Image Credit: Anon
Today I came across an debate on the BBC Home website about a new number called nullity Φ=0/0 invented along with Transmathematics by Dr James Anderson of the University of Reading. “Wow” I thought – a new number. And, finally, someone’s found a way to work around division by zero. At the heart of James’ idea is the splitting of the real number line into 2 infinities – positive infinity and negative infinity: 1/0=+∞ and -1/0=-∞.
Image Credit: Anon
This seems better than just having one unfathomable infinity at both ends of the number line. As I am going through a phase collecting special numbers and looking at their properties I decided to think a bit more about nullity. But something just didn’t feel right about it. I was introduced to real maths by another James – my grandad James Patrick (“Paddy”) O’Neill one day when he returned from one of his usual Saturday walks around the antique shops of Bootle. He called me in from the back garden and said, “Son, sit yourself down. I’ve a good book for you” in his strong Keady accent. I was seven. He plonked down a massive hardback book on the kitchen table with a look of pride shaking the table so hard it caused my nan’s bone china tea-cup to rattle on the saucer. The book was the 1936 edition of “Mathematics for all” and was twice as thick as the Bible. It was written for the “educated layperson” and full of practical uses of mathematics like how to measure the width of a river without having to cross it. I loved it. It was like a wizard’s book of spells. It had passed many hands between coming off the printing press and landing on the tablecloth that day in 1977. Although the pages were yellowed and slightly stiffened due to their drying out over the years, it was without a blemish. Every previous previous owner seemed to have either cherished it (or never read it!) before it finally wound up in the second-hand shop where Paddy found it. At the end of each chapter it had a “teaser” puzzle which could only be solved with common-sense and a sprinkle of logic. So what about Φ? I figure… if I have nothing and share it with no-one then surely “everyone” (noone) gets nothing right? So isn’t Φ=0?
Image Credit: Anon
Now that would be a mathematical revelation: 0/0=0! Maybe it is. Maybe it isn’t. But I like it that way. It’s also then fits nicely in the middle of the number line between -∞=-1/0 and 1/0=+∞ where, as Paddy would say, “it’s sits pretty”. It’s funny that he was also in Athens this time of the year 56 years ago. What triggered him to pick up this particular book for me? Who knows? Maybe memories of smalltalk he had had 30 years earlier with a friendly local in Pireas about geometry and well-proportioned women? I like to think so.
