I’ve always LOVED that concept! And while I’m sure I’m not the first to dream it up, it was new to ME on a certain day, back around 1967.
I was about fourteen, in the “A” stream at Copleston High, when a temporary teacher decided to wind us all up – by presenting us with an unsolvable problem.
The premise was as follows: if you take two objects and divide the distance between them by half – then move them that much closer to one another – then divide THAT distance by half – rinse and repeat – will they ever make CONTACT? Yes or no?
Of course, it’s like the chicken and the egg – which came first? Neither answer works.
And likewise, the two objects. If you constantly HALVE their distance apart, they can never meet. But if they continue to CLOSE on each other – they MUST.
Eventually, I said, “I’ve GOT it.”
Seventy-two eyes swung in my direction.
“You have given us a problem in three dimensions – to which, since those objects are constantly moving towards each other – the answer MUST be YES.
“However, to QUALIFY that answer we must bring in the FOURTH dimension; TIME.
“The question then becomes not IF the two objects will meet – but WHEN.
“And the answer to THAT question is… INFINITY… PLUS ONE!!”
…At which point, the discussion swung to the concept of infinity.
Even the grains of sand on our planet have now been quantified (roughly, of course).
The only thing now – and indeed, back then – that is infinite (well… probably) is the universe – closely followed by a Bangkok long-duration traffic light – but that I won’t trouble you with.
Instead, I’ll pose a question of my own: is infinity plus one… SMALLER than infinity plus TWO?!