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[Solved]: Why have additional symbols on a Turing machine?

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Problem Detail: 

What is the point of non-binary printed letters on a turing machine? I understand that these need to be omitted to get a computable number, but why are they used in the first place?

Asked By : joker

Answered By : Denis

Turing Machines are an abstract model of computation, their purpose is to define in a mathematical way what problems are theoretically computable and which are not.

It is true that a binary alphabet is enough to reach the full expressive power of Turing Machines. However, when playing with them "in practice" to prove theorems and to communicate these proofs, it can be more convenient to use more symbols, instead of encoding everything in binary. We could always go back to binary if it's absolutely needed.

An extreme example of the same sort would be "why are we still using 26 characters to write texts, now that we know that two are enough? It would save time when learning the alphabet!".

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