2005 : WHAT DO YOU BELIEVE IS TRUE EVEN THOUGH YOU CANNOT PROVE IT?

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Writer and Television Producer; Author, Remembering Our Childhood: How Memory Betrays Us
Writer and Television Producer; Author, The Riemann Hypothesis

I believe it is true that if there is intelligent life elsewhere in the universe, of whatever form, it will be familiar with the same concept of counting numbers.

Some philosophers believe that pure mathematics is human-specific and that it is possible for an entirely different type of mathematics to emerge from a different type of intelligence, a type of mathematics that has nothing in common with ours and may even contradict it. But it is difficult to think of what sort of life-form would not need the counting numbers. The stars in the sky are discrete points and cry out to be counted by beings throughout the universe, but alien life-forms may not have vision. 

Intelligent objects with boundaries between being and non-being surely want to be measured— "I'm bigger that you", "I need a size 312 overcoat"—but perhaps there are life-forms which don't have boundaries but are continuously varying density changes in some Jovian sea. Intelligent life might be disembodied or at least lack a discrete body and merely be transmitted between various points in a solid material matrix, so that it was impossible to distinguish one intelligent being from another.

But sooner or later, whether it is to measure the passing of time, the magnitude of distance, the density of one Jovian being compared with another, numbers will have to be used. And if numbers are used, 2 + 2 must always equal 4, the number of stars in the Pleiades brighter than magnitude 5.7 will always be 11 which will always be a prime number, and two measurements of the speed of light in any units in identical conditions will always be identical. Of course, the fact that I find it difficult to think of beings which won't need our sort of mathematics doesn't mean they don't exist, but that's what I believe without proof.