.... "If the brain was so simple that we could understand it, then we would be so simple that we couldn't." -- Emerson M. Pugh


Web mindshavings.blogspot.com

Friday, August 22, 2008

The Berry Paradox

The Berry Paradox comes in a few different forms. Here is one of the simplest examples of it for easy comprehension:

Name "the smallest possible integer NOT definable by fewer than twelve words".

It's easy to imagine examples that DON'T work:

the speed of light in meters per second [only 8 words]
the number of inches in a foot [7 words]
the number of stars in the universe [7 words]
one hundred thirty million, sixty seven thousand, three hundred and thirteen [11 words]

easy enough...

The problem arises however (if it isn't already obvious), that if you did concoct a sentence of 12 or more words to define some integer, and it IS the smallest such definable integer, IT can then be accurately designated (defined) by the original 11-word sentence above ("the smallest possible integer not definable by fewer than twelve words") -- thus a self-referential contradiction!

Another example of where mixing language/semantics with numbers/mathematics proves vexing, throwing light on illogical ambiguity within language.

More on the Berry paradox at Wikipedia:


No comments: