Gulliver Knew His Physics ...

One of the best illustrations of the influence of Isaac Newton, and of the intellectual capability of the eighteenth century readers, pops up in Jonathan Swift's Gulliver's Travels (1726, amended 1735). The official name is Travels into Several Remote Nations of the World, in Four Parts. By Lemuel Gulliver, First a Surgeon, and then a Captain of several Ships.

Most people have heard of Gulliver's visit to Lilliput, home of the little people. Many don't realize that gulliver travelled to several other lands, too. Swift wrote the book as a satire and condemnation of the injustices of society in the century before the great democratic revolutions. But Swift had to be careful. He couldn't just come right out and say, for example, that the king was an ass, or that the British House of Lords was composed of imbeciles, or that justices of the peace were corrupt. Doing so could have got him thrown in jail, or worse.

Instead, he had Gulliver visit lands where the king was an ass and the appointed governing body was composed of imbeciles. When challenged, he could always say that he'd written a book of fiction. He wasn't talking about home, for goodness sake.

Isaac Newton had revolutionized science. He showed that the universe runs on simple mathematical laws. He broke down the distinction between heaven and earth by showing that the same laws of physics that govern the actions of objects on Earth apply to the planets. Prior to Newton, nature was mysterious, and scientists (or natural philosophers, as they were more properly called) were limited to explaining Earthly phenomena. The Heavens were governed by their own laws, and why not? Heaven was the realm of God, and God should not be subject to the same laws that constrained the behaviours of Earthly objects.

A generation before Newton, Kepler found that the planetary orbits follow mathematical rules. The planets travel on elliptical paths at varying speed. (Their speed increases as they get closer to the sun.) And Kepler found a fascinating, but mysterious relationship: the cube of the a planet's average radius of orbit divided by the square of the planet's period of orbit is the same for all planets. In math lingo, T-squared varies directly with R-cubed.

Newton used this relationship, Kepler's elliptical orbits, and the calculus that Newton invented while on summer holidays when he was an undergrad at Cambridge University to come up with the Law of Gravity. He could demonstrate that the same force that makes apples fall keeps the planets in orbit around the sun. When he published his discoveries (some twenty years after he made them) he became an instant celebrity.

So, back to Gulliver. On his voyage, he landed at Laputa, where astronomers studied the heavenly bodies through great telescopes. In Swift's time, no moons of Mars had been discovered, so he decided to pretend that Laputian astronomers made a fascinating discovery. Read this:

They have discovered two lesser stars, or satellites, which revolve about Mars; whereof the innermost is distant from the centre of the primary planet exactly three of his diameters, and the outermost, five; the former revolves in the space of ten hours, and the latter in twenty-one and a half; so that the squares of their periodical times are very near in the same proportion with the cubes of their distance from the centre of Mars; which evidently shows them to be governed by the same law of gravitation that influences the other heavenly bodies.

Did you see what he said? Kepler's T-squared/R-cubed law holds for the moons of Mars, showing them to follow Newton's Law of Universal Gravitation!

I think this speaks volumes about Swift's society. Swift counted on his readers knowing Kepler's and Newton's Laws. He knew that his characters had instant credibility if they were included in Newton's great intellectual revolution.

How many authors of fiction today assume their readers would be as intellectually accomplished?

Tidy rooms...

My wife regularly asks my daughter Debbie to tidy her bedroom. Debbie's response is always either, "I did," or "It is tidy." Here are two photos of the room after my daughter insists it's tidy.

After many years, I still haven't cracked the code. I figure "It is tidy" means one of these:

1. it's good enough for me

2. this matches the definition of "tidy"

3. don't tell me what to do.

To be sure, number 3 applies as a general rule to any suggestion my wife makes to my daughter. "Don't tell me what to do" is a given. But I've come to the conclusion that Debbie actually believes that a room qualifies as tidy even if the floor is covered in paper, empty water bottles, underwear, spilled cat litter, books, CDs, and overturned containers.

Look, my den is often messy. I freely confess it. But, during those times, I don't call it "tidy". Our bedroom is often a mess. (My wife doesn't follow the adage "let she who is without sin cast the first stone.") But I admit the fact.

Debbie's definition of "tidy" is far from my wife's (and mine, but I stay out of it.) There will never be a day when my wife will be able to look in Debbie's room and say, "My, your room is tidy."

And there is only one or two days a year when our bedroom is tidy, and it only stays that way for 24 hours. But that's another story.

Congratulations US Congress ...

As a Canadian, I was pleased to see the Democrats prevail and pass a universal health care bill. Over the past year, I couldn't believe the vitriol from the Republicans. I was disgusted by the distortions, and misinformation, and outright lies about what the various versions of the bill contained and ramifications of ensuring that Americans can get access to health care.

I don't mind paying higher taxes than Americans in return for health care. One of my daughters had a brain tumor operation. No one asked for money for the operation and the three weeks in hospital. My other daughter went in for a seizure-caused dislocated shoulder. We just show our health card, and walk in. If I have a problem, I go to my doctor, flash my card, and that's it. The important thing is that it's the same for everyone, not just those that can afford insurance.

The fact that, in the US, some workers at insurance companies admitted that they automatically reject claims until appealed appalled me. I found it hard to believe that the country with the highest standard of living in the world wasn't embarrassed to see some of its citizens bankrupted by health problems, or worse, see some of its citizens having to forgo medical treatments because they were financially worse off.

That a country wouldn't take care of its citizens on such a basic issue as health care ... well, congratulations for seeing the light.

Shame on Republicans for NOT EVEN ONE voting for the bill. NOT EVEN ONE.

Defeating Obama was more important than doing the right thing for your country. I realize that Republicans will jump all over that statement, saying that they WERE doing the right thing for the country by voting against the bill. But it sure didn't look that way from here.

The Mentalist ... Getting Stupid

I'm getting more and more disappointed with The Mentalist. I cheered the concept at the start, especially when Patrick Jayne said, in the first episode, "There are no such things as psychics." The problem is, the police work in the show is getting far too stupid.

Cases in point:

Case 1

In one episode, the dead victim is in a field, shot from a distance. But where did he stand? We hear Jayne call, "He stood here." Jayne is standing behind a scarecrow, waving its arms. Of course, Jayne would be standing right on top, and thus destroying, possible evidence.

Case 2

A couple of episodes ago (January or February, 2010), The Mentalist never realized that a person was lying to him. Kinda destroys the very concept of The Mentalist, doesn't it.

Case 3 (Last week, March 4)

A second victim dies, right in front of the head of the crime unit (Teresa Lisbon). She sees him drop, eyes open, not breathing, not talking. Does she start CPR? Does she check for a pulse. No. She holds her hand in front of his face and cries, "How many fingers am I holding up?"

Case 4 (Tonight, March 11)

A scientist in a bio lab became exposed to a virus and died. A few hours later, Jayne pulls a prank, admittedly clever, to catch the killer. But it involved announcing to at least 40 other people that they have now been exposed, that they should call their loved ones and say good-bye, and make their final arrangements. They only have an hour or so to live.

It was a fabrication, of course, but how many lives did he just hurt? How many people are going to sue him for pain and suffering.

Going back to Case 3. Where was an editor or consultant to say, "That's stupid. A supposedly experienced person is not going to say 'how many fingers?' to a dead person." Surely Robbin Tunney, if she really knew her role, would balk, and announce, "My character wouldn't say that."

Dealing with unruly students

I have been retired from teaching or four years. I had a wonderful career, teaching high school physics. I was in good schools, got the best students, and had supportive vice-principals and principals. Generally, a more peaceful career than many teachers.

I did have the odd student who was a class disruptor, refused to do assignments, or skipped class. Here is a remedy that fixed the situation.

In brief, they were told to leave and not come back until the after the next test. I explained that each day they could come at the beginning to get page references for the lesson. But they were to learn from the text book, without my aid "Since, by your behaviour," I told them, "you showed that you do not value my contribution to your education, learn without me. We'll see how that works on the next test."

The result was that, after a day or two, the student requested to come back in the classroom. And that's how it should be. Students should be in class because they want to be, not because they have to be. A student isn't doing me a favour by showing up. I am doing him a favour by sharing my expertise. My method gets that point across.

Of course, the process was illegal. Putting a student in the hall meant that he was now, potentially, someone else's discipline problem. And if he left the school and got hit by a car, I might be held responsible because he should have been in the class under my supervision. I took the risk, and was supported by the principal because the system worked.

Here are some methods that ensure success.

Call home. Mention that the student is not learning as much as he should and ask for suggestions. Parents are almost always appreciative of your call, and the fact that you ask them for help shows you care and respect their opinion. Usually, if you are having trouble with the student, they are too. The phone call will be a sharing episode. Then say, "Here's something that might work. Suppose I tell him that he's not allowed to come to class. He's not kicked out of the course. He just has to learn on his own." Then explain the plan. Parents have always agreed to try it. Usually they're desperate to try anything.

Mention the plan to the principal. A couple of times I drew up contracts, on school stationery, for the principal, parent, student, and me to sign. The student always wants to renegotiate after a day or two.

Soon, the student is back in class, under my terms, appreciative of my efforts to help him learn.

Sample Horoscope

One day, I went down the aisles of my grade 10 science class asking the kids their birthdays. Each was given the appropriate horoscope. Here's Aries:

Aries – March 21- April 19

You have had some difficulties in the recent past. Sometimes you wonder who your best friends are, or will be in the future.

Someone's words will take on a tone of intensity for you now. Don't fall into a dark, brooding mood as a result. It's good to clear the air, and time to break your silence.

There's high drama on your schedule for the next couple of days, so prepare yourself. That's not necessarily a bad thing. Still, you might want to warn your close friends.

Some encounters will be a very significant -- some more pleasantly so than others. Think of it this way -- you have a choice about how to use this energy, so use it to its best ends.

You're in the mood to catch up on the latest scoop, but your family and friends have been a little too intense for your tastes -- at the moment, anyway. Let them talk, and just listen closely. Your turn will be coming up soon.

I asked the kids to put up their hand if they felt the horoscope was accurate. Hands went up around the room. Then I had them pass it to the person beside them. They started to laugh because all the horoscopes were the same. (I made it up.) It's so easy to persuade people of the truth of something so loony (luney?) as astrology. And easy to demonstrate how false it is. Still, few believers can ever be persuaded otherwise.

BTW: Not a single person pointed out that in the second paragraph I advised them to speak out, but in the last paragraph to just listen.

What "Christian" means

Shari, a teaching colleague, once told me that she was against evolution because she was a Christian. Of course, what she meant was that she was a fundamentalist Christian.

I asked her if she thought the Pope was a Christian. She agreed that he was. But Roman Catholics are okay with evolution, I told her. So are Anglicans (Episcopalians) and some other Protestant denominations. She was surprised at that.

(The RC's position, stated in March 2009, is that there is no conflict between evolution and religion on the origin of species, but man's soul was a matter of special creation. I am simplifying, but I think that's the kernel of their position.)

I digress. My comments are on the use of the label "Christian". We hear of "Christian Schools". In Canada, we allow two school systems, the public school system (inclusive, open to everyone) and the Roman Catholic School system. Non-Catholics can, theoretically, attend (because tax dollars go to the RC boards), but it's catholic education. Then there are the schools not supported by tax dollars. The label "Christian" school goes to the private schools that are run by Baptists, for example, or other fundamentalist groups. In general usage, the term "a Christian education" does not apply to either of the two official school systems.

The fundamentalists have confiscated the word "Christian". In addition to Christian schools, we have Christian radio stations and Christian literature. Am I over generalizing here? Are there "Christian" televangelists who accept evolution? Are there any "Christian" radio stations that broadcast messages doubting the literal translation of Genesis?

Incidentally, Shari was a biology teacher who did an excellent job of teaching evolution. This despite her proudly announcing herself as "a Christian".

Denying Evolution

I almost feel sorry for the creationists these days. I have a couple of friends who take Genesis literally. There was an actual Adam and Eve, they say. One of them was surprised to hear that man have the same number of ribs as women. The other truly believes the Earth is not much older than six thousand years.

These are not morons--they are intelligent, rational people with good jobs (earning more than me!) But they deny evolution with a vehemence that astounds me. No, I'll take that back. I am not astounded by what adherence to a religious belief does. Witness suicide bombers who feel that
1. non-believers deserve to die, and
2. they themselves will go to eternal paradise by killing infidels with them when they go.

My two creationist friends aren't in that league. That is, contrary to some creationists I see on the web, they don't feel the need to make everyone believe, or else.

I feel sorry for creationists when I assess what they have to give up to maintain their beliefs. Although they might not concede this list, to deny evolution, they must ignore accepted facts in astronomy, geology, the fossil record, comparative anatomy, comparative physiology, genetics, molecular biology, continental drift, and embryology, at a minimum.

One of them even says, "There is no evidence for evolution." This floors me! The evidence for evolution is overwhelming, converging from so many disciplines. How can he say this?

What a wealth of knowledge people have to give up to maintain absolute consistency with a religious belief. So sad!

Sing the Damn Note!

I don't watch Idol because I can't stand the type of singing that everyone seems to do nowadays. Instead of singing the note as the composer wrote it, today's performers hit about five notes per syllable near the correct one, eventually (one hopes) lingering on right one long enough to demonstrate that they are familiar with the tune. I know Streisand did that (in moderation) years ago. Karen Carpenter used to scoop a note here or there, and Petula Clark would put a grace note in occasionally.

But now the instruction to "Make the song your own" means that the tune gets destroyed. I am especially irked when this happens to Christmas carols. When "ger" in "Away In The Manger" is awarded six notes, I feel like yelling "Sing the damn note".

That's one of the reasons I like show tunes. I realize I'm showing my age here, but when Shirley Jones sung a song, she hit the notes and put on the consonants. Same with the quality performs in "Cats", or "Phantom" or "Les Mis".

Of course, we have to give the singers who perform the national anthem permission to butcher the song. That's expected.

Conspiracy theorists

Glenn Beck on the radio; Mark Steyn in Macleans magazine; Conrad Black in the National Post... One thing these men have in common is their loud disbelief that global warming is occurring, much less caused by humans. Do they actually believe what they are saying/writing?

Evidently so. Just as the people who think that the US flew planes into the Twin Towers, that man has not set foot on the moon, that the Holocaust didn't happen, and so on. I sometimes wonder how intelligent people can let themselves be led to ridiculous, unsupported positions.

Of course, these guys are saying the same thing about me; namely, that I've been sucked in by all the baloney and believe that the Earth is getting warmer. Every day I hear new evidence--a study here, an observation there. What do Beck, Steyn, Black, and the other deniers think to themselves when they hear each bit of new evidence? Another deluded scientist has made a mistake (or is lying)?

For the record: I have had a cottage a few hours north of Toronto since 1976, and grew up at my parents' cottage before that. The lake temperature used to peak at 80 degrees F on or around August 1, and stay there for a day or two before starting to cool. In each of the last two years, my lake got to 80 F by July 13, and stayed that warm for over two weeks. And there are new birds in the forest. (I know by the new bird calls.)

Something has changed.

Base 3 Computers

Computers work by having ones and zeros represented by memory locations that either contain magnetism or no magnetism. These memory locations are combined to represent bigger numbers using binary arithmetic. For example 0010 is 2, 0111 is 7, and 1000 is 8. Is there any way of altering and determing the polarity of the magnetism? If there were, then "north-up" could be a 2, "north-down" could be a 1, and no magnetism would be a 0.

That way, the computer could work in base three. A 2 would be 0002, a 7 would be 0021, and an eight 0022. It took two digits to represent an 8 instead of four (not counting the leading zeros.)

In binary, the biggest 4 digit number is 1111, which is 15. So sixteen numbers (0 to 15) can be represented with 4 digits. In base three, however, the biggest 4 digit number would be 2222, which represents 80. Many more numbers (i.e. data) could be packed into the same memory space.

Is anybody working on base three computers?

Amazing? Not

I propose a ban on the use of the word 'amazing'. Just today I heard the following:

The figure skater's performance was amazing.
The Olympics were amazing.
Crosby's goal was amazing.
Avatar was amazing.
The book was amazing.
The video was simply amazing.
The blueberry cheesecake was amazing.
Human reaction time is amazing.
The hummingbird was amazing.
The [sensitivity of a] mousetrap was amazing.
A girl said her boyfriend was amazing, but didn't clarify.
The same girl said her girlfriend was amazing to her.

I'm ready to scream the next time I hear the word. The problem is, of course, that the word is used so widely that it has lost all meaning. To amaze is to overwhelm with surprise or sudden wonder. But people now use it to mean excellent, interesting, better than expected, higher/lower/cooler/warmer/drier/wetter, and very tasty. Human reaction time might be incredibly fast, but it is what it is, so one should not be amazed. Same with the hummingbird, but not that it can hover. If it tried to hover and fell...that should be amazing.

I agree that a hockey player like Ovetchkin can score an amazing goal, like when I see him put the puck through an opponent's legs, twirl around the guy, pick it up again, slip it into his skates to keep it away from the goalie's poke check, then kick it up to his stick, and pop it over the goalie's shoulder with a one-handed shot. Something that makes me blurt out, "Oh!" or "Wow" should rank as amazing.

But not everything else.

How Many Dimensions Are There?

We have three physical dimensions: length, width, and height. A mathematician or physicist might represent them by x, y, and z.

In his Theory of Relativity, Einstein used time as a dimension, expressing the position of an object in space-time with four co-ordinates: x, y, z, and t. Hence the phrase "time is the fourth dimension."

Remember that the number of dimensions is just a convenience. Einstein's formulas, using four dimensions, described the universe better than Newton's equations.

You may have heard of string theory using eleven dimensions. What does this mean? Why eleven? Here's a quick explanation.

An application of the laws of conservation of energy and conservation of momentum, in senior high school physics, is calculating the final velocities of two colliding balls, given the balls' initial masses and velocities. (And the angle between them, technically included in the word "velocity".) There are two unknowns, the final velocities of each object, and two equations to use. You always need the same number of equations as unknowns.

What if there are three balls? You need three equations to find the three final velocities. But we don't have a third equation. This is the famous Three Body Problem. It's unsolved: physicists can't compute an exact answer.

But nature can! How does nature figure out what happens to three simultaneously interacting objects? It's clear that nature does know, because this situation comes up all the time. The sun, moon, and Earth are simultaneously interacting. (An interaction is one object exerting a force on another, and all three objects have gravity, which extends to infinity.)

Physicists attack the problem by dealing with the bodies in pairs, or approximating the situation by saying that the smallest object doesn't influence the others very much. But it would be nice to have a third equation, to get absolute answers instead of numerical approximations.

A special three-body question that can be solved by students is if one object comes in and hits two identical objects, like two balls touching and the third arriving on the mid-line between them. Because the situation is symmetrical, you can find an answer. (The third equation is that the final speed on one ball equals the final speed of the other, through symmetry.)

So you can solve more complex questions if symmetry is involved. Remember this fact.

Now picture a circle. It looks the same from all angles. Perfect symmetry. Even a small circle is the same as a large circle, in one respect, because a small circle is the large circle viewed from farther back.

How about a square and a diamond? Are they the same? Sure: a diamond is a square rotated.

How about a square and a hexagon? (A hexagon has six equal sides.) You can't rotate a square or view it from a different angle and direction and see a hexagon. So in two dimensions, a square and a hexagon are different.

Now use your imagination. If you illuminate a cube with a light directly overhead, the shadow is the shape of a square. But if you turn the cube, you can get a shadow the shape of a hexagon. (To convince yourself, draw a hexagon, and add the "missing lines" to make it look like a 3-D cube viewed at an angle.)

So, if you think in three dimensions, a square and a hexagon are the same thing. They're both 2-D shadows of the same 3-D object. The lesson here is that if you include an extra dimension in your considerations, you can sometimes find symmetries that didn't exist when you were working in fewer dimensions.

And symmetry allows you to solve otherwise unsolvable equations, remember?

The string theorists use eleven dimensions. Their equations are so complex, apparently, that they need eleven dimensions to give them enough symmetries to solve them.

Gun Control and American Over-reaction

(Warning: stereotypes used in this dissertation!)

Last night I had a discussion with a friend, Jim, about gun control. He was an American, now happy to have been granted immigrant status to remain in Canada. He's from New Hampshire (state motto: Live Free or Die) and owns several guns, stored at the home of his parents in the US.

He had been an Obama supporter, but last night made Obama out to be the worst person imaginable. Why? Because, Jim said, Obama was sneaking in legislation under the tax laws to take away people's guns. Jim was furious, and proceeded to bring up the right-to-bear-arms and denial-of-freedom-guaranteed-by-the-Founding-Fathers arguments.

I did some research and it turned out that he was incensed over an internet hoax. (http://www.snopes.com/politics/guns/taxreturns.asp). There was a bill about licensing of firearms (HR 45: Blair Holt...) before Congress--nothing to do with Obama--that Jim thought would permit the government to enter private houses to check the firearms, but the bill said no such thing. A similar bill had been brought before, and never voted on. Likely, that will be the same result here.

What I found surprising (shocking would be a better word, except that I'm no longer shocked because I've seen it so often) is how the barest hint of gun control provokes such a visceral reaction in (many) Americans that it trumps all other considerations. Jim argued that the reaction is against restriction on freedom itself. Okay, I'll buy that. But the scale of the reaction is way out of proportion to the "danger".

First, the reaction is against the mere suggestion of something that could possibly be used by an extremely totalitarian state to remove all weapons from its citizens. In fact the first site I hit when I searched for Obama and gun control displayed his picture beside Hitler, Stalin, Mao, and Pol Pot. Such comparison is ludicrous because the president doesn't have the power over the legislative and judicial arms that those guys had.

Second, there are many limitations on freedom in society that we (Canadians and Americans, both) tolerate. We accept having to contribute some income to the state (taxation), licensing our cars, being required to educate our children, and so on.

Jim made a distinction between privilege and right. Owning guns wasn't a privilege; it was a right. He was on pretty solid ground there, except that the distinction has, historically and in practicality, been that "right" is what a someone demands and "privilege" is what someone else demands but doesn't matter much to me. We saw how society changed on the Smokers' Rights issue, where smoking changed from a right to a limited privilege.

It seems to me, and to most Canadians (I claim), that the American defense of their "right" in the 2nd Amendment is far more vehement than their defense of any hint of infringement on any other right. The reaction looks, to Canadians, way out of proportion. And since we Canadians don't include the right to bear arms as a fundamental freedom, the fact that so many otherwise thoughtful, intelligent Americans demand the right to carry machine guns and rocket launchers down public streets looks preposterous and downright pathological.

Am I exaggerating? Sure, but there is a continuous line between pea-shooters and nuclear weapons. Air pistols, semiautomatics, and the other types of weapons fill the gap. Individual Americans place the line between acceptable and unacceptable somewhere, and there is vast disagreement as to where.

To Americans, I say that I accept that the right to bear arms is incorporated into the very fabric of the creation of your country, both to rid yourself of an oppressive regime and to defend yourself against external threats. So I can pardon the vehemence somewhat. But what's ironic (and scary) is that your vehemence is its own counterargument. Jim said it himself, "If Obama's going to restrict my right to carry a gun, I'll shoot him myself." The very fact that he made that declaration shows that he shouldn't have the right to own a gun. My own Florida relative, visiting my cottage during an earlier presidential campaign years ago, was watching Jesse Jackson on the TV news. She blurted, "That man should be shot." I stared at her in disbelief. Compare her statement to "we should vote against that guy" or "someone should write an editorial against what he's saying". Her automatic reaction perfectly illustrated the difference between Canadians and Americans.

I agree that I'm talking stereotypes. Many Americans favor gun control, and many Canadians are against the drive to register long guns in Canada.

But am I very far off the mark?