In 1759 the British mathematician Francis Maseres wrote that negative numbers "darken the very whole doctrines of the equations and make dark of the things which are in their nature excessively obvious and simple". Because of their dark and mysterious nature, Maseres concluded that negative numbers did not exist, as did his contemporary, William Friend. However, other mathematicians were braver. They took a leap into the unknown and decided that negative numbers could be used during calculations, as long as they had disappeared upon reaching the solution.
Child's Mind
The remarkable physical transformation children undergo as they grow up is matched only by the metamorphosis of their minds. Parents, of course, play a critical role in this aspect of development. But what’s really going on in a child’s head? Kids can’t always tell us what’s on their minds. Psychologists, neurobiologists and other scientists can help fill in the blanks, however.
Learn how children develop morals, why they talk to themselves, and what happens to brain development and function in the face of abuse at an early age. Other articles explore how reading should be taught, how attention-deficit hyperactivity disorder arises and what unique challenges gifted children face. Lastly, sharpen your little one’s powers of concentration, and your own, with a few easy tricks.
The Collector was a Canadiansupernaturaldramatelevision series about a man attempting to help save people who have bargained their souls with the Devil. After over 600 years of "collecting" the souls of people at the end of their 10-year deals, Morgan Pym (Chris Kramer) negotiates with the Devil for the ability to aid the damned in redeeming themselves rather than sending them to Hell. Under the Devil's mocking gaze
After the September 11 attacks on the World Trade Center and Pentagon, many people questioned why no one had anticipated the terrorists' acts, even when events and intelligence seemed to point toward them. John Barell wonders if the attacks speak to a greater societal problem of complacency. He believes many students have become too passive in their learning, accepting information and 'facts' as presented in textbooks, classes, and the media. Drawing on anecdotes from educators and his own life, Barell describes practical strategies to spur students' ability and willingness to pose and answer their own questions. Antarctica expeditions, outer space discoveries, dinosaur fossils, ...
In Greek and Roman times, friendship was thought of as being an essential constituent of both a good society and a good life; a good society because it lay at the heart of participative civic democracy; a good life because it nurtured wisdom and happiness. It is this period which gives us the texts on friendship which, to this day, are arguably the most important of their kind. Amongst their authors is Aristotle, who engaged in one of the great philosophical discussions on the subject. For Aristotle, friendship could fall into three categories: it could be based on utility, pleasure or goodness. In its latter state, Aristotle described it as being 'a single soul dwelling in two bodies'.
So how did the Ancients establish the parameters of the true nature of friendship in the literature and philosophy that followed? How have different forms of friendship helped or hindered creativity and intellectual pursuit? What has been the apparent relationship between friendship and power? And what of the darker aspects of friendship - jealousy, envy and exploitation?
![Negative numbers - how they spread across civilizations [Science; Advanced Listening; mp3]](http://englishtips.org/uploads/posts/2010-03/1268289109_p003hyd9_303_170.jpg "Negative numbers - how they spread across civilizations [Science; Advanced Listening; mp3]")
