Getting Something from Nothing

This last week we read about the creation of zero and how it wasn’t really part of a numerical system until later in civilization. It seems weird that such an essential part of the number system is left out. The reading by the Smithsonian Magazine intrigued me enough to dig into for myself because of the heavy importance writer Amir Aczel puts on it. He talks at the end of his article about if the zero was created or discovered. For the most part it makes sense that zero wasn’t necessary because the old practical reason for a numerical system was to count things and most of my readings supported that. They did not necessarily need a symbol to represent nothing. Their notation served its purpose and was all that was needed back then. The acknowledgement of zero as not only a numerical value, but as an idea has brought mathematics to what it is today, and without math we would never be anywhere close to what we are today.

caption Babylonian numerical system circa 3100 BC. Image: Josell7, via Wikimedia Commons.

Going along periodically throughout time we began to have more systematically efficient numerical systems, including the Roman numerals and the Babylonian counting systems and eventually the Hindu Base ten system. The idea of zero was much more prominent as math theory progressed. The zero was originally just a dot to represent an empty place. It took until the ninth century when Persian Mathmatician Mohammed ibn-Musa- al-Khowarizimi(780-850) started working on equations that equaled zero. Today these equations are known as algebra.

“Russel Peters-Invention of Zero”-Youtube

An Italian mathematician named Leonardo Bonnacci(c.1170-c.1250), more commonly known as Fibonacci, refined and built on Al-Khowarzmi’s work for use in an Abacus book, which spread around European merchants and became the primitive base work for accounting. He spread it as a placeholder so we may distinguish 1 from 10 and 10 from 100. By distinguishing that it exists we can now separate the negatives from the positives, we know have a universal positional notation worldwide because of the simplicity that the base 10 system has. This affected trade and progression of civilization in surrounding areas. What it also affected was the growth of math itself.

But why is zero so substantially symbolic? As an article from Joanne Sacred Scribes from states that zero symbolizes of an eternity. There is no end, nor beginning. It also has to do with the concept of Heaven, that there would be no more suffering, which gave people a tangible idea of what zero was. The symbolism of the zero also came from Rene Descartes(1596-1650), the founder of the Cartesian co-ordinate system. With (0,0) being the origin of all Cartesian planes it fits in the belief that we were created from nothing and we can base ourselves on where we were at our origin.

So now that we have the basics of graphing and algebra the zero has played its importance and is just another number right? Wrong. Perhaps the greatest progressive push the zero has helped create was the creation of physics, engineering and economics through the use of calculus. How did zero play a part in this? Most people know the laws of adding, subtracting and multiplying zero but it wasn’t until the 1600’s that mathematicians Isaac Newton and Gottfried Wilhelm Leibniz understood what it meant to divide by zero in a mathematical sense. This hook in basic arithmetic was observed through the use of infinitesimal quantities, or looking at what happens to a number, or a line as it gets infinitely small towards zero, but not zero. For a better quick history on the development of calculus the author Jason Garver of From Quarks to Quasars gives a fantastic overview.

As Tobias Danzig, a German mathematician says “In the history of culture the discovery of zero will always stand out as one of the greatest achievements of the human race”. When you look back and realize that when we got a standardized numerical system is when we started making vast headway in trade, commerce, expansion and innovation it is amazing to ponder what life would be without it.

Further reading:

-John Matson: Article talks about early uses of zero and its importance to civilization:

-marycneville: Article talks about creation of zero and its importance to religion:

-malinibindra: Slideshow talking about why zero is the most important discovery:

-JJ O’conner and E F Robertson: Article talked about the progression of zero through non western civilizations:

-Joanne Sacred Scribes: Talked about the theological aspect of zero and the symbolism behind it:

Amir Aczel: Article read in class. Gave a broad overview of the development and implementation of zero:

Nils-Bertil Wallin: Talks thoroughly about the importance of zero throughout time and evolving civilizations:

Jason Garver: Gives overview of the creation and development of Newton’s side of Calculus:

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