Think about â€“ nothing.Â Was â€œnothingâ€� discovered or invented?Â Did some fortunate soul discover â€œnothingâ€� when they tripped over it on a walk in the park?Â Or was it some prehistoric laborer who had a long day ahead of them that suddenly realized that the best tool for the job was â€œnothingâ€�?
If you’re confused, you’re not alone.Â What we’re talking about here is the concept of nothing, or an easier way to think about it might be to consider the concept of zero.Â This question about nothing is tied to the larger question of whether you think mathematics was discovered or invented.Â I prefer the question on â€œnothing,â€� however, since it simplifies things.Â There are some very abstract examples in mathematics that I say would be hard to argue are discovered.
To simplify things, let’s look at the counting numbers.Â My guess is that most people would consider 1, 2, 3, 4, â€¦, as naturally occurring and discovered objects.Â Be careful, though.Â Keep in mind that we grew up in a time well past the development of these numbers and their arithmetic rules.Â There are tribes in the world that, even today, do not have such a number system.Â The documentary The Story of 1 introduces us to the Walpri tribe of Australia, in which an elderly man is asked how many children he has.Â Instead of answering â€œfour,â€� as we would, he verbally lists the names of his children.Â The same information is being conveyed, just not in the way we are used to.
I relate this to the lack of the word â€œyesâ€� in Chinese â€“ at least as it is used in the English language.Â In English, the word â€œyesâ€� can answer a variety of questions, but if you were to ask someone in Chinese if they are hungry, they will answer â€œhungryâ€� or â€œnot hungryâ€� rather than answering â€œyesâ€� or â€œno.â€�Â If you then ask if they want to eat pizza, they will say â€œwantâ€� or â€œdon’t want.â€�
As far as nothing, or â€œzeroâ€� is concerned, we have grown up in a time and place where we are so comfortable with the idea of zero that it is hard to imagine otherwise, but the idea of representing â€œnothingâ€� was, at one time, very controversial.Â A literal â€œnothingâ€� can’t be seen, touched, or smelled, and that is exactly what zero is supposed to represent.Â So strange was this idea, that it took hundreds of years to develop into the simple thing we recognize today.
I’ve noticed that language itself tells us that the number zero is more of a modern concept.Â For example, if I were to ask the question, â€œhow many elephants are in your house?â€� the answer would be â€œthere are no elephants in my house.â€�Â There could be some variation on what that answer might be, such as â€œthere are noneâ€� or â€œthere ain’t no elephants,â€� but one answer that would not be given is, â€œthere are ZERO elephants in my house.â€�Â I’ve asked dozens of bilingual people how it works in their first language and so far no one has said the word for zero would be used.Â (Google’s translator says the phrase translates to â€œno hay elefantes en mi casaâ€� in Spanish, but all I remember from my Spanish class is â€œno tengo dinero.â€�)
According to the MacTutor History of Mathematics archive, zero first began making an appearance as a place keeper.Â The archive points out that the number 216 may not have meant two-hundred-sixteen, as we see it today.Â Instead, it might have meant 2,160 or 2,106.Â To figure out what was meant, the context of the number needed to be understood.Â The website gives a nice example, stating,
â€œIf I take a bus to a nearby town and ask what the fare is then I know that the answer â€˜It’s three fifty’ means three pounds fifty pence. Yet if the same answer is given to the question about the cost of a flight from Edinburgh to New York then I know that three hundred and fifty pounds is what is intended.â€�
All this makes me think that â€œnothingâ€� was invented.Â Just like mathematics as a whole, the development of â€œnothingâ€� was as much about the personalities who developed it as it was about â€œnothingâ€� itself.
So what do you think?Â Was â€œnothingâ€� discovered or was it invented?