Ants do trigonometry: a problem for Darwinism


Photo credit: Muséum de Toulouse, CC BY-SA 4.0 , via Wikimedia Commons.

Editor’s Note: The following is an excerpt from the recently published book, Animal algorithms: evolution and mysterious origin of ingenious instincts, from Discovery Institute Press. Don’t miss the next webinar with Eric Cassell and Casey Luskin, Thursday, December 9 from 4 p.m. to 5:30 p.m. PT. register here.

As we have seen, a wide variety of animal navigation and migration patterns strongly suggest complex programmed behaviors. The migration and navigation strategies used by most animals are much more sophisticated than initially assumed when scientists began to study them. The more scientists learn about them, the more complex they appear in many animals.

One way to demonstrate the level of engineering involved in these behaviors is to examine modern air navigation systems. As shown in Figure 3.4, aircraft navigation systems use several redundant sensors (inertial systems, GPS, ground) as well as other essential components.

Chart 3.4. Air navigation system.

The illustration in Figure 3.4 is, of course, a rough simplification. Having been personally involved in the technical design of several systems, including air navigation systems, I can attest that a structured engineering process is essential. The process should be top-down, where the overall concept should first be defined, as shown in Figure 3.5.

The process is as follows. The first step is to define the overall objective, including the purpose of the system. The second step is to develop a concept for the implementation of the system, including the main functions. Next, we perform an analysis of potential design options. This includes evaluating options and evaluating trade-offs, which for artificial systems include performance, complexity and cost. Once a design option is chosen, the next step is to define the specific requirements. Then the system can be manufactured.

Top-down and structured, but why?

There are many reasons why this process needs to be top-down and structured. The first is that, since this is a complex system, there are many interdependencies and therefore the design requirements must take this into account to ensure that the components and operation work consistently. If all functions are not integrated correctly, system performance is significantly degraded.

Chart 3.5. Top-down engineering process.

The overall design of air navigation systems requires thousands of hours of design and development work by engineers. The goal is a system that provides the optimum navigation information to pilots by selecting the navigation source that provides the best performance for specific phases of flight – takeoff, en route, oceanic, terminal area, approach and landing. Functions include the various sensors that provide this information, each of which is itself extremely complex.

As with all modern systems, it includes a combination of hardware (radio receivers, computer processors, cockpit displays) and software containing the computer algorithms for processing aircraft position data, the logic for selecting navigation, map and route information and display interface. All navigation methods require an integrated and consistent combination of physical elements, programmed algorithms, and other related information. It is the same for all migratory animals.

How the elements interact

Referring to Figure 2.2 regarding animal navigation systems, remember how all of these elements interact. Or to take one of the specific examples above, we see it in desert ants (Figure 3.1). While the sensors, brain, algorithm, and physiology can be viewed as separate subsystems, they must function as an integrated system. Remember that the ants of the desert employ three methods of navigation. Note the similarity to the air navigation systems in Figure 3.4. The odometer and polarized light compass in desert ants are the sources of information for integrating paths, while landmarks are the other source of information. The central control function uses this information, in addition to the available clues of external conditions, to make a programmed decision as to which source to use and to calculate the correct navigation route. As we can see from all of this, the control function is a complex algorithm.

And that is only getting more complicated. Referring again to Figure 3.3, the information defining these elements likely resides in different parts of the genome. In addition, the information defining these elements is of a very different nature. For example, the genes that control physiology have no relation to the genes that define navigation or migration algorithms. Even the genes that determine the physiology of sensors (compass sensors, etc.) are very different from the genes that determine migratory physiology (flight characteristics, etc.). All in all, the development of browsing and migrating behaviors requires the independent origin of the physical traits and information necessary for five distinct groups of genes and other genetic information in the genome. As discussed above, the likelihood of getting even a few coordinated genetic changes is very low. The likelihood of obtaining an unknown (but probably high) number of coordinated genetic changes in five different parts of the genome is extremely unlikely. The development of new traits (many of which are related to navigation and migration), which will be discussed in Chapter 4.

Two incidents

I wrote a first draft of this section shortly after there were two incidents in the news where commercial planes landed at airports that were not the intended destination. This is an example of pilots failing to refer to their alternative navigation systems or an actual system failure. In either case, the incidents illustrate how crucial it is to have backup navigation strategies and how difficult it is to program systems that operate correctly on a consistent basis. It is a fundamental concept in engineering that when the availability and reliability of a system is critical, then it is best to design a backup system. A given clue may not be available at certain times, and at other times, it may give ambiguous information. Having another source of information can also help spot wrong signals. We find this rule of thumb followed in desert ants and many other migrating creatures.

Those who program computer algorithms for a living are uniquely placed to appreciate how complex an algorithm would have to be to function as well as the Desert Ant’s navigation algorithm. In this case, the algorithm consists of several logical decisions based on the information detected. Once the algorithm has made a decision on which navigation source to use based on the incoming data and environmental conditions, the control function must then calculate the heading. In some cases, the route is calculated by combining information from two navigation methods. When the ant uses the trajectory integrator, it keeps track of its movement through the odometer and the angular movements determined by the compass, both of which are stored in memory. It can then calculate the direct path to its original nest. This is a complex process that involves trigonometry.

When ants do trigonometry

While we can write a relatively simple segment of computer code to perform this calculation, in this case it has to be programmed into the ant’s brain and integrated with the many other essential elements of the navigation algorithm. The question is twofold: (1) How can a mathematical trigonometric calculation be programmed in the brain of an ant through a neo-Darwinian process of genetic mutation and natural selection? Programming, keep in mind, probably involves a neural circuit and of considerable sophistication. (2) How could a neo-Darwinian process succeed in doing this while simultaneously building other essential subsystems of the larger integrated navigation system? The trigonometric calculus alone would seem difficult to evolve in stages, but without these other subsystems in place, the most beautiful algorithm in the world for calculating a mathematical trigonometric calculation is useless to the ant, and therefore unavailable for input on and preserved by natural selection. This brings up the chicken or the egg problem: what evolved first – physical systems or behavioral algorithms?

The gradual evolution in series does not seem plausible, because each characteristic in itself is not useful. On the other hand, the simultaneous evolution of all physical characteristics and behaviors is not plausible because of its extreme improbability.


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