Number sense and the calculating child: Measure, multiplicity and mathematical monsters

ABSTRACT

Children and animals of all kinds are said to develop some degree of number sense. The search for ‘number neurons’ and neural correlates of computational thinking aims to identify biological primitives to explain the emergence of number sense. This work typically looks for the sources of number sense in organisms, but one might extend this search and study the possibility of a calculating matter more generally. Such a speculative project explores the implications of the non-human turn within the posthumanities. In this paper, I draw primarily on the work of Vicky Kirby and Gilles Deleuze in order to focus on becoming-monster through calculation. I show how calculation, as a machinic and empirical act that both serves and troubles images of mathematical truth, has always played a unique role in the production of mathematical monsters. I then discuss calculating children who participate in abacus clubs and annual abacus competitions, calculating at inhuman rates with imaginary abacuses. I argue that a new materialist philosophy of immanence demands a radically new approach to number sense.

KEYWORDS:

• Number
• calculation
• computation
• immanence
• Deleuze
• Kirby

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1. For various examples in the mathematical bestiary, see Dr Vogel's gallery of calculus pathologies at http://www.math.tamu.edu/~tvogel/gallery/gallery.html.

2. This dilemma can be explored with students using geometric series and simple measurement formulae for area and perimeter of a triangle. With each iteration, smaller triangles are added to the previous stage, generating formulae for perimeter (P) and Area (A) after n iterations:

As n approaches infinity, the perimeter expands without limit, but the area converges.