The difference between intuitive and operational in science and mathematics

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…]

Encouraging reproducibility in science

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…]

Infinities

The concept of infinity is hard to grasp because it is an abstraction. There are no tangible objects in our lives that are truly infinite in number so we really have nothing to compare it to. The only way to get an infinite number of anything is by invoking infinity elsewhere, which doesn’t really clarify matters much. [Read more…]

That’s science, baby!

On Monday, August 6 at 1:30 am Eastern Time in the US, the Curiosity rover will land on Mars. The gravitational field on Mars being roughly twice that of the Moon, its atmosphere being so thin, and Curiosity being so big, all posed immense challenges to the scientists and engineers who had to figure out how to gently drop the vehicle onto the surface. It does not help that Mars is so far away that there will be a time lag of 14 minutes for communications to get from Earth to the spacecraft and vice versa, meaning that no adjustments can be made from Earth once the descent begins. [Read more…]