On the page about infinity we mention that there are things
that go wrong if you rely on your intuition. This page
describes one of them. You may also want to see the page
where Cantor Visits Hilberts Hotel, or the Balls In Barrels page.
Take a block about the size of a paperback book. Or a hardback
book, or a brick. It doesn't really matter. If you try this
for real you might want to use dominoes, CD cases, or something
But start with a bunch of blocks.
Taking the first step
Now put the first block on a table with its edge lined up neatly.
Push it gently out over the edge of the table, and get it as
far out as you can.
How far can it go?
Most people guess, correctly, about half way.
So far so good.
Bit tricky, this ...
Now put two blocks, one on top of the other. Push the top
one out until it's halfway off the bottom one, then start
to push the pair of them together out until they can't go
How far do they get?
Well, the combined centre of gravity can't go further than
the edge of the table, so the second block ends up a quarter
of the way off the table.
That means the top one is actually 3/4 off the table!
How far can we go?
The question now is this: If you're allowed any number of
blocks, just how far can you get the top one hanging over
the edge of the desk.
The answer may surprise you.
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