Asimov Story on Computation

■ N 1958, American science fiction legend Isaac Asimov wrote a very short story called "The Feeling of Power." In it, lowly technician MyI ron Aub discovers that he is capable of duplicating the work of his computer by multiplying two numbers together on a piece of paper. Amazing! This miraculous discovery makes its way up the chain of command, where the generals and politicians are stunned by Aub's black magic. The top general is intrigued by the possibility that human calculations could g...

 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...

 A Minority of Users Account for Majority of Online Comments

In July, NPR.org recorded nearly 33 million unique users, and 491,000 comments. But those comments came from just 19,400 commenters, Montgomery said. That's 0.06 percent of users who are commenting, a number that has stayed steady through 2016. When NPR analyzed the number of people who left at least one comment in both June and July, the numbers showed an even more interesting pattern: Just 4,300 users posted about 145 comments apiece, or 67 percent of all NPR.org comments for the two month...

 The Great Lifespan Escape

At the time when the lines begin, in the mid-18th century, life expectancy in Europe and the Americas was around 35, where it had been parked for the 225 previous years for which we have data.3 Life expectancy for the world as a whole was 29. These numbers are in the range of expected life spans for most of human history. The life expectancy of hunter-gatherers is around 32.5, and it probably decreased among the peoples who first took up farming because of their starchy diet and the diseases ...

 Number Scrabble: Numerical Tic-Tac-Toe

In psychological research on problem-solving, sometimes the game of Tic-Tac-Toe is employed, which, though very simple to learn and play, still offers sufficient problems to the investigator in that it is not at all clear what heuristics are used by the subjects, except avoiding the winning move of the opponent. The same is apparently true for the isomorphic game of Number Scrabble, which is based on the fact that there exists a 3 X 3 magic square, of which rows, columns, and main diagonals a...

 Ways of Being "Good at Math"

It’s a common misconception that someone who’s good at math is someone who can compute quickly and accurately. But mathematics is a broad discipline, and there are many ways to be smart in math. Some students are good at seeing relationships among numbers, quantities, or objects. Others may be creative problem solvers, able to come up with nonroutine ways to approach an unfamiliar problem. Still others may be good at visually representing relationships or problems or translating from one ...

 The Noosphere

Under the impact of this passage from simple to squared numbers, we all become aware that the entrance is open for the hominised consciousness into a new inner world: the world of the Universe as thought. But do we sufficiently notice that simultaneously, in the realm of the measurable and tangible, another form of ' generalisation '—also as the result of reflexion — becomes possible and outlines itself: no longer simply for our knowledge, the systematised perception of total time and tot...

 The Mistake of Not Taking Theories Seriously Enough

This is often the way it is in physics. Our mistake is not that we take our theories too seriously, but that we do not take them seriously enough. It is always hard to realize that these numbers and equations we play with at our desks have something to do with the real world. Even worse, there often seems to be a general agreement that certain phenomena are just not fit subjects for respectable theoretical and experimental effort. . . . The most important thing accomplished by the discovery o...

 Expanding the Scope of School Subjects

We should not retreat to a curriculum advisory committee and ask, “Now where should we fit this topic into the already overloaded curriculum?” Although we cannot discard all the fragmented subjects in our present school system and start from scratch, we can and should ask all teachers to stretch their subjects to meet the needs and interests of the whole child. Working within the present subject-centered curriculum, we can ask math and science teachers as well as English and social studie...

 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...