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...

 Shannon's Learning Mouse Theseus

Theseus was propelled by a pair of magnets, one embedded in its hollow core, and one moving freely beneath the maze. The mouse would begin its course, bump into a wall, sense that it had hit an obstacle with its “whiskers,” activate the right relay to attempt a new path, and then repeat the process until it hit its goal, a metallic piece of cheese. The relays stored the directions of the right path in “memory”: once the mouse had successfully navigated the maze by trial and error, it ...

 Understanding Factors Through Divisibility

This is appropriate for 4th or 5th graders and involves finding the smallest number divisible by 2, 3, 4, 5, 6, 9, and 10. Directions: Teach the students how to tell if a number is divisible by 2, 3, 4, 5, 6, 9, & 10. Give groups ofu00a0two tou00a0four students the divisibility rules on a sheet of paper, and challenge them to find the smallest number divisible by all of the numbers listed above. Eventually the students, with or without help from the teacher, will come to reali...

 There is No End to Mechanical Progress

[To] mechanical progress there is apparently no end: for as in the past so in the future, each step in any direction will remove limits and bring in past barriers which have till then blocked the way in other directions; and so what for the time may appear to be a visible or practical limit will turn out to be but a bend in the road.

 Functions of Analogies and Models in Science

... one of the main functions of an analogy or model is to suggest extensions of the theory by considering extensions of the analogy, since more is known about the analogy than is known about the subject matter of the theory itself … A collection of observable concepts in a purely formal hypothesis suggesting no analogy with anything would consequently not suggest either any directions for its own development.

 Alchemy VS Chemistry

He tapped the papers; the advice had been coming down since early winter. He remembered when Amdijefri had brought in the first pages, pages of numerical tables, of directions and diagrams, all drawn in neat but childish style. Steel and the Fragment had spent days trying to understand. Some of the references were obvious. The Visitor’s recipes required silver and gold in quantities that would otherwise finance a war. But what was this “liquid silver”? Tyrathect had recognized it; the M...

 Knowledge is Indivisible

Knowledge is indivisible. When people grow wise in one direction, they are sure to make it easier for themselves to grow wise in other directions as well. On the other hand, when they split up knowledge, concentrate on their own field, and scorn and ignore other fields, they grow less wise–even in their own field.

 13 Percent of the English Language is Not Spelled Phoneti...

I received a letter today from the "Reading Reform Foundation," which tells me that "23 million (American) adults are functionally illiterate, unable to read an advertisement, a job application, directions on a medicine bottle." They say "30 percent of all schoolchildren have serious reading difficulties." I rather believe this, judging from my own limited experience with people. But why is this? Can it be that part of the reason is the matter of English spelling? The letter tells me that "87...