The Way of Science

b. Objections based on random distribution of surface features

In the same vein, let us look at the other independent way of falsifying the "shrinking apple" model: The prediction that shrinkage should give random distribution of major surface features.

1. Curvilinear distribution of mountains and volcanoes
   On any world map, look at how mountains and volcanoes are distributed. Are they randomly distributed, or do they form patterns? Does this distribution support or contradict the old model?

2. Bimodal distribution
   In the previous section, the only concern was where the high parts (mountains) are on the Earth's surface. Now consider all altitudes, both above and below sea level, and predict how much area (how much of the crust's total surface) would be at any given altitude, assuming the "shrinking apple" model is correct. In order to follow the logic of Wegener's argument, we need a few concepts from statistics.

Figure 2. A bell curve for students' grades. The certical axis is in actual numbers, but could be any measure of frequency (factors, decimals, percent of students).

Take the following three terms: mean, median, mode. The first of these (mean) is what most people are using when they say "average." For example, we might have a mean grade of 70% on an exam; this figure is obtained by adding all grades and dividing by the number of exams graded. The median grade would be the grade that divides the total range of grades into two equal halves; in other words, the median has an equal number of percentages above and below it. The mode is that number (grade) which is most abundant. In the famous "bell curve" (Figure 2), one can easily see that the mean, median and mode are all the same: 70%. Note well! All graphs must have their axes labeled.

Figure 3. Expected bell curve based on SAM. Note: the mean is below the present sea level. The vertical axis could be in percent (as here) or square miles, square km, acres, etc.

If the "shrinking apple" model were correct, then random uplift and subsidence (sinking) would have produced a surface which contained very little area of immense height or very great depth; most of the crust' surface should be near the mean. We would expect to get, in fact, a bell-shaped curve. Figure 3 illustrates such a prediction based on the "shrinking apple" model, using sea level as our handy reference point, The axis labeled "frequency" could represent any units of area (square miles, acres, etc.).

Figure 4. Actual distribution of altitudes of the crust. The axes are identical to Figure 3. One mode is slightly below sea level (continental plains) and the second is deep (at the ocean floor).

When the Earth's surface is graphed in the same way, what one obtains is a bimodal curve (Figure 4). Note what this new graph signifies: Most of the Earth's surface is either slightly above sea level(continental plain) or way down below sea level, on the abyssal ocean floor.

Step back for a moment to compare these two arguments based on randomness, since we expect you to understand them fully, and be able to describe and explain them in class or on an exam.

Suppose we use all the male students at NEC as an analogy for comparison of the two arguments. Blindfold all the students, and let them wander for half a day on campus. At the end of that time, we would expect to see scattered clumps, some solo bodies, some empty areas, etc. We would certainly not expect to see neat lines of males. That's the analogy to random wrinkles producing mountain ranges.

Now let's measure the heights of all the same males. Since most of our students are reasonably well nourished, their heights are determined primarily by genes inherited from their parents. This inheritance is essentially a random process, as you will see when we cover Evolution.

If our students were admitted to NEC without paying any attention to their height, we would expect to see that old bell curve (Figure 2), in which there are very few students above six feet six, and very few very short males. On the other hand, suppose the plotted height gave the bimodal curve of Figure 4. Note that the mean and median are still the same as the bell curve of Figure 2, but there are no students who are at that height! Clearly, something besides randomness is at work. One might suspect that the college has decided to train jockeys and basketball players, or perhaps the Great Dragon had a role to play... In any case, randomness is effectively eliminated as the cause. When you finish the readings for Plate Tectonics, you should be able to explain the bimodal distribution of crustal altitudes, where the continental rock (granitic, mostly) is lighter, and the lower substratum (seabed) is much denser and heavier basalt (plus some other dense materials like gabbro and peridotite. These are good words, but strictly "enrich your life").

You have now finished two of the five major sections on Wegener. Before moving on to the new model, be sure you are comfortable with all the following items:

1. The "shrinking apple" model, including isostasy and land-bridge arguments.
   
   
2. Objections to the "shrinking apple" model, including motion arguments (coastlines, minerals, cratons, fossils; ancient climates, including coal and glacier evidence) and randomness (distribution, frequency).