Bertrand Russell Says

A stupid man's report of what a clever man says can never be accurate, because he unconsciously translates what he hears into something he can understand.

- A History of Western Philosophy

Everything is vague to a degree you do not realize till you have tried to make it precise. 

- The Philosophy of Logical Atomism

If there were in the world today any large number of people who desired their own happiness more than they desired the unhappiness of others, we could have paradise in a few years. 

- Probably paraphrased from a passage in What Desires Are Politically Important

In the part of this universe that we know there is great injustice, and often the good suffer, and often the wicked prosper, and one hardly knows which of those is the more annoying. 

- “Why I Am Not A Christian”

Many people would die sooner die than think - In fact they do so.
- The ABC of Relativity

Our great democracies still tend to think that a stupid man is more likely to be honest than a clever man, and our politicians take advantage of this prejudice by pretending to be even more stupid than nature made them.
- New Hopes for a Changing World

Patriotism… a willingness to kill and be killed for trivial reasons.
- “Freedom in Society”

So far as I can remember, there is not one word in the Gospels in praise of intelligence.
- Education and the Social Order

The good life, as I conceive it, is a happy life. I do not mean that if you are good you will be happy - I mean that if you are happy you will be good.
- New Hopes for a Changing World

The people who are regarded as moral luminaries are those who forego ordinary pleasures themselves and find compensation in interfering with the pleasures of others.
- “Eastern and Western Ideals of Happiness.”

The fundamental cause of the trouble is that in the modern world the stupid are cocksure while the intelligent are full of doubt
- "The Triumph of Stupidity"

To modern educated people, it seems obvious that matters of fact are to be ascer­tained by observation, not by consulting ancient authorities. But this is an entirely modern conception, which hardly existed before the seventeenth century. Aristotle maintained that women have fewer teeth than men; although he was twice married, it never occurred to him to verify this statement by examining his wives' mouths. 

- The Impact of Science on Society

In America everybody is of opinion that he has no social superiors, since all men are equal, but he does not admit that he has no social inferiors. 

- Unpopular Essays

The Colors

In 1665, the plague closed Cambridge for two years. Isaac Newton, who had just gotten his bachelors there, was stuck at home. To fill the time, he made a series of the biggest breakthroughs in physics, ever.

One of these regarded the nature of light and color. People knew that white light shined though a prism resulted in a rainbow of colored light, but they thought that the white light was perfectly pure and the colors were the result of the prism muddying the light. Well, Newton got a hold of two prisms. He used one to split the light, observed the different colored beams of light, and then tried to use the second prism to split one of the colored beams of light. If the prevailing theory was right, more colors should have been added, but no; it remained one color (red). Newton's new, correct, theory was that all colors are already present within the white light and the prism just separates them. In fact, he was able to use mirrors and lenses to recombine the separated colors back into white light. Incidentally, if you've ever heard of ROY G BIV you can thank Newton. He decided the colors of the rainbow were: Red, Orange, Yellow, Green, Blue, Indigo, and Violet. If indigo seems a bit awkward there, you're right. He just added it because he wanted there to be seven colors.

In fact, quite a few languages have done without "blue" entirely. If you ever read the ancient Greek Iliad and Odyssey you can count the usages of each color.  William Gladstone (the British politician) did just that and counted 170 uses of black, 100 of white, 13 uses of red, less than ten each of yellow and green, and not a single use of blue. Homer famously described the sea as "wine dark." If you read the Torah and New Testament in their original ancient Greek and Hebrew you'll, again, find no blue. In 1969 Berlin and Kay proposed a theory based on the study of dozens of languages suggesting that they always follow the same progression of adding color terms. A primitive language will only have black and white. Any dark or cool color will be lumped into black and any light or warm color will be white. If the language has three basic color terms, the next is always red. Then you get green and yellow, then blue. If you think about it, in a way blue is very rare in nature. It's by far the least common color in plants, animals, rocks, or dirt. It's the most difficult pigment to produce. But what about the sky, the sea? Well, we call those blue, but what about air, or water? They're clear, colorless. And these vast features are always background. One can imagine that if one had no concept of blue, no word for it, one could fail to really see that background. See this episode of Radiolab for a good discussion. 

The Lever of Mahomet

Imagine a game: it uses a cart that can move forward and backward along a straight track. The cart can move with any finite speed and acceleration. A straight, uniform rod is attached to the bed of the cart with a hinge. We'll assume the hinge is frictionless, there is no air resistance, etc.

Player 1 assigns the cart a motion that gets it from Point A to Point B. It may start and stop several times, it may reverse direction, but it has to eventually get to Point B. Player 2 is given the motion Player 1 came up with and has to try to find an initial position of the rod such that the rod will never quite fall all the way down. He gets as many tries and as much time as he wants to try and accomplish it. 

The question: Is there any motion that Player 1 can choose that Player 2 can not eventually beat.

It turns out the answer is no. At least as a thought experiment, there is no dance Player 1 can come up with that can not be beat by Player 2 choosing just the right starting position. Think of the extremes. Given the motion, Player 2 knows that if he starts the rod far enough over to the back it will end up all the way down in back. He also knows that if he starts the rod far enough forward it end up all the way down in front. Well, everything we're talking about is continuous, so as he gradually changes the rod angle from back to front there must be some small range of angles where the result transitions from ending up down in back to ending up down in front. Any one of those transition points is a solution where it doesn't end up down at all. 

This problem is from an article by Richard Courant and Herbert Robbins called "The Lever of Mahomet" and can be found in The World of Mathematics.