# Cautionary Conversation: Flying on Empty

An episode of [Cautionary Tales with Tim Harford](https://invisiblenetwork.ai/podcast/1484511465), 9 Sep 2022, 32 min.

Audio: https://podtrac.com/pts/redirect.mp3/pdrl.fm/18db03/tracking.swap.fm/track/SxlTEPDY7xDg35RXkASs/traffic.omny.fm/d/clips/e73c998e-6e60-432f-8610-ae210140c5b1/c0ae8c6e-22f0-4e9b-ac1c-ae390037ac53/2668598e-06ac-416f-9d90-af09013cc1ee/audio.mp3?utm_source=Podcast&in_playlist=7f5a4714-6b10-4ccf-a424-ae390037ac70

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.

## Transcript

[0:15] Speaker 1: Pushkin. On the twentieth of July nineteen eighty three, Air
[0:25] Speaker 1: Canada Flight one four three was being prepared for its
[0:29] Speaker 1: two thousand mile cross country flight from Montreal to Edmonton.
[0:34] Speaker 1: The ground crew loaded her up with a necessary fuel
[0:37] Speaker 1: twenty two thousand, six hundred kilograms according to their calculations.
[0:42] Speaker 1: Those calculations were correct up to a point, but unfortunately
[0:47] Speaker 1: they're mixed up kilograms and pounds, and not in a
[0:51] Speaker 1: good way. Nobody had any idea of this, but the
[0:55] Speaker 1: plane took off for a four hour flight with only
[0:59] Speaker 1: half the fuel it needed to get to Edmonton. The
[1:02] Speaker 1: plane was now on course to run out of fuel
[1:06] Speaker 1: somewhere over Winnipeg. I'm Tim Harford and you're listening to
[1:12] Speaker 1: Cautionary Tales. This is a new experiment for us. Here
[1:37] Speaker 1: at Cautionary Tales. As usual, you'll hear a story of disaster,
[1:41] Speaker 1: but I'll be joined by an expert to help tell
[1:43] Speaker 1: the story and reflect on the lessons. I hope you
[1:46] Speaker 1: like it, and I'm confident you will, because my guest
[1:49] Speaker 1: today is Matt Parker. Matt Parker is a phenomenon, a
[1:53] Speaker 1: stand up comedian, mathematician, YouTuber, podcaster, an author of the
[1:57] Speaker 1: number one bestseller Humble Pie and Humble Pie is a funny,
[2:02] Speaker 1: nerdy book about the real life consequences of mathematical mistakes,
[2:06] Speaker 1: and it's where I first heard the story of air
[2:09] Speaker 1: flight one four three. Matt Parker, Welcome to Cautionary Sales.
[2:13] Speaker 1: Thank you, Tim. It's an absolute honor to be your
[2:16] Speaker 1: zeroth guest on the show zero both guests. Matt counts
[2:20] Speaker 1: in strange wayst this story is a bit like an onion.
[2:24] Speaker 1: It's got layers. Yeah, on the most superficial level, the
[2:27] Speaker 1: sort of papery outer layer of the story. If you like,
[2:30] Speaker 1: why did this plane have too little fuel? The very
[2:32] Speaker 1: simple reading is they had a unit conversion error. So
[2:37] Speaker 1: the people who are meant to be fueling the aircraft
[2:40] Speaker 1: saw a number, they assumed it was pounds of fuel,
[2:43] Speaker 1: when in fact it was kilograms of fuel. And the
[2:46] Speaker 1: reason they're even doing this in mass because if you
[2:48] Speaker 1: fill up a car, you don't put the fuel in
[2:51] Speaker 1: by mass, you do it by volume. Volume changes based
[2:56] Speaker 1: on the ambient temperature. As things warm up, they tend
[2:59] Speaker 1: to expand, if they cool down, they tend to shrink.
[3:01] Speaker 1: And if you're flying an aircraft, it's important you have
[3:05] Speaker 1: the amount of fuel you're supposed to have, and so
[3:08] Speaker 1: they may insure instead of using the straightforward volume, they
[3:12] Speaker 1: were going to use mass instead. And sadly it was
[3:16] Speaker 1: that attempt for extra precision that opened up the door
[3:20] Speaker 1: for this unit conversion error. Yes, you would think they
[3:22] Speaker 1: might just stick in a little bit extra just to
[3:25] Speaker 1: be sure, but there's limits to the amount of extra
[3:27] Speaker 1: fuel you want on a plane because yeah, it's heavy. Yeah,
[3:30] Speaker 1: And so they even allowed enough extra so that twenty
[3:33] Speaker 1: two six hundred kilograms you mentioned, that's twenty two thousand,
[3:37] Speaker 1: three hundred kilograms for the flying bit, and then they
[3:40] Speaker 1: put on the extra three hundred kilograms for like taxiing
[3:44] Speaker 1: and like all the bits that maybe they hadn't factored
[3:47] Speaker 1: into the flight. So they were trying to be careful,
[3:49] Speaker 1: they were being thorough, they just got the units wrong.
[3:53] Speaker 1: What it was it about Canada at this particular time
[3:55] Speaker 1: that made it particularly vulnerable to a unit conversion error.
[3:59] Speaker 1: In Canada, they had just switched so previously they were
[4:04] Speaker 1: using imperial units or like the old school, like English
[4:07] Speaker 1: style units, and they just swopped over to real units
[4:11] Speaker 1: or metric as the rest of US. I was about
[4:15] Speaker 1: to say that as in Australian you're neutral in this fight,
[4:18] Speaker 1: but you're clearly not neutral. Okay, no, no, not since
[4:21] Speaker 1: the nineteen sixties. I love the quirkiness of the imperial system.
[4:26] Speaker 1: That metric is nice and straightforward. Yeah, but if there's
[4:29] Speaker 1: one thing that's worse than using imperiod units, it's using
[4:32] Speaker 1: imperiod units when you think you're using metric units or
[4:35] Speaker 1: vice versa exactly. And it was even obscured by one
[4:39] Speaker 1: layer because when they were doing the calculations, they weren't
[4:42] Speaker 1: actually doing it in terms of the direct mass. They
[4:46] Speaker 1: were using something called the specific gravity, which is like
[4:48] Speaker 1: a measure the density of the fuel, and so they
[4:51] Speaker 1: used that to get back to the volume that they
[4:53] Speaker 1: then had to put into the plane. And because there
[4:56] Speaker 1: was this extra one layer of opaque bit of putting
[4:59] Speaker 1: it into a slightly different way of looking at it,
[5:01] Speaker 1: they didn't realize that the units behind the specific gravity
[5:04] Speaker 1: were based on kilograms and they assume that they were
[5:07] Speaker 1: based the old way on pounds. There's more maths than
[5:10] Speaker 1: I had anticipated in filling up a plane. Yeah, okay,
[5:13] Speaker 1: this is slightly unnerving, but I mean it's not just
[5:16] Speaker 1: planes that suffer from unit conversion. Eras your book Humble
[5:19] Speaker 1: Pie has a whole chapter full of them. I mean,
[5:22] Speaker 1: do you have any favorites with This? Plane is now
[5:24] Speaker 1: my favorite? You said you only came across it because
[5:27] Speaker 1: you were reading the book. I only came across a
[5:29] Speaker 1: researching the book. Prior to that. It was the Mars
[5:33] Speaker 1: Climate Orbiter spacecraft that NASA launched in nineteen ninety eight.
[5:37] Speaker 1: That was my favorite unit conversion era. And that's partly
[5:41] Speaker 1: because a lot of people know about it. There's this
[5:43] Speaker 1: urban legend of when NASA got the maths wrong, and
[5:47] Speaker 1: partly this is something very delightful about NASA, like the
[5:51] Speaker 1: mascot of science and precision and achievement coming undone because
[5:55] Speaker 1: of a unit conversion era. It was actually a bit
[5:58] Speaker 1: more subtle than that, wasn't it. I think NASA we're
[6:00] Speaker 1: using metric, but the sply was using imperial or old
[6:03] Speaker 1: school pounds. Yeah, it was Lockeed Martin was the contractor.
[6:07] Speaker 1: And like you said, NASA use metric. They're scientists, they're engineers.
[6:10] Speaker 1: They're going to use the most efficient, most optimal units,
[6:13] Speaker 1: and so everything they were doing was in metric and
[6:16] Speaker 1: in their documentation that they gave to their contractors, it's
[6:19] Speaker 1: stipulated you're going to do this in metric. Now, the
[6:23] Speaker 1: kind of common understanding of this is when the Mars
[6:26] Speaker 1: Climate orbiter got to Mars, they had to calculate how
[6:30] Speaker 1: far above the surface it was so they could put
[6:32] Speaker 1: it into a nice, neat stable orbit and people go, oh,
[6:36] Speaker 1: isn't that the one where NASA thought it was in
[6:40] Speaker 1: feet but it was actually a meters or vice versa,
[6:42] Speaker 1: And then they got the altitude wrong because they were
[6:44] Speaker 1: measuring the distance incorrectly. And to be fair to this day,
[6:49] Speaker 1: if you look at altitude of things like aircraft, it's
[6:51] Speaker 1: given in feet, which in one sense is a nice
[6:54] Speaker 1: bit of error correction, because if you hear a number
[6:59] Speaker 1: in aviation and its feet, you know it's in the
[7:02] Speaker 1: vertical direction, and if you hear a number and it's
[7:05] Speaker 1: kilometers or meters, you know it's in the horizontal direction.
[7:09] Speaker 1: And so it's a bit of redundancy in terms of
[7:12] Speaker 1: the directions encoded in the units that are used. Which
[7:16] Speaker 1: is maybe the one time I will concede that's an
[7:18] Speaker 1: interesting use for imperial units, but that's not the case. Here.
[7:22] Speaker 1: First time I've ever heard you defend values, I know
[7:24] Speaker 1: I know where defend is a strong word tim but
[7:27] Speaker 1: actually that's not what NASA did. They didn't confuse feet
[7:30] Speaker 1: and meters and kind of just smash this thing into
[7:32] Speaker 1: the surface of mask because they didn't know how high
[7:33] Speaker 1: it was. It is a much more soft lever. It's
[7:35] Speaker 1: always more complicated than that. In this case, as they're
[7:38] Speaker 1: flying the spacecraft from the Earth to Mars, there's a
[7:40] Speaker 1: big flywheel on board, because in space, there's nothing to
[7:43] Speaker 1: push against if you want to change your direction. But
[7:46] Speaker 1: if you have a spinning mass, you get the gyroscopic
[7:49] Speaker 1: effect and you can push against something spinning to reorientate
[7:52] Speaker 1: your spacecraft. The issue with that is sometimes your flywheel
[7:56] Speaker 1: is going incredibly fast and you have to have what
[8:00] Speaker 1: the NASA scientists have deemed a angular momentum desaturation event,
[8:05] Speaker 1: which is just slowing down the flywheel. But to do that,
[8:09] Speaker 1: you've got to fire the thrusters, like the little steering
[8:12] Speaker 1: rockets on the spacecraft to keep it pointing in roughly
[8:15] Speaker 1: the same direction as you're slowing down your gyroscope, and
[8:18] Speaker 1: those little thruster firings slightly change the trajectory of the
[8:24] Speaker 1: spacecraft on its way to Mars. So you want to
[8:26] Speaker 1: keep track of those. This was an external system done
[8:29] Speaker 1: by lockeed Mutton, and they've got a little program that
[8:32] Speaker 1: just logged every single time the thrusters fired how much
[8:35] Speaker 1: force they were firing, and therefore, later on NASA could
[8:39] Speaker 1: calculate the actual trajectory when it gets to Mars by
[8:43] Speaker 1: factoring in all these little thruster firings. And NASA said,
[8:47] Speaker 1: very very clearly, please write these down using mutants the
[8:52] Speaker 1: proper metric unit for force, and lockeed Martin wrote them
[8:56] Speaker 1: down as pounds force, pounds force. It's a ratio of
[9:01] Speaker 1: four point four five ish, very similar. It's pounds pounds
[9:05] Speaker 1: are killers all over again. Really, and this is the
[9:08] Speaker 1: kind of thing little smash your spacecraft straight into Mars.
[9:11] Speaker 1: Oh yeah. Because they assumed that the firings were in
[9:15] Speaker 1: Newton's when they've been written down in pounds fource, they
[9:17] Speaker 1: figured they were going to come in at an altitude
[9:19] Speaker 1: of between one hundred and fifty and one hundred and
[9:21] Speaker 1: seventy kilometers above the surface of Mars. They actually came
[9:24] Speaker 1: in at fifty seven kilometers above the surface of Mars,
[9:28] Speaker 1: much much closer, which means even though there's not a
[9:30] Speaker 1: lot of atmosphere on Mars, there is some The extra
[9:33] Speaker 1: drag of being that much lower slowed the spacecraft down
[9:36] Speaker 1: a lot more than they expected, which meant that it
[9:39] Speaker 1: fell out of the sky. It deorbited very ungracefully, and
[9:44] Speaker 1: billions of US dollars a spacecraft slammed into the surface
[9:47] Speaker 1: of Mars because of one unit conversion error. I wanted
[9:51] Speaker 1: to ask about a really old conversion error, which pleasingly
[9:54] Speaker 1: rhymes with NASA. So it was Vasa Vassa is this ship?
[9:57] Speaker 1: What's the story with there? This was a ship in
[10:01] Speaker 1: Sweden that was launched in the sixteen hundreds, in the
[10:05] Speaker 1: year sixteen twenty eight, and it was a magnificent, massive ship.
[10:09] Speaker 1: They put a lot of cannons on the top of it,
[10:11] Speaker 1: which might have been part of the problem because almost
[10:13] Speaker 1: immediately in its maiden voyage it toppled over. At the
[10:18] Speaker 1: time they're like, it was top heavy. We put too
[10:20] Speaker 1: many cans on the top. The ship was too tall,
[10:22] Speaker 1: and that caused it almost as soon as it left
[10:25] Speaker 1: the harbor, just just fall over on its side and sink.
[10:28] Speaker 1: And it wasn't actually found until the nineteen fifties. And
[10:31] Speaker 1: in nineteen sixty one they dredged it up and they
[10:34] Speaker 1: put it in a museum, which if you're ever in Stockholm,
[10:37] Speaker 1: I highly recommend you good at the Vassa Museum. The
[10:39] Speaker 1: ship was incredibly well preserved, so well preserved that some
[10:43] Speaker 1: people have a good look at it and thought that
[10:46] Speaker 1: looks a little asymmetric, Like the hole is not as
[10:50] Speaker 1: symmetric as you would hope a hole would be on
[10:53] Speaker 1: a ship. I mean that is a property I tend
[10:56] Speaker 1: to associate with ships exactly. Everyone likes a good symmetric
[10:59] Speaker 1: ships as a rule of thumb. So people looked at
[11:03] Speaker 1: it and went, dan, it's not as symmetric as it
[11:05] Speaker 1: should be, as other theory now is. When it was built,
[11:08] Speaker 1: it was built lightly asymmetrically because people were using different units. Specifically,
[11:13] Speaker 1: people were mixing up Swedish feet with the Amsterdam feet.
[11:19] Speaker 1: And we know this because we've found in all the
[11:22] Speaker 1: other bits of paraphernalia that came with the ship rulers
[11:26] Speaker 1: that we assume we're used when building the ship, and
[11:29] Speaker 1: they found both Swedish feet rulers and Amsterdam feet rulers,
[11:34] Speaker 1: which are different lengths, so a foot in Amsterdam is
[11:37] Speaker 1: different to a foot in Sweden. They've even got different
[11:41] Speaker 1: numbers of inches. A Swedish foot is divided up into
[11:44] Speaker 1: twelve inches and an Amsterdam foot divided up into eleven inches,
[11:48] Speaker 1: and of course the inches are then different. So the
[11:49] Speaker 1: theory now is when their ship was built in the
[11:52] Speaker 1: sixteen hundreds and people are like, oh, make it to
[11:54] Speaker 1: this many inches, this many feet. People are using different
[11:57] Speaker 1: rulers that are different lengths divided into different numbers of subdivisions,
[12:01] Speaker 1: and they've got some bits off, and so the ship
[12:04] Speaker 1: ended up a little bit wonky, sadly for them, and
[12:07] Speaker 1: great for us because it preserved this incredible warship. It
[12:11] Speaker 1: toppled over almost as soon as it sets sail. So
[12:14] Speaker 1: let's get back to Air Canada Flight one four three.
[12:17] Speaker 1: I flipped over the page in your book, and almost
[12:20] Speaker 1: the first thing that happens is it lands in Ottawa.
[12:23] Speaker 1: For some reason, they did this before they embarked on
[12:26] Speaker 1: the real journey, which is two thousand miles, and so
[12:29] Speaker 1: I thought, oh, it's a fake ount. Matt has faked
[12:31] Speaker 1: me out. They landed Ottawa, they checked the fuel, they
[12:34] Speaker 1: figure out there's been a near miss, nearly fatal error,
[12:37] Speaker 1: and they top it up and it's all fine. Not
[12:40] Speaker 1: quite so. There are layers and layers of mistakes that
[12:44] Speaker 1: were occurring, and it was a series of very unfortunate
[12:48] Speaker 1: mistakes which caused the plane to take off with the
[12:50] Speaker 1: wrong amount of fuel. But then a stroke of good luck,
[12:54] Speaker 1: they had to land early because they were changing passages
[12:57] Speaker 1: in Ottawa, and whenever you land, you have to redo
[13:00] Speaker 1: the fuel calculations. But as people may have realized based
[13:05] Speaker 1: on the percentage through this podcast, we are at the moment,
[13:07] Speaker 1: that's not the end of the story. They redid the
[13:10] Speaker 1: calculations and made exactly the same unit conversion error. They
[13:15] Speaker 1: once again did the calculations based on pounds instead of
[13:19] Speaker 1: doing it based on kilograms, and they're like, yep, that
[13:22] Speaker 1: checks out. That's the exact amount of fuel we need.
[13:25] Speaker 1: We will carry on with no additional fuel. Well done.
[13:28] Speaker 1: Whoever fueled this plane in the first place. So there
[13:31] Speaker 1: we are. Air Canada Flight one four three has taken
[13:35] Speaker 1: off not once but twice with the wrong amount of fuel,
[13:39] Speaker 1: with the calculations all messed up, and facing imminently the
[13:44] Speaker 1: fate of running out of fuel over the middle of Canada.
[13:46] Speaker 1: And after these messages that Parker and I will explain
[13:50] Speaker 1: what happened next. So we've been following Air Canada flight
[14:11] Speaker 1: on four three. It's taken off from Montreal. It has
[14:15] Speaker 1: pounds of fuel instead of kilograms of fuel. That is
[14:18] Speaker 1: not remotely enough fuel. It then has a second chance
[14:22] Speaker 1: to fix this because it lands after a short hop
[14:24] Speaker 1: land in Ottawa. They do the same calculation, They make
[14:26] Speaker 1: the same mistake. They say, Yep, there's plenty of fuel
[14:29] Speaker 1: in there. Because they're confusing pounds and kilograms. There is
[14:32] Speaker 1: not plenty of fuel in there. And the plane takes
[14:34] Speaker 1: off again, and now it's really in trouble because now
[14:36] Speaker 1: it is going to fly two thousand miles. People listening
[14:38] Speaker 1: to this will be screaming, why didn't they check the
[14:41] Speaker 1: fuel gauge? Does a plane not have a fuel gauge?
[14:43] Speaker 1: My car has a fuel gage, surely a plane has
[14:45] Speaker 1: a fuel gage. So what's going on with the fuel gage?
[14:47] Speaker 1: I mean a plane does have a fuel gage. In fact,
[14:50] Speaker 1: it's kind of got a double fuel gauge. Because redundancy
[14:53] Speaker 1: is the motto of aviation, because you know something goes wrong,
[14:57] Speaker 1: it goes very wrong. And so they had a gauge
[15:01] Speaker 1: that shows the fuel and they've got like a unit
[15:03] Speaker 1: that then does the calculations to work out how much fuel,
[15:06] Speaker 1: and they've got sensors in the fuel tanks that are
[15:09] Speaker 1: measuring how much fuel, and they're all joined together to
[15:11] Speaker 1: give you extra redundancy. There's more than one sensor in
[15:14] Speaker 1: the tank, there's more than one link between the sensors
[15:16] Speaker 1: and the unit. There's the calculation, and then you've got
[15:18] Speaker 1: the display on the gauge. And one flight prior to
[15:21] Speaker 1: this flight. So when the plane was actually in Edmonton
[15:25] Speaker 1: ready to come over to Montreal to start this fateful flight,
[15:28] Speaker 1: they realized there was an issue with the senses because
[15:31] Speaker 1: the gauge had stopped working. And a technician realized, if
[15:35] Speaker 1: you unplug just one of the connections, if you remove
[15:39] Speaker 1: that layer of redundancy, there starts working again. And they're like, oh,
[15:43] Speaker 1: that's interesting, and in theory that should be fine because
[15:46] Speaker 1: they just label their right, I've removed this because it
[15:49] Speaker 1: wasn't working. You now have to do a manual check
[15:51] Speaker 1: as your layer of redundancy. Because we've removed it from
[15:54] Speaker 1: the sensors, You've now got to do it manually. But
[15:56] Speaker 1: this is where the chain of mistakes, the layers of
[15:58] Speaker 1: this onion really kick off, because there was just one
[16:02] Speaker 1: thing after another that went wrong, so that technician poorly
[16:06] Speaker 1: labeled what they had done. They just wrote faulty or
[16:09] Speaker 1: something to that effect. They then didn't write it very
[16:11] Speaker 1: clearly in the log book. They then didn't explain it
[16:14] Speaker 1: very well to the pilot. The pilot understood it as
[16:16] Speaker 1: being an ongoing problem, and it was always the case
[16:19] Speaker 1: that you had to do the manual fuel check, which
[16:21] Speaker 1: is like literally putting a stick in the tank to
[16:23] Speaker 1: see how much fuel there is when they finished the
[16:25] Speaker 1: next flight. The pilot then badly communicated this to the
[16:29] Speaker 1: next pilot, and the technician handover was equally bad. Like
[16:33] Speaker 1: at any point someone could have realized what was going on,
[16:35] Speaker 1: but the communication didn't work, and so the new pilot
[16:39] Speaker 1: was told, don't panic. As long as you do the
[16:41] Speaker 1: manual check, it's fine. Separately, a different technician's popped in,
[16:45] Speaker 1: realized it's unconnected, connected it back in again, rediscovered the
[16:49] Speaker 1: same issue the previous technician had left it plugged in,
[16:52] Speaker 1: went off to order the new part. The new pilot
[16:56] Speaker 1: sees the old label, which is now irrelevant, saying faulty,
[16:59] Speaker 1: but it's plugged back in again, which means none of
[17:01] Speaker 1: the gauges are working. All of this just comes together
[17:05] Speaker 1: as the pilot is sitting there looking at this label,
[17:08] Speaker 1: looking at the blank game age, and everything they've been
[17:10] Speaker 1: told just happens to line up, and they think, oh,
[17:14] Speaker 1: it's fine, as long as we do the manual check,
[17:16] Speaker 1: we can still fly even though the gauge is completely dead,
[17:20] Speaker 1: without realizing it is very much not what they should
[17:23] Speaker 1: be doing. So I did once run out of fuel,
[17:27] Speaker 1: and I fortunately I was on the ground in a car,
[17:29] Speaker 1: but I ran out of fuel because there'd been a
[17:32] Speaker 1: problem with the pump. The pump kept clicking out as
[17:36] Speaker 1: I was refueling in a way that indicated that the
[17:39] Speaker 1: tank was full. Yeah, but the fuel gage was showing
[17:42] Speaker 1: that the tank was nearly empty, and I just assumed
[17:45] Speaker 1: that the pump was correct and the fuel gage was wrong.
[17:48] Speaker 1: So I thought, huh, I got a broken fuel gage,
[17:50] Speaker 1: and off I drove, and I was not full. But yeah,
[17:55] Speaker 1: as I say, fortunately I was on the ground. You're
[17:57] Speaker 1: on the ground, but imagine all that happens, and you're like, huh,
[18:01] Speaker 1: you know what, I'll just get someone at the fuel
[18:03] Speaker 1: station to double check for me, and they put a
[18:04] Speaker 1: stick in your fuel tank. They do the calculation they're like,
[18:07] Speaker 1: oh no, no no, no, no, You've got loads of fuel,
[18:09] Speaker 1: but they've made a unit conversion error, and that parallel
[18:12] Speaker 1: mistake has reinforced your series of mistakes and misunderstandings, and
[18:17] Speaker 1: then you drive off without enough fuel. And there's actually
[18:19] Speaker 1: a theory in accident well, I guess mistake mitigation called
[18:25] Speaker 1: the Swiss cheese principle of avoiding disasters. Will you imagine
[18:31] Speaker 1: each check, each bit of redundancy, each failsafe as being
[18:35] Speaker 1: like a barrier to stop mistakes from getting through. But
[18:38] Speaker 1: no barrier is perfect. Some of them are operated by
[18:41] Speaker 1: humans and we can make mistakes. Some of them are
[18:44] Speaker 1: run by code on machines and they make mistakes. And
[18:46] Speaker 1: so each barrier has a few holes in it, like
[18:49] Speaker 1: a slice of Swiss cheese. But you just hope that
[18:52] Speaker 1: if you've got enough slices of cheese, one of them
[18:54] Speaker 1: will stop the mistake from getting through. But every now
[18:57] Speaker 1: and then your cheese holes just line up, and a
[18:59] Speaker 1: mistake will make it through every single layer, every single barrier,
[19:03] Speaker 1: every single failsafe, and will make it out the fast
[19:05] Speaker 1: side and become a disaster. And that's what happened with
[19:08] Speaker 1: Flight one for three. Just slice of cheese after slice
[19:12] Speaker 1: of cheese had a hole in the wrong spot and
[19:15] Speaker 1: the mistake made it through undetected, and so the plane
[19:18] Speaker 1: runs out of fuel somewhere over Winnipeg. It can't have
[19:22] Speaker 1: been a happy moment for the pilots. It was a
[19:24] Speaker 1: startling moment. I mean, the first indication they had that
[19:27] Speaker 1: something was up was a aero noise in the cockpit
[19:31] Speaker 1: that no one had heard before. They had to look
[19:32] Speaker 1: it up in the manual to see what was going on,
[19:34] Speaker 1: like this came out of nowhere, as only they realize
[19:37] Speaker 1: they're out of fuel. And this plane was one of
[19:39] Speaker 1: the first aircraft that Air Canada had brought on which
[19:43] Speaker 1: used avionics, and so there's a lot more electronics than
[19:46] Speaker 1: normal and suddenly all of it goes dead. The engines
[19:49] Speaker 1: are out, and that they're coasting. They're coasting a Boeing
[19:52] Speaker 1: seven to six seven. There were still some very basic,
[19:55] Speaker 1: rudimentary controls for the aircraft, so they were able to
[19:58] Speaker 1: glide it to some extent. And the reason why this
[20:01] Speaker 1: isn't a tale of absolute disaster, the reason why there
[20:05] Speaker 1: is a sufficiently happy ending is the pilot, before they
[20:08] Speaker 1: became like an airliner pilot for Air Canada. In their
[20:11] Speaker 1: previous career, they were a glider pilot, so the pilot
[20:15] Speaker 1: had sufficient gliding experience and they were able to glide
[20:21] Speaker 1: this bowing seven to six seven to a disused military
[20:25] Speaker 1: runway in a very small town called Gimli, and they
[20:28] Speaker 1: were able to glide this aircraft just over forty miles
[20:32] Speaker 1: and safely. Safely. It was abrupt. It's not actually a glider,
[20:36] Speaker 1: is it. It's not built to do this. No, No,
[20:39] Speaker 1: it's still going to land hard. And they couldn't bring
[20:42] Speaker 1: up like the landing gear and all this. Like they
[20:44] Speaker 1: had so few controls. They basically went straight into the
[20:46] Speaker 1: tarmac and they just like the nose went into it
[20:49] Speaker 1: and they just slid along. I guess, sparks going everywhere,
[20:52] Speaker 1: but there was just enough friction to bring the aircraft
[20:55] Speaker 1: to a halt before the fire end of the runway,
[20:58] Speaker 1: much to the relief of the sixty one passengers and
[21:01] Speaker 1: eight crew members on board, and not to the surprise
[21:04] Speaker 1: of the people currently using the airfield, and much the
[21:09] Speaker 1: big surprise to the people who were camping at the
[21:11] Speaker 1: other end of the runway. So there were people there.
[21:14] Speaker 1: They were on a go karting weekend and I guess
[21:16] Speaker 1: they booked the runway to drive go carts around. And
[21:19] Speaker 1: the crazy thing about a Boeing seven to six seven,
[21:22] Speaker 1: which the engines are turned off. It's pretty quiet, and
[21:25] Speaker 1: so they had no idea what was happening until they
[21:28] Speaker 1: hear this almighty wham and they all look around. There's
[21:31] Speaker 1: a jumbo yet sliding up this they were told disused
[21:35] Speaker 1: runway towards them, stopping just before it got to the
[21:39] Speaker 1: go cuts. So I mean, oh my goodness, once again,
[21:42] Speaker 1: things could have gone very wrong. But the last second,
[21:45] Speaker 1: thank goodness, everyone was okay. No one there. There was
[21:48] Speaker 1: no loss of life in the entire situation. It was
[21:50] Speaker 1: just amazing. I imagine a few people lost, a few hairs,
[21:53] Speaker 1: things were lost. Yeah, there's a note in your book
[21:56] Speaker 1: that they recreated this scenario in a simulator for other
[22:01] Speaker 1: pilots and it did not always go well. No, so
[22:03] Speaker 1: they obviously there's a big investigation afterwards to work out
[22:06] Speaker 1: what went wrong and how and why. And when I
[22:09] Speaker 1: was writing A Humble Pie, a lot of my time
[22:11] Speaker 1: was spent reading through these old investigations because if they
[22:15] Speaker 1: make it public to an extent, and so in there
[22:17] Speaker 1: they talked about the fact that they got other pilots
[22:20] Speaker 1: and put them in flight simulators in the same situation
[22:25] Speaker 1: to see what would happen, and every time they crashed,
[22:28] Speaker 1: no other pilot was in a stimulator was able to
[22:31] Speaker 1: glide a powerless seven six seven that distance and land
[22:35] Speaker 1: it safely. So they were very lucky that they had
[22:39] Speaker 1: the pilot they did, with the experience the pilot had
[22:41] Speaker 1: and was able to land this plane safely. It was
[22:44] Speaker 1: I mean, it very easily could have gone a different way. Yeah.
[22:46] Speaker 1: One of the other unit conversion eras in your book
[22:49] Speaker 1: is celsius fahrenheit thing on a BBC news story and
[22:54] Speaker 1: they were trying to figure out what some scientists or
[22:58] Speaker 1: somebody had basically said that there might be the following
[23:01] Speaker 1: temperature change because a climate change, and here it is
[23:03] Speaker 1: in celsius or centigrade, here it is in fahrenheit. And
[23:07] Speaker 1: the BBC just kept jumping backwards in four with really
[23:10] Speaker 1: very radical different answers to this question of how to
[23:13] Speaker 1: convert between celsius and fahrenheit. They kept changing their mind.
[23:16] Speaker 1: People just couldn't settle on the right answer. Yeah. Thankfully
[23:19] Speaker 1: people log changes to news sites so we can watch
[23:23] Speaker 1: as it went backwards and forwards, and then you're right,
[23:26] Speaker 1: there must have been a shouting match. There must have
[23:28] Speaker 1: been team three point six degrees and team thirty six degrees,
[23:33] Speaker 1: because those were the two Fahrenheits that the news story
[23:36] Speaker 1: kept flipping between two degrees celsius is thirty six degrees
[23:42] Speaker 1: fahrenheit and two degrees celsius is three point six degrees fahrenheit,
[23:47] Speaker 1: depending on if that's an absolute temperature or a change
[23:50] Speaker 1: in temperature. And it's easy to make this mistake because
[23:53] Speaker 1: things like kilograms and pounds they both start at zero.
[23:57] Speaker 1: You've got zero mass and then you have some mass,
[23:59] Speaker 1: and meters and feet both start at zero. Doesn't make
[24:02] Speaker 1: a difference if you're talking about the difference in two
[24:05] Speaker 1: people's height or anything. It changes versus absolute, same deal.
[24:09] Speaker 1: Celsius and Fahrenheits start at different points. They're zeros, are
[24:12] Speaker 1: at different places, and their increments are different. Like if
[24:16] Speaker 1: you're outside and it's two degrees celsius actual temperature and
[24:21] Speaker 1: you look at a thermometer, it would say two degrees
[24:24] Speaker 1: celsius thirty six degrees fahrenheit absolute temperature. But if it
[24:29] Speaker 1: then went up another two degrees, the temperature wouldn't go
[24:34] Speaker 1: up another thirty six degrees fahrenheit, it would go up
[24:37] Speaker 1: another three point six degrees fahrenheit, because that's the relative
[24:42] Speaker 1: ratio between the increments. So you've got a factor in
[24:44] Speaker 1: where they start how much they change. And because those
[24:47] Speaker 1: numbers look very similar, I can imagine why someone like
[24:52] Speaker 1: looked at the news story and went, oh, they've put
[24:55] Speaker 1: they put three point six. It should be thirty six.
[24:58] Speaker 1: They put the decimal point in the wrong place. Or
[25:00] Speaker 1: I'm guessing if you type this into Google or a
[25:03] Speaker 1: similar website and ask for the conversion, you know, what
[25:06] Speaker 1: is two degrees centigrade in fahrenheit. I mean, the answer
[25:10] Speaker 1: to that question is ambiguous, but Google is probably going
[25:13] Speaker 1: to return thirty six fahrenheit because that is the most
[25:16] Speaker 1: common sort of instance people thinking about the weather. Yeah,
[25:20] Speaker 1: the vast mirror of people are looking for the absolute temperature.
[25:22] Speaker 1: That's what Google is going to give you back. But
[25:24] Speaker 1: this was a percentage change in global warming should have
[25:27] Speaker 1: been three point six. Eventually, their solution was just not
[25:31] Speaker 1: to give it in fahrenheit, which is a solution I
[25:33] Speaker 1: wholeheartedly agree with just avoiding the problem, but just give
[25:38] Speaker 1: it in celsius and move on. As a journalist, it
[25:41] Speaker 1: is surprising how often you can solve a problem by
[25:44] Speaker 1: just deleting the sentence you're struggling with, ideally before you
[25:47] Speaker 1: hit publish. But you know it doesn't always work out
[25:50] Speaker 1: like that. So the story, as we've mentioned, comes from
[25:52] Speaker 1: your book Humble Pie, and it's one of dozens and
[25:55] Speaker 1: dozens of stories. A Humble Pie is not your first
[25:57] Speaker 1: book about fun maths. Why did you turn to the
[26:00] Speaker 1: topic of mistakes. I mean, because I've previously written about
[26:05] Speaker 1: kind of enjoying mass doing it, having some fun with it.
[26:07] Speaker 1: I thought, you know what, maths, it's wonderful, it's lovely,
[26:10] Speaker 1: we play with it. I think it's great, but we
[26:12] Speaker 1: do use it in a lot of critical situations, and
[26:14] Speaker 1: we use it like it's behind the scenes in our
[26:16] Speaker 1: modern society and we never really notice it. And so
[26:18] Speaker 1: I thought, you know what, if I write a book
[26:20] Speaker 1: about maths mistakes, I can tick two boxes simultaneously. Partly,
[26:25] Speaker 1: it means people want to read it. I mean, people
[26:27] Speaker 1: love things going wrong, as this podcast is a testament
[26:30] Speaker 1: too right, and we can learn learn from these terrible situations.
[26:34] Speaker 1: And so I was like, Okay, there'll be a good
[26:35] Speaker 1: hook to get people reading a book about mathematics, and
[26:39] Speaker 1: because I'm telling stories of mass going wrong, it's an
[26:42] Speaker 1: excellent excuse to first of all, have to set up
[26:45] Speaker 1: what the maths is and why we're using it. So
[26:47] Speaker 1: it justifies me writing about all these fantastic situations where
[26:51] Speaker 1: maths makes our modern society possible, which I found deeply pleasing.
[26:57] Speaker 1: One more thought, Matt Air, Canada have made this mistake twice.
[27:02] Speaker 1: NASA have made this mistake. Sixteenth century Swedish shipwrights have
[27:07] Speaker 1: made this mistake. The BBC have made this mistake. I mean,
[27:10] Speaker 1: this sort of problem seems to be absolutely all around us,
[27:13] Speaker 1: and it's the kind of thing that does bring planes
[27:16] Speaker 1: out of the sky and causes bridges to collapse? Does it?
[27:19] Speaker 1: Does it make you nervous knowing that we're trusting all
[27:22] Speaker 1: of these people all around us to get these things
[27:24] Speaker 1: right and they sometimes don't. It doesn't. It doesn't. So
[27:29] Speaker 1: then the underlying issue is as humans, we're not naturally
[27:32] Speaker 1: good at mathematics. And that's kind of reassuring because everyone
[27:35] Speaker 1: has ever struggled with maths or found it difficult. We
[27:37] Speaker 1: all do. Everyone finds maths difficult. The human brain doesn't
[27:40] Speaker 1: do maths like natively, it's going to learn it. But
[27:45] Speaker 1: thankfully that's not reassuring at all. I'm not reassured by
[27:49] Speaker 1: the thought that the people be fueling planes can't doing maths.
[27:52] Speaker 1: That's a valid point, allow me to continue. But what
[27:56] Speaker 1: I do find, what I do like is, and I'll
[27:59] Speaker 1: try and land this with a nice happy conclusion that
[28:04] Speaker 1: because we have maths, we can do so much more
[28:06] Speaker 1: than our brains can do. Intuitively, we don't have to
[28:09] Speaker 1: design like we have to make a building by eyeballing
[28:12] Speaker 1: it and like super over engineering it. We can actually
[28:15] Speaker 1: do the mathmakes and work out exactly what we need
[28:17] Speaker 1: and how it's going to work, and using maths we
[28:20] Speaker 1: can do far more than the human brain was ever
[28:23] Speaker 1: designed to do. The cost, however, is that we are
[28:26] Speaker 1: beyond our intuition and we have to do the maths
[28:28] Speaker 1: and do it very carefully and double check everything. And
[28:31] Speaker 1: so I like the fact we can achieve so much
[28:33] Speaker 1: more because we can use maths. I accept that this
[28:36] Speaker 1: is the cost it comes with, and I'm also reassured
[28:39] Speaker 1: all the stories I found, Obviously they're very spectacular, they're
[28:43] Speaker 1: very interesting, there's a lot to learn. I love the
[28:45] Speaker 1: fact now students at school are told pay attention to
[28:48] Speaker 1: units otherwise these things can happen. They are the exception.
[28:51] Speaker 1: The vast majority of the time, we've got all these
[28:53] Speaker 1: redundancies and checks in place, and they work. And so
[28:57] Speaker 1: these stories are interesting because they are such freak occurrence
[29:01] Speaker 1: as they managed to slip through, and thankfully, with a
[29:05] Speaker 1: very statistic minded head, I can still happily lie knowing
[29:10] Speaker 1: that the vast majority of the time it works. Fine, Matt,
[29:13] Speaker 1: What else are you working on at the moment, and
[29:15] Speaker 1: where else can people find your stuff? Oh? My gods. Well,
[29:19] Speaker 1: I'm still writing away on a new book which will
[29:23] Speaker 1: be out at some point in the distant future, you
[29:26] Speaker 1: know what. I don't think it's been announced, but it'll
[29:28] Speaker 1: be a book about trigonometry. So that's a Cautionary Tales
[29:32] Speaker 1: exclusive trigonometry book coming up at some point when I
[29:37] Speaker 1: finished writing it. If you'd like to know when you
[29:40] Speaker 1: sound a lot like my editor around that, I'm still
[29:43] Speaker 1: doing a lot of work obviously on YouTube and live
[29:47] Speaker 1: works picking up again. I just actually I just filmed
[29:50] Speaker 1: the stand up special version of Humble Pie. So I
[29:55] Speaker 1: was on tour with the show that goes with the book.
[29:58] Speaker 1: In twenty nineteen into twenty twenty. We obviously had to
[30:01] Speaker 1: delay and cancel a lot of those shows, and we
[30:04] Speaker 1: only just filmed the stand Up Special a month or
[30:07] Speaker 1: two ago, and that will be out at some point
[30:10] Speaker 1: around September. So if people want to see the live
[30:12] Speaker 1: stage version of all of these, if you've heard of
[30:15] Speaker 1: at a stand Up Mass dot com, that's my website
[30:17] Speaker 1: where everything happens. And if you're going to YouTube dot
[30:20] Speaker 1: com slash stand Up Mass, you'll see all of my
[30:22] Speaker 1: videos as and when they come out. Matt Parker, thank
[30:26] Speaker 1: you very much for joining us on Cautionary Tales. Tim
[30:28] Speaker 1: has been my absolute pleasure. Cautionary Tales is written by
[30:35] Speaker 1: me Tim Harford with Andrew Wright. It's produced by Ryan
[30:40] Speaker 1: Dilley with support from Courtney Guarino and Emily Vaughan. The
[30:44] Speaker 1: sound design and original music is the work of Pascal Wise.
[30:48] Speaker 1: It features the voice talents of Ben Crow, Melanie Gutridge,
[30:52] Speaker 1: Stella Harford, and Rufus Wright. The show also wouldn't have
[30:56] Speaker 1: been possible without the work of Mia LaBelle, Jacob Weisberg,
[30:59] Speaker 1: Heather Fane, John Schnas, Julia Barton, Kylie mcgliori, Eric Sandler,
[31:05] Speaker 1: Royston Berserv, Maggie Taylor, Nicole Murano, Danielle kan and Maya Caning.
[31:11] Speaker 1: Cautionary Tales is a production of Pushkin Industries. If you
[31:15] Speaker 1: like the show, please remember to share, rate and review,
[31:19] Speaker 1: Tell a friend, Tell two friends, and if you want
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[31:24] Speaker 1: exclusive Cautionary Tales shorts. Then sign up for Pushkin Plus
[31:28] Speaker 1: on the show page in Apple Podcasts or at pushkin
[31:32] Speaker 1: dot fm, slash plus

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