Tuesday, 25 May 2010

Making Mountains of Surmise from Molehills of Evidence

The title of this post is taken from an article by the great exponent of popular mathematics and early skeptic, Martin Gardner who died last Saturday. I knew of Gardner because of his books like the Mathematical Carnival, which made maths fun and accessible. These were books that I would read along with my best friend when we were 12-13 and wonder at the beauty of mathematics. Gardner wrote a puzzle column for Scientific American which combined puzzles with magic and shows the strong link between Maths, Logic and Magic.

The particular case he was referring to was the book Atlantis written by Ignatius Donnelly in 1885, which pointed out the possible links between the South American civilisations and Ancient Egypt. They both built pyramids, they both had a calendar of 365 days and they both had flood legends. What he could not have known is that the South American civilisations such as the Incas and Aztec flourished from the 12th century AD over 3500 years after the building of the Great Pyramid. Even the Maya pre-classic period does not begin until 2000 BC, 500 years later.

This is an example of correlation that does not imply causation. They both happen to have discovered the same things. The same calendar is sensible as this is the right one that corresponds to the Earth's orbit. Flood legends are ubiquitous in human civilisations, because floods happen everywhere and pyramids are a strong and simple structure to build if you want a large monument with limited materials.

This is also a perfect example of another phenomenon from biology, that of Convergent Evolution. We end up with the same products from very different histories because of the environmental constraints. This lesson about constraints and convergence is a very important one as it is easy to fall into Donnelly's error and think that events are less probable than they actually are.

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