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Say you want to note down a number to another person, and want it to be unambiguous (perhaps the other person is an alien and has more than 10 fingers or something). So if you say

12345, base 42

That's not enough because they will ask

is 42 in base 42 or in base 10

What is the commonly accepted approach here? Should you specify the base in base-9, because that base's representation only has one digit?

Johannes Schaub - litb
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  • I think it's self-evident that this is a recursive problem unless you can find some way of expressing a quantity using a representation not bound by the concept of basis. – Lightness Races in Orbit Aug 14 '14 at 18:07
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    Base 42 would need 42 different symbols. In base 42 it would be '10'. –  Aug 14 '14 at 18:08

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Then how would you specify that number's bases's base's base? Its turtles all the way down, unless at some point everyone agrees on a convention. I have always assumed the base is given in base ten.

As far as being unambiguous to an alien, this is rather impossible for any symbol. Language requires a common frame of reference. You might make it easier for them to deduce what you mean by providing many examples, in much the same way attacks in cryptography are often more feasible with more ciphertext.

Jonny
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