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Archive for July, 2010

great fools

There is an apostolic injunction to suffer fools gladly. We always lay the stress on the word “suffer,” and interpret the passage as one urging resignation. It might be better, perhaps, to lay the stress upon the word “gladly,” and make our familiarity with fools a delight, and almost a dissipation. Nor is it necessary that our pleasure in fools (or at least in great and godlike fools) should be merely satiric or cruel. The great fool is he in whom we cannot tell which is the conscious and which the unconscious humour; we laugh with him and laugh at him at the same time.

An obvious instance is that of ordinary and happy marriage. A man and a woman cannot live together without having against each other a kind of everlasting joke. Each has discovered that the other is a fool, but a great fool. This largeness, this grossness and gorgeousness of folly is the thing which we all find about those with whom we are in intimate contact; and it is the one enduring basis of affection, and even of respect.

G.K.C.

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First of all, 5OSME is here in Singapore! (Registration is over, but I think there are some portions of this convention for Origami in Science, Math and Education which are open to the public.)

Which explains why Erik Demaine and Robert Lang are here in Singapore!

Erik Demaine gave a talk today at NUS, and among the many amazing things he displayed, he demonstrated a “trick” that makes use of something called monotonous Boolean functions.

Before proceeding, I shall state the problem.

First, suppose we have a picture frame hanging from a nail by a piece of string like so:

If we remove the nail, the frame will fall.

Now suppose we have two nails instead of one. We can hang the frame from both nails in a few ways:

In the leftmost example, the frame will still remain suspended if we remove either nail; only by removing both nails can we cause it to fall. In the middle example, removing the red peg will cause the frame to remain suspended, while removing the green one will cause it to fall. The problem is this:

Is it possible to loop our string around the two pegs in such a way that removing either nail will cause the frame to fall?

This should be relatively simple to solve. (A version of the answer is here. There is no picture frame in the answer, so you have to imagine it hanging from the bottom of the loop, and convince yourself that removing either nail will cause the frame to fall)

Erik demonstrated the above in his talk today. He then asked: can we generalize this to more nails? Can we hang a picture from n nails such that removing any nail causes the picture to fall?

I’ll post about the solution, and its relation to monotone Boolean functions, in subsequent posts.

.

(Picture Credits:

Pictures of curved origami sculptures in glass

Picture frame)

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