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Humble Pi: A Comedy of Maths Errors
An international bestseller
The book-length answer to anyone who ever put their hand up in math class and asked, "When am I ever going to use this in the real world?"
"Fun, informative, and relentlessly entertaining, Humble Pi is a charming and very readable guide to some of humanity's all-time greatest miscalculations--that also gives you permission to feel a little better about some of your own mistakes." --Ryan North, author of How to Invent Everything
Our whole world is built on math, from the code running a website to the equations enabling the design of skyscrapers and bridges. Most of the time this math works quietly behind the scenes . . . until it doesn't. All sorts of seemingly innocuous mathematical mistakes can have significant consequences.
Math is easy to ignore until a misplaced decimal point upends the stock market, a unit conversion error causes a plane to crash, or someone divides by zero and stalls a battleship in the middle of the ocean.
Exploring and explaining a litany of glitches, near misses, and mathematical mishaps involving the internet, big data, elections, street signs, lotteries, the Roman Empire, and an Olympic team, Matt Parker uncovers the bizarre ways math trips us up, and what this reveals about its essential place in our world. Getting it wrong has never been more fun.
The book-length answer to anyone who ever put their hand up in math class and asked, "When am I ever going to use this in the real world?"
"Fun, informative, and relentlessly entertaining, Humble Pi is a charming and very readable guide to some of humanity's all-time greatest miscalculations--that also gives you permission to feel a little better about some of your own mistakes." --Ryan North, author of How to Invent Everything
Our whole world is built on math, from the code running a website to the equations enabling the design of skyscrapers and bridges. Most of the time this math works quietly behind the scenes . . . until it doesn't. All sorts of seemingly innocuous mathematical mistakes can have significant consequences.
Math is easy to ignore until a misplaced decimal point upends the stock market, a unit conversion error causes a plane to crash, or someone divides by zero and stalls a battleship in the middle of the ocean.
Exploring and explaining a litany of glitches, near misses, and mathematical mishaps involving the internet, big data, elections, street signs, lotteries, the Roman Empire, and an Olympic team, Matt Parker uncovers the bizarre ways math trips us up, and what this reveals about its essential place in our world. Getting it wrong has never been more fun.
314 pages, Paperback
First published March 7, 2019
About the author
Matt Parker
4 books387 followersMatt Parker is a former maths teacher who communicates about mathematics via YouTube videos, stand-up comedy, and books.
Librarian note:
There is more than one author in the GoodReads database with this name
Librarian note:
There is more than one author in the GoodReads database with this name
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Displaying 1 - 30 of 1,878 reviews
June 14, 2020
Humble Pi takes us on a tour of the times when math, engineering, and programming have gone wrong, leading to disastrous or sometimes just funny results. The book covers a range of mistakes, including bridge failures, space exploration disasters, game show cheats, financial algorithms gone rogue, and so much more.
I pretty much loved this book from start to finish. I found it thoroughly fascinating and often hilarious. Parker has a great way with explaining technical subjects, distilling it down to layman terms while retaining his humor. Even on events I already know about, Parker's explanations provided a new and interesting take.
The book is organized so that similar themes are grouped together into chapters, but each incident is only a few pages long, so it never feels bogged down or boring. I found it best to read with the internet handy, so I could zip on and find out more whenever it interested me.
It's been a while since I've been this riveted by a nonfiction book. I was tearing through it, chuckling to myself and stopping only to look up videos of Michael Larson on Press Your Luck and Galloping Gertie as it came down. I'm so glad I happened across this book. It totally spoke to the inner engineer nerd in me. After all, the only thing more fascinating than how something works is when it doesn't.
I pretty much loved this book from start to finish. I found it thoroughly fascinating and often hilarious. Parker has a great way with explaining technical subjects, distilling it down to layman terms while retaining his humor. Even on events I already know about, Parker's explanations provided a new and interesting take.
The book is organized so that similar themes are grouped together into chapters, but each incident is only a few pages long, so it never feels bogged down or boring. I found it best to read with the internet handy, so I could zip on and find out more whenever it interested me.
It's been a while since I've been this riveted by a nonfiction book. I was tearing through it, chuckling to myself and stopping only to look up videos of Michael Larson on Press Your Luck and Galloping Gertie as it came down. I'm so glad I happened across this book. It totally spoke to the inner engineer nerd in me. After all, the only thing more fascinating than how something works is when it doesn't.
July 10, 2021
There is an Australian word that is used to describe people that is affectionate, but when you learn its etymology, you wonder how it possibly ever could have come to common use. It is to be called a dag, or more likely, a bit of a dag. It isn’t exactly a compliment, but it almost always implies a fondness for the person being spoken about. You know, if in context you call someone ‘a bit of a dag’ you would not be likely to get into a fight – whereas, if you called them a shit-head or a total-turd or a prick, you really might. The thing is that a dag is a piece of shit that hangs from the wool around a sheep’s bum. Like I said, you couldn’t say being called a dag is a compliment, but it isn't really an insult either. I say all of this because this guy was born in Western Australia and, well, he's a bit of a dag. Oh, and by the way, I’m typing this in Microsoft Word using the Australian English dictionary and I have to say it amuses me very much indeed that ‘dag’ has a red squiggly line under it informing me that I’ve made a spelling mistake. Australian English, indeed.
There is a point in this book where the author started a campaign to have the soccer ball depicted on signs in England changed to ensure that it was not made up only of hexagons, but also included pentagons. He explained that if all of the segments in the ball were hexagons you couldn’t make it into a ball. Now, look, I get it – he’s a maths guy, and so getting it right is important to him – but sometimes you need to move on. It’s a bit like a meme I saw early in the pandemic showing right angle triangles with all sides being 1.5 metres, and then Hawking and deGrasse Tyson holding back Pythagoras who was ready for a fight. My all-time favourite of these things is the fact that it is impossible to see a cube in real life in the way we have all been taught to draw one, with a square on the top of the cube and two sides also being squares. You can get upset about these things, but 2-d representations of 3-d phenomena are, well, you know, 2-d.
Quite a lot of this book discusses mistakes a bit like that. But other mistakes are much more consequential – you know, the sort of mistakes that make planes fall out of the sky. What is really interesting with these things is that those mistakes can be quite difficult to make. Not that you have to really try to make them, or put in lots of effort, the mistakes come easily enough, but a whole lot of things need to go very wrong for some mistakes to happen – that is the lovely thing about this book, it is quite forgiving of those who make mistakes – given that that is all of us, just about all of the time. His point isn’t to point and laugh, but rather to explain that any system based on the assumption that no one would be damn stupid enough to make that particular mistake has been designed to fail. In many of the stories here you might find yourself feeling rather smug – but as they say in the classics, ‘pride comes before a fall’ and ‘there but for the grace of God go I…’ It is really worth while keeping those little quotes in mind here.
The metaphor he uses at the end of this is hot Swiss cheese, but I preferred the straight Swiss cheese one used earlier – that is, there are always holes, you need to make sure that the holes in your defences don't all line up. We probably can’t make sure of that, ultimately, but setting that as your life’s goal is a worthwhile thing to do. If you are smart, the challenge is to create something that will be as close to foolproof as you can, rather than blaming people afterwards for not using it properly.
Right at the end of this there is a quote from him that has ended up being used in mathematics classrooms by teachers – and I love it to bits. It is, “Mathematicians aren’t people who find maths easy; they’re people who enjoy how hard it is”. Isn’t that the best thing you’ve read today? One of the things that always annoys me is that so many people seem to understand some things about sport that they never seem to connect with intellectual effort. One is that no matter how good you are at a sport, you still need to practice. And that if you want to be really good, you have to practice a lot. If I was to wear a ‘I’m too intelligent to play football’ t-shirt, I would, rightly enough, I guess, be considered grossly insulting. But I have seen a ‘I’m too pretty for maths’ t-shirt. The effort required to be good at any skill is almost always actually the point – but too many people seem to think that a skill needs to be 100% innate or it isn’t a real skill.
The other connection to sport is that you can be the best at your sport that has ever been, and you will still fail over and over again. Don Bradman’s last score in a test match was a duck. Michael Jordan once said, ‘I’ve missed more than 9,000 shots in my career’. Yeah, he probably ought to have just given up, he clearly didn’t have any natural talent for that shit. The thing is that people give up on mathematics for far less. I’ve actually a negative interest in sport, zero being far too large a number to fully encompass my boredom – but I find it remarkable that people are so much more likely to give up on things that are really worthwhile, but would ‘never say die’ for shit that doesn't matter at all.
Anyway, I distract myself – while it is worth reading this book if only to see the near endless number of ways we can stuff things up, there are other joys involved here. Some of the stories read like jokes – in the sense that you know there is going to be a punchline coming soon, and so you try to guess it before it comes. Sometimes the punchline will come and then he will explain that the punchline was actually only one of the things that needed to go wrong for the whole thing to come crashing down. He also explains that sometimes stuff ups are necessary, rather than just tragic accidents. Progress in science and engineering often involves someone needing to go beyond the cutting edge, on to the bleeding edge. But to boldly go where no one has gone before is risky business. Not all mistakes are stuff-ups, sometimes they are a necessary consequence of being first.
There is a point in this book where the author started a campaign to have the soccer ball depicted on signs in England changed to ensure that it was not made up only of hexagons, but also included pentagons. He explained that if all of the segments in the ball were hexagons you couldn’t make it into a ball. Now, look, I get it – he’s a maths guy, and so getting it right is important to him – but sometimes you need to move on. It’s a bit like a meme I saw early in the pandemic showing right angle triangles with all sides being 1.5 metres, and then Hawking and deGrasse Tyson holding back Pythagoras who was ready for a fight. My all-time favourite of these things is the fact that it is impossible to see a cube in real life in the way we have all been taught to draw one, with a square on the top of the cube and two sides also being squares. You can get upset about these things, but 2-d representations of 3-d phenomena are, well, you know, 2-d.
Quite a lot of this book discusses mistakes a bit like that. But other mistakes are much more consequential – you know, the sort of mistakes that make planes fall out of the sky. What is really interesting with these things is that those mistakes can be quite difficult to make. Not that you have to really try to make them, or put in lots of effort, the mistakes come easily enough, but a whole lot of things need to go very wrong for some mistakes to happen – that is the lovely thing about this book, it is quite forgiving of those who make mistakes – given that that is all of us, just about all of the time. His point isn’t to point and laugh, but rather to explain that any system based on the assumption that no one would be damn stupid enough to make that particular mistake has been designed to fail. In many of the stories here you might find yourself feeling rather smug – but as they say in the classics, ‘pride comes before a fall’ and ‘there but for the grace of God go I…’ It is really worth while keeping those little quotes in mind here.
The metaphor he uses at the end of this is hot Swiss cheese, but I preferred the straight Swiss cheese one used earlier – that is, there are always holes, you need to make sure that the holes in your defences don't all line up. We probably can’t make sure of that, ultimately, but setting that as your life’s goal is a worthwhile thing to do. If you are smart, the challenge is to create something that will be as close to foolproof as you can, rather than blaming people afterwards for not using it properly.
Right at the end of this there is a quote from him that has ended up being used in mathematics classrooms by teachers – and I love it to bits. It is, “Mathematicians aren’t people who find maths easy; they’re people who enjoy how hard it is”. Isn’t that the best thing you’ve read today? One of the things that always annoys me is that so many people seem to understand some things about sport that they never seem to connect with intellectual effort. One is that no matter how good you are at a sport, you still need to practice. And that if you want to be really good, you have to practice a lot. If I was to wear a ‘I’m too intelligent to play football’ t-shirt, I would, rightly enough, I guess, be considered grossly insulting. But I have seen a ‘I’m too pretty for maths’ t-shirt. The effort required to be good at any skill is almost always actually the point – but too many people seem to think that a skill needs to be 100% innate or it isn’t a real skill.
The other connection to sport is that you can be the best at your sport that has ever been, and you will still fail over and over again. Don Bradman’s last score in a test match was a duck. Michael Jordan once said, ‘I’ve missed more than 9,000 shots in my career’. Yeah, he probably ought to have just given up, he clearly didn’t have any natural talent for that shit. The thing is that people give up on mathematics for far less. I’ve actually a negative interest in sport, zero being far too large a number to fully encompass my boredom – but I find it remarkable that people are so much more likely to give up on things that are really worthwhile, but would ‘never say die’ for shit that doesn't matter at all.
Anyway, I distract myself – while it is worth reading this book if only to see the near endless number of ways we can stuff things up, there are other joys involved here. Some of the stories read like jokes – in the sense that you know there is going to be a punchline coming soon, and so you try to guess it before it comes. Sometimes the punchline will come and then he will explain that the punchline was actually only one of the things that needed to go wrong for the whole thing to come crashing down. He also explains that sometimes stuff ups are necessary, rather than just tragic accidents. Progress in science and engineering often involves someone needing to go beyond the cutting edge, on to the bleeding edge. But to boldly go where no one has gone before is risky business. Not all mistakes are stuff-ups, sometimes they are a necessary consequence of being first.
July 28, 2019
Turns out that pi's not as humble as one could imagine. That many people actually did die as a result of many of the errors is tragic and definitely takes most of fun from the comedy. The unfortunate book name aside, it's a magnificent read into how maths go bump in everywhere.
Q:
‘Plaintiff’s insistence that the commercial appears to be a serious offer requires the Court to explain why the commercial is funny. Explaining why a joke is funny is a daunting task.’ (c)
Q:
I went with my favourite method of comparing big numbers to time. We know a million, a billion and a trillion are different sizes, but we often don’t appreciate the staggering increases between them. A million seconds from now is just shy of eleven days and fourteen hours. Not so bad. I could wait that long. It’s within two weeks. A billion seconds is over thirty-one years.
A trillion seconds from now is after the year 33700CE.
Those surprising numbers actually make perfect sense after a moment’s thought. Million, billion and trillion are each a thousand times bigger than each other. A million seconds is roughly a third of a month, so a billion seconds is on the order of 330 (a third of a thousand) months. And if a billion is around thirty-one years, then of course a trillion is around 31,000 years. (c)
Q:
Even after a lifetime of education dealing with small numbers there is a vestigial instinct that larger numbers are logarithmic; that the gap between a trillion and a billion feels about the same as the jump between a million and a billion – because both are a thousand times bigger. In reality, the jump to a trillion is much bigger: the difference between living to your early thirties and a time when humankind may no longer exist. (c)
Q:
I believe that ‘regardless of flight phase’ is official FAA speak for ‘This could go down mid-flight.’ Their official line on airworthiness was the requirement of ‘repetitive maintenance tasks for electrical power deactivation’. That is to say, anyone with a Boeing 787 had to remember to turn it off and on again. (с)
Q:
A political committee is rarely a good solution to a mathematical problem. (c)
Q:
To get everything back into alignment in the first place, the year 46BCE had a possible-world-record 445 days. (c)
Q:
The building at 20 Fenchurch Street in London … By all measures, it’s a successful building. Except, during the summer of 2013, it started setting things on fire. …
The exterior of the building was designed by architect Rafael Viñoly to have a sweeping curve, but this meant that all the reflective glass windows accidentally became a massive concave mirror – a kind of giant lens in the sky able to focus sunlight on a tiny area. It’s not often sunny in London, but when a sun-filled day in summer 2013 lined up with the recently completed windows, a death heat-ray swept across London.
Okay, it wasn’t that bad. But it was producing temperatures of around 90°C, which was enough to scorch the doormat at a nearby barber’s shop. A parked car was a bit melted and someone claimed it burned their lemon (that’s not cockney rhyming slang; it was an actual lemon). A local reporter with a flair for the dramatic took the opportunity to fry some eggs by placing a pan in the hotspot. (c)
Q:
In July 2011 a thirty-nine-storey shopping centre in South Korea had to be evacuated because resonance was vibrating the building. People at the top of the building felt it start to shake, as if someone had banged the bass and turned up the treble. Which was exactly the problem. After the official investigation had ruled out an earthquake, they found the culprit was an exercise class on the twelfth floor.
On 5 July 2011 they had decided to work out to Snap’s ‘The Power’, and everyone jumped around harder than they usually did. Could the rhythm of ‘The Power’ match a resonant frequency of the building? During the investigation, about twenty people were crammed back into that room to recreate the exercise class and, sure enough, they did have the power. When the exercise class on the twelfth floor had ‘The Power’, the thirty-eighth floor started shaking around ten times more than it normally did. (c)
Q:
When it was reopened, the Millennium Bridge was described as ‘probably the most complex passively-damped structure in the world’. Not an epithet most of us would aspire to. (c)
Q:
… British engineers prided themselves on their stiff upper bridges. (c)
Q:
Obviously, we should do whatever we can to avoid engineering mistakes, but when engineers are pushing the boundaries of what is possible, occasionally a new aspect of mathematical behaviour will unexpectedly emerge. Sometimes the addition of a little bit more mass is all it takes to change the mathematics of how a structure behaves.
This is a common theme in human progress. We make things beyond what we understand, and we always have done. …
When theory lags behind application, there will always be mathematical surprises lying in wait. The important thing is that we learn from these inevitable mistakes and don’t repeat them. (c)
Q:
In the mid-1990s a new employee of Sun Microsystems in California kept disappearing from their database. Every time his details were entered, the system seemed to eat him whole; he would disappear without a trace. No one in HR could work out why poor Steve Null was database kryptonite. (c)
Q:
Carrying on in the same vein as Steve Null, I’d like you to meet Brian Test, Avery Blank and Jeff Sample. The Null problem can be fixed by encoding names in a format for only character data, so that it doesn’t get confused with the data value of NULL. But Avery Blank has a bigger problem: humans.
When Avery Blank was at law school she had difficulty getting an internship because her applications were not taken seriously. People would see ‘Blank’ in the surname field and assume it was an incomplete application. She always had to get in touch and convince the selection committee that she was a real human.
Brian Test and Jeff Sample fell foul of the same problem, but for slightly different reasons. When you set up a new database, or a way to input data, it’s good practice to test it and make sure it’s all working. So you feed through some dummy data to check the pipeline. I run a lot of projects with schools, and they often sign up online. I’ve just opened my most recent such database and scrolled to the top. The first entry is from a Ms Teacher who works at Test High School on Test Road in the county of Fakenham. She’s probably a relation of Mr Teacher from St Fakington’s Grammar School, who seems to sign up for everything I do.
To avoid being deleted as unwanted test data, when Brian Test started a new job, he brought in a cake for all his new colleagues to enjoy. Printed on the cake was a picture of his face, with the following words written in icing: ‘I’m Brian Test and I’m real.’ Like a lot of office problems, the issue was solved with free cake, and he was not deleted again. (c)
Q:
So, when it comes to names, if you inherit a database-killing last name, you can either wear it as a badge of honour or take some deed-poll action. But if you are a parent, please don’t give your child a first name which will set them up for a lifetime of battling computers. And given that over three hundred children in the USA since 1990 have been named Abcde, it’s worth spelling this out: don’t name your child anything like Fake, Null or DECLARE. (c)
Q:
In Los Angeles there is a block of land on the corner of West 1st Street and South Spring Street which houses the offices of the LA Times. It is just down the street from City Hall and directly over the road from the LA Police Department. There may be some rough areas of LA best avoided by tourists, but this is certainly not one of them. The area looks as safe as safe can be … until you check the LAPD’s online map of reported crime locations. Between October 2008 and March 2009 there were 1,380 crimes on that block. That’s around 4 per cent of all crimes marked on the map.
When the LA Times noticed this, it politely asked the LAPD what was going on. … If the computer is unable to work out the location, it simply logs the default location for Los Angeles: the front doorstep of the LAPD headquarters. (c)
Q:
Whenever a computer cannot decipher a location, it still has to fill something in, and so 0,0 became the default location. The island where bad data goes to die. (c)
Q:
For a start, just because something walks like a number and quacks like a number does not mean it is a number. (c)
Q:
For generations, cartographers have been sneaking fictitious places into real maps (often as a way to expose people plagiarizing their work), and it was inevitable that Null Island would take on a life of its own. So, they literally put it on the map. (c)
Q:
So the signs remain incorrect. But at least now I have a framed letter from the UK government saying that they don’t think accurate maths is important and they don’t believe street signs should have to follow the laws of geometry. (c)
Q:
Never put ‘teamwork cogs’ as a search term into a stock image website. For a start, if you’re not used to the cheese-tastic world of inspirational work posters, what you see will come as a shock. The next shock is that a lot of the diagrams supposed to be showing a team working like a well-oiled machine use a mechanism which would be permanently seized in place. …
The longer I think about it, the more I’m convinced that this does actually make a great analogy for workplace teamwork. (c)
Q:
I don’t complain that Picasso’s works are biologically implausible or send Salvador Dalí angry letters about the melting point of clocks. (c)
Q:
It seems they used to do their upper- and lower-body workouts on alternate days but now, due to a lack of time, they wanted to know if there was any risk in doing it all on the same day, making for fewer trips to the gym. I know how they feel: I split my days between geometry and algebra. (c)
Q:
The game designers had deliberately given Gandhi the lowest non-zero aggression rating possible: a score of 1. Classic Gandhi. But later in the game, when all the civilizations were becoming more, well, civilized, every leader had their aggression rating dropped by two. For Gandhi, starting from 1, this calculation played out as 1 − 2 = 255, suddenly setting him to maximum aggression. Even though this error has since been fixed, later versions of the game have kept Gandhi as the most nuke-happy leader as a tradition. (с)
Q:
If you want something unlikely to occur, you simply need the patience to create enough opportunities to allow it to happen. (c)
Q:
The managers and high-up people in NASA were saying that each shuttle launch had only a one in 100,000 chance of disaster. But, to Feynman’s ears, that did not sound right. He realized it would mean there could be a shuttle launch every day for three hundred years with only one disaster. (с)
Q:
What counts as a mistake in finance? Of course, there are the obvious ones, where people simply get the numbers wrong. On 8 December 2005 the Japanese investment firm Mizuho Securities sent an order to the Tokyo Stock Exchange to sell a single share in the company J-COM Co. Ltd for ¥610,000 (around £3,000 at the time). Well, they thought they were selling one share for ¥610,000 but the person typing in the order accidentally swapped the numbers and put in an order to sell 610,000 shares for ¥1 each.
They frantically tried to cancel it, but the Tokyo Stock Exchange was proving resistant. Other firms were snapping up the discount shares and, by the time trading was suspended the following day, Mizuho Securities were looking at a minimum of ¥27 billion in losses (well over £100 million at the time). It was described as a ‘fat fingers’ error. I would have gone with something more like ‘distracted fingers’ or ‘should learn to double-check all important data entry but is probably now fired anyway fingers’.
The wake of the error was wide-reaching: confidence dropped in the Tokyo Stock Exchange as a whole, and the Nikkei Index fell 1.95 per cent in one day. Some, but not all, of the firms which bought the discount stock offered to give them back. A later ruling by the Tokyo District Court put some of the blame on the Tokyo Stock Exchange because their system did not allow Mizuho to cancel the erroneous order. This only serves to confirm my theory that everything is better with an undo button.
This is the numerical equivalent of a typo. (c)
Q:
Some of the ancient Sumerian records were written by a person seemingly named Kushim and signed off by their supervisor, Nisa. Some historians have argued that Kushim is the earliest human whose name we know. It seems the first human whose name has been passed down through millennia of history was not a ruler, a warrior or a priest … but an accountant. The eighteen existing clay tablets which are signed Kushim indicate that their job was to control the stock levels in a warehouse which held the raw materials for brewing beer. I mean, that is still a thing; a friend of mine manages a brewery and does exactly that for a living. (His name is Rich, by the way, just in case this book is one of the few objects to survive the apocalypse and he becomes the new oldest-named human.) (c)
Q:
A salami-slicing rounding-down attack was part of the plot of the 1999 film Office Space (just like Superman III). The main characters altered the computer code at a company so that, whenever interest was being calculated, instead of being rounded to the nearest penny the value would be truncated and the remaining fractions of a penny deposited into their account. Like the Vancouver Stock Exchange Index, this could theoretically carry on unnoticed as those fractions of pennies gradually added up.
Most real-world salami-slicing scams seem to use amounts greater than fractions of a penny but still operate below the threshold where people will notice and complain. One embezzler within a bank wrote software to take twenty or thirty cents out of accounts at random, never hitting the same account more than three times in a year. Two programmers in a New York firm increased the tax withheld on all company pay cheques by two cents each week but sent the money to their own tax-withholding accounts so they received it all as a tax refund at the end of the year. There are rumours that an employee of a Canadian bank implemented the interest-rounding scam to net $70,000 (and was discovered only when the bank looked for the most active account to give them an award), but I cannot find any evidence to back that up. (c)
Q:
Precision and accuracy often get jumbled together, but they are two very different things. Precision is the level of detail given, and accuracy is how true something is. I can accurately say I was born on Earth, but it’s not very precise. I can precisely say I was born at latitude 37.229N, longitude 115.811W, but that is not at all accurate. Which gives you a lot of wriggle-room when answering questions if people don’t demand that you be accurate and precise. Accurately, I can say that someone drank all the beer. Precisely, I can say that an Albanian who holds several Tetris world records drank all the beer. But I’d rather not be precise and accurate at the same time, as it may incriminate me. (c)
Q:
In 2017 it was reported that if the US switched all of its coal power production to be solar power it would save 51,999 lives every year, an oddly specific number. It clearly looks like it has not been rounded; check out all those nines! But to my eye it looks like two numbers of different sizes have been combined and have produced an unnecessary level of precision as a result. I’ve mentioned in this book that the universe is 13,800 million years old. But if you’re reading it three years after it was published, that does not mean that the universe is now 13,800,000,003 years old. Numbers with different orders of magnitude (sizes of the numbers) cannot always be added and subtracted from each other in a meaningful way.
The figure of 51,999 was the difference between lives saved not using coal and deaths caused by solar. Previous research in 2013 had established that the emissions from coal-burning power stations caused about 52,000 deaths a year. The solar photovoltaic industry was still too small to have any recorded deaths. So the researchers used statistics from the semiconductor industry (which has very similar manufacturing processes and utilizes dangerous chemicals) to estimate that solar-panel manufacture would cause one death per year. So 51,999 lives saved per year. Easy.
The problem was that the starting value of 52,000 was a rounded figure with only two significant figures and now, suddenly, it had five. I went back to the 2013 research, and the original figure was 52,200 deaths a year. And that was already a bit of a guess (for all you stats fans, the value of 52,200 had a 90 per cent confidence interval of 23,400 to 94,300). The 2013 research into coal-power deaths had rounded this figure to 52,000 but, if we un-round it back to 52,200, then solar power can save 52,199 lives! We just saved an extra two hundred people!
I can see why, for political reasons, the figure of 51,999 was used – to draw attention to the single expected death from solar-panel production and so to emphasize how safe it is. And that extra precision does make a number look more authoritative. The reduced precision in a rounded number makes them also feel less accurate, even though that is often not the case. Those zeros on the end may also be part of the precision. One in a million people will unknowingly live exactly a whole number of kilometres (door to door) from work, accurate to the nearest millimetre. (c)
Q:
In February 2017 the BBC reported a recent Office for National Statistics (ONS) report that in the last three months of 2016 ‘UK unemployment fell by 7,000 to 1.6 million people.’ But this change of seven thousand is well below what the number 1.6 million had been rounded to. Mathematician Matthew Scroggs was quick to point out that the BBC was basically saying that unemployment had gone from 1.6 million to 1.6 million. (c)
Q:
Simply telling people not to make any mistakes is a naive way to try to avoid accidents and disasters. James Reason is an Emeritus Professor of Psychology at the University of Manchester whose research is on human error. He put forward the Swiss Cheese model of disasters, which looks at the whole system, instead of focusing on individual people.
The Swiss Cheese model looks at how ‘defenses, barriers, and safeguards may be penetrated by an accident trajectory’. This accident trajectory imagines accidents as similar to a barrage of stones being thrown at a system: only the ones which make it all the way through result in a disaster. Within the system are multiple layers, each with their own defences and safeguards to slow mistakes. But each layer has holes. They are like slices of Swiss cheese.
I love this view of accident management because it acknowledges that people will inevitably make mistakes a certain percentage of the time. The pragmatic approach is to acknowledge this and build a system robust enough to filter mistakes out before they become disasters. When a disaster occurs, it is a system-wide failure and it may not be fair to find a single human to take the blame. (c)
Q:
It is my uninformed impression that in some industries, such as medicine and finance, which do tend to blame the individual, ignoring the whole system can lead to a culture of not admitting mistakes when they happen. Which, ironically, makes the system less able to deal with them. (c)
Q:
‘Plaintiff’s insistence that the commercial appears to be a serious offer requires the Court to explain why the commercial is funny. Explaining why a joke is funny is a daunting task.’ (c)
Q:
I went with my favourite method of comparing big numbers to time. We know a million, a billion and a trillion are different sizes, but we often don’t appreciate the staggering increases between them. A million seconds from now is just shy of eleven days and fourteen hours. Not so bad. I could wait that long. It’s within two weeks. A billion seconds is over thirty-one years.
A trillion seconds from now is after the year 33700CE.
Those surprising numbers actually make perfect sense after a moment’s thought. Million, billion and trillion are each a thousand times bigger than each other. A million seconds is roughly a third of a month, so a billion seconds is on the order of 330 (a third of a thousand) months. And if a billion is around thirty-one years, then of course a trillion is around 31,000 years. (c)
Q:
Even after a lifetime of education dealing with small numbers there is a vestigial instinct that larger numbers are logarithmic; that the gap between a trillion and a billion feels about the same as the jump between a million and a billion – because both are a thousand times bigger. In reality, the jump to a trillion is much bigger: the difference between living to your early thirties and a time when humankind may no longer exist. (c)
Q:
I believe that ‘regardless of flight phase’ is official FAA speak for ‘This could go down mid-flight.’ Their official line on airworthiness was the requirement of ‘repetitive maintenance tasks for electrical power deactivation’. That is to say, anyone with a Boeing 787 had to remember to turn it off and on again. (с)
Q:
A political committee is rarely a good solution to a mathematical problem. (c)
Q:
To get everything back into alignment in the first place, the year 46BCE had a possible-world-record 445 days. (c)
Q:
The building at 20 Fenchurch Street in London … By all measures, it’s a successful building. Except, during the summer of 2013, it started setting things on fire. …
The exterior of the building was designed by architect Rafael Viñoly to have a sweeping curve, but this meant that all the reflective glass windows accidentally became a massive concave mirror – a kind of giant lens in the sky able to focus sunlight on a tiny area. It’s not often sunny in London, but when a sun-filled day in summer 2013 lined up with the recently completed windows, a death heat-ray swept across London.
Okay, it wasn’t that bad. But it was producing temperatures of around 90°C, which was enough to scorch the doormat at a nearby barber’s shop. A parked car was a bit melted and someone claimed it burned their lemon (that’s not cockney rhyming slang; it was an actual lemon). A local reporter with a flair for the dramatic took the opportunity to fry some eggs by placing a pan in the hotspot. (c)
Q:
In July 2011 a thirty-nine-storey shopping centre in South Korea had to be evacuated because resonance was vibrating the building. People at the top of the building felt it start to shake, as if someone had banged the bass and turned up the treble. Which was exactly the problem. After the official investigation had ruled out an earthquake, they found the culprit was an exercise class on the twelfth floor.
On 5 July 2011 they had decided to work out to Snap’s ‘The Power’, and everyone jumped around harder than they usually did. Could the rhythm of ‘The Power’ match a resonant frequency of the building? During the investigation, about twenty people were crammed back into that room to recreate the exercise class and, sure enough, they did have the power. When the exercise class on the twelfth floor had ‘The Power’, the thirty-eighth floor started shaking around ten times more than it normally did. (c)
Q:
When it was reopened, the Millennium Bridge was described as ‘probably the most complex passively-damped structure in the world’. Not an epithet most of us would aspire to. (c)
Q:
… British engineers prided themselves on their stiff upper bridges. (c)
Q:
Obviously, we should do whatever we can to avoid engineering mistakes, but when engineers are pushing the boundaries of what is possible, occasionally a new aspect of mathematical behaviour will unexpectedly emerge. Sometimes the addition of a little bit more mass is all it takes to change the mathematics of how a structure behaves.
This is a common theme in human progress. We make things beyond what we understand, and we always have done. …
When theory lags behind application, there will always be mathematical surprises lying in wait. The important thing is that we learn from these inevitable mistakes and don’t repeat them. (c)
Q:
In the mid-1990s a new employee of Sun Microsystems in California kept disappearing from their database. Every time his details were entered, the system seemed to eat him whole; he would disappear without a trace. No one in HR could work out why poor Steve Null was database kryptonite. (c)
Q:
Carrying on in the same vein as Steve Null, I’d like you to meet Brian Test, Avery Blank and Jeff Sample. The Null problem can be fixed by encoding names in a format for only character data, so that it doesn’t get confused with the data value of NULL. But Avery Blank has a bigger problem: humans.
When Avery Blank was at law school she had difficulty getting an internship because her applications were not taken seriously. People would see ‘Blank’ in the surname field and assume it was an incomplete application. She always had to get in touch and convince the selection committee that she was a real human.
Brian Test and Jeff Sample fell foul of the same problem, but for slightly different reasons. When you set up a new database, or a way to input data, it’s good practice to test it and make sure it’s all working. So you feed through some dummy data to check the pipeline. I run a lot of projects with schools, and they often sign up online. I’ve just opened my most recent such database and scrolled to the top. The first entry is from a Ms Teacher who works at Test High School on Test Road in the county of Fakenham. She’s probably a relation of Mr Teacher from St Fakington’s Grammar School, who seems to sign up for everything I do.
To avoid being deleted as unwanted test data, when Brian Test started a new job, he brought in a cake for all his new colleagues to enjoy. Printed on the cake was a picture of his face, with the following words written in icing: ‘I’m Brian Test and I’m real.’ Like a lot of office problems, the issue was solved with free cake, and he was not deleted again. (c)
Q:
So, when it comes to names, if you inherit a database-killing last name, you can either wear it as a badge of honour or take some deed-poll action. But if you are a parent, please don’t give your child a first name which will set them up for a lifetime of battling computers. And given that over three hundred children in the USA since 1990 have been named Abcde, it’s worth spelling this out: don’t name your child anything like Fake, Null or DECLARE. (c)
Q:
In Los Angeles there is a block of land on the corner of West 1st Street and South Spring Street which houses the offices of the LA Times. It is just down the street from City Hall and directly over the road from the LA Police Department. There may be some rough areas of LA best avoided by tourists, but this is certainly not one of them. The area looks as safe as safe can be … until you check the LAPD’s online map of reported crime locations. Between October 2008 and March 2009 there were 1,380 crimes on that block. That’s around 4 per cent of all crimes marked on the map.
When the LA Times noticed this, it politely asked the LAPD what was going on. … If the computer is unable to work out the location, it simply logs the default location for Los Angeles: the front doorstep of the LAPD headquarters. (c)
Q:
Whenever a computer cannot decipher a location, it still has to fill something in, and so 0,0 became the default location. The island where bad data goes to die. (c)
Q:
For a start, just because something walks like a number and quacks like a number does not mean it is a number. (c)
Q:
For generations, cartographers have been sneaking fictitious places into real maps (often as a way to expose people plagiarizing their work), and it was inevitable that Null Island would take on a life of its own. So, they literally put it on the map. (c)
Q:
So the signs remain incorrect. But at least now I have a framed letter from the UK government saying that they don’t think accurate maths is important and they don’t believe street signs should have to follow the laws of geometry. (c)
Q:
Never put ‘teamwork cogs’ as a search term into a stock image website. For a start, if you’re not used to the cheese-tastic world of inspirational work posters, what you see will come as a shock. The next shock is that a lot of the diagrams supposed to be showing a team working like a well-oiled machine use a mechanism which would be permanently seized in place. …
The longer I think about it, the more I’m convinced that this does actually make a great analogy for workplace teamwork. (c)
Q:
I don’t complain that Picasso’s works are biologically implausible or send Salvador Dalí angry letters about the melting point of clocks. (c)
Q:
It seems they used to do their upper- and lower-body workouts on alternate days but now, due to a lack of time, they wanted to know if there was any risk in doing it all on the same day, making for fewer trips to the gym. I know how they feel: I split my days between geometry and algebra. (c)
Q:
The game designers had deliberately given Gandhi the lowest non-zero aggression rating possible: a score of 1. Classic Gandhi. But later in the game, when all the civilizations were becoming more, well, civilized, every leader had their aggression rating dropped by two. For Gandhi, starting from 1, this calculation played out as 1 − 2 = 255, suddenly setting him to maximum aggression. Even though this error has since been fixed, later versions of the game have kept Gandhi as the most nuke-happy leader as a tradition. (с)
Q:
If you want something unlikely to occur, you simply need the patience to create enough opportunities to allow it to happen. (c)
Q:
The managers and high-up people in NASA were saying that each shuttle launch had only a one in 100,000 chance of disaster. But, to Feynman’s ears, that did not sound right. He realized it would mean there could be a shuttle launch every day for three hundred years with only one disaster. (с)
Q:
What counts as a mistake in finance? Of course, there are the obvious ones, where people simply get the numbers wrong. On 8 December 2005 the Japanese investment firm Mizuho Securities sent an order to the Tokyo Stock Exchange to sell a single share in the company J-COM Co. Ltd for ¥610,000 (around £3,000 at the time). Well, they thought they were selling one share for ¥610,000 but the person typing in the order accidentally swapped the numbers and put in an order to sell 610,000 shares for ¥1 each.
They frantically tried to cancel it, but the Tokyo Stock Exchange was proving resistant. Other firms were snapping up the discount shares and, by the time trading was suspended the following day, Mizuho Securities were looking at a minimum of ¥27 billion in losses (well over £100 million at the time). It was described as a ‘fat fingers’ error. I would have gone with something more like ‘distracted fingers’ or ‘should learn to double-check all important data entry but is probably now fired anyway fingers’.
The wake of the error was wide-reaching: confidence dropped in the Tokyo Stock Exchange as a whole, and the Nikkei Index fell 1.95 per cent in one day. Some, but not all, of the firms which bought the discount stock offered to give them back. A later ruling by the Tokyo District Court put some of the blame on the Tokyo Stock Exchange because their system did not allow Mizuho to cancel the erroneous order. This only serves to confirm my theory that everything is better with an undo button.
This is the numerical equivalent of a typo. (c)
Q:
Some of the ancient Sumerian records were written by a person seemingly named Kushim and signed off by their supervisor, Nisa. Some historians have argued that Kushim is the earliest human whose name we know. It seems the first human whose name has been passed down through millennia of history was not a ruler, a warrior or a priest … but an accountant. The eighteen existing clay tablets which are signed Kushim indicate that their job was to control the stock levels in a warehouse which held the raw materials for brewing beer. I mean, that is still a thing; a friend of mine manages a brewery and does exactly that for a living. (His name is Rich, by the way, just in case this book is one of the few objects to survive the apocalypse and he becomes the new oldest-named human.) (c)
Q:
A salami-slicing rounding-down attack was part of the plot of the 1999 film Office Space (just like Superman III). The main characters altered the computer code at a company so that, whenever interest was being calculated, instead of being rounded to the nearest penny the value would be truncated and the remaining fractions of a penny deposited into their account. Like the Vancouver Stock Exchange Index, this could theoretically carry on unnoticed as those fractions of pennies gradually added up.
Most real-world salami-slicing scams seem to use amounts greater than fractions of a penny but still operate below the threshold where people will notice and complain. One embezzler within a bank wrote software to take twenty or thirty cents out of accounts at random, never hitting the same account more than three times in a year. Two programmers in a New York firm increased the tax withheld on all company pay cheques by two cents each week but sent the money to their own tax-withholding accounts so they received it all as a tax refund at the end of the year. There are rumours that an employee of a Canadian bank implemented the interest-rounding scam to net $70,000 (and was discovered only when the bank looked for the most active account to give them an award), but I cannot find any evidence to back that up. (c)
Q:
Precision and accuracy often get jumbled together, but they are two very different things. Precision is the level of detail given, and accuracy is how true something is. I can accurately say I was born on Earth, but it’s not very precise. I can precisely say I was born at latitude 37.229N, longitude 115.811W, but that is not at all accurate. Which gives you a lot of wriggle-room when answering questions if people don’t demand that you be accurate and precise. Accurately, I can say that someone drank all the beer. Precisely, I can say that an Albanian who holds several Tetris world records drank all the beer. But I’d rather not be precise and accurate at the same time, as it may incriminate me. (c)
Q:
In 2017 it was reported that if the US switched all of its coal power production to be solar power it would save 51,999 lives every year, an oddly specific number. It clearly looks like it has not been rounded; check out all those nines! But to my eye it looks like two numbers of different sizes have been combined and have produced an unnecessary level of precision as a result. I’ve mentioned in this book that the universe is 13,800 million years old. But if you’re reading it three years after it was published, that does not mean that the universe is now 13,800,000,003 years old. Numbers with different orders of magnitude (sizes of the numbers) cannot always be added and subtracted from each other in a meaningful way.
The figure of 51,999 was the difference between lives saved not using coal and deaths caused by solar. Previous research in 2013 had established that the emissions from coal-burning power stations caused about 52,000 deaths a year. The solar photovoltaic industry was still too small to have any recorded deaths. So the researchers used statistics from the semiconductor industry (which has very similar manufacturing processes and utilizes dangerous chemicals) to estimate that solar-panel manufacture would cause one death per year. So 51,999 lives saved per year. Easy.
The problem was that the starting value of 52,000 was a rounded figure with only two significant figures and now, suddenly, it had five. I went back to the 2013 research, and the original figure was 52,200 deaths a year. And that was already a bit of a guess (for all you stats fans, the value of 52,200 had a 90 per cent confidence interval of 23,400 to 94,300). The 2013 research into coal-power deaths had rounded this figure to 52,000 but, if we un-round it back to 52,200, then solar power can save 52,199 lives! We just saved an extra two hundred people!
I can see why, for political reasons, the figure of 51,999 was used – to draw attention to the single expected death from solar-panel production and so to emphasize how safe it is. And that extra precision does make a number look more authoritative. The reduced precision in a rounded number makes them also feel less accurate, even though that is often not the case. Those zeros on the end may also be part of the precision. One in a million people will unknowingly live exactly a whole number of kilometres (door to door) from work, accurate to the nearest millimetre. (c)
Q:
In February 2017 the BBC reported a recent Office for National Statistics (ONS) report that in the last three months of 2016 ‘UK unemployment fell by 7,000 to 1.6 million people.’ But this change of seven thousand is well below what the number 1.6 million had been rounded to. Mathematician Matthew Scroggs was quick to point out that the BBC was basically saying that unemployment had gone from 1.6 million to 1.6 million. (c)
Q:
Simply telling people not to make any mistakes is a naive way to try to avoid accidents and disasters. James Reason is an Emeritus Professor of Psychology at the University of Manchester whose research is on human error. He put forward the Swiss Cheese model of disasters, which looks at the whole system, instead of focusing on individual people.
The Swiss Cheese model looks at how ‘defenses, barriers, and safeguards may be penetrated by an accident trajectory’. This accident trajectory imagines accidents as similar to a barrage of stones being thrown at a system: only the ones which make it all the way through result in a disaster. Within the system are multiple layers, each with their own defences and safeguards to slow mistakes. But each layer has holes. They are like slices of Swiss cheese.
I love this view of accident management because it acknowledges that people will inevitably make mistakes a certain percentage of the time. The pragmatic approach is to acknowledge this and build a system robust enough to filter mistakes out before they become disasters. When a disaster occurs, it is a system-wide failure and it may not be fair to find a single human to take the blame. (c)
Q:
It is my uninformed impression that in some industries, such as medicine and finance, which do tend to blame the individual, ignoring the whole system can lead to a culture of not admitting mistakes when they happen. Which, ironically, makes the system less able to deal with them. (c)
October 11, 2021
No es un libro sobre errores matemáticos, y menos sobre errores matemáticos que hayan causado accidentes, o, al menos, yo no he sabido interpretarlo así (aunque haberlos, haylos). Lo que sí me ha quedado claro es que los humanos, desde programadores hasta arquitectos, han de poner sumo cuidado en la elaboración de sus tareas, y no obviar que las matemáticas están ahí para hacernos la vida más fácil. No hacerlo (prestar la suficiente atención), puede derivar en poner en riesgo vidas humanas, y el autor nos muestra algunos ejemplos sobre ello. Pero se enrolla en demasía en asuntos que se me escapan (quede claro que yo soy de letras) consiguiendo con ello que mi mente se escabulla hacia algún otro lugar, lejos de las páginas. Supongo que ha querido dirigir su producto hacia un público más versado en el tema, y es comprensible.
También se me ha escapado parte de su contenido “humorístico”, pero creo que es achacable a que el autor y yo hablamos distintos idiomas (tanto literarios como mentales). En más de una ocasión me ha ocurrido estar bromeando con amigos no muy diferentes al escritor (léase freakis de las matemáticas). Las bromas de uno y de otro rebotaban en alguna especie de muro invisible, y al final cada uno acababa riéndose de sus propios chistes, sin pillar los del otro. ¡Créanme que es más gracioso contarlo que vivirlo!
En cualquier caso, solo espero que la próxima vez que tenga que coger un vuelo, o depender de alguna “maquinita” para la administración de alguna terapia, o incluso cruzar un puente ya sea en coche o caminando, los encargados de poner a punto dichos aparatos y/u obras hayan prestado atención a su trabajo, y que hayan tenido todos los suministros necesarios (¡sin escatimar en gastos!). Y que su sueldo sea proporcional con el de sus estudios matemáticos. Ah, y que no tengan sueño. ¡Y a quién Dios se la dé, San Pedro se la bendiga!
También se me ha escapado parte de su contenido “humorístico”, pero creo que es achacable a que el autor y yo hablamos distintos idiomas (tanto literarios como mentales). En más de una ocasión me ha ocurrido estar bromeando con amigos no muy diferentes al escritor (léase freakis de las matemáticas). Las bromas de uno y de otro rebotaban en alguna especie de muro invisible, y al final cada uno acababa riéndose de sus propios chistes, sin pillar los del otro. ¡Créanme que es más gracioso contarlo que vivirlo!
En cualquier caso, solo espero que la próxima vez que tenga que coger un vuelo, o depender de alguna “maquinita” para la administración de alguna terapia, o incluso cruzar un puente ya sea en coche o caminando, los encargados de poner a punto dichos aparatos y/u obras hayan prestado atención a su trabajo, y que hayan tenido todos los suministros necesarios (¡sin escatimar en gastos!). Y que su sueldo sea proporcional con el de sus estudios matemáticos. Ah, y que no tengan sueño. ¡Y a quién Dios se la dé, San Pedro se la bendiga!
October 14, 2023
Humble Pi: A Comedy of Maths Errors started off with a bang for me. Autor, Matt Parker, intentionally put the pages in reverse order, so that as you read the book, the page number decreases rather than increases. The first story is about the Pepsi points contest where you could win a Harrier (military) jet if you were able to get 7 million Pepsi points. There is a fabulous Netflix documentary about this contest that I highly recommend; it's called Pepsi, Where's My Jet.
The book shares other mathematical situations where innovation outpaced the math calculations and tragedy occurred. In 1940, the Tacoma Narrows Bridge was nicknamed Galloping Gertie and it collapsed four months after being built. It was built cheap and sleek but didn't factor in aerodynamic flutter. Walkways built in a Kansas City Hyatt collapsed when the length of the bolts were tweaked; the collapse caused 114 deaths.
Humble Pi: A Comedy of Maths Errors highlights how mathematical mistakes can have dramatic consequences.
Although the book started off with a bang, it progressed to a whimper and didn't hold my attention in the same way it had in the beginning.
The book shares other mathematical situations where innovation outpaced the math calculations and tragedy occurred. In 1940, the Tacoma Narrows Bridge was nicknamed Galloping Gertie and it collapsed four months after being built. It was built cheap and sleek but didn't factor in aerodynamic flutter. Walkways built in a Kansas City Hyatt collapsed when the length of the bolts were tweaked; the collapse caused 114 deaths.
Humble Pi: A Comedy of Maths Errors highlights how mathematical mistakes can have dramatic consequences.
Although the book started off with a bang, it progressed to a whimper and didn't hold my attention in the same way it had in the beginning.
May 26, 2019
Summary: not very interesting, and it's not about maths errors.
This book is a collection of anecdotes that you can read anywhere: most of them I had read before, and you can find them on the internet, too. They're bundled by theme here, which is convenient, but the writer tries too hard to make them appear connected, and more often than not that results in uninspired paragraphs. Here's an example from a random page:
"But what happens when computers try to divide by zero? Unless they've been explicitly told that they can't divide by zero, they naively give it a go. And the results can be terrifying."
You can almost hear that in that slick documentary voice-over style, where everything spells doom: "Will the team find a way out, ... or will they fail?" And in this case (really, I picked a random page), the writer is wrong. There has been no "naively" dividing by zero for quite some time now. What happens is well defined, and in many languages requires explicit handling. There are more cases where the writer follows this loose, "journalistic" style, almost as if he expects the reader would lose interest without such casual segues.
And that leads me to the next problem: most of the book is not about math errors. Instead, it's about not understanding or not properly modelling the subject matter (physics mostly), not measuring correctly, and not implementing properly. And quite a bit of text is dedicated to explaining probability calculus. Only a small part is about actual mathematical errors.
So, if you want some entertaining reading with a technical streak, this can be your book, provided you've never read about the Challenger report, and don't know anything about collapsing bridges or programming errors that crash rockets. Otherwise, you might want to look for something else.
This book is a collection of anecdotes that you can read anywhere: most of them I had read before, and you can find them on the internet, too. They're bundled by theme here, which is convenient, but the writer tries too hard to make them appear connected, and more often than not that results in uninspired paragraphs. Here's an example from a random page:
"But what happens when computers try to divide by zero? Unless they've been explicitly told that they can't divide by zero, they naively give it a go. And the results can be terrifying."
You can almost hear that in that slick documentary voice-over style, where everything spells doom: "Will the team find a way out, ... or will they fail?" And in this case (really, I picked a random page), the writer is wrong. There has been no "naively" dividing by zero for quite some time now. What happens is well defined, and in many languages requires explicit handling. There are more cases where the writer follows this loose, "journalistic" style, almost as if he expects the reader would lose interest without such casual segues.
And that leads me to the next problem: most of the book is not about math errors. Instead, it's about not understanding or not properly modelling the subject matter (physics mostly), not measuring correctly, and not implementing properly. And quite a bit of text is dedicated to explaining probability calculus. Only a small part is about actual mathematical errors.
So, if you want some entertaining reading with a technical streak, this can be your book, provided you've never read about the Challenger report, and don't know anything about collapsing bridges or programming errors that crash rockets. Otherwise, you might want to look for something else.
November 6, 2020
A delightful, funny, and low stakes way to enjoy the world of “maths.” Chock full of errors—ranging from program bugs to engineering mishaps to faulty Excel formulas to weird rounding mistakes—in Humble Pi, Matt Parker introduces the kind of math mistakes that can afflict the hoi polloi and rankle the experts too!
Matt Parker’s narration of the audiobook made this one even more fun to listen to. I found plenty of humor in his very drawn out rendition of “0.00000000000000000000000000167.” There are bountiful opportunities for him to narrate very large and tiny numbers without using scientific notation, and I personally found this fun. For all those who (realistically) would be annoyed rather than gently amused, I would probably pick up the hard copy instead.
Each chapter houses its own topic that is largely unrelated from one to the next, and various pieces of trivia are launched with Parker’s witty commentary for some interesting discussion. For example, computers using a signed 32-bit counting system to track time will no longer be able to 2,147,483,647 seconds later from the start of 1970 (at which point in 2038, who knows whether the world will have fully chucked out computers forphones tinier gadgets). Or based on the Affordable Care Act’s 3x maximum cap on older individuals’ insurance premiums, the Trump Administration tried to argue that older customers could be charged 3.49x as much. Yunno, because 3.49 ‘rounds down’ to 3. That failed, but yeah, nice try.
Doing math can often be in turns maddening or tiresome. For the average folk, we never fully manage to put a finger on the utility of an integral or the need to prove that an isosceles triangle has two same sides (can’t I just believe it, 8th grade Geometry teacher!?!!?). But for all the chuckles we can derive from laughing at silly mistakes, Matt Parker shows the rampant fallibility in our application of maths, hounding the gambler to the government official to the bridge engineer and certainly to us. Careful counting matters more than ever right now, and we should be wary of math errors—at the very least, Humble Pi offers a useful distraction to seeing numbers other than that everlasting tally for the election.
Matt Parker’s narration of the audiobook made this one even more fun to listen to. I found plenty of humor in his very drawn out rendition of “0.00000000000000000000000000167.” There are bountiful opportunities for him to narrate very large and tiny numbers without using scientific notation, and I personally found this fun. For all those who (realistically) would be annoyed rather than gently amused, I would probably pick up the hard copy instead.
Each chapter houses its own topic that is largely unrelated from one to the next, and various pieces of trivia are launched with Parker’s witty commentary for some interesting discussion. For example, computers using a signed 32-bit counting system to track time will no longer be able to 2,147,483,647 seconds later from the start of 1970 (at which point in 2038, who knows whether the world will have fully chucked out computers for
Doing math can often be in turns maddening or tiresome. For the average folk, we never fully manage to put a finger on the utility of an integral or the need to prove that an isosceles triangle has two same sides (can’t I just believe it, 8th grade Geometry teacher!?!!?). But for all the chuckles we can derive from laughing at silly mistakes, Matt Parker shows the rampant fallibility in our application of maths, hounding the gambler to the government official to the bridge engineer and certainly to us. Careful counting matters more than ever right now, and we should be wary of math errors—at the very least, Humble Pi offers a useful distraction to seeing numbers other than that everlasting tally for the election.
Read
March 22, 2022Entertaining non fic with plenty of stries of maths going wrong in the real world. You know the sort of thing: makes excellent airplane reading except for the number of stories involving airplane crashes. Highly readable and lots of good jokes.
July 19, 2021
This is a book for nerds: math, science, and engineering nerds. I loved it. I was mesmerized.
Mr. Parker examines the relationship humans have with math and what happens when we mess up. The mistakes he describes are fascinating in how they came about. He doesn’t seek to shame anyone. He has an attitude that we all make mistakes and we’re all in this together. A lot of the mistakes are in programming code. He covers calendars and timekeeping, probability, randomness, the effects of rounding, and errors in units.
And just for fun, the page numbers count down instead of up.
He points out how our society punishes mistakes, so we keep them secret and don’t share them. This mean a drug trial may be done over and over without success because the failures are never published, or engineering errors may be repeated a number of times. Employees will cover up their mistakes and not report them. This is a dangerous attitude.
A million seconds from now is just shy of eleven days and fourteen hours. Not so bad. I could wait that long. It’s within two weeks. A billion seconds is over thirty-one years. A trillion seconds from now is after the year 33,700 CE.
If you ever have access to a friend’s phone, go into the settings and change their calendar to the Buddhist one. Suddenly, they’re living in the 2560s. Maybe try to convince them they have just woken up from a coma.
Clean content. (Some deaths from engineering disasters are mentioned.)
Mr. Parker examines the relationship humans have with math and what happens when we mess up. The mistakes he describes are fascinating in how they came about. He doesn’t seek to shame anyone. He has an attitude that we all make mistakes and we’re all in this together. A lot of the mistakes are in programming code. He covers calendars and timekeeping, probability, randomness, the effects of rounding, and errors in units.
And just for fun, the page numbers count down instead of up.
He points out how our society punishes mistakes, so we keep them secret and don’t share them. This mean a drug trial may be done over and over without success because the failures are never published, or engineering errors may be repeated a number of times. Employees will cover up their mistakes and not report them. This is a dangerous attitude.
A million seconds from now is just shy of eleven days and fourteen hours. Not so bad. I could wait that long. It’s within two weeks. A billion seconds is over thirty-one years. A trillion seconds from now is after the year 33,700 CE.
If you ever have access to a friend’s phone, go into the settings and change their calendar to the Buddhist one. Suddenly, they’re living in the 2560s. Maybe try to convince them they have just woken up from a coma.
Clean content. (Some deaths from engineering disasters are mentioned.)
April 5, 2021
This is a marvelous book about all the ways that math errors can infiltrate our day-to-day living. Some of the math errors are just fun (as in older arcade games), while others have life-or-death consequences (like airplanes running out of fuel mid-flight).
Some of the math errors are simply a confusion about units; feet/meters, pounds/kilograms, and so on. One such error was when a jet liner was loaded up with fuel in pounds, instead of kilograms. Luckily, there was a mid-flight landing and refueling. Unluckily, the refueling made the same identical mistake. Luckily, the pilot had experience piloting glider planes! An emergency landing at an abandoned airstrip without engines or power or electricity for the landing gear -- surprised a drag racing party!
Sometimes, a change in versions of equipment or software cause problems when an only partial compatibility is encountered. Sometimes, limited storage for variables (say, 32-bit instead of 64-bit) cause issues when numbers that are expected to be small actually overrun the storage. This happened to the Patriot Missiles that were deployed to protect against incoming missiles during the Desert Storm operation.
Misplaced decimals, misunderstood calculator quirks, bridges and buildings that resonate at unfortunate frequencies, and everyday folk who lack the understanding of how to divide numbers with units, make up many of the fascinating anecdotes in this book.
Matt Parker is an Australian mathematician with a delightful sense of humor. The book is never overly technical--just enough mathematics or engineering background is introduced, to allow an understanding of each episode in the book. Oh--and I did not read this book. I listened to the audiobook, as read by the author. It is absolutely wonderful!
Some of the math errors are simply a confusion about units; feet/meters, pounds/kilograms, and so on. One such error was when a jet liner was loaded up with fuel in pounds, instead of kilograms. Luckily, there was a mid-flight landing and refueling. Unluckily, the refueling made the same identical mistake. Luckily, the pilot had experience piloting glider planes! An emergency landing at an abandoned airstrip without engines or power or electricity for the landing gear -- surprised a drag racing party!
Sometimes, a change in versions of equipment or software cause problems when an only partial compatibility is encountered. Sometimes, limited storage for variables (say, 32-bit instead of 64-bit) cause issues when numbers that are expected to be small actually overrun the storage. This happened to the Patriot Missiles that were deployed to protect against incoming missiles during the Desert Storm operation.
Misplaced decimals, misunderstood calculator quirks, bridges and buildings that resonate at unfortunate frequencies, and everyday folk who lack the understanding of how to divide numbers with units, make up many of the fascinating anecdotes in this book.
Matt Parker is an Australian mathematician with a delightful sense of humor. The book is never overly technical--just enough mathematics or engineering background is introduced, to allow an understanding of each episode in the book. Oh--and I did not read this book. I listened to the audiobook, as read by the author. It is absolutely wonderful!
September 7, 2021
This is billed as a book about when theory bumps up against the real world. I found it more about when the wrong mathematics is chosen rather than when mathematics is done wrongly.
There are plenty of examples to amuse, shock and confound. There is one section called “If the Data Fits” that I will note specifically. Parker is making an important point about how the advent of the computer would make data-processing so much easier. He uses as an example how the U.S. Air Force tried in the 1950s to improve its flight suits. He discusses how over 4,000 personnel were each measured for 132 characteristics. These data were then “computed for the mean, the standard deviation, the standard deviation as a percentage of the mean, the range, and twenty-five different percentile values” The conclusion: There was no “average man.” And, not one of the over 4,000 men measured got a good fit in the “standard (average) uninform.” Parker over-reaches a bit in this section when he describes the cockpits of WW II aircraft as roomy. I don’t believe that the USA’s major fighter aircraft were “roomy” at all. Many potential pilots had difficulty with the space in a P-38 or P-51.
I couldn’t read the book straight through….just too much similarity. But, taken in small doses it captured my interest.
Highly entertaining. 3.5*
There are plenty of examples to amuse, shock and confound. There is one section called “If the Data Fits” that I will note specifically. Parker is making an important point about how the advent of the computer would make data-processing so much easier. He uses as an example how the U.S. Air Force tried in the 1950s to improve its flight suits. He discusses how over 4,000 personnel were each measured for 132 characteristics. These data were then “computed for the mean, the standard deviation, the standard deviation as a percentage of the mean, the range, and twenty-five different percentile values” The conclusion: There was no “average man.” And, not one of the over 4,000 men measured got a good fit in the “standard (average) uninform.” Parker over-reaches a bit in this section when he describes the cockpits of WW II aircraft as roomy. I don’t believe that the USA’s major fighter aircraft were “roomy” at all. Many potential pilots had difficulty with the space in a P-38 or P-51.
I couldn’t read the book straight through….just too much similarity. But, taken in small doses it captured my interest.
Highly entertaining. 3.5*
February 15, 2020
I really enjoyed this book!
I'm one of those people who got labelled "bad at math" at a young age because I struggled with arithmetic (and still do). That resulted in my getting handed a lot of books of "math is fun!" type puzzles when I was a kid, which were definitely much more fun than math class. I learned to differentiate "math" from "arithmetic" and stubbornly took math classes up through calculus, which was fascinating, but which I've sadly never had any occasion to put to use. To make this long story short, I recommend this book to people who think they hate math or who found/find math difficult, as well as technically-inclined types who use math all the time.
The topics covered in this book are wide-ranging, and a lot of them are things you might not even think of as being mathematical (putting a padlock on a door properly, for instance, or people with names that get ignored by computer code). Matt Parker's voice is witty without ever talking down to his audience. He just really loves anything even tangentially mathematical, and loves sharing it with everyone else. And this book made me laugh out loud many times! It's possibly all nerd humor, but it was great.
There are three math errors in this book which I did not catch (but also didn't look for very hard). So this book has a math game in it! Also, it's numbered backwards, which made it tricky to track my process through it here, since Goodreads won't let you update to Page 141 when you started on Page 316. There's also a trick to the index that I didn't figure out (but the index is worth reading for itself, as well). I may reread this sometime and actually try to find the errors and solve the indexing. But there was a waiting list for it at the library, so I zoomed it back as soon as I finished it.
This is some of the most fun I've had reading in quite a while. So seriously, even if your knee-jerk reaction is to recoil in horror from the thought of reading a math book, try it anyway.
I'm one of those people who got labelled "bad at math" at a young age because I struggled with arithmetic (and still do). That resulted in my getting handed a lot of books of "math is fun!" type puzzles when I was a kid, which were definitely much more fun than math class. I learned to differentiate "math" from "arithmetic" and stubbornly took math classes up through calculus, which was fascinating, but which I've sadly never had any occasion to put to use. To make this long story short, I recommend this book to people who think they hate math or who found/find math difficult, as well as technically-inclined types who use math all the time.
The topics covered in this book are wide-ranging, and a lot of them are things you might not even think of as being mathematical (putting a padlock on a door properly, for instance, or people with names that get ignored by computer code). Matt Parker's voice is witty without ever talking down to his audience. He just really loves anything even tangentially mathematical, and loves sharing it with everyone else. And this book made me laugh out loud many times! It's possibly all nerd humor, but it was great.
There are three math errors in this book which I did not catch (but also didn't look for very hard). So this book has a math game in it! Also, it's numbered backwards, which made it tricky to track my process through it here, since Goodreads won't let you update to Page 141 when you started on Page 316. There's also a trick to the index that I didn't figure out (but the index is worth reading for itself, as well). I may reread this sometime and actually try to find the errors and solve the indexing. But there was a waiting list for it at the library, so I zoomed it back as soon as I finished it.
This is some of the most fun I've had reading in quite a while. So seriously, even if your knee-jerk reaction is to recoil in horror from the thought of reading a math book, try it anyway.
August 10, 2022
A GR friend of mine wrote in his review that this is cotton candy for the mind. I'd give it higher marks, but I understand his point. This book is fun, well narrated, & probably informative to those without much experience with math, the history of engineering disasters, & computer programming. I'm not particularly well versed in these subjects, but I recognized many (most) immediately. Still, if you're not familiar with any of that, this would be eye-opening. It's probably a good book for the under 30 crowd down to teens, maybe even somewhat younger.
I liked his point about blame. We want to find a villain in every disaster, but often they were well meaning people who were working at the edge of our knowledge or it was a committee failure. A little larger or heavier construct suddenly passes a limit where previously minor problems become major ones or add up in odd ways. Many of our projects are too complex for anyone to have a full grasp of all the parts &/or market/political forces overshadowed a dire warning. It's instructive, sad, & all too common.
He spent a little too much time with exact, very large numbers which I pretty much ignored since I listened to the audiobook. An exact number in the millions is meaningless to me & everyone else except in very specific situations & this book wasn't one. That's why we have significant digits & scientific notation, a point he made, but could have done better, IMO. He's too young to remember the days of the slide rule. He mentions them, but doesn't really have a feel for them & the way they shaped our thinking since he grew up with calculators & computers, but his example of the increase in numbers is one I use constantly, too.
1,000 seconds = about 17 minutes
1 million seconds = about 12 days
1 billion seconds = about 32 years
1 trillion seconds = about 32,000 years
I can't grasp the last in any personal sense, but this helps me keep some perspective when dealing with large numbers.
His narration was excellent & there was enough humor to keep it interesting. Still, it was simple enough that if I zoned out for a few minutes, I didn't really miss anything. I'll give it 4 stars & recommend it to most with the above reservations.
I liked his point about blame. We want to find a villain in every disaster, but often they were well meaning people who were working at the edge of our knowledge or it was a committee failure. A little larger or heavier construct suddenly passes a limit where previously minor problems become major ones or add up in odd ways. Many of our projects are too complex for anyone to have a full grasp of all the parts &/or market/political forces overshadowed a dire warning. It's instructive, sad, & all too common.
He spent a little too much time with exact, very large numbers which I pretty much ignored since I listened to the audiobook. An exact number in the millions is meaningless to me & everyone else except in very specific situations & this book wasn't one. That's why we have significant digits & scientific notation, a point he made, but could have done better, IMO. He's too young to remember the days of the slide rule. He mentions them, but doesn't really have a feel for them & the way they shaped our thinking since he grew up with calculators & computers, but his example of the increase in numbers is one I use constantly, too.
1,000 seconds = about 17 minutes
1 million seconds = about 12 days
1 billion seconds = about 32 years
1 trillion seconds = about 32,000 years
I can't grasp the last in any personal sense, but this helps me keep some perspective when dealing with large numbers.
His narration was excellent & there was enough humor to keep it interesting. Still, it was simple enough that if I zoned out for a few minutes, I didn't really miss anything. I'll give it 4 stars & recommend it to most with the above reservations.
December 11, 2018
I love maths. I enjoy finding out about mathematical and statistical errors. I was thinking some of my maths teacher friends might enjoy it and find it useful for illustrations in class. Thats where the plot breaks down a little.
I enjoyed the book but was a little disappointed that so much was taken from fields of computing and engineering, where the issue wasn't strictly a mathematical failure, but a failure, for example, to understand the limits of binary, or load-bearing, or resonant frequency. Many of the examples could easily have found themselves in books subtitled "A Comedy of Engineering Errors" or "A Comedy of Programming Errors"
The book is fine if you are looking for a book that shows how mathematics in its many practical applications goes wrong. Having said that there are chapters that are more maths/number/statistics oriented than others. But not as many as I would have liked.
The book is reasonably well written, but a few too many asides to the reader for my liking.
I enjoyed the book but was a little disappointed that so much was taken from fields of computing and engineering, where the issue wasn't strictly a mathematical failure, but a failure, for example, to understand the limits of binary, or load-bearing, or resonant frequency. Many of the examples could easily have found themselves in books subtitled "A Comedy of Engineering Errors" or "A Comedy of Programming Errors"
The book is fine if you are looking for a book that shows how mathematics in its many practical applications goes wrong. Having said that there are chapters that are more maths/number/statistics oriented than others. But not as many as I would have liked.
The book is reasonably well written, but a few too many asides to the reader for my liking.
April 5, 2019
Knew I was going to love this book when I opened it and immediately saw the page numbers going the wrong way.
It is a lot of fun the whole way through. Parker takes us through some of his favourite, or some of the more noteworthy, cases of maths going wrong across a variety of applications. We're talking engineering and computing, from bridges to spacecraft to calendars to ancient sumerian tablets. His enthusiam shines brightly through, and it's hard to not be infected by it. His writing is infused with a dry wit and a good sprinkling of genuine laugh-out-loud humour, which hopefully would make this a fun read ever for those who aren't already invested in the maths stories.
My major criticism is that despite the clear over-arching theme of maths problems, the book still does not feel that cohesive. It has the feeling of a series of articles, and just never quite manages to tie them all together or raise a greater point. This ultimately doesn't matter too much though as it is still a very engaging and enjoyable read. Definitely learnt a new thing or two!
It is a lot of fun the whole way through. Parker takes us through some of his favourite, or some of the more noteworthy, cases of maths going wrong across a variety of applications. We're talking engineering and computing, from bridges to spacecraft to calendars to ancient sumerian tablets. His enthusiam shines brightly through, and it's hard to not be infected by it. His writing is infused with a dry wit and a good sprinkling of genuine laugh-out-loud humour, which hopefully would make this a fun read ever for those who aren't already invested in the maths stories.
My major criticism is that despite the clear over-arching theme of maths problems, the book still does not feel that cohesive. It has the feeling of a series of articles, and just never quite manages to tie them all together or raise a greater point. This ultimately doesn't matter too much though as it is still a very engaging and enjoyable read. Definitely learnt a new thing or two!
March 18, 2019
Matt Parker had me thoroughly enjoying this collection of situations where maths and numbers go wrong in everyday life. I think the book's title is a little weak - 'Humble Pi' doesn't really convey what it's about, but that subtitle 'a comedy of maths errors' is far more informative.
With his delightful conversational style, honed in his stand-up maths shows, it feels as if Parker is a friend down the pub, relating the story of some technical disaster driven by maths and computing, or regaling us with a numerical cock-up. These range from the spectacular - wobbling and collapsing bridges, for example - to the small but beautifully formed, such as Excel's rounding errors.
Sometimes it's Parker's little asides that are particularly attractive. I loved his rant on why phone numbers aren't numbers at all (would it be meaningful for someone to ask you what half your phone number is?). We discover the trials and tribulations of getting calendars right, explore some of the oddities of probability, enjoy a bit of impossible geometry and see how getting units right (or wrong) can make all the difference. Of course there are the big stories, from NASA disasters to the risks of trying to crash onboard systems on planes mid-flight. But it's often those little details like the phone numbers that tickled me. I loved, for example, Parker's attempts to get the footballs on UK signs geometrically correct - totally misunderstood by the bureaucracy - or when Parker points out the problems of graphics featuring multiple cogs interlocked with each other in a way that will lock them solid - not to mention his combinatorial struggles with the McDonald's McChoice menu.
The only thing I did find - and this is the only reason the book doesn't get five stars - is that the final couple of chapters seemed a little samey. Rather than save the best to last, Parker resorts to revisiting rather familiar feeling computer problems, which are interesting (but perhaps more to me, with a background in computing, than many readers), but by now not quite as original and fresh feeling.
However, this is an excellent read, managing to be light and meaty at the same time, and highly recommended for anyone interested in maths, business or computing.
With his delightful conversational style, honed in his stand-up maths shows, it feels as if Parker is a friend down the pub, relating the story of some technical disaster driven by maths and computing, or regaling us with a numerical cock-up. These range from the spectacular - wobbling and collapsing bridges, for example - to the small but beautifully formed, such as Excel's rounding errors.
Sometimes it's Parker's little asides that are particularly attractive. I loved his rant on why phone numbers aren't numbers at all (would it be meaningful for someone to ask you what half your phone number is?). We discover the trials and tribulations of getting calendars right, explore some of the oddities of probability, enjoy a bit of impossible geometry and see how getting units right (or wrong) can make all the difference. Of course there are the big stories, from NASA disasters to the risks of trying to crash onboard systems on planes mid-flight. But it's often those little details like the phone numbers that tickled me. I loved, for example, Parker's attempts to get the footballs on UK signs geometrically correct - totally misunderstood by the bureaucracy - or when Parker points out the problems of graphics featuring multiple cogs interlocked with each other in a way that will lock them solid - not to mention his combinatorial struggles with the McDonald's McChoice menu.
The only thing I did find - and this is the only reason the book doesn't get five stars - is that the final couple of chapters seemed a little samey. Rather than save the best to last, Parker resorts to revisiting rather familiar feeling computer problems, which are interesting (but perhaps more to me, with a background in computing, than many readers), but by now not quite as original and fresh feeling.
However, this is an excellent read, managing to be light and meaty at the same time, and highly recommended for anyone interested in maths, business or computing.
September 27, 2020
Ay las matemáticas. Tan cruciales y tan importantes y tan desapasionadamente que se enseñan. Por eso tanta gente les tiene miedo y por eso muchos huyen tan pronto se libran de ellas.
Un libro de divulgación sobre los usos y abusos y sobre todo, los errores nimios que pueden tener consecuencias devastadoras si se brincan los suficientes filtros puede ser una proposición que no da
Ara un best seller. Pero Parker lo hizo, y a golpe de puro humor. Porque tiene bastantes chistes que ayudan a generar si no pasión, sí un sano interés en el lector.
Obviamente hay capítulos más pesados que otros. Particularmente no soy de computadoras por lo que todo lo que tiene que ver con programación me resulta muy aburrido. Pero me encantaron los capítulos de ingeniería, geometría, probabilidad, aleatoriedad, estadística, sesgos etcétera. Quizá faltó uno de cálculo y uno de topología.
Al igual que el Diablo de los Números, la enseñanza de las matemáticas para ser exitosa debe tener un componente lúdico que enseñe a perder el miedo y a desacralizar. Mis maestros de matemáticas, siempre solemnes y sarcásticos, a duras penas lo lograron conmigo. Pero ojalá Parker hubiera sido mi maestro.
Un libro de divulgación sobre los usos y abusos y sobre todo, los errores nimios que pueden tener consecuencias devastadoras si se brincan los suficientes filtros puede ser una proposición que no da
Ara un best seller. Pero Parker lo hizo, y a golpe de puro humor. Porque tiene bastantes chistes que ayudan a generar si no pasión, sí un sano interés en el lector.
Obviamente hay capítulos más pesados que otros. Particularmente no soy de computadoras por lo que todo lo que tiene que ver con programación me resulta muy aburrido. Pero me encantaron los capítulos de ingeniería, geometría, probabilidad, aleatoriedad, estadística, sesgos etcétera. Quizá faltó uno de cálculo y uno de topología.
Al igual que el Diablo de los Números, la enseñanza de las matemáticas para ser exitosa debe tener un componente lúdico que enseñe a perder el miedo y a desacralizar. Mis maestros de matemáticas, siempre solemnes y sarcásticos, a duras penas lo lograron conmigo. Pero ojalá Parker hubiera sido mi maestro.
April 5, 2021
A Christmas present book from a relative in recognition of my past technical career.
Each chapter a nugget of information about some ‘maths’ error that has caused us problems in everyday life. I put ‘maths’ in inverted commas as many of the issues may be a poor engineering implementation of some analysis. As each chapter is independent of others it’s easy to dip in and out of the book when one fancies light relief from the more serious business of reading fiction!
Not normally a book I’d review on here. I don’t go for popular science of this type, anecdotal though informed, commentary on technical mistakes. I’ve found that in the modern era many science bloggers online can provide up to date light or serious reviews of technical problems in a digestible and easy to understand form. Books on the same topic seem to me too frozen when a lively discussion online, something interactive, is often a better way to understand the problem. Just my view though.
This book is better than most popular ‘wow, isn’t that silly scientists did this’ books. About half of the chapters I did find genuinely interesting (eg how clocks in computer operating systems can be designed to count down from some very high number on the assumption that time zero will be well beyond the expected operating life of the system - guess what?!). Some, such as how numbers placed in spreadsheets in a text format can lead to errors interpreting spreadsheet outputs, had me yawning! But if you’re prepared to ditch out of chapters quickly that you don’t enjoy and move onto the next it’s generally an interesting read.
I think the author has great talent for popularising some difficult science and maths concepts (he does well with probability) and he’s easy to read but it’d be better to see it used for one grand concept in a book rather than this mish mash of the interesting and mundane. I know it’ll be a matter of a reader’s interests but about half of the book covered topics I regarded as dull, so you’ll need to work to find the ones that interest you.
If you get it as a present then worth a read but I wouldn’t go out of my way to recommend it for a purchase, if you want an interesting popular science read.
Each chapter a nugget of information about some ‘maths’ error that has caused us problems in everyday life. I put ‘maths’ in inverted commas as many of the issues may be a poor engineering implementation of some analysis. As each chapter is independent of others it’s easy to dip in and out of the book when one fancies light relief from the more serious business of reading fiction!
Not normally a book I’d review on here. I don’t go for popular science of this type, anecdotal though informed, commentary on technical mistakes. I’ve found that in the modern era many science bloggers online can provide up to date light or serious reviews of technical problems in a digestible and easy to understand form. Books on the same topic seem to me too frozen when a lively discussion online, something interactive, is often a better way to understand the problem. Just my view though.
This book is better than most popular ‘wow, isn’t that silly scientists did this’ books. About half of the chapters I did find genuinely interesting (eg how clocks in computer operating systems can be designed to count down from some very high number on the assumption that time zero will be well beyond the expected operating life of the system - guess what?!). Some, such as how numbers placed in spreadsheets in a text format can lead to errors interpreting spreadsheet outputs, had me yawning! But if you’re prepared to ditch out of chapters quickly that you don’t enjoy and move onto the next it’s generally an interesting read.
I think the author has great talent for popularising some difficult science and maths concepts (he does well with probability) and he’s easy to read but it’d be better to see it used for one grand concept in a book rather than this mish mash of the interesting and mundane. I know it’ll be a matter of a reader’s interests but about half of the book covered topics I regarded as dull, so you’ll need to work to find the ones that interest you.
If you get it as a present then worth a read but I wouldn’t go out of my way to recommend it for a purchase, if you want an interesting popular science read.
February 27, 2022
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April 24, 2020
This was one of the most highly entertaining books I’ve ever read. Whitty and easily digestable I would recommend this to anyone remotely interested in math or engineering.
April 2, 2024
I once read an analysis of the Three Mile Island disaster. It was caused by a stuck pressure relief valve the size of a ping-pong ball. The control console light showed the valve was closed, but the operators did not know that that light signified only that the signal to close had been sent, not that it was actually closed. And so steam continued to vent, water levels continued to drop, and the reactor came closer and closer to meltdown. Finally one engineer, amid chaos and panic in the control room, with sirens wailing and klaxons blaring, was able to mentally trace the sequence of events and realize what must have happened, and then direct the proper response. Disaster averted, but it was a lot closer than the official reports indicated.
Little things add up. Mistakes can accumulate until disaster becomes inevitable. I watched a lecture by a political scientist about how nations collapse: slowly at first, then all at once. That is probably a good general rule for many other situations as well, math and engineering included.
Matt Parker is a former math teacher who clearly loves his subject. There are videos of him on the internet and he always seems to be having a good time. This book looks at incidents where things went seriously off the rails because of math errors. Some of them were ridiculous and some serious, resulting in lost lives, and those cases are treated with appropriate gravity.
On February 25th, 1991, during the Gulf War, a Scud missile was fired at American troops in Saudi Arabia. The launch was detected by a Patriot missile battery, tracked, and a missile was fired. Its intercept calculations were off by 0.00009536743164 percent, but against a missile traveling at 3800 mph, that resulted in a 2000 foot miss. Twenty-eight soldiers were killed and over one hundred injured. The problem was that the Patriot’s computer used a 24-bit number for internal calculations, counting tenths of a second. This meant that the missile battery could be run continuously for 191 days, 10 hours, and 2 minutes before the 24-bit number overflowed and reset. The army knew about this problem, and that it could be avoided simply by having the computers restarted at regular intervals. Instead, vague guidance was issued not to keep the system running for a “long period of time,” without specifying what that meant. A software patch was developed and released on February 16th, but it did not arrive in Saudi Arabia until the 26th, one day after the incident.
There is also a good discussion of the mistakes surrounding the balcony collapse at the Kansas City Hyatt on 17 July 1981 in which 114 people we killed and another 216 injured. In this case the situation was tragic but infuriating. These were dumb mistakes in math calculating the expected load on the balcony supports, compounded by engineering shortcuts approved by the architect that no professional ever should have made. It was almost inevitable that those balconies were going to fail sooner or later. I was happy to see that some of those involved went to jail and others lost their professional licenses.
The book also spends some time in a very good discussion of the calendar, and the efforts that have been made over time to bring it into alignment with the solar year. The calendar changes approved by Julius Caesar were off by 11 minutes and 15 seconds a year, resulting in the calendar slipping one day every 128 years, so that by the early 1500s there was a ten day gap between the official date of the spring equinox and when it actually occurred. Since the calendar was used to schedule planting, this was a serious problem for largely agricultural societies.
Our current calendar was developed by Alousius “Luigi” Lilius, and included the 100/400 year leap calculations. It was accepted by Pope Gregory XIII and implemented in October 1582 by the Catholic world. The Protestant world wanted nothing to do with Pope or his decisions, and it was not adopted in England until 1751, and even then there were furious objections. Russia did not adopt the Gregorian calendar until 1918, after the overthrow of the Czar.
A year is actually 365.2421875 days long, but the Gregorian calendar calculates it at 365.2425, so we are still off by twenty-seven seconds a year. This means we will lose a day every 3213 years, and in half a million years our seasons with reverse if there are no changes. Yep, a Y500k bug is out there. Let’s get right on that.
Other examples are interesting but kind of silly, such as that the original Pacman game used an 8-bit counter to track its levels, and those players who were expert enough make it past level 256 crashed the machine. There is also a discussion of an incident that could have come right out of The Simpsons. The Mars Climate Orbiter was launched in December 1998 and traveled for nine months to its destination. It was destroyed as it entered orbit because two of its critical systems exchanged information incorrectly, one using metric and the other imperial units. “D’oh!”
I must confess that I was partial to Matt Parker after he raised an issue that is near and dear to my heart. In the course of my professional career I have objected over and over to managing projects with spreadsheets. It is always a bad idea, with different versions floating around, and people adding or deleting columns and rows to suit their own needs. Seriously, folks, databases were made for jobs like this, but most managers understand spreadsheets but not databases, so project after project muddled along accumulating errors and delays. As the old saying goes, “I used to be disgusted. Now I’m just amused.”
I enjoyed this book an learned enough interesting things to ensure that I will be the boringest person at any social gathering I attend. I recommend it for anyone with an interest in the subject because let’s face it, we hairless half-apes can screw up anything. Let’s be careful out there.
Little things add up. Mistakes can accumulate until disaster becomes inevitable. I watched a lecture by a political scientist about how nations collapse: slowly at first, then all at once. That is probably a good general rule for many other situations as well, math and engineering included.
Matt Parker is a former math teacher who clearly loves his subject. There are videos of him on the internet and he always seems to be having a good time. This book looks at incidents where things went seriously off the rails because of math errors. Some of them were ridiculous and some serious, resulting in lost lives, and those cases are treated with appropriate gravity.
On February 25th, 1991, during the Gulf War, a Scud missile was fired at American troops in Saudi Arabia. The launch was detected by a Patriot missile battery, tracked, and a missile was fired. Its intercept calculations were off by 0.00009536743164 percent, but against a missile traveling at 3800 mph, that resulted in a 2000 foot miss. Twenty-eight soldiers were killed and over one hundred injured. The problem was that the Patriot’s computer used a 24-bit number for internal calculations, counting tenths of a second. This meant that the missile battery could be run continuously for 191 days, 10 hours, and 2 minutes before the 24-bit number overflowed and reset. The army knew about this problem, and that it could be avoided simply by having the computers restarted at regular intervals. Instead, vague guidance was issued not to keep the system running for a “long period of time,” without specifying what that meant. A software patch was developed and released on February 16th, but it did not arrive in Saudi Arabia until the 26th, one day after the incident.
There is also a good discussion of the mistakes surrounding the balcony collapse at the Kansas City Hyatt on 17 July 1981 in which 114 people we killed and another 216 injured. In this case the situation was tragic but infuriating. These were dumb mistakes in math calculating the expected load on the balcony supports, compounded by engineering shortcuts approved by the architect that no professional ever should have made. It was almost inevitable that those balconies were going to fail sooner or later. I was happy to see that some of those involved went to jail and others lost their professional licenses.
The book also spends some time in a very good discussion of the calendar, and the efforts that have been made over time to bring it into alignment with the solar year. The calendar changes approved by Julius Caesar were off by 11 minutes and 15 seconds a year, resulting in the calendar slipping one day every 128 years, so that by the early 1500s there was a ten day gap between the official date of the spring equinox and when it actually occurred. Since the calendar was used to schedule planting, this was a serious problem for largely agricultural societies.
Our current calendar was developed by Alousius “Luigi” Lilius, and included the 100/400 year leap calculations. It was accepted by Pope Gregory XIII and implemented in October 1582 by the Catholic world. The Protestant world wanted nothing to do with Pope or his decisions, and it was not adopted in England until 1751, and even then there were furious objections. Russia did not adopt the Gregorian calendar until 1918, after the overthrow of the Czar.
A year is actually 365.2421875 days long, but the Gregorian calendar calculates it at 365.2425, so we are still off by twenty-seven seconds a year. This means we will lose a day every 3213 years, and in half a million years our seasons with reverse if there are no changes. Yep, a Y500k bug is out there. Let’s get right on that.
Other examples are interesting but kind of silly, such as that the original Pacman game used an 8-bit counter to track its levels, and those players who were expert enough make it past level 256 crashed the machine. There is also a discussion of an incident that could have come right out of The Simpsons. The Mars Climate Orbiter was launched in December 1998 and traveled for nine months to its destination. It was destroyed as it entered orbit because two of its critical systems exchanged information incorrectly, one using metric and the other imperial units. “D’oh!”
I must confess that I was partial to Matt Parker after he raised an issue that is near and dear to my heart. In the course of my professional career I have objected over and over to managing projects with spreadsheets. It is always a bad idea, with different versions floating around, and people adding or deleting columns and rows to suit their own needs. Seriously, folks, databases were made for jobs like this, but most managers understand spreadsheets but not databases, so project after project muddled along accumulating errors and delays. As the old saying goes, “I used to be disgusted. Now I’m just amused.”
I enjoyed this book an learned enough interesting things to ensure that I will be the boringest person at any social gathering I attend. I recommend it for anyone with an interest in the subject because let’s face it, we hairless half-apes can screw up anything. Let’s be careful out there.
July 29, 2021
3,5⭐️/5
To książka napisana w zabawny sposób, w którym czuć pasje i zamiłowanie autora do królowej nauk.
Możemy z niej wiele wynieść i się nauczyć m.in koniec excela 😅😳.
Według mnie nawet osoba, która nie lubi matematyki może się świetnie bawić przy tej książce. Najciekawsza była dla mnie pierwsza pomyłka (temat) z książki, lecz inne były interesujące.
Mam jedno zastrzeżenie do tej książki. Były tu czasami trudne i skomplikowane dla mnie nazwy.
To książka napisana w zabawny sposób, w którym czuć pasje i zamiłowanie autora do królowej nauk.
Możemy z niej wiele wynieść i się nauczyć m.in koniec excela 😅😳.
Według mnie nawet osoba, która nie lubi matematyki może się świetnie bawić przy tej książce. Najciekawsza była dla mnie pierwsza pomyłka (temat) z książki, lecz inne były interesujące.
Mam jedno zastrzeżenie do tej książki. Były tu czasami trudne i skomplikowane dla mnie nazwy.
August 22, 2022
[21 August 2022]
I love a nonfiction book that makes me laugh out loud. Matt Parker does that. About math.
Math is essential to everyday life. It undergirds most of the technology that we are so dependent upon and the structures that we inhabit. But humans, even engineers and mathematicians, are not always good at math. They make mistakes. Sometimes those mistakes are disastrous. Sometimes less so.
Parker describes many of the situations where a math error caused some kind of failure. Sometimes it's funny. Sometimes it's frightening. Sometimes it's catastrophic. But humans will always make mistakes. Parker argues that we need to allow for that and create our systems and structures with redundancy and error routines to eliminate the effect of the inevitable math mistakes.
I enjoyed this book, but somehow I also felt oddly disappointed when I finished it. I can't quite decide why. It's not a groundbreaking book, sure; you've probably heard of many of these events already. But I wasn't expecting that. I'm not sure what I was expecting. But when I got to the end, I felt like: "Okay, yeah. That's obvious."
Still I would recommend it to most people. It's short and an easy read. Whether or not you like math.
I love a nonfiction book that makes me laugh out loud. Matt Parker does that. About math.
Math is essential to everyday life. It undergirds most of the technology that we are so dependent upon and the structures that we inhabit. But humans, even engineers and mathematicians, are not always good at math. They make mistakes. Sometimes those mistakes are disastrous. Sometimes less so.
Parker describes many of the situations where a math error caused some kind of failure. Sometimes it's funny. Sometimes it's frightening. Sometimes it's catastrophic. But humans will always make mistakes. Parker argues that we need to allow for that and create our systems and structures with redundancy and error routines to eliminate the effect of the inevitable math mistakes.
I enjoyed this book, but somehow I also felt oddly disappointed when I finished it. I can't quite decide why. It's not a groundbreaking book, sure; you've probably heard of many of these events already. But I wasn't expecting that. I'm not sure what I was expecting. But when I got to the end, I felt like: "Okay, yeah. That's obvious."
Still I would recommend it to most people. It's short and an easy read. Whether or not you like math.
February 28, 2020
I have no idea why this book has the average rating of 4.
December 14, 2023
An insightful read on several cases of real world funny and catastrophic accidents that were due to mathematical errors involving simple ones such as discrepancy in conversion between standard measuring systems and also complex ones where flawed mathematical model was the culprit.
August 2, 2021
El libro se subtitula "Cuando las matemáticas fallan en el mundo real", pero solo una pequeña parte de lo que cuenta va realmente de matemáticas. La mayor parte son fallos de diseño ingenieril, negligencias de diseño ingenieril (hay un puente que hacen mal a sabiendas a pesar de que conocían que los cálculos estructurales estaban mal antes de empezar a construirlo, fallos informáticos y un montón de datos curiosos pero inútiles acerca de mil disciplinas, eso sí, relacionadas todas con las matemáticas.
El libro recopila cientos de pequeñas historias, intentando darles una cierta continuidad y agrupándolas por capítulos, pero podríamos decir que este es un libro casi aleatorio porque para describir todo su contenido necesitaríamos casi casi reescribir de nuevo el libro; no hay una buena manera de resumirlo.
La gran mayoría de las historias las he leído por otras partes; el autor ha hecho una labor de recopilación principalmente, aunque ha añadido aportaciones personales, como su petición al gobierno británico de que los balones de fútbol en las señales de tráfico fueran geométricamente correctos y llevaran pentágonos y hexágonos, en lugar de solo hexágonos o su visita a una ciudad indeterminada para ver una obra de ingeniería indeterminada con la que hacerse una foto porque un amigo ingeniero le contó que la habían cagado y les había quedado un empalme medio raro. Obviamente, el amigo entró en pánico (había contratos de confidencialidad firmados por él y por su empresa) y le pidió que no diera detalles, por lo que nos cuenta solo vaguedades muy vagas. Aparte de estas dos historias, las demás creo que andan rulando por ahí desde hace tiempo.
El libro empieza hablando de algo peor que el efecto 2000: El efecto Y2K38, en el que los relojes de sistemas Unix, que empiezan a contar el tiempo en segundos desde 1970, alcancen el límite de 2^31 segundos, que son más o menos 68 años, 2170 millones de segundos (por construcción son 232 segundos, que van desde -2^31 hasta 2^31 ). Nos cuenta historias relacionadas con este tipo de error, como la de 6 aviones F-22 Raptor que al volar de Hawaii a Japón perdieron absolutamente todos los sistemas porque cruzaron la línea internacional de cambio de fecha y sus ordenadores se resetearon. Nos habla luego de puentes como el puente del milenio de Londres y cómo tuvo que cerrar tras su inauguración por culpa de la resonancia. Nos habla también del famoso caso del puente de Tacoma Narrows, y cómo no era exactamente resonancia. Un dato curiosísimo es que nos cuenta que el mito de que los soldados deben romper el paso antes de cruzar puentes es cierto en realidad, y nos documenta el primer puente que se cayó por resonancia cuando lo cruzaron soldados marcando el paso:
Solo he resumido el capítulo 1. Hay mil historias más. Sobre cómo los logos con muchos engranajes suelen estar mal hechos, sobre los interesantísimos errores off-by-one, sobre probabilidad, sobre finanzas, sobre cómo conseguir números aleatorios... La verdad es que ahora que lo estoy comentando veo que el libro trae un montón de historias.
La lectura es entretenida y debe ser visto como una recopilación de historias curiosas y no como un ensayo que tiene principio y fin. Pero merece mucho la pena.
Como parte decididamente mejorable, el autor manifiesta su absoluto desconocimiento en los motivos de los fallos financieros de varios casos. Uno de ellos es el de Knight Capital, una empresa que quebró en una hora por un fallo informático, fallo que se ha documentado extensamente, y otro el de las hipotecas subprime, cuyo origen también conocemos con bastante certeza. Si vas a escribir un libro, esfuérzate un poco en explicar cosas.
El libro recopila cientos de pequeñas historias, intentando darles una cierta continuidad y agrupándolas por capítulos, pero podríamos decir que este es un libro casi aleatorio porque para describir todo su contenido necesitaríamos casi casi reescribir de nuevo el libro; no hay una buena manera de resumirlo.
La gran mayoría de las historias las he leído por otras partes; el autor ha hecho una labor de recopilación principalmente, aunque ha añadido aportaciones personales, como su petición al gobierno británico de que los balones de fútbol en las señales de tráfico fueran geométricamente correctos y llevaran pentágonos y hexágonos, en lugar de solo hexágonos o su visita a una ciudad indeterminada para ver una obra de ingeniería indeterminada con la que hacerse una foto porque un amigo ingeniero le contó que la habían cagado y les había quedado un empalme medio raro. Obviamente, el amigo entró en pánico (había contratos de confidencialidad firmados por él y por su empresa) y le pidió que no diera detalles, por lo que nos cuenta solo vaguedades muy vagas. Aparte de estas dos historias, las demás creo que andan rulando por ahí desde hace tiempo.
El libro empieza hablando de algo peor que el efecto 2000: El efecto Y2K38, en el que los relojes de sistemas Unix, que empiezan a contar el tiempo en segundos desde 1970, alcancen el límite de 2^31 segundos, que son más o menos 68 años, 2170 millones de segundos (por construcción son 232 segundos, que van desde -2^31 hasta 2^31 ). Nos cuenta historias relacionadas con este tipo de error, como la de 6 aviones F-22 Raptor que al volar de Hawaii a Japón perdieron absolutamente todos los sistemas porque cruzaron la línea internacional de cambio de fecha y sus ordenadores se resetearon. Nos habla luego de puentes como el puente del milenio de Londres y cómo tuvo que cerrar tras su inauguración por culpa de la resonancia. Nos habla también del famoso caso del puente de Tacoma Narrows, y cómo no era exactamente resonancia. Un dato curiosísimo es que nos cuenta que el mito de que los soldados deben romper el paso antes de cruzar puentes es cierto en realidad, y nos documenta el primer puente que se cayó por resonancia cuando lo cruzaron soldados marcando el paso:
One of the first bridges to be destroyed by synchronized pedestrians was a suspension bridge just outside Manchester, England (in what is now the city of Salford). I believe that this Broughton Suspension Bridge was the earliest bridge destroyed when people walked over it at the resonant frequency.[...]
The bridge was built in 1826, and people crossed it with no problem at all until 1831. It took a troop of soldiers all marching perfectly in sync to hit the resonant frequency. The 60th Rifle Corps of seventy four soldiers were heading back to their barracks at about midday on April 12, 1831. They started to cross in rows of four and pretty quickly noticed that the bridge was bouncing in rhythm with their steps. This was apparently quite a fun experience and they started to whistle a tune to go with the bouncing. Until about sixty soldiers were bouncing on the bridge at once and it collapsed.
Solo he resumido el capítulo 1. Hay mil historias más. Sobre cómo los logos con muchos engranajes suelen estar mal hechos, sobre los interesantísimos errores off-by-one, sobre probabilidad, sobre finanzas, sobre cómo conseguir números aleatorios... La verdad es que ahora que lo estoy comentando veo que el libro trae un montón de historias.
La lectura es entretenida y debe ser visto como una recopilación de historias curiosas y no como un ensayo que tiene principio y fin. Pero merece mucho la pena.
Como parte decididamente mejorable, el autor manifiesta su absoluto desconocimiento en los motivos de los fallos financieros de varios casos. Uno de ellos es el de Knight Capital, una empresa que quebró en una hora por un fallo informático, fallo que se ha documentado extensamente, y otro el de las hipotecas subprime, cuyo origen también conocemos con bastante certeza. Si vas a escribir un libro, esfuérzate un poco en explicar cosas.
April 9, 2021
Lo disfruté de principio a fin.
Se nota la formación docente del autor y su pasión por las matemáticas.
La lectura es muy amena y no requiere "ningún conocimiento previo" :)
Se nota la formación docente del autor y su pasión por las matemáticas.
La lectura es muy amena y no requiere "ningún conocimiento previo" :)
Read
September 10, 2023Ставить оценку сборнику анекдотов, из которого вы еще до прочтения прекрасно знали две трети — действие бессмысленное, так что не буду.
Оне не скучны сами по себе, скучно читать упрощенный пересказ вещей которые известны вам в деталях.
Из этого выходит моя главная претензия к книге — название обещало, наверное, нечто чуть другое. Математика оказалась (в большинстве рассматриваемых случаев) программированием, и дальше вы и сами знаете и про Therac-25, и про GPS rollover, и про 2038 год.
Про BAC One-Eleven и неправильные болты невероятная история зато, но и тут математика имеет достаточно отстраненное отношение (притягивается через swiss cheese model).
Оне не скучны сами по себе, скучно читать упрощенный пересказ вещей которые известны вам в деталях.
Из этого выходит моя главная претензия к книге — название обещало, наверное, нечто чуть другое. Математика оказалась (в большинстве рассматриваемых случаев) программированием, и дальше вы и сами знаете и про Therac-25, и про GPS rollover, и про 2038 год.
Про BAC One-Eleven и неправильные болты невероятная история зато, но и тут математика имеет достаточно отстраненное отношение (притягивается через swiss cheese model).
November 8, 2022
Summary: An exploration of all the ways we use (and misuse) math in the real world, and the ways our calculations can go badly wrong.
Were you among those who wondered how on earth you would ever use that math you learned in high school? The truth is that even if you do not, there are others using that math in just about every aspect of our physical world from our bridges to our medical hardware to our buildings. The amazing thing is how we can describe and predict how things will work through our calculations. And sometimes, if we make a mistake, or a wrong assumption, those calculations can go badly wrong. Some of those mistakes are just amusing or complete nonsense. But some can be deadly…
Matt Parker explores many of the ways math goes wrong in the real world, citing dozens of real world examples for the different classes of math errors he discusses. He starts with how we lose track of time, particularly with our timekeeping rollover features on our computers. Usually, it’s no problem because they start counting each time we turn them on. But leave it running long enough for the time to roll over, and the world can come to a grinding halt, a real problem if it occurs mid-flight.
He discusses engineering problems, like the failure to calculate resonance effects on bridges and engineer to compensate for them. One of the most famous, and tragic, was the collapse of the Kansas City Hyatt Regency Walkways when the design of how sections of box beams were supported by nuts was changed without recalculating load limits. Then there are the errors that can creep into spreadsheet formulas and calculations that can produce misleading information on which businesses make decisions.
We often make counting mistakes with intervals. Like how many posts do you need to support a five section fence? (Six). We make geometry mistakes, like the example of the diagram of a soccer ball with all the sections, white and black, being hexagonal. This is not possible on a spherical ball which is why the white sections are hexagons and the black ones are pentagons. Shapes are important. Deformations on rocket boosters combined with cold circular O-rings spelled disaster on a space shuttle. Some are the minor difference in precisely engineered parts that are outside tolerances or times when conventions of measurement vary among those on the same project.
Many of the mistakes concerns the peculiarities of computer calculations, including rounding errors and supposed randomization programs and errors of even a single line of code in an algorithm. Another math problem is what “average” means and what you do with that where most people aren’t “average.” So often, math and computer code are part of complex systems, that when changed, involve recalculating or reviewing every part. Often the things overlooked create problems.
Parker explains all of this in language even this non-mathematician can understand and includes many images and illustrations, making this an enjoyable read (while reminding us the acts of faith involved in everything from spreadsheets to suspension bridges to airplane flights). We assume talented people have made, checked, and rechecked calculations and code for accuracy. And most of the time, things work…except when they don’t.
He also alerts us to fallacies that we may encounter with statistics or so-called random numbers or even in how we count. What seems common sense is not in every case.
There’s one other interesting quirk in this book, and that is in the pagination, which is in reverse order, from 313 to zero, and then a roll over number, 4,294,967,294. I kind of liked it personally. How many times have you wondered, “how many pages left in this book?” In this case, the page number you are on is the answer! This feature may give you a sense of the light touch this author takes in a book dealing with ostensibly serious matters making it such a good read.
Were you among those who wondered how on earth you would ever use that math you learned in high school? The truth is that even if you do not, there are others using that math in just about every aspect of our physical world from our bridges to our medical hardware to our buildings. The amazing thing is how we can describe and predict how things will work through our calculations. And sometimes, if we make a mistake, or a wrong assumption, those calculations can go badly wrong. Some of those mistakes are just amusing or complete nonsense. But some can be deadly…
Matt Parker explores many of the ways math goes wrong in the real world, citing dozens of real world examples for the different classes of math errors he discusses. He starts with how we lose track of time, particularly with our timekeeping rollover features on our computers. Usually, it’s no problem because they start counting each time we turn them on. But leave it running long enough for the time to roll over, and the world can come to a grinding halt, a real problem if it occurs mid-flight.
He discusses engineering problems, like the failure to calculate resonance effects on bridges and engineer to compensate for them. One of the most famous, and tragic, was the collapse of the Kansas City Hyatt Regency Walkways when the design of how sections of box beams were supported by nuts was changed without recalculating load limits. Then there are the errors that can creep into spreadsheet formulas and calculations that can produce misleading information on which businesses make decisions.
We often make counting mistakes with intervals. Like how many posts do you need to support a five section fence? (Six). We make geometry mistakes, like the example of the diagram of a soccer ball with all the sections, white and black, being hexagonal. This is not possible on a spherical ball which is why the white sections are hexagons and the black ones are pentagons. Shapes are important. Deformations on rocket boosters combined with cold circular O-rings spelled disaster on a space shuttle. Some are the minor difference in precisely engineered parts that are outside tolerances or times when conventions of measurement vary among those on the same project.
Many of the mistakes concerns the peculiarities of computer calculations, including rounding errors and supposed randomization programs and errors of even a single line of code in an algorithm. Another math problem is what “average” means and what you do with that where most people aren’t “average.” So often, math and computer code are part of complex systems, that when changed, involve recalculating or reviewing every part. Often the things overlooked create problems.
Parker explains all of this in language even this non-mathematician can understand and includes many images and illustrations, making this an enjoyable read (while reminding us the acts of faith involved in everything from spreadsheets to suspension bridges to airplane flights). We assume talented people have made, checked, and rechecked calculations and code for accuracy. And most of the time, things work…except when they don’t.
He also alerts us to fallacies that we may encounter with statistics or so-called random numbers or even in how we count. What seems common sense is not in every case.
There’s one other interesting quirk in this book, and that is in the pagination, which is in reverse order, from 313 to zero, and then a roll over number, 4,294,967,294. I kind of liked it personally. How many times have you wondered, “how many pages left in this book?” In this case, the page number you are on is the answer! This feature may give you a sense of the light touch this author takes in a book dealing with ostensibly serious matters making it such a good read.
July 11, 2019
Šo grāmatu iegādājos tādas kā vainas apziņas mudināts. Es sen senos laikos pirms kādiem diviem gadiem nopirku šī autora grāmatu Things to Make and Do in the Fourth Dimension, bet tā kā ceturtās dimensijas apmeklējums atlikās uz nenoteiktu laiku, es to tā arī neesmu vēl sācis lasīt. Šo gan es veikalā pašķirstīju un sapratu, ka izlasīšu, uzreiz nopirku un noliku plauktā uz kādu laiku.
Lai cik novazāti tas neizklausītos, bet mūsdienu pasaule savos pamatos balstās uz matemātiku un to lielākoties neviens pat nepamana līdz brīdim, kamēr kāds ir aizmirsis kaut kur kādu skaitli un tad sākas briesmu lietas – brūk tilti, mājas sadedzina automašīnas, kosmosa zondes ietriecas planētās, tava rūpīgi slēptā parole viegli atkodējas un loteriju organizētājiem jādodas uz tiesām.
Šī nav ne pirmā, ne pēdējā grāmata, kas veltīta matemātikai, kuru es esmu izlasījis, taču diezgan reti gadās atrast kādu, kas savā būtībā atkāpjas no iebrauktās takas un neatražo standarta “interesantās” lietas. Es nedomāju noniecināt citus autorus, taču ja esi izlasījis pārdesmit grāmatas no sērijas “saistoši par matemātiku”, tad neizbēgami nākas secināt, ka labo piemēru vai nu nav tik daudz, jeb neviens autors nemaz necer, ka kāds cilvēks viņas lasa desmitiem. Tad nu iešauj pāris fibonači piemērus no augu valsts, phi skaitli, interesantas metodes kā aprēķināt skaitli π pēc Montekarlo metodes, un skat – jau pienākušas grāmatas beigas.
Šīs grāmatas lielākais pluss bija tas, ka autora piesauktie matemātikas pielietojuma vai nepielietojuma piemēri nudien bija līdz šim pa pasauli pārāk daudz neizvazāti un pat man rūdītam matemātikas fanam bija uzzināmas jaunas lietas un ar dažām problēmām man pat ir nācies saskarties pašam. Piemēram, ar kļūdām Excel formulās, kur kaut kad ne tā esi novilcis un ne to mainīgo ielicis formulā un tad pusgadu dzīvo laimīgi par savu kļūdu nemaz nenojauzdams. Te gan tas tika pacelts lielo finanšu spēlētāju līmenī, kur neveiksmīgs ekselis var likt zaudēt pārsimts miljonus. Vai arī par to kā reizēm, izmantojot mārketinga departamenta cilvēku nespēju tikt galā ar skaitļiem tikt pie reaktīvās lidmašīnas. Par to, kā gadījuma skaitļi patiesībā un cilvēku uztverē ir tik kardināli atšķirīgi, un kāpēc netrenēts cilvēka prāts nav spējīgs tikt galā ar varbūtību teoriju.
Ja dikti gribās piekasīties, tad jāatzīst, ka grāmata, lai ar izlasās vienā rāvienā, tai pat laikā lasītais diezgan ātri aizmirstas. Tas gan ir raksturīgs daudzām grāmatām, bet manā pieredze tas liecina par daudz nestrukturētiem faktiem, kas baro smadzenes kā cukurs, tai pat laikā pamanoties neatstāt nekādas paliekošas atmiņas!
Grāmatai lieku 9 no 10 ballēm, ja interesē matemātika un vēlies izprast tās vietu savā dzīvē, vari droši lasīt! Pat ja neinteresē matemātika, bet patīk lasīt par cilvēkiem, kas ir smagi kļūdījušies dēļ sīkuma, tad šī grāmata sniegs daudzus uzskatāmus piemērus. Var lasīt arī tad, ja pats esi kaut ko salaidis dēlī un ar prieku konstatēt, ka tavs veikums ir sīkums salīdzinot ar to čali, kurš uzpildot lidmašīnu sajauca kilogramus ar mārciņām.
Lai cik novazāti tas neizklausītos, bet mūsdienu pasaule savos pamatos balstās uz matemātiku un to lielākoties neviens pat nepamana līdz brīdim, kamēr kāds ir aizmirsis kaut kur kādu skaitli un tad sākas briesmu lietas – brūk tilti, mājas sadedzina automašīnas, kosmosa zondes ietriecas planētās, tava rūpīgi slēptā parole viegli atkodējas un loteriju organizētājiem jādodas uz tiesām.
Šī nav ne pirmā, ne pēdējā grāmata, kas veltīta matemātikai, kuru es esmu izlasījis, taču diezgan reti gadās atrast kādu, kas savā būtībā atkāpjas no iebrauktās takas un neatražo standarta “interesantās” lietas. Es nedomāju noniecināt citus autorus, taču ja esi izlasījis pārdesmit grāmatas no sērijas “saistoši par matemātiku”, tad neizbēgami nākas secināt, ka labo piemēru vai nu nav tik daudz, jeb neviens autors nemaz necer, ka kāds cilvēks viņas lasa desmitiem. Tad nu iešauj pāris fibonači piemērus no augu valsts, phi skaitli, interesantas metodes kā aprēķināt skaitli π pēc Montekarlo metodes, un skat – jau pienākušas grāmatas beigas.
Šīs grāmatas lielākais pluss bija tas, ka autora piesauktie matemātikas pielietojuma vai nepielietojuma piemēri nudien bija līdz šim pa pasauli pārāk daudz neizvazāti un pat man rūdītam matemātikas fanam bija uzzināmas jaunas lietas un ar dažām problēmām man pat ir nācies saskarties pašam. Piemēram, ar kļūdām Excel formulās, kur kaut kad ne tā esi novilcis un ne to mainīgo ielicis formulā un tad pusgadu dzīvo laimīgi par savu kļūdu nemaz nenojauzdams. Te gan tas tika pacelts lielo finanšu spēlētāju līmenī, kur neveiksmīgs ekselis var likt zaudēt pārsimts miljonus. Vai arī par to kā reizēm, izmantojot mārketinga departamenta cilvēku nespēju tikt galā ar skaitļiem tikt pie reaktīvās lidmašīnas. Par to, kā gadījuma skaitļi patiesībā un cilvēku uztverē ir tik kardināli atšķirīgi, un kāpēc netrenēts cilvēka prāts nav spējīgs tikt galā ar varbūtību teoriju.
Ja dikti gribās piekasīties, tad jāatzīst, ka grāmata, lai ar izlasās vienā rāvienā, tai pat laikā lasītais diezgan ātri aizmirstas. Tas gan ir raksturīgs daudzām grāmatām, bet manā pieredze tas liecina par daudz nestrukturētiem faktiem, kas baro smadzenes kā cukurs, tai pat laikā pamanoties neatstāt nekādas paliekošas atmiņas!
Grāmatai lieku 9 no 10 ballēm, ja interesē matemātika un vēlies izprast tās vietu savā dzīvē, vari droši lasīt! Pat ja neinteresē matemātika, bet patīk lasīt par cilvēkiem, kas ir smagi kļūdījušies dēļ sīkuma, tad šī grāmata sniegs daudzus uzskatāmus piemērus. Var lasīt arī tad, ja pats esi kaut ko salaidis dēlī un ar prieku konstatēt, ka tavs veikums ir sīkums salīdzinot ar to čali, kurš uzpildot lidmašīnu sajauca kilogramus ar mārciņām.
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