Abstract

A thought provoking history of the origins and basis for algorithmic thinking

Lessons

Preface

Algorithm: an abstract instrument of coordination supplying procedural means to various ends.

The execution of an algorithm is nothing new, and, thus, it may seem that there is nothing truly novel about the digital computer. This disassociation between mind and matter is represented in the world by entities such as bureaucracies which themselves venture to undertake complex algorithms which seem to command some form of intelligence.

However, there is a significant difference between the execution of an algorithm by bureaucracy and a computer.

Introduction

Calculus made modern science possible and serves the imperial vision of mathematical physics. That era is now over. The algorithm has taken over and is retrograde in relation to the world of mathematical physics. Algorithms are just recipes and really nothing new.

1. The Marketplace of Schemes

Gottfried von Leibniz was born in 1646 and died in 1716.

He demonstrated his calculating machine in England in 1673 which was able to multiply, divide, add, and substract. Newton and Leibniz invented calculus which made the scientific revolution possible. He also made several other discoveries.

Aristotelian logic, which is not much more than a syllogism, was the standard in Leibniz’s day.

Categorical statements have syllogisms in which a conclusion follows a major and minor premise. An argument is assessed by the validity of its inference and not the truth of its premises. Thiis didn’t set well with some and Leibniz’s improved it.

He invented the algebraic interpretation of categorical syllogism where symbols represent what was formerly identities. This morphed into a checklist of sorts which allowed for the proveability of its premises. A=AB; B=BC; A=ABC; A=AC. This allowed for reasoning in meta physics and morals.

Leibniz was interested in an encyclopedia of human concepts of which he thought all sprung from God and nothingness (or chaos and order). The alternation between the two, something and nothing, could correalate to 0 and 1.

Concepts are nested and have parts. Every scheme and science is justified by itself or not at all.