Humble Pi
Page 26
After the collapse the bridge was redesigned, with the critical load-bearing beams now having twice the cross-sectional area of the ones from the first attempt. This design was successful and the Quebec Bridge remains in use over a century since it was finished in 1917. But constructing it was not without further problems. When the middle section was being moved into place in 1916 the lifting equipment broke and that section of bridge dropped into the river. Thirteen workers lost their lives. The middle section sank and remains on the riverbed, next to the collapsed first bridge, to this day. Construction is a dangerous job and the slightest mistake can cost lives.
A photo from right before the collapse and one from after.
Being an engineer, or working on any important mathematics, is a terrifying job. Because of the Quebec Bridge disaster, starting in 1925 any student graduating from an engineering degree in Canada can attend a voluntary Ceremony of the Calling of an Engineer, where they are given a steel ring to remind them of the humility and fallibility of engineers. It can be a tragedy when a mathematician makes a mistake which causes a disaster, but that does not mean we can do without mathematics. We need engineers designing bridges, despite the pressure that comes with it.
Our modern world depends on mathematics and, when things go wrong, it should serve as a sobering reminder that we need to keep an eye on the hot cheese but also remind us of all the maths which works faultlessly around us.
Acknowledgements
As always, my wife, Lucie Green, supplied tea and moral support in roughly equal quantities (and put up with me occasionally shouting, ‘This whole book is a mistake!’).
My agent, Will Francis (of Janklow and Nesbit), has once again steered me away from the multiple other books I wanted to write and focused in on this one good idea. My editor, Helen Conford (and substitute editor Margaret Stead), turned my writing into a book, ably assisted by copy-editor Sarah Day and the whole gang at Penguin Random House.
I have no artistic skill so all photographs (other than my holiday snaps and stock images) were taken by Al Richardson and diagrams were drawn by Adam Robinson. The render of the foot-donut is by Tim Waskett of Stone Baked Games; 3D cogs working together was made by Sabetta Matsumoto after I asked very nicely; photo of Kate and Chris was thanks to, well, Kate and Chris; images from Archaic Bookkeeping are thanks to Bob Englund. Everything else was made by me in some combination of Excel, Photoshop, GeoGebra and Mathematica. Any screen-grabs from retro video games were actually being played by me at the time.
Thanks to all the experts who took time out of their schedule to answer my questions and comment on sections of the book. This includes but is not limited to: Peter Cameron, Moira Dillon, Søren Eilers, Michael Fletcher, Ben Goldacre, James Grime, Felienne Hermans, Hugh Hunt, Peter Nurkse, Lisa Pollack, Bruce Rushin and Ben Sparks. I listened to about 93 per cent of their advice.
Plus, much thanks to the many experts who spoke to me off the record. I’ll thank you by not thanking you.
Translations from Latin were thanks to Jon Harvey, and Swiss German was converted to English with great help from the Valori-Opitz family. The book was crunched into index form by code conjured up by Andrew Taylor. The same competition from the previous book is hidden in this book again, thanks to me being a jerk.
Charlie Turner fact-checked the crap out of the book and all remaining errors are hilarious jokes I’ve demanded be left in. Thanks for additional maths research and checking by Zoe Griffiths and Katie Steckles. Final error spotting was done by Nick Day, Christian Lawson Perfect and pedant extraordinaire Adam Atkinson.
Cheers to the group of people who are as close to colleagues as my ridiculous career allows: Helen Arney and Steve Mould at Festival of the Spoken Nerd, everyone at QMUL, Trent Burton of Trunkman Productions, Rob Eastaway of Maths Inspiration, my agent, Jo Wander, and administrator of admin, Sarah Cooper.
The Parker Square is thanks to Bradley Haran. Consider this a sign of my appreciation, mate.
Index
The page references in this index correspond to the print edition from which this ebook was created, and clicking on them will take you to the the location in the ebook where the equivalent print page would begin. To find a specific word or phrase from the index, please use the search feature of your ebook reader.
Advertising Standards Authority: 198.64179–199.41791
Air Canada: 85.20896–85.23881, 87.41791–88.20896
Air Force: 69.00000–73.94216, 286.62687–287.50746
air traffic control: 302.95522–304.00000
Ariane rocket: 20.41791, 26.56530–27.26866, 29.80597–30.59515
attractiveness scores: 68.35821–69.53731
average Australian: 74.62687–75.95522, 77.56716–77.82090
Avery Blank: 258.02985–258.17910
Benford’s Law: 36.80597–40.95709
Big data: 259.62687–259.74627
big enough: 27.17910–27.47761, 40.50746, 73.14925, 171.20896, 196.02799, 303.08955–304.44776, 313.86567
big number: 47.74627, 203.55224, 253.77612, 289.05970, 310.00000–311.72948, 313.80597
Bill Gates: 141.11940, 160.05970
billion seconds: 290.23881–291.44776, 310.23881–310.41791
binary number: 34.29851, 179.38806–180.50746, 182.35821, 185.35821, 189.41791, 191.08955–191.53731, 246.23881, 250.05970–251.92537, 290.35821, 292.65672–292.80597, 301.00000
brewing beer: 147.89552, 149.59701
Brian Test: 258.02985–258.86567
Casio fx: 11.74627, 175.00000
cause problems: 81.23881, 122.29851–122.56716, 144.20896, 249.56716
CEO pay: 131.53731–131.62687, 133.29851–133.41791
cheese slices: 4.74627, 102.95709
classic football: 235.80597, 238.44776
clay tablets: 149.50746–150.89552
clocks going: 112.08955–114.71642
clockwise anticlockwise: 216.26866
Cluster mission: 29.68657–30.86381
computer code: 29.89552, 123.59701, 187.57836, 189.17910, 191.23881–192.68657, 250.14925, 256.56716, 261.80597, 289.53731, 302.38806–303.02985
constant width: 221.59701–222.86567
cot death: 167.56716–167.68657
crescent moon: 229.11940–231.92537
Datasaurus Dozen: 56.53731, 67.95709–68.92537
Date Line: 286.02985–286.56716
daylight saving: 64.11940–65.92537, 112.05970–114.83582
deliberately vague: somewhere in 7 to 10 and maybe 74
Dice O Matic: 52.20896–52.44776
diehard package: 34.00000–35.86567
Dow Jones: 125.29851, 143.00000–144.47761
drug trial: 62.47761–63.53731
electron beam: 184.05970, 186.53731–186.83582
expensive book: 141.14925–142.86567
explain why: 16.68657, 208.11940, 312.86567–312.89552
false positive: 64.62687, 154.74627, 247.08955, 252.50746, 276.86567, 301.20896, 308.26866–309.86567
fat fingers error: 143.44776, 150.11940
feedback loop: 144.35821, 268.08955–269.86567, 274.26866, 276.02985–277.80597
fence post problem: 208.83582–209.47761
Fenchurch Street: 280.20896, 282.35821–283.38806
fibre optic cable: 136.32836–136.89552, 138.08955
flash crash: 143.41791–144.38806
foot doughnut: 235.50933–235.71642
frigorific mixture: 92.44776–92.68657
fuel gauges: 85.05970–87.92537
full body workout: 213.71642–213.95522
functional sausage: 123.44776–123.47761
gene names: 247.00000–248.47761
Gimli Glider: 82.11940–83.68657
GOOD LUCK: 25.74627, 83.47761–84.83582, 288.74440
Gregorian calendar: 288.14925–288.41791, 293.08955–296.92537
Grime Dice: 160.56716–160.90672, 162.14925
Harrier Jet: 311.00000–313.65672
heart attacks: 64.11940–65.89552,
112.11940–114.92537
high frequency trading: 142.53731, 145.44776–146.71642
Hot Cheese: 1.92537, 4.59701
human brains: 149.05970, 159.00000, 266.29851, 308.02985–309.44776
Hyatt Regency: 264.80597, 267.95522
International Date Line: 286.02985–286.56716
JPMorgan Chase: 240.80597–241.68657
Julian calendar: 295.23881–297.59701
Julius Caesar: 206.32836–206.89552, 293.80597, 297.17910–298.56716
Kansas City: 264.80597–264.86567, 267.95522
lava lamps: 31.27612–32.82090
leap years: 206.29851, 288.47761, 295.26866, 297.00000–298.86567
Lego bricks: 201.05970–202.95522
long enough: 55.77425–56.83582, 99.20896–99.26866, 171.08955, 194.50746, 246.86567, 303.44776
Los Angeles: 255.17910–255.65672, 302.20896, 305.53731
magic squares: 6.11940–7.89552
Mars Climate Orbiter: 96.80410–97.87873
maths error: 9.91418, 11.29851, 28.56716, 79.62687, 97.75933, 147.50746, 175.00000, 181.56716, 245.68657, 304.29851–305.86567
maths mistake: 7.35821–8.11940, 89.65672, 149.80597, 174.11940–175.65672, 181.59701, 206.65672–206.71642, 210.14925, 259.71642, 264.41791, 300.08955, 305.47761, 308.74627–308.95522
McChoice Menu: 197.02985, 199.44776–200.00000
Millennium Bridge: 269.68657–269.83582, 274.26866–277.41791, 280.00000–281.68657
mobile phone masts: 57.19403–59.92537
most important: 6.00000, 190.62687
Mr Average: 74.14925–75.53731
NBA players: 166.17910–166.44776
non transitive dice: 141.17910, 160.00000–162.14925
non zero: 157.35821, 183.20896, 185.17910, 192.74627
Null Island: 254.50746–255.95522
null meal: 197.74627, 199.26866–200.50746
oddly specific: 117.2089552238806, 139.1194029850746, 190.5074626865672, 245.7462686567164
off-by-one errors: 206.53731, 209.65672–211.17910
Olympic Games: 293.26866, 300.14925
Parker Square: 5.05970–6.89552
Penney Ante: 163.32836–163.38806
Pepsi Points: 311.69963–313.71642
phone masts: 57.19403–59.92537
plug seal: 100.90672
Pseudorandom number generators: 43.74627–44.44776, 47.56716–48.86567
punch cards: 73.74627–73.77612, 75.08955–76.74627
real world: 38.34328–40.23881, 121.38806, 123.80597, 145.95522, 208.02985, 241.26866, 244.53731–245.95522
resonant frequencies: 269.68657–269.74627, 274.23881–280.95522
Richard Feynman: 154.95522, 222.00000–223.29851
rm -rf: 23.08955–23.47761
Rock Paper Scissors: 163.50746–163.71642
roll over errors: 25.38806, 180.32836, 184.53731, 190.26866–191.20896
Royal Mint: 215.92537–216.85075
salami slicing: 121.35821–123.80597
salt mines: 232.00000–233.80597
scientific notation: 249.32836–250.77612, 252.00000–253.83582
Scud missile: 179.00000–181.65672
sea level: 89.17910–89.83582
seemingly arbitrary: 53.20896, 190.38806, 296.86567, 302.23881
Sesame Street: 230.00000–230.26866
should open: 225.53731–225.62687, 227.41791–227.44776
skin tight garments: 73.23881–73.26866
something else: 57.29851, 64.65672, 247.02985, 270.11940, 301.14925
Space Invaders: 19.59701–21.83396
space shuttle: 4.10448–4.34328, 152.26866–153.50746, 223.14925–223.35821, 230.80597–230.89552
SQL injection: 250.11940, 256.02985
standard deviation: 34.35821–34.53731, 66.93097–68.83582, 73.65672, 132.86381
Steve Null: 258.00000–259.80597, 261.47761
Stock Exchange: 123.71642, 125.08955–125.65672, 145.29851–145.62687, 150.26866–151.92351
stock options: 131.14925–133.92537
street signs: 233.29851–234.38806, 238.35634–238.50746
survivor bias: 13.89552, 21.32836, 65.53731–66.77612
Swiss Cheese model: 4.56716–4.83582, 13.23881, 103.80597
synchronous lateral excitation: 276.38806–277.38806, 280.62687
T shirt: 5.00000–5.02985, 313.41791–313.62687
tabulating machines: 73.74627, 75.08955–76.65672
Tacoma Narrows Bridge: 268.47761–270.29851
tallest mountain: 115.11940–116.89552
tax return: 36.71642–36.80597, 38.61194, 41.05970–42.92537
Therac machine: 13.00000, 185.05970–185.80597
three cogs: 214.00000–215.74813, 219.02985–220.35821
Tokyo Stock Exchange: 125.38806, 150.26866–151.92351
torsional instability: 268.17910–271.89552
trading algorithms: 138.77612, 142.53731–142.74627, 144.23881–146.68657
Traffic Control: 302.20896–305.68657
Trump administration: 128.17910–129.89552
UK government: 52.47761, 233.23881–234.83582, 238.86567, 256.44776
UK lottery: 155.38806–155.86567, 159.41791–159.92537, 308.08955–308.14925
UK street signs: 238.35634–238.50746
US army: 179.77612, 181.68657–181.71642
USS Yorktown: 175.20896–175.77425
Vancouver Stock Exchange: 123.71642, 125.08955–125.65672
waka waka: 189.95709
went wrong: 27.62687, 29.80597, 84.41791, 134.80597–134.92537, 145.77612, 265.20896, 267.50746, 280.62687, 286.65672, 305.89552
Wobbly Bridge: 97.66978, 280.11940–280.41791
Woolworths locations: 60.00000–60.62687
world record: 119.11940–121.77612, 135.35261, 298.77612
wrong bolts: 99.02985–99.74627, 101.17910–102.70149, 104.77612
X rays: 185.86567–186.80597
THE BEGINNING
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ALLEN LANE
UK | USA | Canada | Ireland | Australia
India | New Zealand | South Africa
Allen Lane is part of the Penguin Random House group of companies whose addresses can be found at global.penguinrandomhouse.com.
First published 2019
Copyright © Matt Parker, 2019
The moral right of the author has been asserted
Cover image: Emilija Manevska/Getty Images
ISBN: 978-0-141-98913-6
This ebook is copyright material and must not be copied, reproduced, transferred, distributed, leased, licensed or publicly performed or used in any way except as specifically permitted in writing by the publishers, as allowed under the terms and conditions under which it was purchased or as strictly permitted by applicable copyright law. Any unauthorized distribution or use of this text may be a direct infringement of the author’s and publisher’s rights and those responsible may be liable in law accordingly.
One: Losing Track of Time
1 Of course, you cannot save a + or – symbol in a binary number, so a system is used to indicate positive or negative using the binary itself, but it still takes up a bit of space.
Three: Little Data
1 For any programmers thinking there is no way this is still a problem, I’m referring to an XMLEncoder problem in Apache Flex. Check out bug report FLEX-33644.
2 Most online maps show nothing but water where Null Island should be – except the open-source map data Natural Earth, which has included a 1-metre-square spot of land at 0,0 si
nce version 1.3.
3 Download them all at https://oeis.org/A262222. Fun fact: they were computed by my maths buddy Christian Lawson-Perfect of Perfect-Herschel Polyhedron fame.
4 This sounds slightly worse than it is because formulas travel in packs: a single formula can be ‘dragged down’ to repeat across multiple cells. If you discount duplicates, the spreadsheets had an average of 17.5 unique mistakes each.
Four: Out of Shape
1 See my book Things to Make and Do in the Fourth Dimension for a guide to making your own.
Five: You Can’t Count on It
1 I appreciate some of this weirdness comes down to semitones (and the definition of a major scale). But they’re only semi to blame.
2 An exclamation mark is used to indicate a factorial and, given how startlingly large the answers can be, it seems appropriate.
3 Always ready for a challenge, mathematicians gave the name ‘McCombination’ to any value n! − n (sequence A005096 in the On-Line Encyclopedia of Integer Sequences) and are trying to find a use for these numbers. No such use has yet been found.
4 The McChoice Menu was one of the few times McDonald’s sold hotdogs. And that somehow wasn’t the biggest mistake in all of this.
5 To be fair, in 1983, the US did expand its zip codes to be nine digits with ‘zip+4’ but freedom-loving Americans did not take kindly to being assigned specific numbers. It was all a bit Nineteen Eighty-Four. So since then the public-facing postcodes have stayed a mere five digits but, behind the scenes, the mail barcodes printed on letters use ‘zip+6’ to assign an eleven-digit code to every building in the country.
Six: Does Not Compute