Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
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The Wilson Cycle involves the breakup of a supercontinent, dispersal of the fragments, and subsequent reassembly into a new supercontinent. In the last three quarters of a billion years, the supercontinent of Rodinia, with North America at the center, broke up. The pieces reassembled into Pangaea, which broke apart to create the present continents. So what's the problem?
The problem is that this is not a "cycle" in the sense of something that inevitably returns to its initial state. The seasons and the phases of the Moon are true cycles. Their cyclic nature is inherent in the orbital motions of the earth and moon. The hydrologic cycle is the evaporation of water from the oceans, precipitation on land, and eventual return to the ocean. Although many variations are possible, the fact that water flows downhill, and the oceans contain most of the earth's surface water, guarantees that most water will eventually return to the oceans.
The cycle of oceanic crust creation in plate tectonics is also a real cycle. As crustal plates pull apart, new material from the mantle rises because it's hot and therefore buoyant. It intrudes the fissures created as plates pull apart. The weight of the descending portion of the plate pulls the plate down into a subduction zone, eventually to be reabsorbed into the earth's interior. The cycle is driven by gravity and the earth's internal heat.
Most real cycles enable some level of prediction. Astronomical cycles are rigorously predictable. We can be confident a developing low pressure system will draw warm air up from the south and colder air down from the north and it will spin counterclockwise in the northern hemisphere. We can assume that hurricanes in the Atlantic will travel west for a while, then curve north and east. We can't predict what any given water molecule in the hydrologic cycle will do, but a hydrologist can measure the properties of a drainage basin and predict how much water will be stored in aquifers versus being carried off as runoff. there are many such cycles on the earth, like the carbon cycle. We can't predict where any given carbon atom will be in a million years but we can describe the movements of carbon into and out of reservoirs like the biosphere, the oceans, or carbonate rocks. These are more webs than cycles.
On the other hand, the Rock Cycle, widely used as a heuristic tool, depicts igneous rocks weathering, being recycled into sedimentary rocks, being heated and changed into metamorphic rocks, and finally being remelted. Very few rocks ever follow a complete cycle. Far more often, sedimentary rocks are reworked into new sedimentary rocks, and metamorphic rocks are weathered and eroded and recycled into sedimentary rocks. It's a "cycle" only in the sense that it's theoretically possible for a rock to traverse the loop igneous-sedimentary-metamorphic-igneous, even though it hardly ever happens that way. And of course, there's no way to predict what the evolutionary history of the granite in a road cut will be in the future. The Rock "Cycle" is also more a web than a cycle.
And it's only in this sense that the Wilson Cycle is a "cycle." There's no inherent reason why some particular configuration of continents has to repeat. The earth is about 30% covered with continental crust. If you jam ten people into a totally dark broom closet and tell them $10,000 is hidden in there somewhere, it's pretty much inevitable that they'll clump together frequently as they move around, but their movement is in no sense a "cycle.". Similarly, if you allow the continents to move around with only twice their area to spare, it's inevitable they'll clump together.
Worst of all, the term "Wilson Cycle" leads some people to think there's something inherently predictable about the motions of the continents. Many writers have claimed that in another 50, 100 or whatever million years, subduction will begin along the margins of the Atlantic and the Americas will begin to converge on Europe and Africa. But why? It's true that North America has broken off on the eastern side along roughly the same line three times, but South America and Africa joined out of disparate pieces around 500-600 million years ago and broke apart along completely different lines around 120 million years ago. There's no reason to suppose that the continents will change course until they converge across the Pacific in perhaps 200 million years.
Spectacular comets like Hale-Bopp, the last really great comet to be easily visible in 1997, travel extremely elongated orbits that take them far from the Sun on journeys lasting many thousands of years. In 1950, Dutch astronomer Jan Oort hypothesized that there had to be a distant reservoir of comets to supply replacements for comets that eventually dissipate all their volatile materials. These comets occupy a spherical shell extending up to a light year from the sun. There would have been too little material that far from the proto-Sun to form solid bodies, so Oort Cloud comets must have formed in the outer Solar System and been flung outward by encounters with the giant outer planets.
So far, so good. But then, these comets are widely supposed to be started on their inward journeys by gravitational disturbances of passing stars, and if a star passes close to the Oort Cloud, as one red dwarf (Gliese 710) will do in about a million years, it can trigger a storm of comets. Most of these models assume, implicitly or explicitly, that these Oort Cloud objects are moving in roughly circular orbits.
And that's the part I don't believe. Initially, the Oort Cloud comets would have been flung outward into extremely elongated orbits that might take a million years to traverse. These orbits are supposed to have been circularized by occasional close passages of stars, tidal effects of the galaxy, and so on. A comet with a period of a million years would have an average distance from the Sun 10,000 times that of Earth (10,000 AU, or Astronomical Units), and its maximum distance would be twice that, 20,000 times earth's distance. (At that scale, for all intents, the Sun is at one end of the ellipse) That's about 1/3 of a light year. At that distance, the Sun's gravity is pretty feeble, but it's still 180 times stronger than that of Alpha Centauri.
Consider, if you will, Halley's Comet. Halley's Comet circles the Sun in 76 years. How fast is it moving when farthest from the Sun? We can solve this problem using the geometry of ellipses and Kepler's Second Law, which states that a line from the comet to the sun sweeps out equal areas in equal times. So what's the area of the orbit of Halley's Comet? The area of an ellipse is pi(ab), where a is half the length of the long axis and b is half the length of the short axis. For Halley's Comet, a = 2.67 billion km. Astronomers measure the shape of an orbit by a number called eccentricity, e. A circular orbit has an eccentricity of zero and a very elongated orbit like Halley's has e = 0.967, that is, the Sun is 96.7 per cent of the way from the center of the orbit to one end. The formula for b = a*Sqrt(1-e*e) or 680 million km for Halley's Comet. The total area is thus 5.7 x 10^18 square km. The area swept out per year is 7.5 x 1016 sq km, or 2.4 x 109 square km/sec. That sounds like a lot, but recall that the area when Halley's Comet is farthest from the Sun is a long, skinny triangle whose apex is at the Sun, 5.2 billion km away. The area of a triangle is 1/2bh, where b is the base and h is the height, so we have area swept out per second = 1/2 bh = 2.4 x 10^9 sqk km/sec. h is 5.2 billion km, so b = 4.8/5.2 = 0.92 km, which is the distance Halley's Comet moves in one second. Halley's Comet is moving about a kilometer per second when farthest from the Sun (920 meters/second).
Now how fast would something be moving if it were in a circular orbit equal in radius to the farthest distance of Halley's Comet? Another of Kepler's Laws helps us. Kepler's Third Law is that the period of an object, squared, is proportional to its mean distance cubed. This circular orbit has a radius twice that of Halley's Comet, so its period is the square root of 2 cubed = 2.8 times that of Halley's Comet, or 215 years. The circumference of this body's orbit is 2pi r = 33.5 billion km. The object travels 33.5 billion km in 215 years, or 156 million km per year, or almost five kilometers per second - five times faster than Halley's Comet.
There's almost no limit to how slowly something in a very elongated orbit might be moving when farthest from the Sun. Let's imagine our hypothetical Oort cloud object in an initial orbit 10,000 times the radius of the earth's. It was probably plodding along in the outer Solar System, maybe a billion kilometers from the Sun, so let's assume the b value is a billion kilometers. The total area of the orbit is pi (10,000 AU)(a billion km) = 4.7 x 1021 square km. It takes a million years to orbit the Sun so a line from the Sun to the comet sweeps out 4.7 x 1015 square km./year, or 150 million square km/sec. But at its farthest, it's 3 trillion kilometers from the Sun. In one second, the comet sweeps out a hair-thin triangle 3 trillion kilometers long and with an area of 150 million square km. The base of the triangle, the distance the comet travels in one second , is 150 million square km/(1/2*3 trillion km) = .0001 km = 10 meters. The comet is only traveling 10 meters per second. surely the merest nudge can change its orbit.
How much do we have to change it to make the orbit circular at that distance? At its farthest, the comet is three trillion km from the Sun or 20,000 times the Earth's distance. So distance cubed is 8 trillion and the square root of that gives us the period, 2.8 million years. So a comet traveling in a circular orbit with a radius of 3 trillion kilometers travels 2pi times that, or 19 trillion km, in 2.8 million years. That's 67 million km per year or 2.1 km per second. That means random passing stars will have to speed up the comet by a factor of over 200 to make the orbit circular. And bear in mind that even the closest stars will exert gravitational pulls less than a per cent that of the Sun. Also, a close stellar encounter will last a few hundred thousand years but the Sun is pulling on the comet hundreds of times more powerfully the whole time.
But it gets even worse. The encounters that flung objects into the Oort Cloud pretty much randomized their orbits. Unlike the planets, Oort Coud comets have orbits all over the sky, and many are retrograde, or opposite the motions of the planets. So any stellar encounter that speeds up one comet will slow another one down. Also, before closest approach, a passing star will pull on a comet one way, and the opposite way after close approach.
According to one list on line, Ludwig Wittgenstein, Sir Isaac Newton and Voltaire had IQ's of 190, Leonardo da Vinci and Michelangelo had IQ's of 180, and so on. Lists like this are utterly meaningless for a host of reasons. For one thing, they're historical figures who never took an IQ test, so their IQ's have to be estimated from their accomplishments. Getting numbers accurate within even 20 points this way is dubious, let alone hair-splitting claims like Johannes Kepler (175) beating out that dullard John Stuart Mill (174). Then there are absolutely preposterous claims, notably that William J. Sidis, a celebrated child prodigy turned crank, had an IQ between 250 and 300.
The range of acceptable human intellectual performance is actually pretty narrow. Someone "half" as intelligent as an average person with an IQ of 100 would have an IQ of 50. He wouldn't say, take twice as long to learn French or do a math calculation - he'd be unable to do them at all and probably wouldn't be able to live independently. And someone with an IQ of 100 won't take 50% longer to learn differential equations or quantum mechanics than someone with an IQ of 150. There is a strong likelihood he won't be able to learn it at all.
Defining intelligence is fraught with practical difficulties. There are many kinds of intelligence: verbal, spatial, social, practical, and so on, and the whole issue is politically and semantically loaded. But if we restrict our discussion to people with reasonably well balanced skill sets, as opposed, say, to people who can learn languages quickly but are absolutely incapable of learning to read a map or tighten a bolt, we might measure intelligence by the speed with which people can learn complex skills and apply them intuitively. Using that measure as a guide, it looks like the relationship between intelligence and IQ is highly non-linear. Even the most profoundly handicapped people with mental ages of small children have some intelligence, but it's very small compared to normal intelligence. On the other hand, a person with an IQ of 80 might be notably less intelligent than someone with an IQ of 100, but certainly much more than a quarter or half as intelligent. Perhaps in the mid-range of IQ, IQ and intelligence are roughly proportional. But beyond 100 we also encounter people who can master complex material that people of lower intelligence simply cannot. A person with an IQ of 80 might learn French over a period of years by immersion; how do we compare that person to someone who can become proficient in months? If we use facility of learning complex material as a measure of intelligence, a person with an IQ of 150 probably isn't 50% more intelligent than someone with an IQ of 100, but several times as intelligent.
So it seems that at both the low and high ends of the scale, IQ and intelligence are not related linearly. If we were to graph IQ on the vertical axis of a graph against "real" intelligence (whatever that means) on the horizontal axis, we'd probably find that the curve is very low and gently sloping for the lowest IQ's, meaning a small change in IQ means a fairly big change in intelligence. Someone with an IQ of 80 is at the low end of the normal range and is far more intelligent than someone with an IQ of 40, not merely twice as intelligent. In the mid-range of the scale, say from 80 to 120 IQ, the curve is probably a lot steeper, then it would flatten out again for very high IQ's, meaning the difference between 140 and 150 is greater than between 100 and 110. This is a very familiar curve in science, called a sigmoid curve.
What's the limit? We could compile similar curves for, say height or time in a mile run, and extrapolate the curve to estimate how many people are eleven feet tall or can run two minute miles. But it's nonsense. There aren't any. And we can extrapolate our IQ curve out to 200, but there probably aren't any people out there, either.
And this is why the wildly inflated IQ scores attributed to great thinkers are probably rubbish. You don't need an IQ of 190 to be an Isaac Newton, if an IQ of 150 makes you, say, three times as intelligent as an average person. I strongly doubt that most of the great thinkers of history had IQ's of 170, 180 or higher. 140 would have been more than ample to accomplish what they did.
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Created 14 October 2011; Last Update 24 May, 2020
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