audience seemed like it had a poor sense of humor. Lots of missed jokes. My personal favorite was "the first of n Iraq wars"

  42. Millenium bug … it's not only using two units for "year". It's about setting the year field to "99" for marking data entries to delete, too. The reason behind is that on a following sorting process (done by batch processing) the data is sorted at the end of file making the deletion easy. A typical way of data handling in COBOL programmed main frame applications in times where memory space was expensive, saving three bytes, two in the year field, one for an extra field of marking "deletion".
    Btw: In Europe they dealt with that mostly while reprogramming their applications due to the double currency introduction of the EURO.

  43. I would love to see you go over what was wrong with the math they used to say stuff as they will never break the sound barrier, that the earth atmosphere was going to catch fire if they explode the atom bomb.

  44. Dude, you say that the contractor got the unita wrong. You say that they fueled the aircraft in pounds not kilos, twice.

    Perhaps the American government could bring America up to speed with the twentieth century so we can remove some of these errors. ?

  45. @17:45 "Pushing against" a gyroscope will only allow you to change your orientation, it can't change the trajectory. Wikipedia: "Specifically, software that calculated the total impulse produced by thruster firings produced results in pound-force seconds. The trajectory calculation software then used these results–expected to be in newton seconds (incorrect by a factor of 4.45)–to update the predicted position of the spacecraft."

  46. I've seen footage on Youtube of stars being seen through the Moon. Hidden in plain sight, maybe? The is not what NASA says it is

  47. Great last question. I wish we'd know if Google's postmortem of mistakes blames the human (as like medicine) or blames the system (as like aviation)?

    Good point that if blame the people then never learn from the mistake. As the system is the issue.

  48. Why do speakers on ted, you tube generally waffle, "my wifes friend etc" …stick to the fucking subject..succinctly

  49. Matt, can you explain non-interger exponents of negative numbers? E.g. -2^2 = 4; -2^3 = -8; -2^2.5 = ? My calculator says it’s an error, but surely it’s evaluable (right?).

  50. Matt, I'm not happy about that circle around the moon on the number plate, you've been a bit too left-wardly generous with the centre and the radius is too long. You'll have to redo it.

  51. That's marvelous.

    There's one other famous airline mistake, & nobody died. They called her "the Gimli Glider". Air Canada had just bought their first A300s, & a flight out of Toronto loaded the usual amount of fuel–only somebody (the Captain?) used pounds instead of kilos, which the aircraft readout used, & they ended up with only half as much fuel as they needed…& the aircraft came down on a drag strip (formerly an airstrip) in Gimli, Manitoba.

    The only other case I can think of where there wasn't enough fuel aboard was the La Mia wreck that killed the soccer team–& that was because the crew were flying on an illegally-low fuel load & expecting they could make it.

  52. With that lovely picture of St Pancras railway station in the background, I could mention the time, about 50 years ago, when that railway system was decimated and almost destroyed by bad maths. Specifically, by creative accounting. It wasn't just a single mistake, but a systematic series of errors, each to the railway system's detriment. Many even believe, and not without reason, that it was deliberate sabotage.

    Around 1960, British Railways was indeed in a bit of a pickle. WW2 had practically bankrupted the Big Four companies, forcing them to be nationalised, and the subsequent 15 years had been marked by several badly mismanaged investment programs – first, a large order of new steam locomotives to replace the worn-out engines from war service, then a crash dieselisation program when someone realised how much steam engines cost to run in an economy in which wages were high, skilled labour scarce, and all the good coal was being exported to service a crippling national debt. There were now dozens of diesel locomotive types in service, many of them hopelessly unreliable and complicated to service, alongside all of the existing steam loco types of which the final examples were still being built!

    The Government were keen to rein in the waste, so they commissioned some "outside industry experts" to report on how to make the railways pay for themselves. It just so happened that these experts came from the road and petrochemical industries, so were hardly neutral observers.

    The ensuing report correctly identified that much of the railways' costs stemmed from low-traffic branch lines which were not very efficiently run. There were some stations which had not sold a single ticket in months or years, yet still employed a stationmaster, a booking clerk, a porter, a signalman or crossing keeper, and even someone to run the tea room. Steam engines were fired up each morning, and kept in steam all day, to haul one or two nearly empty carriages up and down the line a few times, and maybe a few wagons for a change. Signalboxes and crossing houses were manned by highly trained staff, two or three shifts a day, merely to let this meagre traffic through in safety.

    It must have seemed like a very simple equation. If sum(costs) > sum(receipts) then close(line).

    They did not think to check, however, what happened on a bank holiday weekend. Excursion trains would then descend on these sleepy branch lines like locusts, their tickets having been sold in major stations elsewhere and thus not appearing in local accounting books. On many lines there was also heavy seasonal freight traffic, as farmers sent their crops or herds to market. The dense network had also proved its resilience against war damage, as any closure forced by an air raid could be bypassed on some alternative line. That was why this expensive infrastructure had been maintained in place, even though it went unused so much of the time.

    But the beancounters missed all of this. The maths seemed simple, so they believed they had it right.

    Nobody even bothered to check whether some of the cost overheads could be reduced, through relatively modest investments like replacing the steam trains with some of the new DMUs, while still keeping the valuable railway service in place. If the staffing at some stations was excessive, make do with fewer staff, augmented seasonally by roving assistants if required. Rig up signalboxes so that they could be left unmanned if traffic was light, and install automatic crossings to replace the swing gates and their keepers. Institute containerised freight to avoid the cost of shunting whole wagons into trains. Obvious solutions to a railwayman directed to look into these things – but the men in charge were not railwaymen, and those solutions would only complicate the equations.

    As a result, there are no more trains to the formerly popular beaches of the North Devon & Cornwall coast. Main and secondary lines, sorely needed today, were closed despite protests, and new lines must now be built to replace them. Much of the railways' utility to passengers and freight traffic alike, that of being able to get from anywhere to anywhere by a singe mode of transportation, was forever lost, accelerating the move to the roads and driving up the death rate accordingly.

    All because of bad maths.

  53. Funny I'm working for this company who is making and installing this axle counter. Thales if somebody is intrested. If somebody is intressted in more information I'll see what I can do.

  54. Did anyone ever publish the deal where some guy tried to assign PI an invalid value? I think that it happened in Illinois??

  55. Christopher Columbus thought the world was smaller than everyone else and that there was just water between Europe and Asia. He thought it was so small in fact, that he barely had enough supplies to get across the Atlantic. Not sure how true this is, but it would be a good jumping off point for a larger point.

  56. What about the math error at the Savannah River nuclear plant that was regularly cracking the pressure vessels. Everyone kept checking the materials used, and engineering practices, but no one verified the actual operating pressures of the vessels, and it turns out that they ran for 40 years at 115% power levels because some engineer had a slide-rule error during its initial construction documentation.

  57. NO NO NO! Those aren't stars shining through the moon. They're the sun glinting off reflective deposits on the moon's surface!

  58. For the F-22 story that's 100 percent true, the navigation system failed at the dateline. As for the windows boot up sound I didn't hear that part of the story but I doubt it's true because all of the computers in the F-22 are custom built and run custom operating systems. I worked on testing a system for the F-22 and I briefly worked with a guy that worked on a team that tested the navigation code. What happened was that they had done simulated flight around Lockheed's center in Texas and verified that the navigation system worked. However, the equation they used in the system led to a divide by 0 error at the date line. So now when they simulate flights they cover crossing the date line, flying over the poles, flying around the pole so you cross all the time zones quickly.

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