Triangles on Earth Exceed 180 Degrees

The idea that space and time can be curved or warped is fairly recent. For more than 2,000 years the axioms of Euclidean geometry were considered to be selfevident. As those of you who were forced to learn geometry at school may remember, one of the consequences of these axioms is that the angles ot a triangle add up to 180 degrees. However, in the last century people began to realise that other forms of geometry were possible in which the angles of a triangle need not add up to i8o degrees...

 The Anthropic Principle

As an example of the power of the Anthropic Principle, consider the number of directions in space. It is a matter of common experience that we live in three-dimensional space. That is to say, we can represent the position of a point in space by three numbers. For example, latitude. longitude and height above sea level. But why is space three-dimensional? Why isn't it two, or four, or some other number of dimensions, hke in science fiction? In fact, in M-theory space has ten dimensions (as wel...

 Scientific Laws Mean That God has No Freedom

he one remaining area that reHgion can now lay claim to is the origin of the universe, but even here science is making progress and should soon provide a definitive answer to how the universe began. I published a book that asked if God created the universe, and that caused something of a stir. People got upset that a scientist should have anything to say on the matter of religion. I have no desire to tell anyone what to believe, but for me asking if God exists is a valid question for science...

 Probability is Truth-Resembling

The study of mathematical uncertainty is called probability. According to Richard Epstein, "The word 'probability' stems from the Latin probabilis, meaning 'truth-resembling'; thus the word itself literally invites semantic misinterpretation." [1]What Epstein means by "semantic misinterpretation" is that if something is "truthresembling," then it isn't actually truthful; at the same time, the truth is exactly what the something does resemble.

 Redundancy in the English Language

Whenever we communicate, rules everywhere restrict our freedom to choose the next letter and the next pineapple.I Because these rules render certain patterns more likely and certain patterns almost impossible, languages like English come well short of complete uncertainty and maximal information: the sequence “th” has already occurred 6,431 times in this book, the sequence “tk” just this once. From the perspective of the information theorist, our languages are hugely predictable— al...

 Our Modern Worldview and Morality is Shaped by Science

To begin with, the findings of science imply that the belief systems of all the world’s traditional religions and cultures—their theories of the genesis of the world, life, humans, and societies—are factually mistaken. We know, but our ancestors did not, that humans belong to a single species of African primate that developed agriculture, government, and writing late in its history. We know that our species is a tiny twig of a genealogical tree that embraces all living things and that e...

 Euclid's Elements as a Game

"If video games had been around in 350 BC, Euclid would have made a video game," Devlin told me. The thirteen books of Euclid's Elements would have been the supplemental material, a PDF file that you could read if you wanted to. "People think I'm joking—I absolutely mean that. Euclid would not have written a textbook, he would have designed a video game." Peek at any of his proofs, Devlin said, and you'll quickly find that the great Greek mathematician, often called the father of geometry, ...

 A Student's Skill-Level Should be Private

A student's skill level should be a private matter, between him and the teacher, and students who are behind should be able to work comfortably, without embarrassment. "They know they should know more. They know they should not be working on tens and ones when their friends are doing division and fractions and all that, and there's no shame in working on it with the computer." Actually, the same principle applies to kids who are off-the-charts advanced: if they just want to relax and do high-...

 Games Allow for Low-Cost Failure

What Prensky and Gee had realized early on was that game designers had lowered the cost of failure so players would take risks. They'd figured out that well-designed problem solving that gives players a second chance and a way to share their successes is almost irresistibly attractive. In just a few years, game designers had discovered the principles of deep and pleasurable learning that it had taken educators more than a century to apply in schools. Game studios had hit upon "profoundly good...

 Health Concerns Spark Adult Interest in Science

Beginning in middle age and continuing through later adulthood, individuals are often motivated by events in their own lives or the lives of significant others to obtain health-related information.^^ Health-related concerns draw many adults into a new domain of science learning. At the same time, with retirement, older adults have more time to devote to personal interests. Their science learnmg addresses long-standing scientific interests as well as new areas of interest.^^ Adults differ fr...