Zero ideas: Reflections on nothing

For someone who is a Maths Person, I don’t really like reading books on maths. I don’t mean textbooks from back in the day, I mean ‘popular science’ books on maths. 101 Fun Factoids You Didn’t Know About Math.
I’m thinking it’s similar to comedy. I like telling – and making – jokes/puns, but certainly don’t like written comedy.  So the double whammy of writers who think they are funny, then write about maths and science…well…good manners prevent me from … 🙂
But it’s not an absolute thing. I do like to occasionally grab one of the more Maths Facts for Grown-Ups type of book. And I think it was in one of those I first read interesting things about nothing.
Or zero to be more precise.

Do Nothing, Destroy or worse.

So, this number zero has some interesting properties. Particularly in the way it acts on other numbers (or things, represented by numbers).

It can do nothing

Add zero to a number and there’s no change. Subtract zero and there’s no change. Do either – or both – 36 or 38 more times: no change.  x ± 0 = x

Yet it can destroy

Take any number, multiple it by zero and bye-bye number. You’ve basically destroyed it. 36 * 0 = 0.

Worse is to come

Dividing by zero is basically NOT ALLOWED in maths.  More formally: “division by zero is undefined”.  From the same source, have a look at what happens when we calculate 1/5, 1/4, 1/3 etc and graph it for a whole lot of values.  As we approach 1/0 the value goes shooting off to approach infinity.  Note: we can never get to 1/0.
Coming the other way  -1/5, -1/4, -1/3  (as the legend below says) it approaches negative infinity.

 

Coping Mechanisms

All modern calculating tools should pick up this ‘dividing by zero’ attempt:

The History of Zero

One source writes “The first evidence we have of zero is from the Sumerian culture in Mesopotamia, some 5,000 years ago. There, a slanted double wedge was inserted between cuneiform symbols for numbers, written positionally, to indicate the absence of a number in a place (as we would write 102, the ‘0’ indicating no digit in the tens column).”
It’s quite an abstract piece of thinking, this zero thing:  a number that sort of represents the absence of a number. Plus all the associated maths that goes along with it.
I wonder what came first, negative numbers (“I owe you 2 goats”) or zero (“I have no goats to give you”)?   I wonder if space-time going infinite inside a black hole (the singularity) has anything to do with division by zero? Time for more reading and learning.