Quotes of the day

In the current political environment, size in the business community has been demonized, but the fact is that some businesses require size in order to make necessary investments, take extraordinary risks and provide vital support globally. ... We need to continue to foster a sense of responsibility in all participants in the economy. Bad outcomes are not always someone else’s fault – we need to cultivate an environment where consumers, lenders, borrowers, businesses and investors all take responsibility for their actions and don’t look for someone else to blame. We have to stop slipping into a cacophony of finger-pointing and blame.--Jamie Dimon

When numbers are spread out evenly on a ruler, the scale is called linear. When numbers get closer as they get larger, the scale is called logarithmic. And it turns out the logarithmic approach is not exclusive to Amazonian Indians – we are all born conceiving numbers this way. In 2004, Robert Siegler and Julie Booth at Carnegie Mellon University in Pennsylvania presented a similar version of the number-line experiment to a group of kindergarten pupils (average age: 5.8 years), first-graders (6.9) and second-graders (7.8). The results showed in slow motion how familiarity with counting moulds our intuitions. The kindergarten pupil, with no formal maths education, maps out numbers logarithmically. By the first year at school, when the pupils are being introduced to number words and symbols, the curve is straightening. And by the second year at school, the numbers are at last evenly laid out along the line. There is a simple explanation. Imagine a Munduruku is presented with five dots. He will study it closely and see that five dots are five times bigger than one dot, but 10 dots are only twice as big as five dots. The Munduruku – and the children – seem to be making their decisions about where numbers lie based on estimating the ratios between amounts. When considering ratios, it is logical that the distance between five and one is much greater than the distance between 10 and five. And, if you judge amounts using ratios, you will always produce a logarithmic scale.--Alex Bellos