The idea of writing a column about nothing has a certain appeal. After all Jerry Seinfeld created a situation comedy series that ran for years on television and it was about nothing. Today we’ll explore some of the characteristics of the nothing known as zero.
The concept of zero may have developed around 4,000 to 5,000 years ago by people in the Mesopotamian city-state of Sumer. It appears to be used as a position indicator as their counting systems. They did not use our base-10 number system but if they did then this positional counting scheme would work like this: Record numbers in columns of 1’s, 10’s, and 100’s. So to record 105 sheep, there would be a 5 in the first column, a pair of diagonal lines in the 10’s column and a 1 in the 100’s column. The diagonal lines indicating no 10’s or zero in the tens column. The Babylonians around 300 B.C. seemed to do the same thing.
The Romans avoided the whole issue with their system of Roman numerals which have no zero. The 105 sheep could be indicated as CV.
The Mayans used the concept of zero as a placeholder around 350 CE in their calendar systems.
The concept of zero appears in many other places; India and China primarily but others worked on the concept too.
The symbol of 0 to stand for zero may be due to “a Persian mathematician, Mohammed ibn-Musa al-Khowarizmi, [who] suggested that a little circle should be used in calculations if no number appeared in the tens place. The Arabs called this circle ‘sifr,’ or ’empty.’ Zero was crucial to al-Khowarizmi, who used it to invent algebra in the ninth century [CE].” (Szalay)
The developers of the Gregorian calendar (Late 17th and early 18th centuries CE) designated the year 1 BCE as year 0. Thereby solving the need for an actual year zero but confusing everyone as to when a new century begins. We all thought year 2000 began the 21st century but we were wrong. It began in 2001.
Zero has a number of unique properties. It exists between one and negative one. Zero itself is neither negative nor positive. If you multiply a number by zero the answer is zero. However, numbers raised to the zero power equal one. Even zero to the zero power equals one.
“The concept of dividing by zero is even more senseless, so much so there is no property for it; the concept simply doesn’t exist since it can’t be carried out. Even mathematicians often struggle to explain why dividing by zero doesn’t work. The reason is essentially related to the multiplication property. When dividing a number by another number, for example 6/2, the result (in this case, 3) can be meaningfully plugged into a formula where the answer multiplied by the divisor equals the dividend. In other words, 6/2=3 and 3×2=6. This doesn’t work with zero when we replace 2 with it as the divisor; 3×0=0, not 6. The concept of dividing by zero is fraught with illogical consequences.”(Clark)
An interesting thought puzzle about nothing.
“… zero doesn’t have to exist to be useful. In fact, we can use the concept of zero to derive all the other numbers in the universe.
“Imagine a box with nothing in it. Mathematicians call this empty box ‘the empty set.’ It’s a physical representation of zero. What’s inside the empty box? Nothing.
“Now take another empty box, and place it in the first one.
“How many things are in the first box now?
“There’s one object in it. Then, put another empty box inside the first two. How many objects does it contain now? Two. And that’s how ‘we derive all the counting numbers from zero … from nothing’ …” (Resnick)
References
- Apologies to William Shakespeare for usurping a title to one of his plays.
- Was Seinfeld really ‘about nothing’?, Jennifer Keishin Armstrong, BBC, June 2015.
- The Zero Project. An organization with the purpose to “elucidate the
origin of the numeral ‘zero’ in the history of mankind and to date the issue remains unresolved.” - How Zero Works, Josh Clark, How Stuff Works.
- Who Invented Zero?, Jessie Szalay, Live Science, September 18, 2017.
- The Origin of Zero, John Matson, Scientific American, August 21, 2009.
- Zero to the power of zero, Wikipedia.
- The mind-bendy weirdness of the number zero, explained, Brian Resnick, Vox, December 5, 2018.
Resnick attributed the puzzle above to John von Neumann.
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