My purchase was $1.17, I handed the clerk $20 and she promptly told me my change was $17.83, while handing me $21.83. When I told her she had made a mistake, she gave me a blank look and pointed at the display on the cash register display.
There were no customers in line behind me, so I spent the next couple of minutes attempting to teach her how to count back change, an arcane skill that seems to have vanished a generation ago, along with manners, common sense, and the ability to use turn signals.
My attempt failed. It became apparent that whatever amount the cash register told her to return, she would trustingly count it out as best she could. I gave up, asked her if she could give me two tens for a five, collected my money and left the store.
The problem is that most people today have a horribly declining sense of numeracy—the ability to understand numbers and to use simple math to solve problems in everyday life. (Or, to use an analogy, numeracy is the math version of literacy).
A basic general understanding of numbers seems to be slipping from our society, and there is ample proof of this. Take, for example, the latest internet meme rapidly spreading across social media—that a recent audit revealed that the Defense Department had misplaced funds. I’m not going to give any detail since I would hate to inadvertently spread this nonsense any further, but the amount mentioned is more than the total budget for the Defense Department for the entirety of the 20th Century!
Anthropologists have recorded many societies whose entire number system was limited to ‘one’, ‘two’, and ‘many’. These were societies whose levels of technology had never advanced to the point where larger numbers were ever needed.
For some reason, lately the idea that ‘one, two, many’ societies ever actually existed has become politically incorrect. According to a few nagging nitpickers, such notions are not only factually incorrect, but are proof of some form of racism or cultural insensitivity. I would apologize…were it not for the fact that a few of these cultures can still be found. The language of the Walpiri of Australia have no words for numbers higher than two, while the vocabulary of the Pirahã of the Amazon Basin contains no words for any abstract concept. They have no words for numbers, colors, or any way of discussing the past or the future. (As I write this, it occurs to me that this describes my interactions with both my grandchildren and my cat.)
Most languages, including English, contain linguistic evidence of a time when our own number sense was also limited to ‘one, two, many’. Consider the words for our cardinal numbers versus our ordinal numbers:
one – first
two – second
three – third
four – fourth
five – fifth
six – sixth
Obviously, after the first two, the words for the ordinal numbers were based on the words for the cardinal numbers, indicating that these words were developed later. This example remains valid for several other languages. Here are the same words in Spanish:
uno – primera
dos – segunda
tres – tercera
quatro – cuarto
cinco – quinta
seis – sexta
Despite our expanded vocabulary, we still have trouble understanding and using numbers, particularly large numbers. You can prove this with a simple experiment that will annoy your friends. Ask them to tell you how many miles away the moon is from the earth. Then ask them how much further the sun is from earth. There is almost no chance that anyone over the age of ten has not heard the correct numbers, but do they really understand the answer? (The answer is roughly a quarter of million miles to the moon, and about 400 times that to the sun.)
A better way to illustrate our uncomfortableness with numbers can be illustrated with Mt. Everest. As soon as the British learned of the mountain, originally named Kangchenjunga, Nepalese for Five Treasuries of the Great Snow, the curiosity to measure the height of the mountain drove the British crazy. Starting in 1840, George Everest began the arduous task of actually measuring a remote mountain.
Note. George Everest was opposed to renaming the mountain, and in part, got his wish. His pronunciation of his last name, "Eve-Rest", is used today by absolutely no one.
Carrying a 1,200 pound theodolite (think of a big telescope merged with a compass) up and down the frozen Himalayas eventually ruined George’s health, but his work was continued by Andrew Waugh and John Armstrong. After taking careful measurements from multiple locations, in 1852, they were able to accurately calculate the height of the mountain—that Waugh insisted on renaming after his former boss—as exactly 29,000 feet above sea level.
29,000? Exactly 29,000?
Waugh and Armstrong knew that no one would believe their measurement was anything but an estimate. If you have spent over a decade in the freezing cold of the Himalayas, waiting for the weather to clear just long enough to take a telescope reading, all the while living in a rotting tent with spoiled food and contaminated water, the last thing you want is for the entire world to take your work as a crude, rough estimate.
If the world will not believe you when you say the mountain is 29,000 feet tall, you simply add two feet to the number and report it as 29,002 feet above sea level. No one at the various geographical societies that sponsored the expedition ever questioned the number.
While the height reported may have been bogus, the number remained the official height for more than half a century. Even today, it is not uncommon to find books or articles that still report the mountain’s height as 29,002 feet. And slightly altering the official record had another real advantage: Not only is 29,002 feet a more believable number, but technically, it means that Andrew Waugh and John Armstrong were the first men to put two feet on the top of Mount Everest.
Eat your heart out, Sir Edmund Hillary.