Numbers as a cognitive and social technology: on the nature of conventional number sequences used in economic systems

authors: David A Harper year: 2010 See in Zotero

Literature Notes

Gives a different perspective on what numbers are.

Numbers aren’t representations of some perfect form that exists outside of time and space (Platonism). They also aren’t completely fictional objects that exist only inside our heads (fictionalism).

Numbers are linked to humans and their social institutions. They are determined by the information they need to convey. They must have internal and external compatibility.

Internal means the number system must have symbols and have a general logic to determine order. Plus, can’t be redundant or have missing elements for necessary knowledge (it can’t skip from quantities that signify ‘1’, x, x, ‘4’).

External compatibility means the number system must convey information effectively for the system we need to communicate about. Number systems are chosen by humans to describe and communicate. ‘Bad’ systems are not chosen, as ‘good’ ones remain through experimentation.

Mathematics is not the study of the numbers, it is a study of the system (of constraints and uses) that we imbued upon the system. Number systems can also have an effect on humanity by expanding an individual’s cognitive ability. Humans working together build a number system (or mathematics) that in mutual communication with each other can create algorithms and rules for the number system that increase the possibilities for single members - and the collective with emergent properties.