1 Million Seconds Is 11 Days; 1 Billion Is 31 Years

10 Mathematical Quirks from “Humble Pi”

Mathematics is the language of God. Modern-day miracles like vaccines, satellites and AI have an underlying mathematical foundation. Logic is a branch of mathematics. Yet, as Matt Parker’s hilarious “Humble Pi” showcases, we make mathematical errors all the time. I’ve compiled a few of my favourite takeaways from this nifty little book. Here’s hoping these inform and entertain in equal measure.

• We are not good at judging large numbers. 1 million seconds is over 11 days. 1 billion seconds is over 31 years. Imagine how much richer a billionaire is compared to a millionaire!
• There are 10 types of people in the world: one who understands binary and the other who doesn’t. The binary system is the bedrock of all computing systems. Unlike the Base-10 decimal system we use for counting, computers understand binary. Binary comprises only two digits: 1 & 0. Each binary digit is called a “bit”. 8 binary digits are called a “byte”. Half a byte is a “nibble”. Mathematicians aren’t renowned for their humour.
• At approximately 3:14 AM on Tuesday, 19th January 2038, all modern microprocessors, and computers will stop working. The dreaded YK38 bug. Why? In 1970, the Institute of Electrical & Electronics Engineers (IEEE) decreed that all computer systems should count every second from the start of 1971. This count was stored in a 32-bit number. The highest 32-bit number is 1111 1111 1111 1111 1111 1111 1111 1111. Which when converted to decimal gives you: 2,147,483,647 seconds. Which is 68 years. Which is that fateful day in January 2038 when everything will stop.
• The electrical generators on a Boeing 787 aircraft count-up every 10 milliseconds and store this value in a 32-bit number. Which means engines could shut off mid-flight if the plane is turned on continuously for 248 days. So, what solution has the $120 Billion aviation behemoth adopted? It turns the planes off and on again. Like how you would your broadband router when the Wi-Fi is flaky.
• Our current calendar, called the Gregorian calendar, is repetitive. It repeats every 400 years. Which means, today is the same day it was 400 years ago and will be the same 400 years from now. History, and the future, repeat themselves. Literally.
• Notice how WhatsApp group chats can have a maximum of 256 members? That’s because 256 = 11111111 in binary. WhatsApp stores each person in a group chat as an 8-bit number.
• You are always older than your age. It’s because of “index zero” counting system. We like counting things from “1”. In fact, the more natural way of counting is from “0”. 1 is actually the second number. Not the first. So, when you celebrate your 40th birthday, you have already lived 40 years — from the day you were born (Year 0) to now (Year 40). You don’t turn 40. We are all a year closer to middle-age, unfortunately.
• We have all experienced The Gambler’s Fallacy. “If some random event has not happened for a while, then it is due!”. Imagine playing roulette and watching a red number appear 18 times in a row. A black number is surely due, right? We should bet our house on it. The truth, unfortunately, is that random events have no memory. No mysterious force is keeping a tab on how many times a particular event has occurred. No one controls the number of “tails” and “heads” in a series of coin tosses so that they come out roughly 50–50. Random events are exactly that: random. And random events also include familiar sequences. The chance of winning the lottery with the sequence “1 2 3 4 5” is the same as winning it with “11 19 34 39 40”.
• The oldest discovered mathematical mistake is from a clay tablet from the Sumerian city of Uruk (now in modern-day Southern Iraq), believed to be at least 5000 years old. The clay tablet was a ledger of stock levels in a brewery. Beer gave us humankind’s first calculations and the first mathematical mistake. Cheers!
• Between 1993 and 2008, tens of thousands of euros were wasted to find Germany’s notorious serial killer: a woman whose DNA had been found at over 40 crime scenes. A €300,000 bounty was declared for her capture. Turns out, this “criminal mastermind” was the woman who worked in the factory that produced the cotton swabs for DNA samples. CSI Anticlimax.
• Causation doesn’t equal correlation. Almost half of us will discover we have cancer at some point in our lives. It’s not because cancer has become more prevalent. It’s because we are living longer and not dying of what we used to die of before. Cancer is now more noticeable. Similarly, as the mobile phone masts in a particular area increase, the number of children born increase. Is the radiation from mobile masts increasing fertility? No. More mobile phone masts are built in heavily populated areas. Our brains jump to the direction of causality that our intuitions most readily believe.

So, there you have it. My thoughts on my ten favourite snippets from Matt Parker’s zesty, light-hearted, and informative “Humble Pi”. It’s unique, intelligent and jampacked with numerical titbits. Pick it up!