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Representing numeric values using positional notation is one of the milestones in the history of arithmetic. Babylons used a base 60 system, Maya a base 20 system; base 10 system became "the standard" used by modern civilizations; digital computers use the Binary numeral system, ....

But if we look at nature, we found that life itself "heavily rely" on an alphabet of 4 symbols: the DNA has four (chemical) bases: adenine, cytosine, guanine and thymine (A, C, G, T) that are used to store the "instructions and information" to generate and drive the parts of a living organism.

But on a higher level, are there "natural algorithms" (algorithms found in natural processes, in animal behaviours or in everyday human behaviours) that take advantages of "numeral systems" other than the unary representation.

To be more precise I would like to know whether or not natural processes or living creatures make use of a finite, discrete alphabet of "symbols" and use them in a manner similar to a positional notation: the symbols are placed together and used as a whole to represent "something" (an action, an information, an object, ...) among many other possibilites ... a sort of "index" in an exponential number of possibilites.

Another (obvious) non numeric example is the human language where (in general) a combination of finite number of sounds ("alphabet") are combined to form the words.

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    $\begingroup$ DNA isn't really a "base 4" system in the sense that the base-pairs are representing integers; it's just an alphabet with four symbols. So what you seem to be asking is whether or not other living creatures seem to make use of a finite, discrete alphabet to store information or to use as instructions to drive their behaviour. If that's so, you might want to re-phrase your question in that way. $\endgroup$ – Niel de Beaudrap Oct 6 '12 at 19:36
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    $\begingroup$ That sounds like information/instruction storage to me; much as we're using symbols right now from a quite literal alphabet to communicate meanings with the whole sequence of the words formed from the letters. But "base 4" and "unary" sound like you're talking about specifically storing numbers. $\endgroup$ – Niel de Beaudrap Oct 6 '12 at 19:56
  • $\begingroup$ @NieldeBeaudrap: thanks, I tried to rewrite the question using your comment. Do you think it can be improved? $\endgroup$ – Vor Oct 6 '12 at 20:18
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There is at least one example where a string of symbols from an alphabet is also used: proteins.

Proteins consist of chains of 20 different amino acids (usually, in some cases, it's 21 or 22) and the sequence of amino acids determines what given protein does.

This example is closely related to the DNA example you gave, because each amino acid in a protein is encoded by a triplet of bases in DNA.

For more information, see the article Genetic code on Wikipedia.

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The Aufbau principle, which controls the electron configuration of atoms, is an example of a "positional" notation. Electrons (more or less) fill shells in some fixed order, and the outer shell determines the chemical properties of the atom.

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