About my father, plate tectonics and non-linear thinking

My father passed away almost ten years ago. He was 76 years old at the time. Of course, de mortuis nil nisi bonum. That being said, I do remember he had difficulty accepting that gorges and valleys were the product of a river cutting down into its bed or, in the case of a valley, a glacier grinding down its floor and sides. In fact, he had actually difficulty accepting other ‘scientific truths’ as well.

Although he was not acquainted with the Himalayas, I must assume that he would probably also have reservations about the now generally accepted story of its formation: Tibet was once a fairly shallow sea, the Thetys Sea, separating the supercontinent of Laurasia in the north from Gondwana in the south, until about 50 million years ago, when India (a continental fragment of Gondwana) collided with the Eurasian plate (Laurasia). The Thetys Sea became the Tibetan plateau, and the collision zone is the Himalayan mountain range. The collision actually continues and so the Himalayas are still rising by about 5 to 10 mm per year and, as a result, the whole area is seismically extremely active still: here in Kathmandu, everyone is waiting for the next Big Earthquake which, according to geologists, is long overdue.

This is obviously more than just a theory: it is supported by evidence, such as the presence of marine fossils and abundant salt reserves in Tibet  (Tibet’s main export a couple of centuries ago), and scientists can actually observe the ongoing tectonic shifts with modern GPS technology. Still, it is mind-boggling and so I do understand the reservations of my skeptical father. In addition, I also note that the theory of plate tectonics only got general accepted in the 1950s and 1960s, when associated phenomena such as seafloor spreading could finally be observed. My father was entering the second half of his life by then and, hence, probably somewhat less ready to accept such theories, or at least less ready than today’s average schoolboy. [By the way, isn’t it amazing how recent most of our scientific understanding actually is? Think, for instance, about the discovery of the Higgs particle, which completed our understanding of matter and energy (or of the universe in general), or think about the recent advances in biology and medical science, which revolutionized our understanding of life itself.]

I guess one of the main difficulties in my father’s understanding of it all (apart from his lack of a more formal education beyond secondary school) might have been his lack of understanding of geological age. What is 50 million years after all? That’s a lot of time of course, but is it enough really to create something as big and as vast as the Himalayas?

Maybe it helps to note that adding a zero, or a digit, to a number is not a matter of simply adding a quantity to another quantity: it is a matter of multiplying the previous quantity. In our common base 10 number system, it is a multiplication with factor 10. Moreover, adding another zero is another multiplication and, importantly, it is not a multiplication of the original number but of the previous result. As such, it reminds one of the famous fable of the king and the wise man, whom the king wanted to reward: when the king asked the wise man what he wanted, the wise man took a chessboard and said he would just like to have one grain of rice on the first square of the chess board, double that number of grains of rice on the second square, and so on: double the number of grains of rice on each of the next 62 squares on the chess board. The king agreed, thinking that the man had asked for a relatively small reward, but after some quick calculations his treasurer informed him that the reward would be far greater than all the rice that could conceivably be produced. To be precise, the total number of grains would be equal to 263. That’s a figure with 19 digits. To be even more precise, the number is equal to 9,223,372,036,854,775,808. Now, one kilogram of rice is about 50,000 grains of rice [yes: I know you think that’s not so much – but that fact in itself underscores once again our difficulty in imaging big numbers] so that number is equivalent to more than 184 billion (metric) tons of rice. The current world production of rice is about 700 million tons only. Hence, yes, the king’s treasurer was right: at current rice production rates (which are much higher now than at the time when this story was first told), it would take about 260 years to produce such amount of rice – provided the rice could be kept for such a long time.

Likewise, I think my father had difficulty accepting he could simply not imagine what a period of 50 or 60 million years actually means. Our active life as a human being spans a period of some 60 to 80 years. From 60 years to 600 years… Well… That brings us back to the Black Death epidemic, or the Hundred Years War. We can imagine that, can’t we? Sure. But can we imagine a period of 6,000 years, or a period of 60,000 years? I don’t think so, let alone a period of 600,000 years, or periods spanning millions of years. It’s like the king who could not imagine how much rice he had promised to give the wise man.

The following graph may help to illustrate the point. It displays an exponential function with base 10. The graph below actually only goes to 10 raised to the power of 5, i.e. up to 100,000 only. Now see how that graph soars, and then just note that we are not talking 100,000 years when we talk geology, but millions of years. Indeed, adding zeroes to a number is a process of repeated multiplication (with a factor 10 in our decimal system), and repeated multiplication amounts to exponentiation. I must assume my father always had linear functions in mind when thinking about time and distance, as opposed to exponential functions. Indeed, despite all of the talk about us human beings thinking non-linearly, can we actually do that – in a mathematical sense? I don’t think so. In daily life, we’re used to adding stuff, and perhaps even to adding stuff repeatedly (i.e. multiplication), but we’re surely not used to multiplying stuff repeatedly with itself, i.e. our mind is not very familiar with the mathematical process of exponentiation.

graph

How and when does man appear on these vast geological timescale? Well… The first traces of man go back 200,000 years ago. Now, 60 million years… Hey ! That’s only 300 times 200,000 years, isn’t it? So we can imagine that, can’t we? 300 times 200,000 years. Perhaps my father was right: that surely cannot be long enough to create something as formidable as the Himalayas, or the Alps for that matter? Or can it?

Yes. Read the story above once again: don’t make the mistake which that naive king made – and my father most probably too. I don’t think we can imagine a period of 200,000 years, let alone a period of 60 million years. Our mind is just not made for it. We need fables and graphs such as the one above to remind us of that. When it comes to math, our mind works linearly.

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