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.

Taste

We perceive taste though chemical reactions that take place on the tongue. The tongue has different receptors that react with different types on molecules and ions in the food. This gives us information about the chemical content of the food. 

We now generally recognize five categories of taste:

• Sweet taste is a reaction with dissolved glucose (or sucrose or some other similar molecule). This tells us the food has a lot of easily accessible energy content. If you're an animal this is a very good thing, so sweet tastes good.
• Salty taste is the detection of Na+ ions. Salt (NaCl) dissolves into Na+ and Cl- ions in water, so if our saliva has a lot of Na+ ions we must be eating something salty. Again, in nature salt can be scarce, but is critical for survival, so it tastes good. 

• Sour taste is detection of H+ ion concentration in the saliva. This means that sourness is the same as acidity. 
• Bitter is triggered by a variety of molecules, many are alkaloids which tend to be basic in pH. This usually comes from plants that are producing it as a defensive poison, so the body's first reaction tends to be to label the taste as bad or even gag. Bitter foods like coffee and beer tend to be acquired tastes.   
• Umami is detected by reacting with various proteins, and thus indicates protein-rich foods like meat. This is a savory taste. 

Earth Gravity

If you think about what we have previously learned about gravity, every bit of mass pulls on every other bit. So the dirt right under your feet is exerting gravity, and dirt on the other side of the globe is as well. But the r² term in that equation says that the stuff close to you pulls much harder. It seems that if you want to know how all the earth together pulls on you, you must sum the effects of each individual bit.

The problem is simpler if we can think of the earth (or whatever) as an onion of nested spherical shells, where each shell is about uniform density. This is a fair assumption because for any very large object, gravity itself will collapse the thing down into a sphere shape and roughly sort the material of the sphere with denser material closer to the center. The Shell Theorem, proved by the ubiquitous Issac Newton, says that for any one of these shells, for the purposes of calculating the gravitational effect of the whole, it is equivalent to assume all of the mass is at a point in the center. Now, as you add the shells together, each tells you to model it’s mass at the same center point, so it’s valid to do that for the whole solid sphere.

The interesting flip side of that theory is that at any point Inside a hollow shell, you will feel no gravity from the shell. At the center this is not surprising, it’s pulling you in all directions equally and it cancels out. And with some thought it makes sense when you’re near the edge (but still inside) also. If you consider the part of the shell that is pulling you generally out from the center, it’s small but close to you. The remainder pulling you in toward the center is much larger, but farther away, so the effects balance out.

So, if you were to tunnel down into the earth, the further you went the less gravity you would feel until weightlessness at the center. Similarly, the gravitational effect of the atmosphere on you is roughly cancelled out to zero, because you are inside that shell.

Some have held the theory that the earth actually is a hollow shell, and that others inhabit the interior face with their own atmosphere, and even their own small sun at the center. We see now one reason this is would not work well. The inhabitants of the interior would feel no gravity holding them to the ground, only a slight (about 2 oz) centrifugal force.  The gravitational effect of the atmosphere inside the hollow earth and the small sun would likely overcome that effect and cause everything to  drift up into the center.

G. K. Chesterton Says

Ideas are dangerous, but the man to whom they are least dangerous is the man of ideas. He is acquainted with ideas, and moves among them like a lion-tamer. Ideas are dangerous, but the man to whom they are most dangerous is the man of no ideas. The man of no ideas will find the first idea fly to his head like wine to the head of a teetotaller.

- Heretics

What fairy tales give the child is his first clear idea of the possible defeat of bogey. The baby has known the dragon intimately ever since he had an imagination. What the fairy tale provides for him is a St. George to kill the dragon.

- Tremendous Trifles

The above was aptly paraphrased by Neal Gaiman in Coraline as "Fairy Tales are more than true; not because they tell us that dragons exist, but because they tell us that dragons can be beaten."

Truth must of necessity be stranger than fiction ... for fiction is the creation of the human mind, and therefore is congenial to it. 

- The Club of Queer Trades

The only way to be sure of catching a train is to miss the one before it.

- According to Pierre Daninos

The traveler sees what he sees, the tourist sees what he has come to see.

- The Temple of Silence & Other Stories

I say that a man must be certain of his morality for the simple reason that he has to suffer for it.

- Illustrated London News, Aug. 4, 1906

To have a right to do a thing is not at all the same as to be right in doing it. 

- A Short History of England

The whole modern world has divided itself into Conservatives and Progressives. The business of Progressives is to go on making mistakes. The business of the Conservatives is to prevent the mistakes from being corrected. 

- Illustrated London News, Apr. 19, 1924

I believe what really happens in history is this: the old man is always wrong; and the young people are always wrong about what is wrong with him. The practical form it takes is this: that, while the old man may stand by some stupid custom, the young man always attacks it with some theory that turns out to be equally stupid.

- Illustrated London News, Jun. 3, 1922

Without a gentle contempt for education, no gentleman's education is complete. 

- The Common Man

Precisely because our political speeches are meant to be reported, they are not worth reporting. Precisely because they are carefully designed to be read, nobody reads them. 

- "On the Cryptic and the Elliptic," All Things Considered

Nine times out of ten, the coarse word is the word that condemns an evil and the refined word the word that excuses it.

- The Everyman Chesterton

Coin Toss

Consider the coin toss. Flip a coin; the result is heads (H) or tails (T).

Each time we flip it there are two possible outcomes with equal likelihood, so the probability of getting heads is 50% or 0.5 and the same is true for tails. But what if we want to know the probability of flipping twice and getting heads the first time and tails the second time? If we look at column B below, we can see all the possibilities. If we flip twice, there are four: heads-heads, heads-tails, tails-heads, and tails-tails. One of those equaly possible four outcomes is the one we're looking for, so the probibility is 1/4 = 0.25 or 25%. Note that for each flip the total number of possible outcomes (Column D) doubles. This is because for each of the previous outcomes we've added two variations, two branches on the probability tree we see in Column B. It turns out that if we want to know the probability of multiple events occurring, we can multiply the individual probabilities. So for if we want the chance of getting HT it's the chance of getting H first (1/2) times the chance of getting tails on the second flip (1/2), (1/2) * (1/2) = (1/4).

Okay, but what if we don't care about the order? What if we just want to know the chance of getting one heads and one tails in two flips? Either HT or TH counts, so it's 2/4 = 0.5. In Column C we can see the groupings of outcomes if we don't care about order. They present an interesting pattern. Look at the coefficients, the multiple of each item. They follow a pattern we call Pascal's Triangle.

Coefficients also follow Pascal's Triangle when we do binomial expansion. To find (A + B)³ we look at the fourth row of the triangle (we consider the first row to be more like the zeroth row) for the coefficients and get A³ + 3*(A²*B) + 3*(A*B²) + B³. But this is basically row three of our Column C above, but with A and B instead of H and T, if we say HHH is like H³. If we extend that metaphor, then flipping three times is like (H + T)³. It's interesting that the math seems to work on events like it does on numbers or variables. Really, that's the power of statistics and probability, doing math on events.

Hair

A hair is essentially a very tall thin stack of flattish cells. The strength and toughness of hair comes from a protein coating on the surface. This protein has long tough filaments that tie the column of cells together along it's length. This is the same protein (keratin) that makes skin and fingernails tough.

The individual strands of hair can be round in cross section or more of a flattened oval, with flatter sections resulting in curlier hair. Think of string vs ribbon. 

Each hair goes through a phase of growth, followed by a period of near static length, before being shed and growing anew. Your maximum hair length is determined by the duration and rate of the growth period. Typical values would be a duration of five years at six inches a year, resulting in hair two and a half feet long. But depending on the individual it could be twice as long, mostly depending on a longer growth duration. World record hair lengths can be over 18 feet long, but it's unclear how much such lengths rely on braiding or matting. 

If you have a tabby cat, look closely at it's hairs. You may observe that in addition to body stripes, the individual hairs may, themselves, be striped. These are called agouti hairs and result in a finely speckled pattern.

Frequency Illusion

It is a common but striking experience to encounter a word or idea or factoid for the first time in your life and then immediately run across it again, seemingly against all probability.

There are several names for this experience:

Diegogarcity - The concept is close to Serendipity. Serendipity is named after an old name for the island of Sri Lanka (Sarandib), Diego Garcia is another island close to Sri Lanka.

Baader-Meinhof Phenomenon - In 1986 Terry Mullen wrote about his experiencing this phenomenon with the Baader-Meinhof Group (or Red Army Faction), a violent political gang in West Germany. The story was published in the St. Paul Pioneer Press which soon received a flood of similar stories and coined the term Baader-Meinhof Phenomenon to collect them.

Frequency Illusion - A linguist named Arnold Zwicky coined the term and explained that it was the result of three very human traits:
1. Gathering and sifting through tremendous amounts of information
2. High sensitivity to patterns and to assuming potential patterns
3. The tendency to filter incoming data to select for things that fit a previously assumed pattern.

Rat King

A rat king is the name given to a group of rats living as one with their tails tangled or fused together. It’s unpleasant enough to encounter one rat, so there should be little surprise that the discovery of a rat king was regarded as a very bad omen through history. It was thought to prophesy a plague, which makes sense because where there is sufficient density of rats to make a rat king possible, conditions are probably ripe for plague. The occurrence of rat kings seems to have diminished (along with the occurrence of plagues) but preserved specimens can be seen. The one pictured below has 32 members.

Recently a similar construct of six squirrels with tails glued together by sap, a squirrel king, was discovered in Canada. Veterinarians separated the squirrels and expect them to recover.

Crepuscular Rays

A fan of sun rays streaming through a cloud or tree or horizon at sunset are called crepuscular rays. It’s a striking and beautiful phenomenon, but may seem to present a quandary.

We know that the sun’s rays that reach the earth do so along almost perfectly parallel lines. The Sun and Earth are so far apart that even if two rays are coming to your location from opposite ends of the vastly large sun, the angle between them is still just over half a degree, and the vast majority of the rays you see are much more parallel than that.

So how is it that crepuscular rays seem to be at very large angles to one another? It seems like the Sun must be much closer than they say...

Actually, it’s just a trick of perspective that can be tricky to get your brain to recognize. Imagine you are in a tremendously long tunnel. Say there are lines painted along the length of the tunnel on the walls. These lines are parallel, but to you they seem to converge at a point.

The suns rays are doing something similar, they are all coming toward you from far away and passing by your head on all sides, so they have this tunnel perspective.

In fact, we can take this further. Consider if you turn around and look the other way in your tunnel, you should get the same effect. Well in fact sometimes if crepuscular rays are visible at sunset, you can turn around and see anti-crepuscular rays on the opposite horizon.

Vonnegut Says

We are what we pretend to be, so we must be careful about what we pretend to be.
- in the introduction to Mother Night

Well, I've worried some about, you know, why write books ... why are we teaching people to write books when presidents and senators do not read them, and generals do not read them. And it's been the university experience that taught me that there is a very good reason, that you catch people before they become generals and presidents and so forth and you poison their minds with ... humanity, and however you want to poison their minds, it's presumably to encourage them to make a better world.
- "A Talk with Kurt Vonnegut. Jr." by Robert Scholes

One of the great American tragedies is to have participated in a just war. It's been possible for politicians and movie-makers to encourage us we're always good guys. The Second World War absolutely had to be fought. I wouldn't have missed it for the world. But we never talk about the people we kill. This is never spoken of.
- Interviewed by Roger Friedman

I have wanted to give Iraq a lesson in democracy — because we’re experienced with it, you know. And, in democracy, after a hundred years, you have to let your slaves go. And, after a hundred and fifty years, you have to let your women vote. And, at the beginning of democracy, is that quite a bit of genocide and ethnic cleansing is quite okay. And that’s what’s going on now.
- Interviewed by Jon Stewart on The Daily Show

[When Vonnegut tells his wife he's going out to buy an envelope] Oh, she says, well, you're not a poor man. You know, why don't you go online and buy a hundred envelopes and put them in the closet? And so I pretend not to hear her. And go out to get an envelope because I'm going to have a hell of a good time in the process of buying one envelope. I meet a lot of people. And, see some great looking babes. And a fire engine goes by. And I give them the thumbs up. And, and ask a woman what kind of dog that is. And, and I don't know. The moral of the story is, is we're here on Earth to fart around. And, of course, the computers will do us out of that. And, what the computer people don't realize, or they don't care, is we're dancing animals. You know, we love to move around. And, we're not supposed to dance at all any more.
- Interview by David Brancaccio

During my controlled near-death experiences, I've met Sir Isaac Newton, who died back in 1727 as often as I've met Saint Peter. They both hang out at the Heaven end of the blue tunnel of the Afterlife. Saint Peter is there because it’s his job. Sir Isaac is there because of his insatiable curiosity about what the blue tunnel is, how the blue tunnel works. It isn't enough for Newton that during his eighty-five years on Earth he invented calculus, codified and quantified the laws of gravity, motion and optics, and designed the first reflecting telescope. He can’t forgive himself for having left it to Darwin to come up with the theory of evolution, to Pasteur to come up with the germ theory, and to Albert Einstein to come up with relativity. “I must have been deaf, dumb, and blind not to have come up with those myself,” he said to me. “What could have been more obvious?”
- God Bless You, Dr Kevorkian

For some reason, the most vocal Christians among us never mention the Beatitudes. But, often with tears in their eyes, they demand that the Ten Commandments be posted in public buildings. And of course that’s Moses, not Jesus. I haven’t heard one of them demand that the Sermon on the Mount, the Beatitudes, be posted anywhere. "Blessed are the merciful" in a courtroom? "Blessed are the peacemakers" in the Pentagon? Give me a break!
- Cold Turkey

Weight and Mass

What we call weight is the effect of gravity on mass. On the surface of earth, weight = mass x g (gravitational acceleration). That’s simplified from Newton’s Law of Universal Gravitation: F = G * M₁ * M₂ / r², which describes the attraction between any two masses. You can use it to find out how much gravity attracts you and the Eiffel tower together, if you want (the answer will be very very small). But the earth is big enough that the force becomes significant, G * M_earth * M_you / (radius of earth)² = g * M_you. Note that this force always goes both ways. You attract the earth as much as it does you (Newton’s third law).

And if you fall to earth, it falls up to you. It’s just that it’s acceleration toward you is extremely small due to it’s large mass (Newton’s second law).

People like to think that in space you are weightless. If by space we mean in orbit around the earth, than not really. Or rather you are only weightless in the way you are in free fall. In fact, we can think of being in orbit as constantly falling to earth, but missing. Think of it this way: if you threw a ball straight ahead, it would fall to the ground. If you threw it hard enough, it would still fall to the ground, but the ground would have curved down a bit first, since the earth is round. 

Now if you threw it even harder, at some point the ground will be falling away as fast as the ball is falling and it will never hit the ground, but remain in orbit. That’s exactly what astronauts do: they use rockets to throw themselves hard enough that they miss the ground.

The Zipper Merge

A common situation: On the highway, a lane is closed ahead. So everyone gets over into the lane that goes through, leaving a terrific jam in that lane, and the other completely empty. And if anyone should drive down he empty lane and merge when it ends, they earn the sincere hate of everyone waiting in the ridiculous line. This is called "early merge." I'm here today to preach the new gospel: the late merge, aka zipper merge, aka zipper method.

Per the late merge, drivers would use both lanes until right before the one ends, and then merge every other car into the continuing lane

Points for the late merge:
1. Length of road filled with traffic is cut in half. This helps prevent the jam from affecting intersections behind and multiplying into gridlock.
2. Merges occur at low speed, with plenty of time to prepare. Where the early merge requires one to merge at full highway speed and with no advance notice. The late merge is safer.
3. More robust against cheating. The early merge can be completely subverted by anyone who wants or who doesn't know or understand the convention, enraging everyone doing it correctly and potentially leading to road rage. The late merge can be cheated, if one refuses to allow the other lane to merge in when it's their turn, but in this case only one car is cheated, instead of all. This greatly reduces rage and requires no advance knowledge, simply drive where you can.
4. The above effects are multiplied when more than two lanes are to merge.
5. Jon Stewart, of the Daily Show, who said on that program to Drew Barrymore: "To me, the hallmark of civilization, and I believe this on its core foundational level, is the every-other-car merge..." Also at the Rally to Restore Sanity:

Visit NBCNews.com for breaking news, world news, and news about the economy

Points against the late merge:
1. Most of the country doesn't do it that way now, and attempting to change will cause resistance. Item 3 for the late merge points out that know advance knowledge is required, but that is almost literally true. If the drivers have knowledge of the early merge they will be very upset when others do the late merge around them.
2. The early merge is preferable where the merge will not necessarily result in a jam. Ideally the early merge would be employed until a jam occurs, at which time traffic would switch to late merge.

Henry Ford Stories

There are certain people in history who accumulate stories and quotes. If you have a quote that is cuttingly witty, it'll be said to be by Oscar Wilde or Winston Churchill. If it's more folksy and witty - Mark Twain.  Here we look at a family of stories and quotes that accrue to Henry Ford. He's legendary as the platonic model of the modern American industrialist.

Left to Right: Ford, Edison, Harding, Firestone

Henry Ford had a problem at one of his factories. The main generator had stopped working and no one could figure out why. Work was stopped and the shutdown was costing the company dearly. Finally Ford, who was familiar with many of the great minds of the age, called Charles Steinmetz to come as a consultant and figure out what was wrong. After listening to a few minutes of explanation, Steinmetz shooed away all of Ford's engineers and drew out his notebook and pencil. After two days of careful listening and occasional bursts of calculation, Steinmetz mounted a ladder and made a chalk mark on the side of the generator. He said "replace 12 loops of the coil at this point." They did, and it worked. Later, Ford received a bill for $10,000. This was a remarkable sum in that time, and Ford asked, respectively, for an itemization from Steinmetz. The reply read: Piece of chalk - $1, Knowing where to mark with chalk - $9,999.

One day there was a small disaster at the Ford factory. An employee had set a metal punch to the wrong position and $1,000 worth of parts were ruined before it was caught. The employee felt terrible and went to Henry Ford himself to apologize and be fired. To his surprise, Ford did not fire the employee, but sent him back to work. When asked why, Ford said "I'm not going to fire an employee I just invested $1,000 in educating!" 

"Whether you think you can, or think you can't - you're right." - Henry Ford

It's said that Henry Ford had a team of engineers who he would send to junkyards around America. They were tasked with assessing the condition of the various parts - what was falling apart, what was still in good shape. They found that a certain cotter pin that was made of a high quality alloy and of a thick gage was always in particularly great shape. The engineers thought "Ah, great, now we know to use this material and technique in other parts." But when they reported to Henry Ford, he listened to what they said, but shook his head and told them to just reduce the quality of the over-designed pin. 

"If I had asked people what they wanted, they would have said faster horses." - Henry Ford.

A VIP was being shown around the factory by Henry Ford himself. At one point Ford indicated the vehicle under construction and stated that the finished product would contain "exactly four thousand, seven hundred, and eighteen parts!" This struck the visitor, so later he cornered a company engineer and asked if there were really exactly four thousand, seven hundred, and eighteen parts in that model. The engineer shrugged and said "I don't know, but I can't think of a more useless piece of information!"

"You can get the Model T in any color you like, as long as it's black." - Henry Ford

It's said that Henry Ford would take job applicants out to lunch, but immediately reject any who salted their food before tasting it. 

"Failure is simply the opportunity to begin again, this time more intelligently" - Henry Ford

Henry Ford hired an efficiency expert to go through his plant. He said, "Find the nonproductive people. Tell me who they are, and I will fire them!" The expert made the rounds with his clipboard in hand and finally returned to Henry Ford's office with his report. "I've found a problem with one of your administrators," he said. "Every time I walked by, he was sitting with his feet propped up on the desk. The man never does a thing. I definitely think you should consider getting rid of him!" When Henry Ford learned the name of the man the expert was referring to, Ford shook his head and said, "I can't fire him. I pay that man to do nothing but think - and that's what he's doing."

Tau Day

Happy Tau (τ) day! It’s June 28th, so here at Preciseish we celebrate 6/28 3:19 (6.283185) This is what we should use instead of pi. Everyone loves pi, but it really should not exist. Tau does everything pi does, but better.

Pi is what you get when you divide the circumference of a circle by it's diameter, but tau is the circumference divided by the radius. After you've defined pi, you'll almost never use the diameter again because it is the radius that makes a circle. A circle is defined as the set of points on a plane a constant distance (radius) from a point. If you draw a circle, you maybe do it by using a compass, or a bit of string, but always by enforcing a radius.

So what if we replaced pi with tau? Working in radians would become much more intuitive. We know that as a unit of angle measurement, 360° = 2 π. But why is one time around two times pi? It's confusing. 360° = 1 τ. Much better. Now you can immediately see how big the angle is. If you have ¼ τ, that's just one quarter of the way around, or 90°. Even better, sine and cosine become intuitive. Instead of memorizing some points like sin(π/2) = 1 without understanding what it means, now you can just learn that the sine is just the height on a unit circle at the angle. Now knowing sin(τ/4) is just knowing how high you are on a circle when you're a quarter the way around: you're on top, so 1.

One thing that seems, at first, like an advantage for pi is that the expression for the area of a circle comes out neater: π r² seems simpler than ½ τ r². But if you work with math or physics enough you'll realize that the ½ (constant variable)² form is very natural and makes sense. It comes from calculus. Consider falling. The fundamental constant for falling is gravitational acceleration, g, and our variable is time. To start with, all we know is g. Integrate that and get g t, that’s the speed you’re falling. integrate again and you get ½ g t² which is how far you've fallen. This is what is going on with the circle too. We start with the fundamental constant, tau. integrate and get τ r, that’s the circumference of the circle, integrate again and you get ½ τ r², the area of the circle. It's natural.

How about the beautiful and strange Euler's Identity that features pi so prominently? Euler's Identity is the following: e^{i π} + 1 = 0. It seems amazingly improbable that Euler's number, the imaginary square root of negative one, and pi should so succinctly combine to a non-imaginary, non-irrational zero. But would using tau do any damage? It turns out to give e^i τ = 1. Not only is this more elegant, in my opinion, but it results more directly from the underlying relationship involved: e^{i x} = cos(x) + i sin(x). If x is taken as pi, the result is an awkward -1. It takes some rearranging to get the more pleasing form above. If x is taken as tau, the result is a perfect 1 right off.

If you still aren't convinced, you must watch Vi Hart's quick and entertaining video on the subject, and enjoy this thorough but relative light and quick paced Tau Manifesto.

Acceleration

Acceleration is the rate of change in velocity. Remember that velocity is properly understood as a combination of speed and direction, so acceleration can refer to the rate of change in direction as well as change in speed, or some combination of both. For example, something orbiting at a constant speed is still accelerating. In the figure below, note that the length of the velocity vector (representing speed) is not changing, because the acceleration (due to gravity) is always orthogonal (perpendicular to) to the velocity.

That acceleration due to gravity is usually expressed by the constant, g = 9.8 meters per second per second. That number is approximate, and only valid near the surface of the planet, but it means that every second you're falling you'll be falling 9.8 m/s (22 mph) faster. In three seconds you'll be going highway speeds. The fastest production cars can just barely match that, doing 0-60 mph in just under three seconds. That's also about the acceleration that a cheetah can pull in a straight line. All of those things can accelerate at about 1 g. Impressive in a different way is the remarkable mantis shrimp. The mantis shrimp packs a punch that has it's foreleg accelerating at about 10,600 g! That's on the level of a bullet fired out of a gun. This motion is so tremendous that it can even cause cavitation for additional damage.

Food Origins

Before international shipping, most things that we ate were very local. For example, peaches were only found in China and no one else ate them. And this is true of most of the foods that we cultivate.

One of the most dramatic changes to this condition came with the exploration of the Americas by European explorers and conquerors. The plant life of the Americas was largely isolated from the rest of the world which led to the evolution of foodstuffs that could be found no where else, including much of what we consider standard fare now. It may be surprising to learn that Italians were not cooking with tomatoes until maybe 1592, for example. They are from Mexico and were completely unknown to Europeans before about 1550. Other examples of foods from the Americas:

• Potatoes
• Bell peppers
• Peanuts
• Chocolate
• Tobacco
• Vanilla
• Corn
• Squash (all kinds, including zucchini)
• Avocado
• Chili peppers
• Strawberries
• Pineapples
• Sweet potatoes 

And some other food origins:

• Oranges - southeast Asia
• Bananas - southeast Asia
• Rice - China
• Sugar - India
• Cucumbers - India
• Plums - east Europe
• Asperagus - central Eurasia (widespread)
• Cherries - Europe
• Cabbage - Europe and Britian
• Apples - Turkey
• Apricots - Armenia
• Spinach - Persia
• Wheat - the Levant
• Carrots - Iran (although they were bred orange in the Netherlands)
• Lettuce - Egypt
• Grapes - the near east
• Broccoli - bred from northern Mediterranean plants
• Peas - Mediterranean
• Olives - north Africa
• Coffee - Ethiopia
• Watermelon - southern Africa

Be glad that you live in such an interesting culinary time.

Charcoal

Charcoal can seem like a strange thing. Why do we want to burn something that has already been burnt? 

Well, charcoal is the result of burning, but a very specific and careful kind of burning. It might more accurately be considered refining. The original, raw, organic fuel found in nature (say, wood) is refined into a more effective fuel, charcoal.

The chemical reaction you really want when burning something organic for fuel is carbon and oxygen becoming carbon dioxide. Something like wood has a lot of carbon, but also a lot of other stuff that can get in the way of a good fire, like water. The slow way that wood is burnt into charcoal, mostly without oxygen, gets rid of most of that, leaving almost pure carbon.

Since charcoal is almost pure carbon, it: 

1. Has a lot more potential energy for it’s weight 
2. Burns hotter and 
3. Burns more cleanly with less smoke and less toxic smoke.

The higher heat obtainable is what made it most desirable through history because very high temperatures were required for working metal.

Hiccups

Many types of animals get hiccups besides humans. But all are mammals. A hiccup is a spasm of the diaphragm, and it seems only the mammalian diaphragm is susceptible. However, some amphibians have a similar reflexive gulp which leads some to suspect that hiccups are a vestigial amphibian trait. This is further supported by some embryonic similarities between amphibians and mammals. Another theory observes that only mammals get hiccups, and that babies and the young are especially afflicted, and suggests that it is related to mammalian reflexes that coordinate breathing and milk sucking. 

The longest known case of hiccups belonged to Charles Osborne, who had them from 1922 to 1990 - 68 years. That would be about 430 million hiccups. 

Utilitarianism

One of the major modern philosophical systems of ethics is Utilitarianism. The basic idea is that 1. everyone is fundamentally equal and has an equal claim to happiness. To be selfishly interested in helping only yourself or your family or friends is not ethically defensible. 2. The best thing to do is what maximizes happiness. Usually taken as the most happiness for the most people, although there have been other interpretations. 

This system is attractive because it’s relatively simple and relatively difficult to counter. Consider the volunteer asking you to donate a trifling amount of money to provide vaccines to children in struggling countries. How do you justify not doing it? Is it more important to buy yourself a can of soda with that dollar than to potentially save the life of a stranger? Utilitarianism is the recognition that obviously it is not and you should donate the dollar.

So okay, now you’re a utilitarian. You donate the dollar. What next? Well, for every subsequent dollar you think of spending you have to consider whether it would better be spent fighting the serious problems of the world and saving innocent lives. Starbucks? Nope. See a movie? Nope. Go out to dinner? Nope. It seems like maybe you should give of yourself until there is no one who needs help more than you. Or maybe you can do more good by being successful so you have more to give, but surely every luxury is still immoral.

Okay, so maybe you aren't a utilitarian. It’s hard to argue with the logic of the system, but at the same time it seems self-apparent that it is flawed; that’s just not how people work.

Probably, the value of utilitarianism, as with most philosophical ideas, is in the contemplation of them. And when faced with a difficult ethical question, it can be valuable to have a number of carefully thought through perspectives to consider. For example, maybe utilitarianism isn't very useful for an individual human, but maybe it can be of use to something less personal like a government or other organization.

Fun With Archaic Measurements

A league is a unit of distance that used to be more useful. It's the distance one could walk in an hour, reckoned to be about three miles.

Similarly, a league in a nautical context is the distance one can see from the deck of a boat and about equal to three nautical miles.

A nautical mile, then, is about 1 arc minute of latitude, or 6076 ft. This is about 15% longer than a regular mile.

The name "mile" comes from the Latin word millia which means thousand, as in a thousand paces. Isn't that more satisfying than the awkward 5280 ft? A mile is also an even 8 furlongs.

The name furlong is just "furrow long" rendered in Old English. It's the fairly standard length of a plowed furrow. It turns out that a square one furlong on each side is ten acres.

Acre is Old English for "open field", and is about the area that can be plowed with a pair of oxen in one day. Picture a football field excluding endzones and sidelines. It's an area one furlong by one chain.

A chain is a length taken from an actual chain a clergyman named Gunter used for measuring land. It had 100 links and was the length of four rods.

A rod is about 16.5 ft. People who did a lot of measuring for engineering or land surveying would have an actual metal rod of that length to use for their standard.

This was more rigourous than the ancient cubit. The word comes from the Latin word cubitum for "elbow" and the length was the distance along one's forearm from the elbow to the tip of the middle finger, about two spans. 

A span is the distance from the tip of one's thumb to the tip of one's pinkie finger with the fingers spread wide, approximately 9 inches. 

The inch has, at one point, been defined as the length of three grains of barley laid end to end, but the word "inch" is from the Latin word uncia for one twelfth part because it was (and now is again) one twelfth of a foot. 

The foot is, guess what, about the length of a person's foot.

Ship of Theseus Paradox

The greek historian Plutarch wrote in the year 75 that the ship of the legendary Theseus was preserved by the people of Athens for hundreds of years. Whenever some part got too worn out they would replace it. Eventually, it was not clear if any part of the ship was still original  And if every part had been replaced, is it still the same ship?

And what if you found and gathered all the original, replaced and discarded parts and reassembled them into a boat - which of the two would be the true Ship of Theseus? 

Similarly, we know our own bodies are always replacing parts. How much of you is the same as the you that existed when you were a small child? Enough to say that you are the same person?

The answer, of course, is that we are the same person. And most would say the Ship of Theseus is the same ship, but it's instructive to think about why. It seems a thing does not derive it's thingness from it's parts alone. It's the relationship of those parts that is important, and the persistence (and evolution) of that relationship through time.