September 9, 2022 • 32 mins
A meter is longer than a yard. An ounce is heavier than a gram. We harmlessly mix them up sometimes, but a "unit conversion error" when you're filling up the fuel tanks of an airliner can be fatal. Which is exactly what happened to Air Canada Flight 143.
Tim Harford talks to mathematician and comedian Matt Parker about how the aircraft came to take off without the proper fuel load, how no one noticed until it was too late, and why such errors give us an insight into just how important maths is to keeping our complex world working as it should.
For more "unit conversion errors" check out Matt's book Humble Pi.
See omnystudio.com/listener for privacy information.
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Episode Transcript
Available transcripts are automatically generated. Complete accuracy is not guaranteed.
Speaker 1 (00:15):
Pushkin. On the twentieth of July nineteen eighty three, Air
Canada Flight one four three was being prepared for its
two thousand mile cross country flight from Montreal to Edmonton.
The ground crew loaded her up with a necessary fuel
(00:37):
twenty two thousand, six hundred kilograms according to their calculations.
Those calculations were correct up to a point, but unfortunately
they're mixed up kilograms and pounds, and not in a
good way. Nobody had any idea of this, but the
plane took off for a four hour flight with only
(00:59):
half the fuel it needed to get to Edmonton. The
plane was now on course to run out of fuel
somewhere over Winnipeg. I'm Tim Harford and you're listening to
Cautionary Tales. This is a new experiment for us. Here
(01:37):
at Cautionary Tales. As usual, you'll hear a story of disaster,
but I'll be joined by an expert to help tell
the story and reflect on the lessons. I hope you
like it, and I'm confident you will, because my guest
today is Matt Parker. Matt Parker is a phenomenon, a
stand up comedian, mathematician, YouTuber, podcaster, an author of the
(01:57):
number one bestseller Humble Pie and Humble Pie is a funny,
nerdy book about the real life consequences of mathematical mistakes,
and it's where I first heard the story of air
flight one four three. Matt Parker, Welcome to Cautionary Sales.
Thank you, Tim. It's an absolute honor to be your
zeroth guest on the show zero both guests. Matt counts
(02:20):
in strange wayst this story is a bit like an onion.
It's got layers. Yeah, on the most superficial level, the
sort of papery outer layer of the story. If you like,
why did this plane have too little fuel? The very
simple reading is they had a unit conversion error. So
the people who are meant to be fueling the aircraft
saw a number, they assumed it was pounds of fuel,
(02:43):
when in fact it was kilograms of fuel. And the
reason they're even doing this in mass because if you
fill up a car, you don't put the fuel in
by mass, you do it by volume. Volume changes based
on the ambient temperature. As things warm up, they tend
to expand, if they cool down, they tend to shrink.
And if you're flying an aircraft, it's important you have
(03:05):
the amount of fuel you're supposed to have, and so
they may insure instead of using the straightforward volume, they
were going to use mass instead. And sadly it was
that attempt for extra precision that opened up the door
for this unit conversion error. Yes, you would think they
might just stick in a little bit extra just to
be sure, but there's limits to the amount of extra
(03:27):
fuel you want on a plane because yeah, it's heavy. Yeah,
And so they even allowed enough extra so that twenty
two six hundred kilograms you mentioned, that's twenty two thousand,
three hundred kilograms for the flying bit, and then they
put on the extra three hundred kilograms for like taxiing
and like all the bits that maybe they hadn't factored
into the flight. So they were trying to be careful,
(03:49):
they were being thorough, they just got the units wrong.
What it was it about Canada at this particular time
that made it particularly vulnerable to a unit conversion error.
In Canada, they had just switched so previously they were
using imperial units or like the old school, like English
style units, and they just swopped over to real units
(04:11):
or metric as the rest of US. I was about
to say that as in Australian you're neutral in this fight,
but you're clearly not neutral. Okay, no, no, not since
the nineteen sixties. I love the quirkiness of the imperial system.
That metric is nice and straightforward. Yeah, but if there's
one thing that's worse than using imperiod units, it's using
(04:32):
imperiod units when you think you're using metric units or
vice versa exactly. And it was even obscured by one
layer because when they were doing the calculations, they weren't
actually doing it in terms of the direct mass. They
were using something called the specific gravity, which is like
a measure the density of the fuel, and so they
used that to get back to the volume that they
(04:53):
then had to put into the plane. And because there
was this extra one layer of opaque bit of putting
it into a slightly different way of looking at it,
they didn't realize that the units behind the specific gravity
were based on kilograms and they assume that they were
based the old way on pounds. There's more maths than
I had anticipated in filling up a plane. Yeah, okay,
(05:13):
this is slightly unnerving, but I mean it's not just
planes that suffer from unit conversion. Eras your book Humble
Pie has a whole chapter full of them. I mean,
do you have any favorites with This? Plane is now
my favorite? You said you only came across it because
you were reading the book. I only came across a
researching the book. Prior to that. It was the Mars
Climate Orbiter spacecraft that NASA launched in nineteen ninety eight.
(05:37):
That was my favorite unit conversion era. And that's partly
because a lot of people know about it. There's this
urban legend of when NASA got the maths wrong, and
partly this is something very delightful about NASA, like the
mascot of science and precision and achievement coming undone because
of a unit conversion era. It was actually a bit
(05:58):
more subtle than that, wasn't it. I think NASA we're
using metric, but the sply was using imperial or old
school pounds. Yeah, it was Lockeed Martin was the contractor.
And like you said, NASA use metric. They're scientists, they're engineers.
They're going to use the most efficient, most optimal units,
and so everything they were doing was in metric and
in their documentation that they gave to their contractors, it's
(06:19):
stipulated you're going to do this in metric. Now, the
kind of common understanding of this is when the Mars
Climate orbiter got to Mars, they had to calculate how
far above the surface it was so they could put
it into a nice, neat stable orbit and people go, oh,
isn't that the one where NASA thought it was in
(06:40):
feet but it was actually a meters or vice versa,
And then they got the altitude wrong because they were
measuring the distance incorrectly. And to be fair to this day,
if you look at altitude of things like aircraft, it's
given in feet, which in one sense is a nice
bit of error correction, because if you hear a number
in aviation and its feet, you know it's in the
(07:02):
vertical direction, and if you hear a number and it's
kilometers or meters, you know it's in the horizontal direction.
And so it's a bit of redundancy in terms of
the directions encoded in the units that are used. Which
is maybe the one time I will concede that's an
interesting use for imperial units, but that's not the case. Here.
First time I've ever heard you defend values, I know
(07:24):
I know where defend is a strong word tim but
actually that's not what NASA did. They didn't confuse feet
and meters and kind of just smash this thing into
the surface of mask because they didn't know how high
it was. It is a much more soft lever. It's
always more complicated than that. In this case, as they're
flying the spacecraft from the Earth to Mars, there's a
big flywheel on board, because in space, there's nothing to
push against if you want to change your direction. But
(07:46):
if you have a spinning mass, you get the gyroscopic
effect and you can push against something spinning to reorientate
your spacecraft. The issue with that is sometimes your flywheel
is going incredibly fast and you have to have what
the NASA scientists have deemed a angular momentum desaturation event,
which is just slowing down the flywheel. But to do that,
(08:09):
you've got to fire the thrusters, like the little steering
rockets on the spacecraft to keep it pointing in roughly
the same direction as you're slowing down your gyroscope, and
those little thruster firings slightly change the trajectory of the
spacecraft on its way to Mars. So you want to
keep track of those. This was an external system done
(08:29):
by lockeed Mutton, and they've got a little program that
just logged every single time the thrusters fired how much
force they were firing, and therefore, later on NASA could
calculate the actual trajectory when it gets to Mars by
factoring in all these little thruster firings. And NASA said,
very very clearly, please write these down using mutants the
(08:52):
proper metric unit for force, and lockeed Martin wrote them
down as pounds force, pounds force. It's a ratio of
four point four five ish, very similar. It's pounds pounds
are killers all over again. Really, and this is the
kind of thing little smash your spacecraft straight into Mars.
Oh yeah. Because they assumed that the firings were in
(09:15):
Newton's when they've been written down in pounds fource, they
figured they were going to come in at an altitude
of between one hundred and fifty and one hundred and
seventy kilometers above the surface of Mars. They actually came
in at fifty seven kilometers above the surface of Mars,
much much closer, which means even though there's not a
lot of atmosphere on Mars, there is some The extra
drag of being that much lower slowed the spacecraft down
(09:36):
a lot more than they expected, which meant that it
fell out of the sky. It deorbited very ungracefully, and
billions of US dollars a spacecraft slammed into the surface
of Mars because of one unit conversion error. I wanted
to ask about a really old conversion error, which pleasingly
rhymes with NASA. So it was Vasa Vassa is this ship?
(09:57):
What's the story with there? This was a ship in
Sweden that was launched in the sixteen hundreds, in the
year sixteen twenty eight, and it was a magnificent, massive ship.
They put a lot of cannons on the top of it,
which might have been part of the problem because almost
immediately in its maiden voyage it toppled over. At the
(10:18):
time they're like, it was top heavy. We put too
many cans on the top. The ship was too tall,
and that caused it almost as soon as it left
the harbor, just just fall over on its side and sink.
And it wasn't actually found until the nineteen fifties. And
in nineteen sixty one they dredged it up and they
put it in a museum, which if you're ever in Stockholm,
I highly recommend you good at the Vassa Museum. The
(10:39):
ship was incredibly well preserved, so well preserved that some
people have a good look at it and thought that
looks a little asymmetric, Like the hole is not as
symmetric as you would hope a hole would be on
a ship. I mean that is a property I tend
to associate with ships exactly. Everyone likes a good symmetric
(10:59):
ships as a rule of thumb. So people looked at
it and went, dan, it's not as symmetric as it
should be, as other theory now is. When it was built,
it was built lightly asymmetrically because people were using different units. Specifically,
people were mixing up Swedish feet with the Amsterdam feet.
And we know this because we've found in all the
(11:22):
other bits of paraphernalia that came with the ship rulers
that we assume we're used when building the ship, and
they found both Swedish feet rulers and Amsterdam feet rulers,
which are different lengths, so a foot in Amsterdam is
different to a foot in Sweden. They've even got different
numbers of inches. A Swedish foot is divided up into
(11:44):
twelve inches and an Amsterdam foot divided up into eleven inches,
and of course the inches are then different. So the
theory now is when their ship was built in the
sixteen hundreds and people are like, oh, make it to
this many inches, this many feet. People are using different
rulers that are different lengths divided into different numbers of subdivisions,
and they've got some bits off, and so the ship
ended up a little bit wonky, sadly for them, and
(12:07):
great for us because it preserved this incredible warship. It
toppled over almost as soon as it sets sail. So
let's get back to Air Canada Flight one four three.
I flipped over the page in your book, and almost
the first thing that happens is it lands in Ottawa.
For some reason, they did this before they embarked on
the real journey, which is two thousand miles, and so
(12:29):
I thought, oh, it's a fake ount. Matt has faked
me out. They landed Ottawa, they checked the fuel, they
figure out there's been a near miss, nearly fatal error,
and they top it up and it's all fine. Not
quite so. There are layers and layers of mistakes that
were occurring, and it was a series of very unfortunate
mistakes which caused the plane to take off with the
(12:50):
wrong amount of fuel. But then a stroke of good luck,
they had to land early because they were changing passages
in Ottawa, and whenever you land, you have to redo
the fuel calculations. But as people may have realized based
on the percentage through this podcast, we are at the moment,
that's not the end of the story. They redid the
calculations and made exactly the same unit conversion error. They
(13:15):
once again did the calculations based on pounds instead of
doing it based on kilograms, and they're like, yep, that
checks out. That's the exact amount of fuel we need.
We will carry on with no additional fuel. Well done.
Whoever fueled this plane in the first place. So there
we are. Air Canada Flight one four three has taken
off not once but twice with the wrong amount of fuel,
(13:39):
with the calculations all messed up, and facing imminently the
fate of running out of fuel over the middle of Canada.
And after these messages that Parker and I will explain
what happened next. So we've been following Air Canada flight
(14:11):
on four three. It's taken off from Montreal. It has
pounds of fuel instead of kilograms of fuel. That is
not remotely enough fuel. It then has a second chance
to fix this because it lands after a short hop
land in Ottawa. They do the same calculation, They make
the same mistake. They say, Yep, there's plenty of fuel
in there. Because they're confusing pounds and kilograms. There is
(14:32):
not plenty of fuel in there. And the plane takes
off again, and now it's really in trouble because now
it is going to fly two thousand miles. People listening
to this will be screaming, why didn't they check the
fuel gauge? Does a plane not have a fuel gauge?
My car has a fuel gage, surely a plane has
a fuel gage. So what's going on with the fuel gage?
I mean a plane does have a fuel gage. In fact,
it's kind of got a double fuel gauge. Because redundancy
(14:53):
is the motto of aviation, because you know something goes wrong,
it goes very wrong. And so they had a gauge
that shows the fuel and they've got like a unit
that then does the calculations to work out how much fuel,
and they've got sensors in the fuel tanks that are
measuring how much fuel, and they're all joined together to
give you extra redundancy. There's more than one sensor in
(15:14):
the tank, there's more than one link between the sensors
and the unit. There's the calculation, and then you've got
the display on the gauge. And one flight prior to
this flight. So when the plane was actually in Edmonton
ready to come over to Montreal to start this fateful flight,
they realized there was an issue with the senses because
the gauge had stopped working. And a technician realized, if
(15:35):
you unplug just one of the connections, if you remove
that layer of redundancy, there starts working again. And they're like, oh,
that's interesting, and in theory that should be fine because
they just label their right, I've removed this because it
wasn't working. You now have to do a manual check
as your layer of redundancy. Because we've removed it from
the sensors, You've now got to do it manually. But
(15:56):
this is where the chain of mistakes, the layers of
this onion really kick off, because there was just one
thing after another that went wrong, so that technician poorly
labeled what they had done. They just wrote faulty or
something to that effect. They then didn't write it very
clearly in the log book. They then didn't explain it
very well to the pilot. The pilot understood it as
(16:16):
being an ongoing problem, and it was always the case
that you had to do the manual fuel check, which
is like literally putting a stick in the tank to
see how much fuel there is when they finished the
next flight. The pilot then badly communicated this to the
next pilot, and the technician handover was equally bad. Like
at any point someone could have realized what was going on,
but the communication didn't work, and so the new pilot
(16:39):
was told, don't panic. As long as you do the
manual check, it's fine. Separately, a different technician's popped in,
realized it's unconnected, connected it back in again, rediscovered the
same issue the previous technician had left it plugged in,
went off to order the new part. The new pilot
sees the old label, which is now irrelevant, saying faulty,
(16:59):
but it's plugged back in again, which means none of
the gauges are working. All of this just comes together
as the pilot is sitting there looking at this label,
looking at the blank game age, and everything they've been
told just happens to line up, and they think, oh,
it's fine, as long as we do the manual check,
we can still fly even though the gauge is completely dead,
(17:20):
without realizing it is very much not what they should
be doing. So I did once run out of fuel,
and I fortunately I was on the ground in a car,
but I ran out of fuel because there'd been a
problem with the pump. The pump kept clicking out as
I was refueling in a way that indicated that the
tank was full. Yeah, but the fuel gage was showing
(17:42):
that the tank was nearly empty, and I just assumed
that the pump was correct and the fuel gage was wrong.
So I thought, huh, I got a broken fuel gage,
and off I drove, and I was not full. But yeah,
as I say, fortunately I was on the ground. You're
on the ground, but imagine all that happens, and you're like, huh,
you know what, I'll just get someone at the fuel
(18:03):
station to double check for me, and they put a
stick in your fuel tank. They do the calculation they're like,
oh no, no no, no, no, You've got loads of fuel,
but they've made a unit conversion error, and that parallel
mistake has reinforced your series of mistakes and misunderstandings, and
then you drive off without enough fuel. And there's actually
a theory in accident well, I guess mistake mitigation called
(18:25):
the Swiss cheese principle of avoiding disasters. Will you imagine
each check, each bit of redundancy, each failsafe as being
like a barrier to stop mistakes from getting through. But
no barrier is perfect. Some of them are operated by
humans and we can make mistakes. Some of them are
run by code on machines and they make mistakes. And
(18:46):
so each barrier has a few holes in it, like
a slice of Swiss cheese. But you just hope that
if you've got enough slices of cheese, one of them
will stop the mistake from getting through. But every now
and then your cheese holes just line up, and a
mistake will make it through every single layer, every single barrier,
every single failsafe, and will make it out the fast
side and become a disaster. And that's what happened with
(19:08):
Flight one for three. Just slice of cheese after slice
of cheese had a hole in the wrong spot and
the mistake made it through undetected, and so the plane
runs out of fuel somewhere over Winnipeg. It can't have
been a happy moment for the pilots. It was a
startling moment. I mean, the first indication they had that
something was up was a aero noise in the cockpit
(19:31):
that no one had heard before. They had to look
it up in the manual to see what was going on,
like this came out of nowhere, as only they realize
they're out of fuel. And this plane was one of
the first aircraft that Air Canada had brought on which
used avionics, and so there's a lot more electronics than
normal and suddenly all of it goes dead. The engines
are out, and that they're coasting. They're coasting a Boeing
(19:52):
seven to six seven. There were still some very basic,
rudimentary controls for the aircraft, so they were able to
glide it to some extent. And the reason why this
isn't a tale of absolute disaster, the reason why there
is a sufficiently happy ending is the pilot, before they
became like an airliner pilot for Air Canada. In their
previous career, they were a glider pilot, so the pilot
(20:15):
had sufficient gliding experience and they were able to glide
this bowing seven to six seven to a disused military
runway in a very small town called Gimli, and they
were able to glide this aircraft just over forty miles
and safely. Safely. It was abrupt. It's not actually a glider,
(20:36):
is it. It's not built to do this. No, No,
it's still going to land hard. And they couldn't bring
up like the landing gear and all this. Like they
had so few controls. They basically went straight into the
tarmac and they just like the nose went into it
and they just slid along. I guess, sparks going everywhere,
but there was just enough friction to bring the aircraft
to a halt before the fire end of the runway,
(20:58):
much to the relief of the sixty one passengers and
eight crew members on board, and not to the surprise
of the people currently using the airfield, and much the
big surprise to the people who were camping at the
other end of the runway. So there were people there.
They were on a go karting weekend and I guess
they booked the runway to drive go carts around. And
(21:19):
the crazy thing about a Boeing seven to six seven,
which the engines are turned off. It's pretty quiet, and
so they had no idea what was happening until they
hear this almighty wham and they all look around. There's
a jumbo yet sliding up this they were told disused
runway towards them, stopping just before it got to the
go cuts. So I mean, oh my goodness, once again,
(21:42):
things could have gone very wrong. But the last second,
thank goodness, everyone was okay. No one there. There was
no loss of life in the entire situation. It was
just amazing. I imagine a few people lost, a few hairs,
things were lost. Yeah, there's a note in your book
that they recreated this scenario in a simulator for other
pilots and it did not always go well. No, so
(22:03):
they obviously there's a big investigation afterwards to work out
what went wrong and how and why. And when I
was writing A Humble Pie, a lot of my time
was spent reading through these old investigations because if they
make it public to an extent, and so in there
they talked about the fact that they got other pilots
and put them in flight simulators in the same situation
(22:25):
to see what would happen, and every time they crashed,
no other pilot was in a stimulator was able to
glide a powerless seven six seven that distance and land
it safely. So they were very lucky that they had
the pilot they did, with the experience the pilot had
and was able to land this plane safely. It was
I mean, it very easily could have gone a different way. Yeah.
(22:46):
One of the other unit conversion eras in your book
is celsius fahrenheit thing on a BBC news story and
they were trying to figure out what some scientists or
somebody had basically said that there might be the following
temperature change because a climate change, and here it is
in celsius or centigrade, here it is in fahrenheit. And
(23:07):
the BBC just kept jumping backwards in four with really
very radical different answers to this question of how to
convert between celsius and fahrenheit. They kept changing their mind.
People just couldn't settle on the right answer. Yeah. Thankfully
people log changes to news sites so we can watch
as it went backwards and forwards, and then you're right,
there must have been a shouting match. There must have
(23:28):
been team three point six degrees and team thirty six degrees,
because those were the two Fahrenheits that the news story
kept flipping between two degrees celsius is thirty six degrees
fahrenheit and two degrees celsius is three point six degrees fahrenheit,
depending on if that's an absolute temperature or a change
(23:50):
in temperature. And it's easy to make this mistake because
things like kilograms and pounds they both start at zero.
You've got zero mass and then you have some mass,
and meters and feet both start at zero. Doesn't make
a difference if you're talking about the difference in two
people's height or anything. It changes versus absolute, same deal.
Celsius and Fahrenheits start at different points. They're zeros, are
(24:12):
at different places, and their increments are different. Like if
you're outside and it's two degrees celsius actual temperature and
you look at a thermometer, it would say two degrees
celsius thirty six degrees fahrenheit absolute temperature. But if it
then went up another two degrees, the temperature wouldn't go
(24:34):
up another thirty six degrees fahrenheit, it would go up
another three point six degrees fahrenheit, because that's the relative
ratio between the increments. So you've got a factor in
where they start how much they change. And because those
numbers look very similar, I can imagine why someone like
looked at the news story and went, oh, they've put
(24:55):
they put three point six. It should be thirty six.
They put the decimal point in the wrong place. Or
I'm guessing if you type this into Google or a
similar website and ask for the conversion, you know, what
is two degrees centigrade in fahrenheit. I mean, the answer
to that question is ambiguous, but Google is probably going
to return thirty six fahrenheit because that is the most
(25:16):
common sort of instance people thinking about the weather. Yeah,
the vast mirror of people are looking for the absolute temperature.
That's what Google is going to give you back. But
this was a percentage change in global warming should have
been three point six. Eventually, their solution was just not
to give it in fahrenheit, which is a solution I
wholeheartedly agree with just avoiding the problem, but just give
(25:38):
it in celsius and move on. As a journalist, it
is surprising how often you can solve a problem by
just deleting the sentence you're struggling with, ideally before you
hit publish. But you know it doesn't always work out
like that. So the story, as we've mentioned, comes from
your book Humble Pie, and it's one of dozens and
dozens of stories. A Humble Pie is not your first
book about fun maths. Why did you turn to the
(26:00):
topic of mistakes. I mean, because I've previously written about
kind of enjoying mass doing it, having some fun with it.
I thought, you know what, maths, it's wonderful, it's lovely,
we play with it. I think it's great, but we
do use it in a lot of critical situations, and
we use it like it's behind the scenes in our
modern society and we never really notice it. And so
I thought, you know what, if I write a book
about maths mistakes, I can tick two boxes simultaneously. Partly,
(26:25):
it means people want to read it. I mean, people
love things going wrong, as this podcast is a testament
too right, and we can learn learn from these terrible situations.
And so I was like, Okay, there'll be a good
hook to get people reading a book about mathematics, and
because I'm telling stories of mass going wrong, it's an
excellent excuse to first of all, have to set up
what the maths is and why we're using it. So
(26:47):
it justifies me writing about all these fantastic situations where
maths makes our modern society possible, which I found deeply pleasing.
One more thought, Matt Air, Canada have made this mistake twice.
NASA have made this mistake. Sixteenth century Swedish shipwrights have
made this mistake. The BBC have made this mistake. I mean,
(27:10):
this sort of problem seems to be absolutely all around us,
and it's the kind of thing that does bring planes
out of the sky and causes bridges to collapse? Does it?
Does it make you nervous knowing that we're trusting all
of these people all around us to get these things
right and they sometimes don't. It doesn't. It doesn't. So
then the underlying issue is as humans, we're not naturally
(27:32):
good at mathematics. And that's kind of reassuring because everyone
has ever struggled with maths or found it difficult. We
all do. Everyone finds maths difficult. The human brain doesn't
do maths like natively, it's going to learn it. But
thankfully that's not reassuring at all. I'm not reassured by
the thought that the people be fueling planes can't doing maths.
(27:52):
That's a valid point, allow me to continue. But what
I do find, what I do like is, and I'll
try and land this with a nice happy conclusion that
because we have maths, we can do so much more
than our brains can do. Intuitively, we don't have to
design like we have to make a building by eyeballing
it and like super over engineering it. We can actually
(28:15):
do the mathmakes and work out exactly what we need
and how it's going to work, and using maths we
can do far more than the human brain was ever
designed to do. The cost, however, is that we are
beyond our intuition and we have to do the maths
and do it very carefully and double check everything. And
so I like the fact we can achieve so much
more because we can use maths. I accept that this
(28:36):
is the cost it comes with, and I'm also reassured
all the stories I found, Obviously they're very spectacular, they're
very interesting, there's a lot to learn. I love the
fact now students at school are told pay attention to
units otherwise these things can happen. They are the exception.
The vast majority of the time, we've got all these
redundancies and checks in place, and they work. And so
(28:57):
these stories are interesting because they are such freak occurrence
as they managed to slip through, and thankfully, with a
very statistic minded head, I can still happily lie knowing
that the vast majority of the time it works. Fine, Matt,
What else are you working on at the moment, and
where else can people find your stuff? Oh? My gods. Well,
(29:19):
I'm still writing away on a new book which will
be out at some point in the distant future, you
know what. I don't think it's been announced, but it'll
be a book about trigonometry. So that's a Cautionary Tales
exclusive trigonometry book coming up at some point when I
finished writing it. If you'd like to know when you
(29:40):
sound a lot like my editor around that, I'm still
doing a lot of work obviously on YouTube and live
works picking up again. I just actually I just filmed
the stand up special version of Humble Pie. So I
was on tour with the show that goes with the book.
In twenty nineteen into twenty twenty. We obviously had to
(30:01):
delay and cancel a lot of those shows, and we
only just filmed the stand Up Special a month or
two ago, and that will be out at some point
around September. So if people want to see the live
stage version of all of these, if you've heard of
at a stand Up Mass dot com, that's my website
where everything happens. And if you're going to YouTube dot
com slash stand Up Mass, you'll see all of my
(30:22):
videos as and when they come out. Matt Parker, thank
you very much for joining us on Cautionary Tales. Tim
has been my absolute pleasure. Cautionary Tales is written by
me Tim Harford with Andrew Wright. It's produced by Ryan
Dilley with support from Courtney Guarino and Emily Vaughan. The
(30:44):
sound design and original music is the work of Pascal Wise.
It features the voice talents of Ben Crow, Melanie Gutridge,
Stella Harford, and Rufus Wright. The show also wouldn't have
been possible without the work of Mia LaBelle, Jacob Weisberg,
Heather Fane, John Schnas, Julia Barton, Kylie mcgliori, Eric Sandler,
(31:05):
Royston Berserv, Maggie Taylor, Nicole Murano, Danielle kan and Maya Caning.
Cautionary Tales is a production of Pushkin Industries. If you
like the show, please remember to share, rate and review,
Tell a friend, Tell two friends, and if you want
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(31:28):
on the show page in Apple Podcasts or at pushkin
dot fm, slash plus
Pushkin. On the twentieth of July nineteen eighty three, Air
Canada Flight one four three was being prepared for its
two thousand mile cross country flight from Montreal to Edmonton.
The ground crew loaded her up with a necessary fuel
(00:37):
twenty two thousand, six hundred kilograms according to their calculations.
Those calculations were correct up to a point, but unfortunately
they're mixed up kilograms and pounds, and not in a
good way. Nobody had any idea of this, but the
plane took off for a four hour flight with only
(00:59):
half the fuel it needed to get to Edmonton. The
plane was now on course to run out of fuel
somewhere over Winnipeg. I'm Tim Harford and you're listening to
Cautionary Tales. This is a new experiment for us. Here
(01:37):
at Cautionary Tales. As usual, you'll hear a story of disaster,
but I'll be joined by an expert to help tell
the story and reflect on the lessons. I hope you
like it, and I'm confident you will, because my guest
today is Matt Parker. Matt Parker is a phenomenon, a
stand up comedian, mathematician, YouTuber, podcaster, an author of the
(01:57):
number one bestseller Humble Pie and Humble Pie is a funny,
nerdy book about the real life consequences of mathematical mistakes,
and it's where I first heard the story of air
flight one four three. Matt Parker, Welcome to Cautionary Sales.
Thank you, Tim. It's an absolute honor to be your
zeroth guest on the show zero both guests. Matt counts
(02:20):
in strange wayst this story is a bit like an onion.
It's got layers. Yeah, on the most superficial level, the
sort of papery outer layer of the story. If you like,
why did this plane have too little fuel? The very
simple reading is they had a unit conversion error. So
the people who are meant to be fueling the aircraft
saw a number, they assumed it was pounds of fuel,
(02:43):
when in fact it was kilograms of fuel. And the
reason they're even doing this in mass because if you
fill up a car, you don't put the fuel in
by mass, you do it by volume. Volume changes based
on the ambient temperature. As things warm up, they tend
to expand, if they cool down, they tend to shrink.
And if you're flying an aircraft, it's important you have
(03:05):
the amount of fuel you're supposed to have, and so
they may insure instead of using the straightforward volume, they
were going to use mass instead. And sadly it was
that attempt for extra precision that opened up the door
for this unit conversion error. Yes, you would think they
might just stick in a little bit extra just to
be sure, but there's limits to the amount of extra
(03:27):
fuel you want on a plane because yeah, it's heavy. Yeah,
And so they even allowed enough extra so that twenty
two six hundred kilograms you mentioned, that's twenty two thousand,
three hundred kilograms for the flying bit, and then they
put on the extra three hundred kilograms for like taxiing
and like all the bits that maybe they hadn't factored
into the flight. So they were trying to be careful,
(03:49):
they were being thorough, they just got the units wrong.
What it was it about Canada at this particular time
that made it particularly vulnerable to a unit conversion error.
In Canada, they had just switched so previously they were
using imperial units or like the old school, like English
style units, and they just swopped over to real units
(04:11):
or metric as the rest of US. I was about
to say that as in Australian you're neutral in this fight,
but you're clearly not neutral. Okay, no, no, not since
the nineteen sixties. I love the quirkiness of the imperial system.
That metric is nice and straightforward. Yeah, but if there's
one thing that's worse than using imperiod units, it's using
(04:32):
imperiod units when you think you're using metric units or
vice versa exactly. And it was even obscured by one
layer because when they were doing the calculations, they weren't
actually doing it in terms of the direct mass. They
were using something called the specific gravity, which is like
a measure the density of the fuel, and so they
used that to get back to the volume that they
(04:53):
then had to put into the plane. And because there
was this extra one layer of opaque bit of putting
it into a slightly different way of looking at it,
they didn't realize that the units behind the specific gravity
were based on kilograms and they assume that they were
based the old way on pounds. There's more maths than
I had anticipated in filling up a plane. Yeah, okay,
(05:13):
this is slightly unnerving, but I mean it's not just
planes that suffer from unit conversion. Eras your book Humble
Pie has a whole chapter full of them. I mean,
do you have any favorites with This? Plane is now
my favorite? You said you only came across it because
you were reading the book. I only came across a
researching the book. Prior to that. It was the Mars
Climate Orbiter spacecraft that NASA launched in nineteen ninety eight.
(05:37):
That was my favorite unit conversion era. And that's partly
because a lot of people know about it. There's this
urban legend of when NASA got the maths wrong, and
partly this is something very delightful about NASA, like the
mascot of science and precision and achievement coming undone because
of a unit conversion era. It was actually a bit
(05:58):
more subtle than that, wasn't it. I think NASA we're
using metric, but the sply was using imperial or old
school pounds. Yeah, it was Lockeed Martin was the contractor.
And like you said, NASA use metric. They're scientists, they're engineers.
They're going to use the most efficient, most optimal units,
and so everything they were doing was in metric and
in their documentation that they gave to their contractors, it's
(06:19):
stipulated you're going to do this in metric. Now, the
kind of common understanding of this is when the Mars
Climate orbiter got to Mars, they had to calculate how
far above the surface it was so they could put
it into a nice, neat stable orbit and people go, oh,
isn't that the one where NASA thought it was in
(06:40):
feet but it was actually a meters or vice versa,
And then they got the altitude wrong because they were
measuring the distance incorrectly. And to be fair to this day,
if you look at altitude of things like aircraft, it's
given in feet, which in one sense is a nice
bit of error correction, because if you hear a number
in aviation and its feet, you know it's in the
(07:02):
vertical direction, and if you hear a number and it's
kilometers or meters, you know it's in the horizontal direction.
And so it's a bit of redundancy in terms of
the directions encoded in the units that are used. Which
is maybe the one time I will concede that's an
interesting use for imperial units, but that's not the case. Here.
First time I've ever heard you defend values, I know
(07:24):
I know where defend is a strong word tim but
actually that's not what NASA did. They didn't confuse feet
and meters and kind of just smash this thing into
the surface of mask because they didn't know how high
it was. It is a much more soft lever. It's
always more complicated than that. In this case, as they're
flying the spacecraft from the Earth to Mars, there's a
big flywheel on board, because in space, there's nothing to
push against if you want to change your direction. But
(07:46):
if you have a spinning mass, you get the gyroscopic
effect and you can push against something spinning to reorientate
your spacecraft. The issue with that is sometimes your flywheel
is going incredibly fast and you have to have what
the NASA scientists have deemed a angular momentum desaturation event,
which is just slowing down the flywheel. But to do that,
(08:09):
you've got to fire the thrusters, like the little steering
rockets on the spacecraft to keep it pointing in roughly
the same direction as you're slowing down your gyroscope, and
those little thruster firings slightly change the trajectory of the
spacecraft on its way to Mars. So you want to
keep track of those. This was an external system done
(08:29):
by lockeed Mutton, and they've got a little program that
just logged every single time the thrusters fired how much
force they were firing, and therefore, later on NASA could
calculate the actual trajectory when it gets to Mars by
factoring in all these little thruster firings. And NASA said,
very very clearly, please write these down using mutants the
(08:52):
proper metric unit for force, and lockeed Martin wrote them
down as pounds force, pounds force. It's a ratio of
four point four five ish, very similar. It's pounds pounds
are killers all over again. Really, and this is the
kind of thing little smash your spacecraft straight into Mars.
Oh yeah. Because they assumed that the firings were in
(09:15):
Newton's when they've been written down in pounds fource, they
figured they were going to come in at an altitude
of between one hundred and fifty and one hundred and
seventy kilometers above the surface of Mars. They actually came
in at fifty seven kilometers above the surface of Mars,
much much closer, which means even though there's not a
lot of atmosphere on Mars, there is some The extra
drag of being that much lower slowed the spacecraft down
(09:36):
a lot more than they expected, which meant that it
fell out of the sky. It deorbited very ungracefully, and
billions of US dollars a spacecraft slammed into the surface
of Mars because of one unit conversion error. I wanted
to ask about a really old conversion error, which pleasingly
rhymes with NASA. So it was Vasa Vassa is this ship?
(09:57):
What's the story with there? This was a ship in
Sweden that was launched in the sixteen hundreds, in the
year sixteen twenty eight, and it was a magnificent, massive ship.
They put a lot of cannons on the top of it,
which might have been part of the problem because almost
immediately in its maiden voyage it toppled over. At the
(10:18):
time they're like, it was top heavy. We put too
many cans on the top. The ship was too tall,
and that caused it almost as soon as it left
the harbor, just just fall over on its side and sink.
And it wasn't actually found until the nineteen fifties. And
in nineteen sixty one they dredged it up and they
put it in a museum, which if you're ever in Stockholm,
I highly recommend you good at the Vassa Museum. The
(10:39):
ship was incredibly well preserved, so well preserved that some
people have a good look at it and thought that
looks a little asymmetric, Like the hole is not as
symmetric as you would hope a hole would be on
a ship. I mean that is a property I tend
to associate with ships exactly. Everyone likes a good symmetric
(10:59):
ships as a rule of thumb. So people looked at
it and went, dan, it's not as symmetric as it
should be, as other theory now is. When it was built,
it was built lightly asymmetrically because people were using different units. Specifically,
people were mixing up Swedish feet with the Amsterdam feet.
And we know this because we've found in all the
(11:22):
other bits of paraphernalia that came with the ship rulers
that we assume we're used when building the ship, and
they found both Swedish feet rulers and Amsterdam feet rulers,
which are different lengths, so a foot in Amsterdam is
different to a foot in Sweden. They've even got different
numbers of inches. A Swedish foot is divided up into
(11:44):
twelve inches and an Amsterdam foot divided up into eleven inches,
and of course the inches are then different. So the
theory now is when their ship was built in the
sixteen hundreds and people are like, oh, make it to
this many inches, this many feet. People are using different
rulers that are different lengths divided into different numbers of subdivisions,
and they've got some bits off, and so the ship
ended up a little bit wonky, sadly for them, and
(12:07):
great for us because it preserved this incredible warship. It
toppled over almost as soon as it sets sail. So
let's get back to Air Canada Flight one four three.
I flipped over the page in your book, and almost
the first thing that happens is it lands in Ottawa.
For some reason, they did this before they embarked on
the real journey, which is two thousand miles, and so
(12:29):
I thought, oh, it's a fake ount. Matt has faked
me out. They landed Ottawa, they checked the fuel, they
figure out there's been a near miss, nearly fatal error,
and they top it up and it's all fine. Not
quite so. There are layers and layers of mistakes that
were occurring, and it was a series of very unfortunate
mistakes which caused the plane to take off with the
(12:50):
wrong amount of fuel. But then a stroke of good luck,
they had to land early because they were changing passages
in Ottawa, and whenever you land, you have to redo
the fuel calculations. But as people may have realized based
on the percentage through this podcast, we are at the moment,
that's not the end of the story. They redid the
calculations and made exactly the same unit conversion error. They
(13:15):
once again did the calculations based on pounds instead of
doing it based on kilograms, and they're like, yep, that
checks out. That's the exact amount of fuel we need.
We will carry on with no additional fuel. Well done.
Whoever fueled this plane in the first place. So there
we are. Air Canada Flight one four three has taken
off not once but twice with the wrong amount of fuel,
(13:39):
with the calculations all messed up, and facing imminently the
fate of running out of fuel over the middle of Canada.
And after these messages that Parker and I will explain
what happened next. So we've been following Air Canada flight
(14:11):
on four three. It's taken off from Montreal. It has
pounds of fuel instead of kilograms of fuel. That is
not remotely enough fuel. It then has a second chance
to fix this because it lands after a short hop
land in Ottawa. They do the same calculation, They make
the same mistake. They say, Yep, there's plenty of fuel
in there. Because they're confusing pounds and kilograms. There is
(14:32):
not plenty of fuel in there. And the plane takes
off again, and now it's really in trouble because now
it is going to fly two thousand miles. People listening
to this will be screaming, why didn't they check the
fuel gauge? Does a plane not have a fuel gauge?
My car has a fuel gage, surely a plane has
a fuel gage. So what's going on with the fuel gage?
I mean a plane does have a fuel gage. In fact,
it's kind of got a double fuel gauge. Because redundancy
(14:53):
is the motto of aviation, because you know something goes wrong,
it goes very wrong. And so they had a gauge
that shows the fuel and they've got like a unit
that then does the calculations to work out how much fuel,
and they've got sensors in the fuel tanks that are
measuring how much fuel, and they're all joined together to
give you extra redundancy. There's more than one sensor in
(15:14):
the tank, there's more than one link between the sensors
and the unit. There's the calculation, and then you've got
the display on the gauge. And one flight prior to
this flight. So when the plane was actually in Edmonton
ready to come over to Montreal to start this fateful flight,
they realized there was an issue with the senses because
the gauge had stopped working. And a technician realized, if
(15:35):
you unplug just one of the connections, if you remove
that layer of redundancy, there starts working again. And they're like, oh,
that's interesting, and in theory that should be fine because
they just label their right, I've removed this because it
wasn't working. You now have to do a manual check
as your layer of redundancy. Because we've removed it from
the sensors, You've now got to do it manually. But
(15:56):
this is where the chain of mistakes, the layers of
this onion really kick off, because there was just one
thing after another that went wrong, so that technician poorly
labeled what they had done. They just wrote faulty or
something to that effect. They then didn't write it very
clearly in the log book. They then didn't explain it
very well to the pilot. The pilot understood it as
(16:16):
being an ongoing problem, and it was always the case
that you had to do the manual fuel check, which
is like literally putting a stick in the tank to
see how much fuel there is when they finished the
next flight. The pilot then badly communicated this to the
next pilot, and the technician handover was equally bad. Like
at any point someone could have realized what was going on,
but the communication didn't work, and so the new pilot
(16:39):
was told, don't panic. As long as you do the
manual check, it's fine. Separately, a different technician's popped in,
realized it's unconnected, connected it back in again, rediscovered the
same issue the previous technician had left it plugged in,
went off to order the new part. The new pilot
sees the old label, which is now irrelevant, saying faulty,
(16:59):
but it's plugged back in again, which means none of
the gauges are working. All of this just comes together
as the pilot is sitting there looking at this label,
looking at the blank game age, and everything they've been
told just happens to line up, and they think, oh,
it's fine, as long as we do the manual check,
we can still fly even though the gauge is completely dead,
(17:20):
without realizing it is very much not what they should
be doing. So I did once run out of fuel,
and I fortunately I was on the ground in a car,
but I ran out of fuel because there'd been a
problem with the pump. The pump kept clicking out as
I was refueling in a way that indicated that the
tank was full. Yeah, but the fuel gage was showing
(17:42):
that the tank was nearly empty, and I just assumed
that the pump was correct and the fuel gage was wrong.
So I thought, huh, I got a broken fuel gage,
and off I drove, and I was not full. But yeah,
as I say, fortunately I was on the ground. You're
on the ground, but imagine all that happens, and you're like, huh,
you know what, I'll just get someone at the fuel
(18:03):
station to double check for me, and they put a
stick in your fuel tank. They do the calculation they're like,
oh no, no no, no, no, You've got loads of fuel,
but they've made a unit conversion error, and that parallel
mistake has reinforced your series of mistakes and misunderstandings, and
then you drive off without enough fuel. And there's actually
a theory in accident well, I guess mistake mitigation called
(18:25):
the Swiss cheese principle of avoiding disasters. Will you imagine
each check, each bit of redundancy, each failsafe as being
like a barrier to stop mistakes from getting through. But
no barrier is perfect. Some of them are operated by
humans and we can make mistakes. Some of them are
run by code on machines and they make mistakes. And
(18:46):
so each barrier has a few holes in it, like
a slice of Swiss cheese. But you just hope that
if you've got enough slices of cheese, one of them
will stop the mistake from getting through. But every now
and then your cheese holes just line up, and a
mistake will make it through every single layer, every single barrier,
every single failsafe, and will make it out the fast
side and become a disaster. And that's what happened with
(19:08):
Flight one for three. Just slice of cheese after slice
of cheese had a hole in the wrong spot and
the mistake made it through undetected, and so the plane
runs out of fuel somewhere over Winnipeg. It can't have
been a happy moment for the pilots. It was a
startling moment. I mean, the first indication they had that
something was up was a aero noise in the cockpit
(19:31):
that no one had heard before. They had to look
it up in the manual to see what was going on,
like this came out of nowhere, as only they realize
they're out of fuel. And this plane was one of
the first aircraft that Air Canada had brought on which
used avionics, and so there's a lot more electronics than
normal and suddenly all of it goes dead. The engines
are out, and that they're coasting. They're coasting a Boeing
(19:52):
seven to six seven. There were still some very basic,
rudimentary controls for the aircraft, so they were able to
glide it to some extent. And the reason why this
isn't a tale of absolute disaster, the reason why there
is a sufficiently happy ending is the pilot, before they
became like an airliner pilot for Air Canada. In their
previous career, they were a glider pilot, so the pilot
(20:15):
had sufficient gliding experience and they were able to glide
this bowing seven to six seven to a disused military
runway in a very small town called Gimli, and they
were able to glide this aircraft just over forty miles
and safely. Safely. It was abrupt. It's not actually a glider,
(20:36):
is it. It's not built to do this. No, No,
it's still going to land hard. And they couldn't bring
up like the landing gear and all this. Like they
had so few controls. They basically went straight into the
tarmac and they just like the nose went into it
and they just slid along. I guess, sparks going everywhere,
but there was just enough friction to bring the aircraft
to a halt before the fire end of the runway,
(20:58):
much to the relief of the sixty one passengers and
eight crew members on board, and not to the surprise
of the people currently using the airfield, and much the
big surprise to the people who were camping at the
other end of the runway. So there were people there.
They were on a go karting weekend and I guess
they booked the runway to drive go carts around. And
(21:19):
the crazy thing about a Boeing seven to six seven,
which the engines are turned off. It's pretty quiet, and
so they had no idea what was happening until they
hear this almighty wham and they all look around. There's
a jumbo yet sliding up this they were told disused
runway towards them, stopping just before it got to the
go cuts. So I mean, oh my goodness, once again,
(21:42):
things could have gone very wrong. But the last second,
thank goodness, everyone was okay. No one there. There was
no loss of life in the entire situation. It was
just amazing. I imagine a few people lost, a few hairs,
things were lost. Yeah, there's a note in your book
that they recreated this scenario in a simulator for other
pilots and it did not always go well. No, so
(22:03):
they obviously there's a big investigation afterwards to work out
what went wrong and how and why. And when I
was writing A Humble Pie, a lot of my time
was spent reading through these old investigations because if they
make it public to an extent, and so in there
they talked about the fact that they got other pilots
and put them in flight simulators in the same situation
(22:25):
to see what would happen, and every time they crashed,
no other pilot was in a stimulator was able to
glide a powerless seven six seven that distance and land
it safely. So they were very lucky that they had
the pilot they did, with the experience the pilot had
and was able to land this plane safely. It was
I mean, it very easily could have gone a different way. Yeah.
(22:46):
One of the other unit conversion eras in your book
is celsius fahrenheit thing on a BBC news story and
they were trying to figure out what some scientists or
somebody had basically said that there might be the following
temperature change because a climate change, and here it is
in celsius or centigrade, here it is in fahrenheit. And
(23:07):
the BBC just kept jumping backwards in four with really
very radical different answers to this question of how to
convert between celsius and fahrenheit. They kept changing their mind.
People just couldn't settle on the right answer. Yeah. Thankfully
people log changes to news sites so we can watch
as it went backwards and forwards, and then you're right,
there must have been a shouting match. There must have
(23:28):
been team three point six degrees and team thirty six degrees,
because those were the two Fahrenheits that the news story
kept flipping between two degrees celsius is thirty six degrees
fahrenheit and two degrees celsius is three point six degrees fahrenheit,
depending on if that's an absolute temperature or a change
(23:50):
in temperature. And it's easy to make this mistake because
things like kilograms and pounds they both start at zero.
You've got zero mass and then you have some mass,
and meters and feet both start at zero. Doesn't make
a difference if you're talking about the difference in two
people's height or anything. It changes versus absolute, same deal.
Celsius and Fahrenheits start at different points. They're zeros, are
(24:12):
at different places, and their increments are different. Like if
you're outside and it's two degrees celsius actual temperature and
you look at a thermometer, it would say two degrees
celsius thirty six degrees fahrenheit absolute temperature. But if it
then went up another two degrees, the temperature wouldn't go
(24:34):
up another thirty six degrees fahrenheit, it would go up
another three point six degrees fahrenheit, because that's the relative
ratio between the increments. So you've got a factor in
where they start how much they change. And because those
numbers look very similar, I can imagine why someone like
looked at the news story and went, oh, they've put
(24:55):
they put three point six. It should be thirty six.
They put the decimal point in the wrong place. Or
I'm guessing if you type this into Google or a
similar website and ask for the conversion, you know, what
is two degrees centigrade in fahrenheit. I mean, the answer
to that question is ambiguous, but Google is probably going
to return thirty six fahrenheit because that is the most
(25:16):
common sort of instance people thinking about the weather. Yeah,
the vast mirror of people are looking for the absolute temperature.
That's what Google is going to give you back. But
this was a percentage change in global warming should have
been three point six. Eventually, their solution was just not
to give it in fahrenheit, which is a solution I
wholeheartedly agree with just avoiding the problem, but just give
(25:38):
it in celsius and move on. As a journalist, it
is surprising how often you can solve a problem by
just deleting the sentence you're struggling with, ideally before you
hit publish. But you know it doesn't always work out
like that. So the story, as we've mentioned, comes from
your book Humble Pie, and it's one of dozens and
dozens of stories. A Humble Pie is not your first
book about fun maths. Why did you turn to the
(26:00):
topic of mistakes. I mean, because I've previously written about
kind of enjoying mass doing it, having some fun with it.
I thought, you know what, maths, it's wonderful, it's lovely,
we play with it. I think it's great, but we
do use it in a lot of critical situations, and
we use it like it's behind the scenes in our
modern society and we never really notice it. And so
I thought, you know what, if I write a book
about maths mistakes, I can tick two boxes simultaneously. Partly,
(26:25):
it means people want to read it. I mean, people
love things going wrong, as this podcast is a testament
too right, and we can learn learn from these terrible situations.
And so I was like, Okay, there'll be a good
hook to get people reading a book about mathematics, and
because I'm telling stories of mass going wrong, it's an
excellent excuse to first of all, have to set up
what the maths is and why we're using it. So
(26:47):
it justifies me writing about all these fantastic situations where
maths makes our modern society possible, which I found deeply pleasing.
One more thought, Matt Air, Canada have made this mistake twice.
NASA have made this mistake. Sixteenth century Swedish shipwrights have
made this mistake. The BBC have made this mistake. I mean,
(27:10):
this sort of problem seems to be absolutely all around us,
and it's the kind of thing that does bring planes
out of the sky and causes bridges to collapse? Does it?
Does it make you nervous knowing that we're trusting all
of these people all around us to get these things
right and they sometimes don't. It doesn't. It doesn't. So
then the underlying issue is as humans, we're not naturally
(27:32):
good at mathematics. And that's kind of reassuring because everyone
has ever struggled with maths or found it difficult. We
all do. Everyone finds maths difficult. The human brain doesn't
do maths like natively, it's going to learn it. But
thankfully that's not reassuring at all. I'm not reassured by
the thought that the people be fueling planes can't doing maths.
(27:52):
That's a valid point, allow me to continue. But what
I do find, what I do like is, and I'll
try and land this with a nice happy conclusion that
because we have maths, we can do so much more
than our brains can do. Intuitively, we don't have to
design like we have to make a building by eyeballing
it and like super over engineering it. We can actually
(28:15):
do the mathmakes and work out exactly what we need
and how it's going to work, and using maths we
can do far more than the human brain was ever
designed to do. The cost, however, is that we are
beyond our intuition and we have to do the maths
and do it very carefully and double check everything. And
so I like the fact we can achieve so much
more because we can use maths. I accept that this
(28:36):
is the cost it comes with, and I'm also reassured
all the stories I found, Obviously they're very spectacular, they're
very interesting, there's a lot to learn. I love the
fact now students at school are told pay attention to
units otherwise these things can happen. They are the exception.
The vast majority of the time, we've got all these
redundancies and checks in place, and they work. And so
(28:57):
these stories are interesting because they are such freak occurrence
as they managed to slip through, and thankfully, with a
very statistic minded head, I can still happily lie knowing
that the vast majority of the time it works. Fine, Matt,
What else are you working on at the moment, and
where else can people find your stuff? Oh? My gods. Well,
(29:19):
I'm still writing away on a new book which will
be out at some point in the distant future, you
know what. I don't think it's been announced, but it'll
be a book about trigonometry. So that's a Cautionary Tales
exclusive trigonometry book coming up at some point when I
finished writing it. If you'd like to know when you
(29:40):
sound a lot like my editor around that, I'm still
doing a lot of work obviously on YouTube and live
works picking up again. I just actually I just filmed
the stand up special version of Humble Pie. So I
was on tour with the show that goes with the book.
In twenty nineteen into twenty twenty. We obviously had to
(30:01):
delay and cancel a lot of those shows, and we
only just filmed the stand Up Special a month or
two ago, and that will be out at some point
around September. So if people want to see the live
stage version of all of these, if you've heard of
at a stand Up Mass dot com, that's my website
where everything happens. And if you're going to YouTube dot
com slash stand Up Mass, you'll see all of my
(30:22):
videos as and when they come out. Matt Parker, thank
you very much for joining us on Cautionary Tales. Tim
has been my absolute pleasure. Cautionary Tales is written by
me Tim Harford with Andrew Wright. It's produced by Ryan
Dilley with support from Courtney Guarino and Emily Vaughan. The
(30:44):
sound design and original music is the work of Pascal Wise.
It features the voice talents of Ben Crow, Melanie Gutridge,
Stella Harford, and Rufus Wright. The show also wouldn't have
been possible without the work of Mia LaBelle, Jacob Weisberg,
Heather Fane, John Schnas, Julia Barton, Kylie mcgliori, Eric Sandler,
(31:05):
Royston Berserv, Maggie Taylor, Nicole Murano, Danielle kan and Maya Caning.
Cautionary Tales is a production of Pushkin Industries. If you
like the show, please remember to share, rate and review,
Tell a friend, Tell two friends, and if you want
to hear the show, adds free and listen to four
exclusive Cautionary Tales shorts. Then sign up for Pushkin Plus
(31:28):
on the show page in Apple Podcasts or at pushkin
dot fm, slash plus
Host
Tim Harford
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