software is mathematics

  • mathematics is a language
  • languages are written with symbols
  • symbols are abstract ideas, more abstract more powerful
  • symbols need not be watched by humans to have meanings
  • computaions don’t process electrons, computations process symbols
  • bits must be organized into syntax
  • the mathematical language my also be given some non mathematical interpretations
  • algorithms are manipulations of the uninterpreted symbols and their syntactic arrangement
  • algorithms and computations are not physical entities but contents
  • mathematicians have discovered a special category of algorithms called universal algorithms, such as universal Turing machine, instruction cycle, Horn clauses, normal order B-reduction
  • a program is data
  • most modern general purpose computers are built according to a common engineering pattern called the stored program computer architecture
  • we say software is mathematics because the execution of all computer programs is the execution of a universal mathematical algorithm. What the computer does is a mathematical computation according to a mathematical algorithm.
Published at 02 December 2012
Tags mathematics 1