Tuesday, 11th March, 2008

Relativity Limericks – with apologies to Einstein

Versions of these (but with worse scansion) can be found almost anywhere. This may be what caused Einstein’s hair to look the way it does. einstein_cartoon_1.jpg

There was a young lady called Bright
Who could travel much faster than light;
She departed one day
On the 13th of May
And returned on the previous night.

There was a smart fellow called Fisk
Whose fencing was really quite brisk;
So fast was his action
The Lorentz contraction
Converted his foil to a disc.

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Tuesday, 18th December, 2007

How to Prove Anything You Want

Believe it or not, you can prove absolutely anything you want.

For instance, you might wish to prove that the moon is made of green cheese. paradoxical triangleTake the statement you want to prove and insert it at number 3 in the box below:

1. There are three numbered statements in this box.

2. Exactly one of these statements is true.

3. The moon is made of green cheese.

 Now we look at each statement in turn.

Statement 1 is true, as we can see from looking at the box.

Statement 2 cannot be true, for the following reasons: we know that 1 is true, and if 2 is also true, then there would be at  least two true statements, not one, in the box. Therefore we mark statement 2 as false.

This means that there are the number of true statements in the box is either none, two or three. It’s not none, because 1 is true. It’s not three, because we’ve just decided that 2 is false.

Therefore there are exactly two true statements in the box. We already know that 1 is true, and 2 is false; thus 3 must be true regardless of what it says!). Thus we can prove that the moon is made of green cheese.

(I first ran across this problem many years ago, in a magazine advertisement for the logic training game Wff n Proof.)

This is an example of the type of paradox first attributed to Epimenides the Cretan (circa 500BC according to Plato, or 600BC according to Aristotle [Britannica]), who said "All Cretans are Liars". It surfaces later in the barber paradox propounded by Bertrand Russell, and arises from the fact that we are using statements to describe themselves.

In its purest form, the paradox resolves to "This statement is false".

There’s an interesting site describing most of the famous mathematical paradoxes at: http://eluzions.com/Puzzles/Logic/Paradox/

 

 

 

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Wednesday, 28th November, 2007

An Escher-type Tessellation

Here’s a tessellation on a sphere, in the style popularised by the Dutch artist, Maurits C Escher. This one has been generated by computer, whereas Escher did his by hand and eye, which is almost beyond human understanding.

 

Escher also produced more interesting pictures related to the natural world, for example, this one of tessellated fish.

 escher type sphere tesselation

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Sunday, 11th November, 2007

Six Impossible Things Before Breakfast: Number 1

minus 1 paradox

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