|Logic Through History||A Chronology of Digital Computing Machines (to 1952)|
as Deductive Science
The Greeks transform mathematics from a body of technique to a deductive science. Aristotle invents logic.
Leibniz dreams of a universal logical language in which all disputes can be settled by computation.
The theory of real numbers and the foundations of the calculus get straightened out.
In the hands of Frege logic at last becomes adequate for mathematics. Russell & Whitehead's Principia Mathematica shows that mathematics can be formalised.
Alan Turing casts light on the limits of computation and breaths life into the idea of intelligent computers.
As digital computers get off the ground formal notations proliferate. Formal expression is a prereqisite of getting a computer to solve a problem.
As computing power gets ever cheaper mass media migrate from analogue to digital representation and global broadband networking ushers in the information megaload.
Digital isn't the whole story. Evolution of delivered functionality depends upon evolution of the logical structure information representation.
Where the network is king, its how you communicate that counts. Representation is just a part of the communication problem, protocol is another part.
The network gets good at formalised mathematics, surpassing in rigour and problem solving capability the majority of todays professional mathematicians.
Computer Aided Design software based on mathematical modelling techniques enables ordinary people to design almost anything.
Work, Learn and Play
In the future many people will do creative work using mathematically based CAD tools. Those same tools (with some simpler models) will be used in education. Good games software demands realistic computer modelling techniques than CAD tools and turns out to be the best way to train in engineering design.
The search for ways of making diverse software interwork and integrate in delivering solutions to business needs leads to the emergence of a de-facto standard Characteristica Universalis.
Threads in the Web of Mathematics