A Computer Algorithm for Randomization

Back in the early days of computers, one of the more popular methods of generating a sequence of random numbers was to employ the following scheme: 1. Choose a starting number between 0 and 1. 2. Multiply the starting number by 4 ("stretch" it). Subtract 4 times the square of the starting number from the quantity obtained in step 2 ("fold" the interval back on itself in order to keep the final result in the same range). 3.Given a starting number between 0 and 1, we can use the proce-dure�...

 Flatland Science: Dimensions

What and where is Flatland? A Square gives us several interesting answers, many of th contradictory. We know that it’s flat, big (but how big?), and very thin, the most important question of all is “how thin?” A lot depends on the answer… A Square himself eliminates the version that’s easiest for three-dimensional readers to understand; a world that’s thin – maybe only a few atoms thick - but nevertheless has some physical height. It would have some sort of solid or semi-solid ...

 What People Can Achieve Grows Exponentially

The mathematics of cooperation of men and tools is interesting. Separated men trying their individual experiments contribute in proportion to their numbers and their work may be called mathematically additive. The effect of a single piece of apparatus given to one man is also additive only, but when a group of men are cooperating, as distinct from merely operating, their work raises with some higher power of the number than the first power. It approaches the square for two men and the cube fo...

 Abusing the Evolving Nature of Science to Find Faith

It is unreasonable to expect science to produce a system of ethics—ethics are a kind of highway code for traffic among mankind—and the fact that in physics atoms which were yesterday assumed to be square are now assumed to be round is exploited with unjustified tendentiousness by all who are hungry for faith; so long as physics extends our dominion over nature, these changes ought to be a matter of complete indifference to you.

 The "Second Half of the Chessboard"

 

 Political, Social, and Scientific Values Should be Mathem...

[P]olitical and social and scientific values … should be correlated in some relation of movement that could be expressed in mathematics, nor did one care in the least that all the world said it could not be done, or that one knew not enough mathematics even to figure a formula beyond the schoolboy s=(1/2)gt2. If Kepler and Newton could take liberties with the sun and moon, an obscure person ... could take liberties with Congress, and venture to multiply its attraction into the square of its...

 Newton's Law of Universal Gravitation

Every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them