Preachers and Prophets

Since I have had to pay college tuition for five daughters, I have chosen to play the role of preacher. I preach to all who will listen the gospel of manifest destiny. The destiny which I am preaching is not the expansion of a single nation or of a single species, but the spreading out of life in all its multifarious {134} forms from its confinement on the surface of our small planet to the freedom of a boundless universe. This unimaginably great and diverse universe, in which we occupy one...

 1/9998 Produces Binary Output

The pattern will break down once you get past 8192, which is 2^13. That means that the pattern continues for an impressive 52 significant figures (well, it actually breaks down on the 52nd digit, which will be a 3 instead of a 2). The reason it works is that 9998 = 10^4 - 2. You can expand as   1 / (10^n - 2) = 1/10^n * 1/(1 - 2/10^n) = 1/10^n * (1 2/10^n 2^2 /10^2n 2^3 /10^3n ...) which gives the observed pattern. It breaks down when 2^k has more than n digi...

 The Teacher Who Inspired Thomas Jefferson

In the spring of 1760, [I] went to William and Mary college, where I continued two years. It was my great good fortune, and what probably fixed the destinies of my life, that Dr. William Small of Scotland, was then Professor of Mathematics, a man profound in most of the useful branches of science, with a happy talent of communication, correct and gentlemanly manners, and an enlarged and liberal mind. He, most happily for me, became soon attached to me, and made me his daily companion when not...

 The One Piece of Dogmatism Allowed the Scientist

It is the business of science to offer rational explanations for all the events in the real world, and any scientist who calls on God to explain something is falling down on his job. This applies as much to the start of the expansion as to any other event. If the explanation is not forthcoming at once, the scientist must suspend judgment: but if he is worth his salt he will always maintain that a rational explanation will eventually be found. This is the one piece of dogmatism that a scientis...

 The Unique Properties of Ice

By the standard of other substances, the properties of ice are bizarre, yet ice is so perfectly suited to our purpose that if it didn't exist we should have to invent it. With few exceptions, the solid phase of matter is more dense than the liquid phase; water. alone among common substances, violates the rule. As water begins to cool, it first contracts and becomes more dense, in the typical way. But about four degrees above the freezing point, something peculiar happens. It ceases to contrac...