claremarieegan Mar/ 25/ 2019 | 0
A couple weeks ago, I read a great CNN article called “Scientists say bees can do basic math.” It details the results of a study conducted by scientists at the Royal Melbourne Institute of Technology in Melbourne, Australia.
The scientists constructed a maze (you can see a diagram of the maze on the CNN article) to train honeybees how to add and subtract. Pretty cool, right? The maze itself had a single entrance with some number of geometric shapes in either blue or yellow representing addition and subtraction, respectively. If the bees, say, saw three blue shapes (let’s say triangles), then when they fly through the maze, they should be looking for four blue triangles (remember, blue = addition). The maze would have two possible exits - one displaying the correct number of shapes (four blue triangles), and the other displaying an incorrect answer (let’s say two blue triangles). The scientists would give the bees a drop of sugar water if they flew through the correct exit and a drop of quinine if they flew through the incorrect exit.
The scientists reported the honeybees picked the correct answer anywhere from 63% to 72% of the time - figures well above random chance, demonstrating the bees were indeed grasping the concepts of addition and subtraction.
Honeybees join a rather exclusive list of animals who have demonstrated the ability to add and subtract - that list includes chimps, African grey parrots, and spiders (although there are even more animals that have demonstrated the ability to grasp the concepts behind numeral quantities).
My first reaction to this article was wow - I had no idea that animals, besides maybe chimpanzees, could add or subtract. My second reaction was more of a question. I wondered how the scientists decided on using colors (blue and yellow) to represent addition and subtraction. Now, I don’t know anything about honeybees or how their brains work, but I’m assuming the scientists realized it would be easier to use two colors to convey the ideas rather than trying to train bees to associate addition and subtraction with the plus and minus signs we humans use.
This got me thinking, where did + and - come from? And what about all the other symbols we use in mathematical notation today? What about numbers? When I am looking at figures or writing equations, I don’t give a second thought about where the symbols come from - at least not until I read this article. I started thinking about how we use symbols in mathematics. After all, mathematical notation is a universal language. So when did all this notation begin to become standardized? I decided to do some research, and actually, the history of mathematical notation is pretty interesting!
Let’s start with our numeral system. Evidence of ancient societies counting goes back as far as 25,000 to 30,000 years ago. Tally marks were found on ancient objects, indicating our ancestors were counting this far back, which in itself is a pretty interesting fact. But numerical systems, and the system we use today took awhile to come into existence.
Different ancient socities had different methdologies of counting. Some societies basically had different representations for each quantity. Ancient Egypt used hieroglyphics (pictographic symbols) and ancient Greece used different combinations of their letters (what if aa = 5?). In theory, these methods might not seem so bad, but imagine if we didn’t have digits 0 - 9 and instead had a different symbol for every number we used. Things would get complicated FAST.
Thank goodness we have digits, but where did this idea of having a few symbols and then rearranging them to represent bigger numbers come from?
The ancient Babylonians (who lived in what is now Southern Iraq) decided to (somewhat) simplify their numerical system by using a base 60 system (so having 59 symbols and then rearranging them to create all their numbers). Other societies - such as the Mayans - used a base 20 system.
If you want to learn more about numeral systems, watch this Ted Talk!
So where did our base 10 system come from? Well, our digits 0 - 9 are called the Hindu Arabic numerals. They originated in the North African region of the Arab Empire called Maghreb and then were introduced in India around the 6th century.
Indian mathematicians made an immense amount of mathematical progress - especially in areas like numerical algebra - and the base 10 counting system using the Hindu Arabic numerals became standard practice in India during the 6th to 8th centuries and finally spread to Europe around the 12th century through Middle Eastern mathematical texts. European mathematicians began to adopt the Hindu Arabic numerals and there we go, we have our digits!
But what about other mathematical symbols? There are hundreds of mathematical symbols, but I have found a few stories that you might be interested in learning about. After all, we use these symbols all the time!
Let’s start with the basics (and the bees): + and -
The concepts of addition and subtracting were around for centuries before the + and - signs we know today were invented and standardized. One example of a more ancient notation is the post-Hellenistic era mathematician Diophantus who simply placed quantities (in those times represented by combinations of ancient Greek letters) directly next to each other to represent addition.
As late as the 15th century, mathematicians were still using multiple different ways to represent addition and subtraction. One method was using the letters p and m, which come from the Latin words plus and minus. Then, in 1489, the + and - signs appeared in a German text written by Johannes Widmann to represent surpluses and deficits in business.
The Infinity Symbol:
We all know the sideways figure-8 that we use to represent infinity, but did you know this symbol was used on a Tarot card?
In 1655, the mathematician J. Wallis used the infinity symbol in a text on conic sections. The concept of infinity, of course, had been around long before this. This symbol began to catch on in the mathematical world, but it also entered broader society. People used the symbol to represent the idea of eternity and it appeared on a Tarot card called the Magus (the Juggler).
The Equals Sign:
I’ll end with the equal sign. In 1557, mathematician Robert Recorde was working on a text when he wrote the words “is equal to” over 200 times. He realized how repetitive (and probably annoying) this was and decided to design a symbol to cut down on time.
He designed the equal sign to be a pair of parallel lines. (If you don’t remember the definition of parallel lines - they are two lines in a plane that never intersect.) When asked how he decided to create the symbol, Recorde stated that no two things could be more equal than a pair of parallel lines. (I have to admit, this is my favorite story.)
So why should we care about all of these symbols and their history? Well, for one thing, we use them on a daily basis. Before a couple weeks ago, I never gave a thought to where the digits came from although without them we’d all be lost. I thought it would be a good idea to share some of these stories so we can get an idea of the long history behind mathematics (notation practice is just a small part of that history).
It’s pretty incredible that around the world we all use the same symbols to communicate about math! I hope you enjoyed learning a little more about how this universal language originated! And please read the sources I've linked in this post. They have a lot of great information!