numbers as a shared illusion, philosophers’ thoughts on 65

Roman finger-counting system and 112, 113

vote counting in 99, 100, 101–11, 103, 112

Gregorian calendar 160

Gutenberg, Johannes 174

halved-body procedure 242–3

hand, counting by

cave art and 1, 47–56, 47, 73

number bases and 60–1

Oksapmin and 237–9

origins of 1, 31, 47–56, 47, 58, 60–1, 62, 73

Roman system of hand-signs for numbers 112–17, 113, 149

Yup’ik and 260

Haridatta 139

Hawaii 246, 250

Hebrew 85, 148, 160, 162

Hellenistic period 69

hieroglyphic script 95–8, 135

Hittites 86

Hollerith, Herman 206–14

Hollerith tabulator 206–14, 210, 217

hominid species 24, 32, 43, 48, 57, 231

Homo genus 32

Homo erectus 43

Homo sapiens

Africa, spread out of 6, 43, 57, 59, 62, 69

emergence of 33–4

Hong Gongshou 188–95

Hooke, Robert 176

House of Representatives, US 206, 211

Hugo of Lerchenfeld 161–3

hunter-gatherer societies 40, 53, 61, 263, 279

Iberia 151, 153

ice ages 45, 50, 51–2, 57, 71, 256

Ichitaro, Kawaguchi 205–7, 214

ideograms 86, 197

Indian number symbols 6

Arabic world, appearance of in 147–56, 155

Brahmi numerals 136–41, 145, 145, 147–9, 155, 160, 183, 193

Ibn Mun’im/dust numerals 147–54

place-value system 141–6, 149, 154, 150–1, 161, 164, 174, 184, 193

Toledan numerals and 157–65, 163

western Arabic form 155–6, 155

Indo-European languages 104, 136, 140

Indonesia 43, 225, 229, 231, 250

Indus Valley 98, 148

innate abilities 6, 11–30, 64, 287, 289

estimating 13–25, 20

subitising 26–30, 27

International Business Machines Corporation (IBM) 212–13, 217