Mathematics has always been a beautiful discipline, but its appeal is of an austere kind that takes some effort to fully appreciate. But computers and simulations now enable people to create visualizations of the beauty that they could formerly only create in their minds. The beautiful patterns generated by the Mandelbrot set is one example. [Read more…]

A book given to people taking the GRE exam advises them that “Exercise great caution if you decide to change an answer. Experience indicates that many students who change answers change to the wrong answer.”

This advice represents a widespread belief that our instincts, our intuitive senses, are the most reliable guides to decisions. It is based on the assumption that instincts are based on prior knowledge and experiences and that our brains integrate all these things to enable us to make quick judgments that tend to be sound. This is the idea heavily promoted by Malcolm Gladwell in his book Blink. [Read more…]

It would be a shock if it does but a series of nine experiments done in 2011 by Daryl Bem a professor at Cornell University and published in the prestigious Journal of Personality and Social Psychology seemed to find this remarkable effect in nine different experiments. [Read more…]

A long time ago, before I began blogging, I read an article or book by an evolutionary biologist that said that dogs and wolves had evolved to have rules in their packs that gave the smallest members a great amount of latitude and that the bigger members of the pack would not be rough with them. This results in what appears to be the smaller animals ‘bullying’ the larger ones with impunity. [Read more…]

All the cooks out there know that there comes a time when recipes require you to separate the egg yolks from the whites. I remember when I was a little boy seeing people do that by breaking the shell roughly in two and pouring the egg into one of the halves. The yolk would get caught while the white would overflow the shell and pour into the bowl beneath. You would then pour the remainder into the now empty other half of the egg shell, with more white dripping down. By doing this several times, you get get a pretty good separation, though it required some skill to not shatter the shell while breaking it and not break the yolk on the jagged edges. [Read more…]

One of the features of evolution is that once we have passed the age when we can have and raise children to a point where they can survive on their own and go on to have children, we have played our part in the process and have become redundant, evolutionarily speaking. Although our own bodies start to decay, this has no biological effect on our children. [Read more…]

Anyone who has a dog as a pet knows to avoid getting close to them when they are wet because they have a remarkable ability to shake themselves in such a way that the water flies off and drenches everything nearby. The interesting questions are why they do that and how they do that. [Read more…]

Where does our sense of justice, fair play, and morality come from? Is it acquired as a part of our culture or are the basic instincts innate? [Read more…]

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…]