ABSTRACT
How best to quantify the information of an object, whether natural or artefact, is a problem of wide interest. A related problem is the computability of the object. This chapter describes practical examples of a new way to address this problem. Most interestingly, the algorithmic complexity is related to the length of the class of objects, rather than to the length of the object. The notion of ultrametric information was introduced both to handle interactive as opposed to static information and by taking a dynamic view of information, with analogies to metric or Kolmogorov–Sinai information. The wavelet transform has traditionally been used for image and signal processing, based on functions in Hilbert space. The perspective, based on some hierarchically structured, appropriate representation or encoding of our object family, and an associated algebra, is that it is so much easier to grow the object! Algorithmic complexity traditionally is related to the length of the object.
