Buzz
What’s really hidden in a number? Apparently, a great deal. Though we may not often ponder the significance of our numbers and numeral system, it has a fascinating history.
The numeral system most of us use today is known as the Arabic numeral system, or more accurately, the Hindu-Arabic numeral system. The original name is somewhat misleading, as it was actually developed in India, not in the Middle East. They are called 'Arabic numerals' because Europeans mistakenly believed they were created by the Arabs.
The numeral system itself isn’t the only part with an intriguing origin; individual numbers also carry their own fascinating and often surprising histories. Here are ten of those stories.
10. 'Billion'
A billion, which is one followed by nine zeros, traditionally represents a thousand million. However, decades ago, the term 'billion' had two different meanings. The first refers to a thousand million (a one and nine zeros), which still holds true today, while the second referred to a million million (a one and twelve zeros), a figure now known as a trillion.
This discrepancy arises from the differences between American and British English. In American English, a billion has always been defined as a thousand million, while in British English, it once meant a million million. Additionally, British English used to refer to a thousand million as a 'milliard.'
Similarly, there were two definitions of a trillion. In American English, a trillion always referred to a million million (a one and twelve zeros), whereas British English used to define it as a million million million (a one and eighteen zeros). In 1974, however, British English adopted the American definitions for billion and trillion, abandoning the term 'milliard.'
9. 40
The correct spelling of 40 is 'f-o-r-t-y,' not 'f-o-u-r-t-y.' This has caused confusion among native English speakers, who sometimes mistakenly add a 'u.' The confusion stems from the assumption that 'forty' derives from 'four,' which contains a 'u.' Interestingly, 'fourty' was once the accepted spelling of 40.
To understand why there is a difference in spelling, we must first recognize that the word 'forty' didn’t come from 'four.' Instead, it was derived from the Old English 'feowertig,' which itself was formed from 'feower' meaning 'four,' and 'tig,' meaning 'group of tens.' The word 'four' in Old English was 'feower.' Over time, 'feowertig' and 'feower' evolved into 'fourty' and 'four.'
This pronunciation shift occurred between the 15th and 17th centuries, during the Great Vowel Shift. This linguistic change caused some English words to lose vowel sounds and alter their pronunciation. By the 16th century, 'forty' emerged. By the 1800s, 'forty' became more common and eventually replaced 'fourty' as the standard spelling.
8. 'Million'
The term 'million' entered the English language in the 14th century, originating from the Old French 'million' and the Italian 'millione' (meaning 'great thousand'), both of which were derived from the Latin 'mille,' meaning 'thousand.' For centuries, English lacked a specific term for 'million,' as there was no need for such large numbers. People didn’t have possessions or wealth that would require counting in the millions.
However, everything changed when people began counting in millions. Initially, they relied on the word 'thousand,' which had previously been the highest numerical term in English. 'Thousand' was called 'þusend,' meaning 'strong hundred,' with 'þ' being an extinct letter known as the thorn. A million was referred to as 'þusend þusend' (thousand thousand) before 'million' was borrowed from Old French.
7. Googol
A googol is the number 1 followed by 100 zeros. In 1996, the search engine we now know as Google was originally called BackRub. In 1997, Larry Page, one of the co-founders, began brainstorming with friends about a new name for the search engine. Sean Anderson, a friend of Larry’s, suggested 'Googolplex,' a term for a number represented by a googol of zeros. But Larry decided on the simpler 'googol.'
Sean went online to check if 'googol.com' was already taken. Unfortunately, he misspelled 'googol' as 'google.' Larry liked the new spelling, and thus, Google was born. What many don’t know is that the terms 'googol' and 'googolplex' were invented by a nine-year-old boy in 1920. Milton Sirotta, the nephew of mathematician Edward Kasner, came up with the terms after Kasner asked him how to name the number 1 followed by 100 zeros.
Sirotta believed that only a playful name like 'googol' would be suitable for such a large number. He also proposed the name 'googolplex' for a number represented by as many zeros as the person writing it down felt like. Later, Kasner defined a googolplex as a number consisting of a googol of zeros.
6. Pi
Pi is the mathematical constant representing the ratio of a circle’s circumference to its diameter. This infinite number is typically approximated as 3.14 or 3.142. The concept of pi has intrigued people for millennia, with the earliest recorded estimation occurring around 1900 BC by the ancient Babylonians, who calculated it as 3.125. The ancient Egyptians had a slightly higher estimate of 3.16. Archimedes of Syracuse is believed to be the first to accurately calculate pi, estimating it between 3.1408 and 3.14285.
In 1874, William Shanks managed to compute pi to 707 digits, though his calculation was only accurate up to the 527th digit. By 1945, D.F. Ferguson extended the calculation to 620 digits, and by 1947, he had calculated it to 710 digits. Fast forward to 1999, when Takahashi Kanada expanded pi’s digits to an extraordinary 206,158,430,000, and in 2011, Shigeru Kondo took it even further, calculating pi to an astounding ten trillion digits.
A rather amusing episode involving pi took place in 1897 when the Indiana state legislature nearly passed a bill that would have set its value at 3.2. Although the bill wasn’t intended to alter pi’s value, but rather aimed to address the old problem of squaring the circle, it would have mistakenly altered pi from its true value of 3.14 to 3.2.
The concept behind this bill was to determine the area of a circle by using a ruler and compass to construct a square with an equal area, and then measuring it. No mathematician has ever solved this problem, but in 1894, Edward Goodwin claimed to have found the solution. He copyrighted his answer and insisted that anyone wishing to view it pay royalties.
Goodwin, however, offered his solution for free to Indiana schools, but only if the state legislature passed a bill confirming the validity of his work. The issue arose because Goodwin used the incorrect value of 3.2 for pi. The state of Indiana was on the verge of passing the bill, but they ultimately reconsidered when Professor C.A. Waldo of Purdue University pointed out that they were about to unintentionally adopt 3.2 as pi’s true value.
5. Zero
Zero was first used by the Sumerians between 4,000 and 5,000 years ago. At that time, it wasn’t used as a number or to represent the concept of nothing. Instead, the Sumerians used it as a placeholder added to single digits to indicate multiples of tens or hundreds. The full concept of zero as we know it today was invented twice. The first occurrence was in Babylon around 400 to 300 BC, but it still functioned as a placeholder for nothing. Meanwhile, the Maya also independently discovered zero in the early centuries of the Common Era.
In the 5th century, the Indian mathematician Brahmagupta became the first person to truly use zero as a number in its own right. He represented it by placing a dot beneath other numbers. By AD 879, zero had taken the oval shape we recognize today, though it was still not universally accepted as a full number, often written in smaller characters compared to other digits.
Zero became widely recognized as a legitimate number after the Italian mathematician Fibonacci introduced it to Europe around 1200, alongside Arabic numerals. Fibonacci had learned about these numerals from the works of the Muslim scholar Mohammed ibn-Musa al-Khowarizmi, who referred to zero as 'sifr.'
Italian merchants and German bankers quickly adopted the use of zero, but many European governments banned Arabic numerals due to concerns about how easily they could be manipulated. Despite this, merchants and bankers continued to secretly use zero in their transactions, often substituting it with a code. This is where the word 'cipher,' meaning 'code,' originated. It came from 'sifr,' the term used by al-Khowarizmi for zero.
4. Belphegor’s Prime
Belphegor’s Prime is a number consisting of a 1 followed by 13 zeros, then three sixes, another 13 zeros, and ending with a 1. In numerical form, it appears as 1,000,000,000,000,066,600,000,000,000,001. The number is named after Belphegor, one of the seven princes of Hell, and it stands out for several unique characteristics.
Despite its lengthy structure, Belphegor’s Prime is a prime number, meaning it is divisible only by one and itself. Additionally, it is a palindrome, remaining identical when read forwards or backwards. It also includes the infamous number 666, the 'number of the beast,' right in its center. As if that weren’t enough, the number has 31 digits, which, when reversed, form '13,' a number often considered unlucky.
Belphegor’s Prime was first discovered by Harvey Dubner, who had a passion for finding new prime numbers. He stumbled upon it after realizing that palindromic prime numbers, like 16,661, could be expanded by inserting zeros at both ends to create new prime numbers. In this case, 13 zeros were placed between the ones and sixes at both ends. It remained just another palindromic prime until mathematician Cliff Pickover named it after Belphegor, the prince of Hell, due to the presence of 666.
3. 100
The term we use for the number 100 is 'hundred.' However, centuries ago, the word 'hundred' had two different meanings. One referred to five scores, which is today’s 'hundred,' while the other referred to six scores, or 120. This difference can be traced back to Old Norse, where 'hundred' was called 'hundrath' and actually meant 120.
This discrepancy caused confusion when the word was introduced into English, where 'hundred' came to be understood as 100. To resolve the issue, the five-score version was called the 'new hundred,' 'short hundred,' or 'decimal hundred' (hundrath ti-raett), while the six-score version was referred to as the 'old hundred,' 'long hundred,' or 'duodecimal hundred' (hundrath tolf-roett). Eventually, the five-score 'hundred' became the standard.
2. 666
Most people are familiar with 666, the infamous number associated with the Biblical beast that is said to rule the Earth during the final days. This is mentioned in Revelation 13:18, which reads: 'Here is wisdom. Let him that hath understanding count the number of the beast: for it is the number of a man; and his number is six hundred threescore and six.' A score is 20, and three scores add up to 60, making 'six hundred threescore and six' equal to 666. Or does it?
However, a fragment of the Book of Revelation discovered in 2005 suggests that the number of the beast is actually 616, not 666. This fragment, the oldest known copy of the Book of Revelation, was written in Greek at the end of the third century and was found in Egypt. When Peter Gilmore, high priest of the Church of Satan, heard the news, he commented that while their movement has embraced 666 due to its negative Christian associations, they would readily adopt 616 if Christianity shifted to recognize it instead.
1. 5,040
To most of us, 5,040 might appear to be a random number. But to ancient Greek philosopher Plato, it was the epitome of perfection. 5,040 is classified as a highly composite number, or anti-prime, a rare category of numbers that are divisible by a large quantity of divisors. Unlike prime numbers, which can only be divided by 1 and themselves, anti-primes like 5,040 have 60 divisors.
Plato considered 5,040 to be the ideal number, suggesting that a perfect city should never exceed this figure in population. He believed that such a number would allow for effective governance and an easy distribution of citizens into different social groups. To uphold this ideal, he proposed that newly established cities be divided into 5,040 plots, each assigned to one of the 5,040 citizens. However, in ancient Greece, women, children, and slaves were not recognized as citizens, so the total population would actually surpass 5,040.
To ensure that land plots were not divided, Plato recommended that when a citizen passed away, their entire plot should be inherited by one designated son. Any additional sons would be allocated to citizens without male heirs, while daughters would be married off. Plato also advised that the government discourage citizens from having too many children; in cases where this occurred, the excess children should be sent to another city.
