Mark Chu-Carroll beat me to this BBC story about a computer science professor in England claiming to have resolved a twelve-hundred year old problem. The story begins:
Dr James Anderson, from the University of Reading’s computer science department, says his new theorem solves an extremely important problem – the problem of nothing.
“Imagine you’re landing on an aeroplane and the automatic pilot’s working,” he suggests. “If it divides by zero and the computer stops working – you’re in big trouble. If your heart pacemaker divides by zero, you’re dead.”
Computers simply cannot divide by zero. Try it on your calculator and you’ll get an error message.
But Dr Anderson has come up with a theory that proposes a new number – ‘nullity’ – which sits outside the conventional number line (stretching from negative infinity, through zero, to positive infinity).
It will come as news to mathematicians that there is any mystery about dividing by zero. Suppose x is some non-zero real number, and suppose that x divided by 0 gave you some other real number y. Then it would also have to be true that x is equal to 0 times y. And since 0 times anything is 0, we have reached a contradiction.
So there is no way of assigning a numerical value to x divided by zero in a way that is consistent with everything else we know about arithmetic, and that is why children learn early on that division by zero is a very bad thing indeed. Dr. Anderson is free to define whatever symbols he likes and assign them whatever values he wants, but he hasn’t resolved anything by doing so. Mark makes the important points:
What this guy has done is invent a new number, which he calls “nullity”. This number is not on the number line, can’t be compared to other numbers by less than or greater than, etc. In other words, he’s given a name to the basic mathematical concept of “undefined”, and proclaimed that this is somehow a solution to a deep and important problem.
The thing is, there is no problem. We understand what division by zero means. You can’t do it. There is no number that meaningfully expresses the concept of what it means to divide by zero. (Emphasis in original).
Read the rest of Mark’s post for some further commentary.
The BBC article also contains a short video of Dr. Anderson using his nifty new number to “solve” the old problem about the value of 00. Turns out it equals his new number. Most mathematicians would not bother to hang around for the proof of the fact, however. You see, Dr. Anderson begins his demonstration by drawing a number line. He labels the positive integers 1, 2, 3 and the negative integers -1, -2, -3 and so on.
Then he wants to indicate that these numbers go on until you reach positive infinity and negative infinity. He indicates this by placing infinity at the far right hand-side of the line and minus inifinty at the far left side. He then places a dot next to these symbols, as if they are actual numbers residing on the line.
This is where most mathematicians would leave the room in disgust.
Infinity and minus infinity are not numbers. They are not points on the number line. When mathematicians use an expression like “the limit as x goes to infinity” they do not mean that inifnity is an actual location on the number line where x will eventually end up if it wanders for long enough. This sort of sloppiness is a big tip-off that crankery is afoot.
I explained some of this in more detail here.
The BBC article shows a group of high school students looking pretty impressed as Dr. Anderson shows them his novel theory. So, just in case the biologists were thinking they were the only ones having to deal with cranks trying to get their hands on school children, it seems the mathematicians have to start paying attention as well.