The number 4,294,967,295 was the most attractive one the author mentions in the first chapter, more so because for a few pages it was kept suspense before revealing to us that this happens to be the 32-digit '1's full capacity (in binary form), attaining which, any system would restart. Quite similar to BSOD, the dumping of memory and the micro-second timed restart of the PC went unnoticed in California’s airport, leading to loss of radio connections with almost 800 aeroplanes. Now that this memory has been replaced with 64-bit ones, it might take 584.9 million years for the system to restart upon reaching the maximum limit of that capacity by a memory device!
The subtle account of Earth’s rotation around the sun has been considered for accuracy calculations of periods. The difference between sidereal and tropical year has been discussed thus. There is this mention about the Y2K38 bug that would make microprocessors stop working on 19th January 2038 for the same reasons mentioned above. The info that February 1847 has 31 days did not prove to be true when the author asks the readers to check their iPhones for this ‘feature’. Probably it has been corrected.
The next chapter is an elaborate account on Engineering mistakes with ample examples that I never thought would be the result of miscalculations. A building in Fenchurch London designed with a sweeping curve behaved like a massive concave mirror in a season such that it set fire to everything that came in its way of convergence. A few suspension bridges in UK had matched severely with a frequency of 1 Hz leading to wobbling and collapsing. It was Boston tower that collapsed when 167th person entered it, a threshold for the frequency mentioned as the bolts and nuts used had an individual capacity bearing (approx. 9280 kg, integrated). We are considered as approximation machines and maths can get us to correct values.
That
some English names have been making us go crazy is well known and Steve Null
was a name whose entry was often non-existent wherever he tried to enter. So it
was important that the names are well defined (reserved words). Similarly, the
flaws in open spread sheets in excel is mentioned with some examples. A similar
incident with data entry led to vanishing of war in Afghanistan!
A wrong design of a road signal in UK was brought to
notice legally by a person as he found that the football image over the signal
light was not in tune with a regular one where one pentagon is surrounded by
hexagons. The author goes on to describe the efficacy of bee-hive type
structures. The Apollo program’s space
craft had a door that opened inside, finds a vital mention to prove the
structural efficiency. Similarly, the ‘Challenger’
disaster had a design flaw. Richard Feynman who was in the inquiry team
demonstrated that the O-rings (rubber gasket), that separated two fuel tanks,
failed to spring back when the temperature was cooled to ice’s. Though a simple
one, the place it was used has a significant impact that was not rightly
addressed. A brief discussion on gears and mechanism ensues till the end of
this chapter.
Someone going to gym was very particular about the number of days in a week. Though the concept is silly, but in a month as weeks get repeated working every alternate day would actually let you do so four times a week! A few pages are devoted to McDonald’s menu in which some combination of the menu legends did not mean breakfast or meal. The customer once chose such a combination on flavours and refused to pay on par with meal in the menu as prescribed by the outlet. The number of ways to arrange these eight menus are given as 8x7x6x5x4x3x2x1=81.
The number of digits on zip codes is discussed with regard to USA. A game on M K Gandhi, who is revered in India, was responsible for losing the reputation merely because the game ‘Civilization’ treated a number 255 as aggressive. Downloaded and played by more than 33 million, a 1-2 subtraction was resulting in '255', which was a flaw in binary system. Remember 255 contacts as the limit in WhatsApp? (256 being the order of 8-bits). This 255-type problem was there with Swiss rail system as well. The author writes that this rail network was probably the only one which issued bureaucracy patch rather than software – 256 axles should not be engaged in the system.
The 256- error was a life
taking issue with Therac-25 a medical radiation device which was used to treat
cancer patients with electron beam bursts. A setup required a routine check-up
as class 3=0. A subroutine would slightly activate whenever the class was zero
and the beam would fire the electrons. Unfortunately, it was 8-digit binary
number which should roll back to zero after it had maxed out. Every 256th
time it would roll back 0.4% of time to skip running. This error led to continued
bursts resulting in the death of a patient in 1987.
An interesting truncation
error that was encountered during the first Gulf war. Every time a 'Scud' was fired 'Patriot' would destroy it before it reached the target. Due to a mathematical
oversight in ‘Excel’ the fraction of 1/3rd of a second was omitted
leading to a lapse of about 500 meters. This accumulated calculation error
misled the Patriot, and it could not fire on time. The software error was later
located, patched up and imported from US for later use.
A large number of examples on
probability can be found in this part of the book which is titled ‘probably
wrong’. A woman was wrongly sentenced twice in UK due to statistical error. The
work out was there but it did not evince any interest in me. Factors like these
were also documented when using dice and lotteries. But the probability of
error with regard to the Columbia shuttle drew my attention. When Feynman was inquiring
into its disaster, he was told by over-confident engineers that the probability
of errors was like 1 in 100000. Feynman put it as ‘it would mean a daily launch
of the shuttle for 300 years with only one disaster', and which
was probably improbable. That was just some data like 46087 road deaths were in
USA in spite of them driving about 1838240000000 miles that year!
Putting money where your mistakes is all about stock
exchange and commerce related. 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. It was described as a ‘fat fingers’ error.
The world’s most expensive book ‘The making of a fly’ was purchased by the author. What made it so expensive? Well, the seller used algorithm that raised the price of the book each day by 26.8% when the buyer visited the site. It was a whopping 23,698,000 USD! After Stocks and Commerce, political issue finds a way into the book. The election in Schleswig Holstein where an MP can get seat only if he scores 5, got a breakthrough when his actual number 4.97 was rounded off to 5. Trump also gets a mention.
Salami slicing is the term used when something
is gradually removed one tiny un-noticeable piece at a time.
Because we had no accurate clock in the 1917 someone might have actually run faster than the present-day athlete whose clocks now show accurate times. When the US switches all coal power to solar it would save 51999 lives - roughly 52000 lives, and each life matters. 13.8 million years do not mean 13,800,003 years when mentioned 3 years later. In view of all the above a round-about is always essential but with a caveat. R Sikdar of Kolkata actually calculated the tallest mountain, but GTS which was run by someone not aware of minute details about calculations, ignored the value and put forth the name of Everest so that this became the tallest mountain in the world!
Hubble Space Telescope was put into orbit in 1990, and its first images were blurred - out of focus due to mirrors’ wrong shape. The wrong paraboloid 1G to 0G lead to edges of 2.4 m mirror - about 2.2 µm longer. The correction was carried out in the repair mission.
Mecca of mistakes carries the photo of Mecca over a mobile phone having a compass app on play. The direction is not straight towards it, but rather tilted. Due to small uncorrected errors proper west is not thus shown. Similarly, a small error in a flight windshield bolts A211 had two almost similar notations - 7D and 8C. A lot of difference was there in size at the micro level. A BAC 1-11 jet liner of British Airways fixed wrong bolt and during the flight the wind screen exploded outward. The chronology of this event, right from checking to take off is mentioned in great detail showing the ignorance of the minute mathematical error leading to major accident when the pilot was flown out!
The conventional unit mistake, often quoted in many books, when in 1998 NASA’s Mars Climate Orbited flopped due to discrepancy in units, finds a mention.
The funny thing about British prime minister was a
question “how long has Theresa been pm?” and the engine threw an answer 1.72
trillion pm! PM was for minister and the pm it mentions is ‘Pico-meter’!
Aircraft fuel is calculated in mass and not in volume. Flight
T143 of Air Canada was wrongly fuelled but accident was avoided during a cross
check. The two-way connection from the aircraft’s two wings over a common
sensor circuit is discussed clearly and was a pleasure to read.
Defining average has always
been a serious task, particularly in Australia. An average Australian meant a 37-year-old
living with a spouse and two children and to fit this data a man at a place
emerged from nowhere during a survey. There are often incidents of people
appearing from nowhere, just like people disappearing. The concept of average
gets a go all along this chapter. Fitting of clothes with average in mind is
another example when dress makers carry out the region wise average assessment.
Some statistical measurements have more than one formula to produce desired
result and many examples are quoted in this chapter.
Sampling bias like conducting a survey about what people might think of modem tech but only accepting submission by fax, makes a lighter read of the bias. A negative result from a drug trial is twice as likely to remain unpublished as positive result (should be published). In 1980 anti-arrythmias drug trial was conducted whereby out of 48 patients, 9 died but only 1 of the 47 given placebos died. And it took 13 years for this fact to get published. It is in Maths that you can find any pattern you want as long as you are prepared to ignore enough data.
Direct correlation between the number of mobile phone towers and number of births in UK was fun to read - with every tower 17.6 birth was recorded. Woolworth a chain shop went bankrupt, the GPS coordinates of 800 ex Woolworth was downloaded, and they revealed a kind of equilateral triangle between nearest locations, and it was illustrated for us to understand. The author mentions that everywhere the triangular pattern was found the Woolworth went bankrupt. Did Aliens help?
Totally Random: Netscape navigators id generation was
random so was IBM’s randomness calculation about any id. Chrome had to fix a random number generator because
math.random, a java script they used was returning used numbers after few
million tasks. It was then that the chrome download was shown as zero even
though thousands downloaded it.
Three things are certain in
life: death, taxes and people trying to cheat on taxes.
If you can write a short computer program to generate s
sequence of numbers, then the sequence cannot be random – Kolmogorov complexity.
ESA’s Ariane 5 in June 1996 went on self-destruction mode 40 seconds after launch. Inquiry revealed that the on-board computer tried to copy a 64-bit number into a 16-bit space. The space craft was using an old sensor meant for Ariane 4. This tracked the rocket based on inertia and as the space exceeded the available space, the SRI (Inertial Reference System) device which gets raw data to convert into meaningful one calculated that the trajectory was different, and it meant that rocket was going haywire. To avoid debris damage in the residential area the self-destruction mode, programmed inside, was invoked and it blasted the entire system over the sea.
There was this case of University of North Carolina not able to send mail to far off places. it was a problem with sendmail.cf and is a classic case of a program trying to digest data that was not intended for it. More than 500 miles, an update set the things right.
So, the advice to the
programmer is to recheck and reverify the code that is written. The metaphor the
author uses at the end of the book is hot Swiss cheese, that is, there are
always holes, you need to make sure that the holes in your defences don't all
line up or rather line up when you want a get-through. If you are smart, the
challenge is to create something that will be as close to fool proof as you
can, rather than blaming people afterwards for not using it properly.
