Wednesday, June 28, 2006

Finding the Ultimate Question? Easy... maybe.

In "The Hitchhikers Guide to the Galaxy," a civilization constructed a gigantic computer to discover "the ultimate answer." It took hundreds of years to complete its calculations, so long that the ancient machine was surrounded by a more modern world when it was done. A huge ceremony was held to find the ultimate answer, and it turned out to be:
42

The people were completely and utterly confused, having no idea what the answer meant. As a result, they turned their civilization into a giant machine to eventually find the ultimate question.

However, to their ignorance, the answer lies in basic Calculus.

Derivation is the process of "reducing" an equation from one form to another, producing an equation that allows one to form a tangent line to any function at a given point. Integration is the opposite of this, taking the equation and undoing the derivation. Integration may also be applied to any function to find the area under that function.

When I took Calculus I, I was taught to think of integration and derivation in the following terms:
When deriving, you are given the question, what is the answer?
When integrating, you are give the answer, what is the question?

Bam! Case solved!

If the answer is a(x)=43, and the above is true, then:

integral(a(x))=q(x)
integral(43)=43x + C
q(x)=43x + C
Q.E.D.

This leaves another question--what is C? Ergo, the ultimate question has left us with another question and cannot be the ultimate question. Because the integral of the ultimate answer should provide us with the ultimate question--and it has failed to do so--one can presume that 42 is not the ultimate answer, and the machine which derived the forestated answer is flawed.

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