Saturday, January 30, 2010

Donkey Geometry

A formal system consists of axioms (propositions whose truth is taken for granted) and theorems (statements derived from axioms using valid inference rules). Because every statement that is not an axiom must be proved on the basis of axioms or previously-proved theorems, it is sometimes necessary to provide formal proofs for propositions that may appear self-evident. Not surprisingly, some people find such proofs pedantic and unnecessary. I will illustrate the point with an anecdote I recently read.

The Epicureans, who esteemed feeling over reasoning, had no patience for the arguments of Euclid, and deemed his science ridiculous. To prove their case, they pointed to Book I, Proposition 20 of the Elements, where Euclid labours to show that in any triangle, the sum of any two sides is greater than the third side. This proposition, said the Epicureans, is evident even to an ass.

For a hungry ass standing at A will go directly to a bale of hay at B, without passing through any point C outside the straight line AB; it is evident to the beast that AB must be shorter than AC+CB.

It is an amusing little anecdote in its own right, but I was all the more amused because it reminded me of a certain journal entry, and more particularly, its comment thread.


Anushka said...

Do you know, I used to confuse Epicure with Epicurean.

Abhiroop said...

I think the proof would be equally accurate if you replaced the Donkey with the Quaker, and the hay bale with a really really tiny pair of hot pants.

Rahul Saha said...

What if the Donkey was a fitness freak or wanted a longer walk to boost his appetite? IT must therefore be clarified that we are talking about a lazy, very hungry donkey otherwise the proof is not proper.

Shrabasti Banerjee said...


Sroyon said...

@Anushka: And understandably so.

@Abhiroop: Also, the Quaker would walk much, much faster than any donkey, thereby ensuring that the experiment would take less time.

@Saha: That is not the only thing wrong with the proof.

@Shrabasti: ...