Sir Arthur's magic orbit

As objects in space get further from the mass they are orbiting around, the orbit takes longer. The space shuttle and other objects in low earth orbit, can go around in about 90 minutes. The moon takes about a month to complete an orbit. Arthur C. Clarke, author of "2001, a Space Odyssey" noticed clear back in 1945 that we could take advantage of this fact to do a few special things with satellites. He noted that in an orbit at about 35,800 kilometers out a satellite would take 24 hours to go around the earth. Since the earth rotates in 24 hours, a satellite in orbit in the equatorial plane would appear to be stationary in the sky. This is the geosynchronous or Clarke orbit. If a satellite is in such an orbit a very narrowly focused telescope or antenna can be pointed at it without it leaving the field of view. You can use a lot of magnification, or antenna gain, because the satellite appears to stay put. The small carefully pointed antenna dishes used for direct-from-satellite TV work on this principle.
The orbit must be in exactly the equatorial plane or the satellite will appear to bob up and down, so the limited number of parking spots in Clarke orbit are extremely valuable and regulated by treaty. In addition the satellites aren't visible from polar areas due to the bulge of the earth getting in the way. In spite of these minor drawbacks, use of the Clarke orbit has brought worldwide wireless telephony, global data linkage for business, educational programming to poor rural areas worldwide and allowed millions of people to access programs their governments would prefer to censor, in general furthering communication and knowledge throughout the world.

This is magical enough, but recent advances in materials technology have generated new interest in an even more miraculous use that Clarke thought up for geosynchronous orbit. Take a satellite in geosynch orbit. Build towers below and above it, so that its center of mass stays at geosynch. The portion below center is traveling slower than orbital speed, so it tends to fall, pulling down. The portion above center is going faster than orbital speed and tends to fly outward. The system is stable, and is loaded in pure tension, so we can replace the towers with cables and it will remain 'tidally locked' in a straight line perpendicular to the orbit. We can even extend the bottom cable all the way to the surface of the earth, where it will have zero speed relative to the ground. If we anchor the bottom and add a little extra weight on the outer end we have a skyhook, or orbital elevator. We can grab onto the cable and pull ourselves upward to orbit for only the energy cost of doing so - pennies per pound instead of tens of thousands of dollars.!
The catch is that the cable has to be able to support its own weight. The best steel, for example, will break when you hang a vertical length of only 50 kilometers, far short of what we need. When Clarke used this idea in the science fiction novel "The Fountains of Paradise" he envisioned it as being built of diamond, the strongest material then known, and even then had to taper the cable severely - very fat at geosynch, tapering almost to a point at the ends. Constructing and setting the cable would be a nightmare, even if we could make that much diamond. Since a Mars-synchronous orbit requires 24 hours 40 minutes at an altitude of only 20,460 kilometers in the weaker Martian gravity field, it would actually be easier to build a skyhook for Mars than Earth.
We have recently invented a new form of carbon, the nanotube. This is a hollow filament only 10 atoms or so across, but capable of being made in macroscopic lengths. This material has awesomely better strength-to-weight than even diamond -so much better that a film less than a millimeter thick and tapering from 1/3 meter to only a meter wide could span earth-to-Clarke orbit and carry useful loads! There seems to be no reason we can't learn to make nanotubes in the quantities required, and we have boosters capable of carrying an entire skyhook like this to orbit, where we could simply unreel it.
There are people seriously planning on doing this in less than 20 years. The result will be an advance in space travel comparable to having replaced Columbus's ships within 100 years with a 6-lane freeway bridge across the Atlantic.
This seems a good point to introduce another idea that Sir Arthur C. Clarke thought up, known as Clarke's third law:

ANY sufficiently advanced technology is indistinguishable from magic.

Really simple evolution model

Evolution requires something that can almost perfectly copy itself. Adaptation requires a way for those copies to interact with their surroundings that affects their ability to make more copies. Given these conditions, evolution and adaptation are inevitable. You can prove it with a game requiring only a sheet of lined paper, a pen or pencil, and a coin. Here are the rules:
1) drawing is freehand.
2) draw two circles on the first line, approximately the same size.
3) flip the coin.
a) if it comes up heads, each circle gets one copy , as exact as you can draw it, on the next line.
b) if it's tails, the least circular (by eyeball) gets two copies of itself, mistakes and all, as exact as you can draw them, on the next line. The other(s) get one.
4) repeat.
5)Watch how quickly you evolve something that doesn't look at all like a circle. Rule 3b is an adaptation that yields reproductive advantage. Without rule 3b you will still evolve things that don't look like circles, but not as fast, and they won't crowd the line so much. If we replace rule 3 with a rule that says when the line gets full eliminate those copies that look most like circles there is a survival advantage. The combination will evolve faster than either alone.
This is an absurdly simple system where the figure can't even make a copy without you helping. Still, it evolves.
If you would like to get a better appreciation of how evolution works, there are many computer simulations that involve 'genes', 'competition', even 'sex' in addition to adaptation to modify evolution. http://www.alcyone.com/max/links/alife.html contains a number of fascinating links for simulated and computational evolution, at levels from grade school to cutting edge research.
Competitive advantage, 'survival of the fittest' , complex organisms, even life itself, are all results of evolution and adaptation that are frequently mistaken for necessary parts of the process. The discovery that much of our DNA is evolutionarily neutral, just 'along for the ride', was probably held back for quite some time because of our focus on 'survival of the fittest' and adaptive significance. We have evolved both straight and naturally curly hair, but neither is of any particular survival significance. If they were, adaptation would cause one to crowd out the other. Focusing on the simple model helps us remember that evolution does not have to follow our logic, we use our logic to find out what evolution does.

Statistics - NOT in simple models.

Statistics have no place in simple models because NOBODY has a 'feel' for statistics . We can illustrate this with a really simple statistical system, the coin flip. An honest coin gives 50-50 odds on each flip - either heads or tails. Consider though, what happens if we get 10 heads in a row. If they are betting, most people will shift their bet to tails, with the feeling that the coin has to come up tails more often in the next few flips to 'even things out'. In a trial of several thousand flips, though, you can expect 10 in a row of either heads or tails to occur multiple times. What has gone before has absolutely no effect on the current flip. The odds remain 50-50, but our feelings about the odds vary dramatically, even when we know they don't change.
Good statisticians know that expectations can influence not only our perception of the odds but even the way we report the events. This is why they go to extreme measures to set up 'double-blind' experiments, so the experimenters and the subjects don't know what to expect.
Feynman illustrated another problem with statistics, that of remembering only 'significant' results. His line was approximately:
"On the way in from the parking lot today I noticed the license plate ABR165. Now, consider the odds that THAT particular license would be there today. It's over 10 million to one!"
The point was that the license had to have SOMETHING on it. If we consider it significant, we note it and say "wow !" and otherwise we don't notice it. We never remember when we have a premonition that a phone call will be bad news about a relative and it turns out to be a telemarketer.
We set up simple models to force ourselves to look at what is actually happening without fooling ourselves. Statistics are an extremely powerful tool for checking reality, but the probability of self-delusion is so high that they are most useful in disproving a simple model, rather than setting one up.

Plate tectonics - the tape recorder

As molten rock solidifies, it records the magnetic field it is exposed to. This means that the oceanic crust flowing away from the mid-ocean ridge is a continuous tape recording of the earth's field. Since new crust flows both ways from the ridge, the recording is in duplicate, as mirror images. It yields two continuous slabs of rock with one edge at zero age and the other edge up to 100 million years old, depending on how far it is from the ridge crest, exactly as a tape recording goes from 'now' under the record head back to the beginning of the song at a distance told by the tape counter.
As rock cools, it contracts, so the ocean floor gets deeper away from the ridge. We can measure the heat flow out of the rock to see how fast it is cooling. Likewise, radioactive decay can be measured in the rock. Finally, oceanic sediment, away from the continents, depends not on river-born mud but on the planktonic life constantly dying in the ocean above, sifting down to the bottom along with a very small amount of windborn dust. There is no sediment on the newly formed rock, and it increases in thickness away from the ridge.
In thousands of holes bored by the Deep-Sea Drilling Project worldwide, the thickness of sediment above the bottom rock, the age of the rock, the depth the rock has receded to, the heatflow out of the rock, the magnetization of the rock, and the distance the hole is from the ridgecrest, all correspond to the measured rate at which new rock is being created at the ridgecrest. We have a continuous record, in duplicate, of the latest 100 million years of the planet, spread over more than 2/3 of the globe. Nowhere on the continents can we duplicate this beautiful simplicity.

Plate tectonics, an elegantly simple model

Plate tectonics appeals to me as the most elegant model of physical processes since Newton. It provides a unified basis for over 200 years of hard-slogging geological research.
Molten rock surfaces and solidifies into new crust at the mid-ocean ridge. The newly solidified crust slides away from the ridge at about the rate that fingernails grow. When the oceanic crust encounters a continent that can't slide with it the oceanic crust dives under the lighter and thicker continental crust. The wrinkling from pushing the two together forms an offshore trench and an inshore mountain range. New continental crust forms from the sediment scraped off the top of the thinner, heavier oceanic crust. As the oceanic crust dives deeper into the earth and gets heated bubbles of molten rock rise from it and add to the continental crust above, pushing mountains higher. That, in a nutshell, is plate tectonics.
Continental geology is so difficult to study and visualize essentially because the continents consist of all of the foam scraped from the top of oceanic crust since the plane cooled, plus all of the lighter remelt as the oceanic crust dives back into the mantle, plus whatever bending, stretching and erosion has happened to the rocks since they were first scraped or bubbled off. I find it amazing that geologists prior to the mid-twentieth century, when we got tools to study the ocean bottom, were able to make as much sense as they did from the reworked continental mess.