My post on infinities and the accompanying video generated some interesting discussions and illustrated the difficulties that people have the idea of ‘operational definitions’ in science and mathematics. While scientists and mathematicians, like everyone else, use everyday language to communicate with one another, they are well aware that language contains traps in the form of implicit meanings and hidden concepts that can lead to ambiguities and even paradoxes in unfamiliar situations. These arise because our intuitive concepts are developed from our experience with the everyday world and while they may work well there, problems can arise when they are extended to regions beyond our immediate experience. [Read more…]

There is a problem in the current science climate which seems to reward original and exciting new research more and seems to value whether the results are true less. I have written before about the problem of journals publishing papers where the results don’t hold up under subsequent examination and how difficult it is to get them to publish articles that contradict earlier ones. [Read more…]