Here are a couple of short extracts from chapter 5 (about the relationship between numbers/math and our minds) of my new book 'Embracing the Wide Sky: A Tour Across the Horizons of the Mind':
"How is this mental number line organized in the human mind? There are several clues. One is found when you ask people to think of a number at random between 1 and 50. Though it might be supposed that each response would occur around 2% (1 in 50) of the time, in fact, given a large enough sample of people, a systematic bias can be observed: people will tend to produce smaller numbers more frequently than larger ones. This suggests that numbers are mentally represented rather like the logarithmic scale on a slide rule where roughly equal space is given to the interval between 1 and 2, between 2 and 4 or between 4 and 8. Our ‘mental ruler,’ it would seem, compresses larger numbers into a smaller space, which is why smaller numbers are more accessible to our minds."
(From a later part of the chapter:)
"As many as 10-15% of people report some kind of graphic mental representation of numbers. Francis Galton, a psychologist and cousin of Charles Darwin, carried out the first of these surveys back in 1880. The responses he obtained offer a fascinating glimpse into the sheer variety of mental number representations... some of the number lines had twists and bends, some turned upside down or back on themselves. A physicist replying to Galton’s questionnaire described seeing numbers in the form of a horseshoe, with 0 at the bottom right, 50 at the top and 100 at the bottom left. Another respondent, a barrister, described visualising the numbers 1-12 as though on the face of a clock, with the following numbers tailing off afterwards into an undulating stream with the tens – 20, 30, 40, etc. – at each bend."
The book is now available for purchase online here: www.amazon.com/Embracing-Wide-Sky-Across-Horizons/dp/1416569693