Why is information a string of digits?

NOTE HXA7241 2012-05-13T11:16Z

“The fundamental form of information seems to be a string of digits, e.g. DNA, text, bits. Why?”

This appears to be a peculiarly intriguing question. It is about something apparently very simple, yet it seems somehow profound.


Initially, one might say:

  • One-dimensionality is simplest.
  • The sequence maps to time.
  • Grouping is also a common feature: codons, words, bytes.
  • A string of digits is a product-type (the string) of sum-types (the digits).
  • The digits are abstract.
  • Information works by ‘reference’ in some sense . . . so it does not need to represent structure directly . . . a single symbol can control a whole machinery.

There a various things to observe and note, but none individually amount to a satisfying answer. The last, though, is the main lead.


Information is like data-structure: the definition, the meaning of it is really in what is done with it. Information is information – it has the features it has – because it is computed with. When we say ‘information’ we are really saying, in a shortened form, ‘the thing we do computation with’.

So what is computation? This must be left for another note, but computation seems fundamentally about time, and action, and causality, and change (it is just a particular way of using those elements). Computation is action, and that must take place in time. But it is also completely general, so it cannot fix any other structure.

Information drives computation. So information is really a (temporal) sequence of instructions that are entirely general: so there cannot be any structure beside time, because that would be a constraint and so no longer general.


(Besides just seeing the relevant facts and features, any profundity is a false impression. It is like sensing a profundity in asking what makes a table table-like – what is the essence that makes it a table? Ultimately, information (and computation) is like information simply because that is what it is.)