# Humble Pi

Matt Parker was a math teacher who has set himself as a life goal to be a math and science communicator. He is well known as a guest in tv-shows, by his stage shows and Numberphile videos on Youtube, and as the author of *Things to make and do in the fourth dimension* (2014). The current book got the subtitle "*A comedy of maths errors*", and a slapstick comedy it is, because of all the things "that went not exactly as planned" because of the "mathematical" errors behind the wrong decisions made. Unfortunately some of the consequences were rather dramatic and caused a loss of lives, money, and energy. Parker warns us in the introduction that he has deliberately left three errors in the book for the reader to detect. Also the cover of the book represents a funny Boeing plane with the wings wrongly attached. That is very unlikely to happen in reality, but unfortunately accidents with planes happen all too often and it is sometimes just a tiny programming or construction error that has caused the death of many passengers and crew in the history of commercial aviation.

This book is not the first to describe a collection of errors with numbers or mathematical errors. For example, read about math errors made by students in *Magnificent Mistakes in Mathematics* (2013) by A.S. Posamentier and I. Lehman while J.A. Paulos wrote his book *Inumeracy* (1988) to warn the man in the street not to be blind for blatant mathematical misconceptions, and more on the informatics side, there is *Weapons of math destruction* (2016) by O'Neil and the more recent *Bits and Bugs* (2019) by T. Huckle and T. Neckel. Also Parker includes many software errors in his collection. So the "maths errors" have to be understood in a broader sense. The fact that if integers are represented by one byte or 8 bits and thus can at most be 11111111 or 255 in decimal notation, will cause an overflow problem when 256 is reached much like the dreaded (but anticipated) millennium bug. The 256 overflow problem however has often been overlooked and has been a source of many mistakes and disasters when a count suddenly dropped from the maximal 255 to zero. This caused Twitter, Minecraft, and Pac-man to break when reaching level 256 but it also can turn an X-ray medical instrument into a deadly weapon.

Other tangentially mathematical errors are related to the unwanted interpretation that is made by Excel of what you type: the leading zeros of telephone numbers are removed when inserted as a number, if an hexadecimal number contains an E it can be interpreted as a scientific notation for a decimal number, it may think to recognize a date in strings of biological information with names for enzymes like MARCH5 or SEP15, or in strings of the form 6/11, etc. It is obviously a bad idea to misuse excel sheets with many formulas. Parker makes an analysis of a large set of excel sheets that are interconnected by a large set of formulas with an inevitable daunting amount of errors. Calenders have changed in the course of history and this has been the reason why the Russian delegation arrived two weeks late at the Olympic Games in 1908 because in Russia the Julian calendar was still in use while the rest of the world had switched to the Gregorian calendar. The different units for weights or volumes, and distances nearly crashed a plane that fell out of fuel in mid-air or another one was heavily overweighted and just made it to its destination (kg and lb are not the same). But there are of course the genuine mathematical problems when engineers do not make the correct computations (or make last moment changes and neglect to redo the computations) during the construction of a bridge or a building. The video of the Tacoma bridge is legendary, but there are many other bridges that had stability problems like the wobbly Millennium bridge in London. The Walkie-Talkie is a nickname for a London skyscraper with parabolic glass facade that reflected sunlight and melted things and set carpets on fire in the focal point. Parker is also the man behind a petition protesting against the UK road signs pointing to football stadiums with the wrong football logo. The classic football is an inflated truncated icosahedron with 20 white hexagons and 12 black pentagons. The logo consisted completely of hexagons. Rounding and statistical errors have upset the financial markets, and were misused in politics. Non-causal correlations are often used as arguments by activists or pressure groups. It's not all strictly mathematics, but Parker keeps going on and on. It's misunderstanding and misinterpretation galore, and often a sequence of coincidences for which Parker borrows the image of a Swiss cheese from James Reason: there are holes in every level of the security checks, like holes in every slice of cheese, but the holes have to line up to let the error slip past them all. Unfortunately that happens from time to time.

On the nerdy side: The pages of the book are numbered from 314 down to 0 and then switches to count down from 4,294,967,295 which is 232-1 for the appendix with the list of illustrations and the index, an example of underflow in binary countdown. A similar type of error played an important role in the first disaster example where the time was stored in 4-bytes and all electrical power was shut down in the Boeing 787 plane when the counter reached 2,147,483,647. The index of the book is automatically produced by a code written by Andrew Taylor. The code selects interesting couples of two successive words from the text. References are given to pages and lines where these couples appear, like for example Richard Feynman: 154.95522, 222.00000-223.29851 meaning that the text "Richard Feynman" appears on the bottom line of page 154 and is discussed on pages 222 top line to page 223 line 11 from the top. This allows to figure out that lines are numbered as multiples of about 2985 starting from line 0 at the top. The more precise value 2985.074662686... is probably a conversion into some units that I have not figured out. There is an exception for the index entry "oddly specific" where lines are shown with 13 digits instead of 5. For example the first is pointing to 117.2089552238806 and "oddly specific" appears indeed on page 117, line 8 from the top, which should on other pages correspond to 117.20896. Another funny and deliberately vague entry is "deliberately vague: somewhere between 7 and 10 and maybe 74". There you can indeed find the phrase "deliberately vague" in connection with the hush up of some errors in the system. It is fun figuring out for yourself how the index is produced. More details below after the "Spoiler alert". Whether the title of the book has any relation with the name of the supergroup of Humble Pie of the late 60's is not clear either. In any case, if pi stands for mathematics, then engineers, programmers, and anyone applying mathematics as a humble tool in their great creative design should be aware of the importance of this humble tool that can safe the life of many that should not die because of a miscalculation.

All of these mistakes with amusing and not so amusing consequences are told by Parker in general in a funny way, even though there are a lot of people dying in this book. Notwithstanding the long list of examples of what went wrong, probably many other mistakes were never discovered or were swept under the rug after investigation, so that the public doesn't even know they ever happened. Newly discovered mistakes create new safety regulations. But new boundaries will always be explored, that is just human's nature, and humans will always make mistakes. We just have to learn to be alert and do the mathematics properly. Read the book! You'll enjoy it! Mathematics is required in life, but not for enjoying this book.

**Spoiler alert** If you scroll down, you might read things that you prefer to find out for yourself.

There is some hint in the "oddly specific" item of the index on how the lines are numbered. That entry refers to places 139.1194029850746 and 117.2089552238806 where the text appears on line 5 of page 139 and line 8 of page 117. Dividing 1194029850748 by 4 gives 298507462687, which is to be the oddly specific value of the distance between lines (multiplied by 10,000,000). The bottom line (line 33) corresponds to 298507462687 × 32 = 9552238805984, which is rounded to 95522. The first (hard cover) edition of *Things to make and do in the fourth dimension* had no index. But in the paperback edition an index was added, also produced by Andrew Taylor. There the references were given in 3D: first the page number and then the coordinates of a square like on a map: columns are indicated with a letter (A,B,C) and rows with a number (1-5), giving 15 squares per page to approximately locate the place where the item of the index can be found.

Another bit worth noting is that in the hardback edition of *Things to make and do*, Brady Haran in the acknowledgements was misspelled as Bradley Haran. Parker promised to have the error corrected in the paperback edition. In this book he thanks again Bradley Haran to which he adds "Consider this a sign of my appreciation, mate". Haran popularized the Parker Square, which Parker produced on Numberphile. It was supposed to be a 3 x 3 kind of magic square containing 9 unique squared numbers with the same sum along rows, columns and diagonals, an unsolved problem in mathematics. Parker is however proud to have found one sloppy approximation in which squared numbers are repeated and one diagonal sum fails. This became known as the Parker Square, an inside joke on Numberphile.

**Submitted by Adhemar Bultheel |

**22 / Aug / 2019