23. Darwin and Aristotle

Perhaps the most important aspect of Newton’s model was that it defined inertia through an ideal case. It was the property evoked when a body failed to abide by a given ideal constraint. In Newton’s model, that constraint is Galileo’s discovery of unrestricted and perpetual motion. The degree of failure to abide by that constraint is the measure of a body’s inertia. Although the exponential law, for example, is suggested as a model, it is not used to define an inertia in the style of Newton and that will then allow a biological reading for a similar failure.

The reason for Newton’s very different approach is made clear in Murray:

The physical world is not simple. Physicists simplify the world in order to study it. Biologists do not simplify the world (Murray, 2001, p. 266).

Like Darwin and Gauss, and as Murray attests, Newton knew how to restrict himself to essentials. He also set a very high standard. He understood very well the significance of Galileo’s discovery, and he proposed a model that incorporated Galileo’s constraint—i.e. the behaviour of objects when free from all other possible constraints. And with Galileo’s conception of perpetual motion in place as the sole possible constraint, Newton could then demonstrate the power and mastery of his quantitative and calculus-based methods.

Another of Newton’s important achievements, with his approach, was to propose and thoroughly analyse the simplest of all possible cases:

Thus, Newton’s mathematical model has only one planet orbiting a point on space; his physical model has only one planet revolving around one star. And Newton was correct; the three-body problem has not yet been solved (Murray, 2001, p. 266).

Although moving from two bodies to three puts Newtonian gravitational analysis beyond all hope of resolution, nobody would suggest that we throw away the two-body case and all it implies. Neither the two- nor the three-body case can exist in reality, yet even though the one is solvable and the other is not, they together form the backbone of science. We must also find a simplest possible case.

Figure 22: Galileo's Thought Experiment
Galileo's Thought Experiment

Murray also points out the difficulties for any proposed model for ecology—including any attempts to base one on Newton’s. As in Figure 22, he refers to Galileo’s famous thought experiment highlighting his constraint of perpetual motion … now the foundation of all science:

Inertial motion, by whomever’s conception, is necessarily abstract. What does observation tell us about inertia ? Nothing. Einstein & Infeld give us an idea of what Galileo may have been thinking. Suppose we take a cart and give it a push. It will move some distance, slow down, and come to a stop. Suppose that we smooth the road, streamline the cart, and then give the cart a push. It will move further, but it will nevertheless come to a stop. No matter how often we do the experiment, we get the same result. One could justifably conclude that ‘a moving body comes to a standstill when the force which pushes it along can no longer so act as to push it’. Now, this is Aristotle’s hypothesis, which has been repeatedly verified. Aristotle, however, was wrong. How did Galileo come to a different conception? Einstein & Infeld suggested that Galileo asked, how is it possible to increase the distance that the cart goes before stopping? He noticed that after he streamlined the cart and smoothed the road, the cart moved further. Suppose, Galileo thought, there were no impeding forces. He guessed that the cart would move in a straight line at a constant speed forever, an idea that was completely contrary to experience. Aristotle’s conclusion regarding the nature of motion was consistent with appearances, but the appearances gave him ‘false clews’ (Murray, 2001, p. 265).

This simply emphasizes the role and importance of models.

As far as biology and ecology are concerned, Aristotle is rightly regarded as ‘the father of biology’, his zoological work being a pivotal moment in science (Shuttleworth, 2010; Lennox, 2011). Perhaps his greatest compliment, as a biologist, came from his greatest successor, Darwin:

The conceptual sophistication of Aristotle’s biology accounts for the vitality and continuity of the tradition he founded but often comes as a surprise to people who have never taken the trouble to read him, dissuaded, no doubt, by his undeserved image as a scholastic logic chopper and antiempirical dogmatist. Darwin is a case in point. … Darwin had a great respect for neoclassical biology. Thus, it is intriguing to find him in his ripe old age reading Aristotle for the first time, when William Ogle sent him a copy of his Oxford translation of Aristotle’s Parts of Animals. Rather wittily Ogle wrote:

I feel some importance in being a kind of formal introducer of the father of naturalists to his great modern successor. Could the meeting occur in the actual flesh, what a curious one it would be. I can fancy the old teleologist looking sideways with no little suspicion at his successor, and must astounded to find that Democritus, whom he thought to have been effectually and everlastingly squashed, had come to life again in the man he saw before him. (Ogle to Darwin, January 17, 1882)

Darwin responded:

You must let me thank you for the pleasure which the introduction to the Aristotle book has given me. I have rarely read anything which has interested me more, though I have not read as yet more than a quarter of the book proper. From quotations which I had seen I had a high notion of Aristotle’s merits, but I had not the remotest notion what a wonderful man he was. Linnaeus and Cuvier have been my two gods, but they were mere school-boys to Aristotle. I never realized before reading your book to what an enormous summation of labour we owe even our common knowledge. (Darwin to Ogle, February 22, 1882 in F. Darwin 1887 vol. 2, p, 427) (Depew and Weber, 1995, p. 43).

Aristotle’s broader taxonomic classifications may now appear eccentric, but when his limited equipment is considered, his work stands as a tribute to his systematic methods in conjunction with an admirably empirical approach. He cannot, therefore, be criticized simply because he did not observe, and he certainly cannot be criticized because he did not analyze and theorize.

There is a profound similarity between Aristotelian and contemporary or Darwinian biology: neither has a coherent model. And since biology still lacks a model there is thus no reason to attack Aristotle’s biological observations for his errors do no real damage … although there are certainly some that cause a measure of irritation to many contemporary biologists and ecologists. His are simply observations for they have no real reference to any rigorous model. But then … Darwin’s observations also have no reference to any model, but he is in his case left open to attack. This juxtaposition demonstrates both the strength and the weakness of the lack of a model. That lack of a model has allowed some of Aristotle’s observations to endure when they should long since have been jettisoned … and that same lack of a model has prevented the proper adoption of Darwin’s far superior theory.

We can now draw another apposite parallel with meteorology. Fired by Bjerknes’ inspiration, Richardson divided Europe up into a set of discrete cells 200 miles across in each direction, and used numerical analysis to predict the weather:

Lewis Fry Richardson used the polar front theory as the basis for his classic work, Weather Prediction by Numerical Process, published in 1922. In that book he used a technique that he felt would allow him to forecast the weather over central Europe based on the weather locations within a 500-mile radius of the designated area. Unfortunately, his numerical technique failed in its first trial. Using his formula, he predicted a pressure drop of 145 millibars (~4 inches of mercury) within six hours. Such a massive drop in barometric pressure over such a period of time had never been known to occur. Even the strongest hurricanes rarely achieved pressure drops of more than 100 millibars during their development, which normally takes place over a period of several days. (Fishman and Kalish, 1994, p. 50).

Yet even though Richardson failed, few doubted the validity or efficacy of his methods … i.e. of his model, which was thoroughly scientific. So in spite of his failure, his basic model was later revived. Such was the confidence in his procedures that instead of considering the entire process flawed, the assumption was rather that there must be errors either in his analysis, or else in the train of his argument. There was nothing wrong with his model.

Six years later, the German mathematician Richard Courant discovered the “computational stability criterion” which explained Richardson’s failure. The Courant–Friedrichs–Lewy, or CFL, condition states the conditions necessary for partial differential equations to converge on a solution in the ‘time-marching’ schemes widely used in meteorology (Courant et al, 1967). This states that if the time step is greater than a certain value then any computer simulation will produce wildly incorrect results. In this Richardson case, the differential equations used in any one cell depended upon the speed at which the information arrived from neighbouring cells to be computed. If the windspeeds across the cell were greater than was anticipated for, or could be handled by, the computers employed to calculate the differential equations employed, then the predictions for that cell could not match the actuality. By the computational stability criterion, Richardson’s predictions could only have been accurate if the winds had remained below 33 miles per hour, 53 kilometres per hour (Fishman and Kalish, 1994). This is classified, on the popular Beaufort scale, as a strong breeze: “large waves, some spray; large branches move, wires whistle, umbrellas are difficult to control” (Rowlett, 2001). Thus Richardson’s failure was explained not by a lack of robustness, or by an incapability, in his model, but by the fact that wind speeds on the ground exceeded that value in some of his cells, with airborne wind speeds in excess of three times that being extremely common in the jet streams—whose existence was then also unknown—in the upper reaches of almost all his cells. His failure lay not in his model, but in contemporary computation speeds (along perhaps with an overly large number of variables, an issue later dealt with by Rossby). This is the clear advantage of a good model. It is robust.

It is again worth comparing Aristotle to Darwin. The issue is not simply observation; and nor is it conclusions drawn from observations. As was Darwin’s, Aristotle’s corpus was a treasure of knowledge built upon careful observation. He used empirical methods and his records were meticulous. The prevailing view in his day was that all organs were present at the time of conception, and developed simply by growing in size. He was admittedly incorrect in believing that the heart was the seat of thought, and therefore that it would be developed first. He thus mistook the developing spinal cord for the heart (Shuttleworth, 2010; Lennox, 2011). But correct information was not possible until the advent of the microscope. All such factors taken into account, his insight into the reality of development was against contemporary dogma and a masterpiece of a conclusion born from experiment and data. This earliest of all observational accomplishments in biology was achieved by his dissection of bird’s eggs at their various stages of development in order that he could understand the precise order in which the various organs developed. It was to be many centuries before his conception of a strict developmental order for the embryo was established as the correct one. He described the embryological development of a chick; appreciated that whales and dolphins were not fish; described the chambered stomachs of ruminants; noted the social organization of bees; and noticed that some sharks give birth to living young. Many of his observations on animals were not confirmed for centuries. Perhaps his greatest contribution was his classification of species. His was the first known attempt to classify animals into groups according not just to their behaviour, but also to their similarities, and differences, in physiology. This again required careful observation and dissection.

But then comes the underlying theory … the model. Without Darwin’s discoveries, there was no reason to attack Aristotle’s biology. But with the advent of Galileo, there was suddenly ample reason to roundly attack his physics. Aristotle’s physics had been attacked before Galileo and Newton, but the ones following these latter two are considerably better known and far more justified. This is, of course, because of their far superior model.

From our perspective, and for what it says about the reach and scope of models, one of the most interesting of the pre-Galilean attacks on Aristotle came from Bishop Nicole d’ Oresme. A fourteenth century cleric, he translated Aristotle for his patron, King Charles V the Wise of France. In his On the Heavens, Oresme provided the first recorded allusion to Einstein’s theory of relativity. Although Oresme had no model to substantiate his ideas, he nevertheless made a most interesting observation. He insisted that all motion was relative. He argued against Aristotle by pointing out that it would make no practical difference to what was observed whether the stars stood still while the Earth moved, or whether the Earth stood still while the stars moved:

I suppose that local motion can be perceived only when one body alters its motion relative to another … just as it seems to a man in a moving boat that the trees outside the boat are indeed in motion (Menut and Denomy, 1968).

But what Oresme lacked, to support his brave contention, is what Darwin also lacks … but that Einstein certainly had: a sound mathematical model. Without such a model it is impossible to make or validate predictions, which is what Oresme could not do. It was also Galileo and Newton’s advantage, for as soon as their model became available, Aristotle’s physics could at last be thoroughly tested against it. He promptly failed.

There is a complementarity at work. As we have seen, even the very worst of predictions do not undermine a good model. This is a strength of meteorology, no matter how much its predictions may be scorned. But the converse also holds. If a sound and accurate analysis is not substantiated with a good model, then even the worst and most improbable of statements can pose apparent threats to its entire structure.

Since Oresme did not have a model to support his case, he did not have the courage of his convictions. More than that, he emulated Aristotle in the latter’s biology, and turned to “other criteria” to make his final decision:

In the end, Oresme believed, the choice between believing in a moving or a stationary Earth had to be a matter of faith. (Linton, 2004, p. 115).

Oresme therefore concluded his ruminations by saying “… everyone maintains, and I think myself, that the heavens do move and not the Earth”. (Menut and Denomy, 1968).

If biology wishes to resist invasions by such dubious criteria, then it—urgently—needs a model. We can begin to construct our own model by first noticing that Galileo and Newton’s was built on the constraint of perfect and perpetual motion. As Oscar Morgenstern (who with John von Neumann founded game theory) pointed out when speaking in June 1963 at a Symposium on Mathematics and the Social Sciences sponsored by the American Academy of Political and Social Sciences on the “Limits of the Uses of Mathematics in Economics” … there are some clear advantages to this strategy:

Although some of the profoundest insights the human mind has achieved are best stated in negative form, it is exceedingly dangerous to discuss limits in a categorical manner. Such insights are that there can be no perpetuum mobile, that the speed of light cannot be exceeded, that the circle cannot be squared using ruler and compasses only, that similarly an angle cannot be trisected, and so on. Each one of these statements is the culmination of great intellectual effort. All are based on centuries of work and either massive empirical evidence or on the development of new mathematics or both. Though stated negatively, these and other discoveries are positive achievements and great contributions to human knowledge. All involve mathematical reasoning; some are, indeed, in the field of pure mathematics, which abounds in statements of prohibitions and impossibilities (Morgenstern, 1963).

We obviously need to follow Galileo and Newton and find the “perfect” biological cycle that can act as the basis for a model.