Archive for April, 2010

Across and Back

Suppose you have a river 100 feet wide, flowing 3 feet per second. Suppose that two perfectly matched swimmers have a contest in which one will swim 100’ upstream and then 100’ downstream while the other swims across and back again. Both swimmers swim 5’ per second the whole way.

Who wins?

Obviously, the one who swims up and down is slowed by the stream going up and helped going down; the one who swims across is slowed a little the whole time, but the intuitive sense is that their trips should come out the same. Right?

Seems right, but let’s check the math.

Joe is going upstream 5’ per second, but actually, he only goes 2’ per second because of the river flowing down at 3’ per second. So it takes him 50 seconds to go 100’. Returning, he goes a speedy 8’ per second, swimming 5’ per second plus 3’ per second from the sweep of the river. Thus it takes him only 12.5 seconds. (12 x 8 = 96; so 12.5 x 8 = 100)

Joe’s whole trip is 62.5 seconds.

Ben swims across. Since the stream sweeps him 3’ downstream every second, he needs to aim upwards to get straight across. If he chooses the correct angle, he’ll get four feet across for every five feet he swims. This is the famous 3-4-5 right triangle where he’s swept 3’ downstream, and goes 4’ across while swimming 5’ on a well-chosen diagonal.

Every second, he’ll get four feet closer to the other side, and the same speed considerations govern his return. 100 / 4 = 25. He can go 100 feet in 25 seconds. Twice 25 is 50. He’ll be there and back in a cool 50 seconds. How did that happen?

Well, never mind how it happened. Just face it. The intuition that upstream and downstream is the same as across and back is wrong. Across and back is faster.


That is how Michelson explained things to his daughter as he (and Morley) prepared a famous experiment to test for the existence of the ether. He had devised  an ether test based on the difference in speed between going upstream and down vs going across and back.

After all, if there is an ether, the earth is traveling through it. And if the earth is traveling through the ether, there should be an “ether wind” blowing across the earth. A very gentle wind, mind you, but a real one. Now, if the earth is also rotating on its axis, then there must be one moment a day when any given spot on the earth is moving exactly parallel to the motion of the ether wind, and one time a day when it’s moving exactly opposite that motion. This is still true even if we consider that the sun and the whole solar system are in motion, as is the galaxy so that the ether’s motion might be in some unexpected direction. No matter how many motions you have to take into account, the end result must be that at some time of day,  the motion of, say, a man on top of Mount Everest, is parallel to the ether, and one time when it’s opposite. At those two times each day, couldn’t you send one light beam up and down the ether wind and one beam across?

Now, what Michelson did was too clever to explain quickly, but you can look up the Michelson-Morley experiment. The idea was that his apparatus would catch those two moments. Indeed, light goes so fast that if you put the beams on a turntable, you should be able to catch a flash of interference at any time of day. Here’s how:

A beam of light would travel across a turntable, be split into two beams in the middle (by a half-silvered mirror) and those two beams would travel across the rest of the table and return home. At some moment, one half-beam would be traveling parallel to the ether, like Joe, and one half-beam at right angles, like Ben. When they got home, and the slow one would make an interference pattern with the fast one.

An interference pattern?

Well, think of the waves in a pond when they come from two directions. Where they meet with one crest meeting one trough, the water is still. Where two crests meet, there is a high crest; where two troughs met, there is a deeper trough.

Light waves can also make an interference pattern, so that at their still point, certain colors go missing, or so that there are light and dark bands instead of a steady light. That was what Michelson was hoping to see.

You see, one beam would be like the stone in the wheel, just in top and bottom positions, first fighting the ether and then going with it. The other beam would be like a stone at the side of the wheel, going at an even speed and, like the swimmer who crosses the river both ways, making his trip faster. When the two beams returned, you would be able to detect the difference in their trips, because they would create an interference pattern.

Did it work?

So what happened?

Well, there was a tiny interference, but it was only 1/40th of what Michelson expected. Or, rethinking things,  maybe one sixth of what he should have expected. Was this because the apparatus was badly designed? Or was it just experimental error – because the apparatus was not sensitive enough? Or was there no ether?

The experiment was conducted again and again. The apparatus was redesigned to be more sensitive. It always gave a result, always too small.

The consensus over time has been that there is no ether. Michelson himself never accepted that consensus.

How can you have a ripple without a pond?

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Let’s think about wheels.

If a car is going down the road 30 miles an hour, all its parts are traveling that fast, and you, too, inside the car. The wheels come along with the car, and they travel at that same speed, 30 miles an hour.


Now suppose the tire treads have ink coming out of them; that ink is printing the road with the tire tread pattern at 30 mph. Does that make sense?

(If someone will make me a drawing, I’ll post it.)

But suppose the treads have a little stone stuck between them. How fast does that stone travel?

If you think it’s 30 miles an hour, consider this: the stone has to go around the axle at 30 miles an hour, because that’s how the car moves, and how the tread prints along the road at 30 mph. So you could say it travels 30 mph.

But in relation to the axle, the stone is sometimes going forward and sometimes going backward. As the stone comes up over the top of the wheel, the axle is going forward at 30 mph and, for a moment, there at the top, the stone is moving forward 30 mph in relation to the axle. So it’s going 60 mph in relation to the ground!

When, on the other hand, the stone is at the bottom of the wheel, the axle is going forward at 30 mph, and the stone is moving back towards the rear of the car; it’s going backwards in relation to the axle — also at 30 mph. Well, you can’t go forwards and backwards both at once, right? You have to combine the speeds: so for a moment, the stone is actually standing still: that is, in relation to the ground, it is standing still under the wheel, just for a moment.

Now, let’s finish up: when the stone is going down at the front edge of the wheel, it travels forward 30 mph, just like the axle, – so though it’s going around the axle at 30 mph, it’s not actually moving forward relative to the axle; it’s just going 30 mph relative to the ground, same as the axle. Then it will slow down to 0 mph at the bottom of the wheel. Also when the stone is coming up at the back of the wheel, it travels forward at 30 mph, just like the axle, and then it speeds up to 60 mph at the top of the wheel.

Thus, the speed of the stone is constantly changing. In relation to the axle, it’s always traveling around at 30 mph, but in relation to the ground, its speed is doubling up and slowing down – to zero! – every time the wheel turns.

(We need a drawing for these four possibilities.)

Think about this for a while. It’s an exercise in what we call Galilean relativity – the fact that the speed of a moving object can be understood in different ways depending on whether the viewer is moving along with it, or standing still, or moving in some other direction. It was an idea that Galileo understood; no need for Einstein to understand this one. Just a little time.

It’s a strange idea, the travels of this little stone, but a very important one. It would be silly to try to talk about Einstein without getting this straight.

By the way, in Corey’s Bow, the story of the Jumblies was about Galilean relativity.

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So you are probably thinking: what’s this all about? How did Einstein ever get to talking about clocks and dice anyway? I thought that relativity was about everything depending on everything else so nothing is just itself.


What time did you say it was just now? And how fast are you moving? And in what direction are you moving relative to me? Because I need to know that or your “time” doesn’t really tell me anything.

See how messy it is?

The original problem was very specific. (It’s always worth knowing what was the hold-up at a specific moment in physics. One man will have an insight that is brilliant, and he’ll run with it and then one day, it just loses steam. He meets a problem that can’t be solved with his bright new tools, and everyone has to sit back and re-think everything to find the place where one of their assumptions could possibly have a leak.)

The problem Einstein had is not difficult to understand, and you’d be asking about it too, if you had thought about it a little.

Think about the ripples in a pond. How beautiful they are! If you stand up, and if the pond is very still, you can close your eyes for one minute and your friend can throw a stone in the pond, and when you open your eyes, you know just where the stone went in. The ripples tell you. You can study waves all day and learn all the principles of wave motion right there by the pond.

Then you can go home and study sound, and the waves are all following the same rules, so you are ready to be very insightful about the way sound works. Sound is carried by air and wood and metal – by lots of things. It ripples outwards just like the ripples in a pond. Sound is carried – it makes waves in — practically everything except emptiness – that is, except a vacuum. When we look around the galaxy, we see some gas clouds that have waves in them. What a sound there must have been where that exploded! But the sound does not reach us because sound waves have to wave in a medium. You can’t have a wave without a medium – like the Alice in Wonderland’s Cheshire cat having a smile without a face. You can’t have a ripple without a pond. Something – some thing – has to be rising and falling, squeezing and puffing, expanding and contracting, so that a wave can travel through it.

You know this; it’s easy.

So then, how does the starlight reach us? Light is a wave, and it follows all the rules of waves, but what does it wave in? Space doesn’t have anything in it to wave. It’s empty.

Isn’t it?

Well, for hundreds of years, it was thought that there had to be something out there – it was called ether. Or aether. Ether was the last remnant of the concept of quintessence, that perfect solid of the heavens. It had to be out there because otherwise light would have nothing to wave in. It had to be very subtle, too, so you could see through it, but it had to be there, perfectly elastic and completely filling all the cracks so that the slenderest beam of starlight could wave it.

Funny to be so solid, and so elastic, and so utterly invisible… How could anything have all those qualities?

But if there’s no ether, what is the light waving in?

Is the ether really there or not? That was the question everyone was wrestling with.

To be continued.

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Notice that this idea of a world shaped by the throw of dice actually goes back to Democritus, the first atomist. Democritus is often portrayed as the amazing philosopher-scientist who lived 2,000 years before his time and proposed an idea that the rest of the benighted world, (including most of the Greeks, including Aristotle), were just too timid to accept. In fact, part of the difficulty with Democritus’ concept of the atom, an idea substantially different from our own, was that he believed that all reality was formed by the chance interactions of these hard little pellets that rained about and bumped into each other at random, sometimes clumping into more interesting stuff until they formed the whole universe, or at least the rather smaller world known to the Greeks.

The concept of Darwinian evolution is tame by comparison. At least it starts from something.

Or does it?

When you read more deeply about Democritus, you get the feeling that was here, not on the Galapagos Islands, that the concept of accidental evolution took its origin. It’s so similar it’s eerie. It’s the same unreasonable idea that a shuffled pack of monochrome cards will yield an elephant if it’s large enough and if you shuffle long enough; only for Democritus it had to yield the sun, moon and stars as well as yogurt, oregano, rivers, elephants, and men who think about the First Cause, all alongside enough apparent causes – such as: dog barks; Dad wakens — to slow the acceptance of accident as a total cosmology.

This causeless cosmology is the soul of Darwinist biology, and it was in competition for the soul of chemistry for a long time. Our present idea of atoms is, of course, quite orderly: the Periodic Table has about 100 elements, give or take a few depending on how long something has to hang around to be considered an active part of the universe. The list is tidy, orderly, predictable in its outlines, specific in its causes, and yet full of merry surprises whose cause is tucked in to a corner you weren’t looking at.

Meantime, the assertion of ultimate randomness has had to back up a step. The modern physics text now says that the atom is quite real but the electron is not an entity, just a cloud of probability, the same philosophical randomness rearing the same ugly head for no good reason except that the electron can’t be photographed with a sparkling trail coming along behind, as it orbits the atomic nucleus.

Einstein was not happy about this. He correctly understood that just because you can’t see, or even measure something, doesn’t mean it isn’t there. Even if the only thing you can be sure of is an average or “probable” behavior, still, there may be things doing the behaving.

But physics got stuck as the home of the Uncause, and it’s going to take a battle to unstick it.

To be continued.

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Einstein 101

If Tom Bethel and his mentor, the physicist Petr Beckman, are to be believed, the principal difficulty in understanding Einstein is much more accessible that has been commonly understood. The basic idea of relativity is this:

Because you move, my watch slows down.

It is an outrageous idea, and so stated, it leaves a trail of insurmountable chaos. Because you move, my watch slows down? Not because I move, which would be bad enough, but because you move? People and stars and systems are moving around me all the time. The Earth moves around the Sun and the Sun moves around its little locus in the arm of the Milky Way, which is spinning around its center and also responding to the gravity pull of the Andromeda Nebula. Never mind that my daughter is out for a run and my husband is driving his truck into the meadow and a tree is falling. If all those things make my clock wobble, why even have one?

The relativity answer would be that only things close to the speed of light change your watch enough to matter – i.e. be measurable.

But this is not satisfying. Don’t you feel it? Because you move, my watch slows down is not a principle that allows anything orderly to take place. We are all of us no more than fluttering leaves in the storm of reality!

It’s one thing to say that everything is connected by gravity; this is an orderly idea even though the complexities are potentially quite intricate. In fact, our universal gravity connection does suggest that movements of things, movements which change the distance and direction of a whole series of gravity interactions, could pull us about some; still, that’s not so bad.

But relativity theory goes so far beyond gravity that the chaos is intractable. It is not just difficult to calculate — in fact, the calculations are not particularly difficult if everything would just sit still a minute – but the imagination simply stops. It can’t go down that road.

If the whole universe stood still,

only excepting my watch,

and if you and I looked at each other

across the darkness of space,

and if you started walking,

my watch would slow down;

not yours, mine.

Petr Beckman rejected this idea — promptly, spontaneously, and permanently — when he first heard it – and he heard it as a student of physics. For the rest of his life, he looked to see how such an idea had taken hold and he saw that it needn’t have taken hold. He even saw the Einstein had been dissatisfied and had pointed the way out of his dilemma, but this time he could not attract a following.

Why not?

Beckman, perhaps wisely, does not really answer this one. You must recognize that there is a philosophical issue. The idea that the universe is fundamentally unreasonable is dear to the heart of the atheist, and Einstein seemed to offer an incredibly powerful support for this. When his idea became part of a synthesis that we may call “the cosmology of accident,” he was famous for saying, “God does not play dice with the world,” but he couldn’t turn things around.

For physicists, Petr Beckman wrote a book called Einstein Plus Two. For the rest of us, he wanted to write a simpler book, but died quite unexpectedly, and his good friend Tom Bethel, not a physicist, sought another mentor to help him write things out.

I’ll tell you more about it.

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When we look at the early history of biology, we are simply looking at the curiosity of ordinary human beings as they look at the living things around them. We do not have the names of the first people to recognize that trees and flowers grow from seeds, or the first to recognize the medicinal values of various plants. How could we? It happened long before writing! For that matter, even animals are sometimes aware of the medicinal value of herbs – you’ve seen your dog eating grass when he’s feeling sick, and you have read about Peter Rabbit wanting parsley after too rich a foray into the garden. (Though I never did think of French beans as rich… Wait a second… who grows French beans?)

But by way of remembering all those herbalists, let’s take a moment to learn about just one herb, oregano. You know the taste of oregano – it is the taste that, added to bread and tomatoes, makes pizza. But what else?

Oregano belongs to the mint family, and, like all mints, carries its little oval leaves in opposite pairs along a square stem. Little leaves – oregano’s leaves are like your baby’s fingernails, just little. Once the plant is established, it blooms freely with tiny, clustered flowers just a few millimeters wide. If you are growing it for kitchen use, you’ll want to harvest the leaves before they put their fragrance and energy into flowers. Like all mints, oregano has a strong scent, although it is unusual in being stronger dried than fresh.

Oregano plant, leaves and flowers

As far as I know, none of the mints are poisonous, but inevitably a few people are allergic to different ones, especially basil, sage, and thyme; anyway, enough is enough of anything.

Besides, oil of oregano has medicinal uses, and that should clue you that it can act strongly.

How much oil is there in oregano?

Not much. You could make a tea and never see drops of oil on the cup. But the oil is extracted and sold as oreganol, and as such it can be a strong medicine.

Oregano was known to the great Greek doctor, Hippocrates, the Father of Medicine; he used it for an antiseptic and for stomach and respiratory ailments. Paracelsus, 2,000 years later, used it for these and for fungal problems as well. Modern herbalists suggest it for all sorts of things, from skin rashes to parasites and warts. Most of the things for which you might use metholatum are also said to be responsive to oreganol; you can use it as an inhalant, for example. Since mint is cheaper and you don’t want to go around smelling like a pizza, there’s no likelihood of a general substitution, but it’s an interesting point. Mint is mint, even when it’s oregano.

On the other hand, not all oregano is the same. Origanum vulgare hirtum is the spice in Italian food, O. onites and O. heracleoticum are used in Greek and Turkish dishes, and the less pungent, common oregano, O. vulgare, is used in English and French cooking. There is a Mexican oregano, lippia graveolens, which is actually in the verbena, not the mint family, but it has a similar flavor and some prefer it to the Greek oregano. For one thing, it stands up better as a freshly chopped leaf, and its leaves are much larger, maybe an inch or more.

Marjoram is a close relative of oregano, but with a sweeter flavor. In fact, oregano is sometimes called pot marjoram.

The name oregano is often said to have Greek roots and to mean “joy of the mountains.” It does grow freely in the mountains of Greece, but this etymology is uncertain; the word may not be Greek at all, its origin, like the herb’s first use, being lost in the mists of time.

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Biology is the study of life. As such, it incorporates botany, the study of plants, zoology, the study of animals, and anatomy, the study of the human body as a biological system. Underlying all of these, though beyond the reach of human vision and therefore unknown until the development of the microscope, is the cell, the unit of living creatures. A modern biology book begins with cytology, the study of the cell, and maybe even with the study of DNA and heredity; but the actual beginnings of biology would have involved the plants and animals we can see.

Surrounding all biology is the landscape — or seascape — which supports life, with different settings for each living creature. Ecology is the study of the land, the water, and the living community that surrounds and supports each kind of living creature.

Observing and domesticating plants

The study of plants would have started early in our history since plants are a source of food. Farming, the systematic cultivation of plants began about 10,000 years ago and very soon involved – deliberately or by accident – immediate changes in the plant. For example, wild wheat does not easily come off the stalk, and by clinging, it ensures that the seeds will come off only in such a high wind or other tumult that they are not likely to fall right together under the mother plant, but be spread abroad. This keeps them from choking each other out. Cultivated wheat is removed more easily, an advantage to the thresher who wishes to remove it for storage. It is then up to the farmer to broadcast the seed next year.

But even farming may not be the oldest biological investigation. From times as old as records reach, we know that some plants were used for healing and for assistance with digestion. These would have been noticed even before they were cultivated; even now, many are gathered from the wild.

Studying animals

The study of animals likewise reaches back into ancient times. The appearance and the habits of predatory animals on the one hand, and of those that might be food, friends, or servants on the other, would have been an immediate value. At least the dog has been man’s companion as far back as record go, for they are intelligent and loyal; they can help with hunting and guarding and also with the isolation of life. As soon as man moved up from hunter-gatherer to herdsman, dogs had a new value as protectors of the herds.

Herding for the value of meat undoubtedly led to the use of animal milk – as drink, as yogurt, and eventually as cheese. It is not clear how far back dairying goes, but it must reach at least as deep into time as farming.

How could we know this?

We know this because the word for cow is shared by several languages whose separation from an earlier language implies such dates. Strange to think that we have evidence from such a source as the words themselves, but so it is. Farming words such as plow are also shared in the Indo-European languages, but these and the grains themselves can be found by archeology as well as language.

So that is the beginning of biology, and for thousands of years, it developed anonymously and worldwide as food, service, and medicine.

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