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How Do Ants Know Trigonometry?
Nov 1, 2020

Think of yourself as a desert ant. You leave your nest to search for food early in the morning in the deserts of Tunisia, except you do not know where to find food. You, therefore, walk randomly in the desert in a circuitous outward path from your nest until you find food. If you would find food, how do you get it back to your home? How do you go back without having left for yourself any traces or signs in the wasteland, without knowing where you located, and most importantly, without ending up stranded in the scorching heat of the desert? Could you accomplish coming back each day with food? Well, desert ants can.

To find out how ants can do this, scientists observed their behavior, and surprisingly they have found that ants did not follow back on the same trail they randomly took after they left their nests. Instead, ants took a direct route as if they already knew where the nest exactly located. How do these ants find the closest way and shortest distance to their nest from their current locations? Former studies had found that red and forest ants secrete a chemical substance to mark their paths. They leave a trail of chemical scents or visual traces behind them—like leaving a trail of breadcrumbs to help you find your way home. However, the structure of desert sands and conditions are not consonant with containing chemicals that will carry an odor or leave visual cues. Even if such markings have made, it is hard to guarantee that they will remain intact long enough considering the harsh conditions of the desert. As in Hansel and Gretel fairy tale kids who could not return home for the breadcrumbs they had left on the trail eaten by birds. Therefore, these desert ants must be equipped with another cognitive mechanism so that they can return to their nests before succumbing to the midday heat.  

Black desert ants (Cataglyphis fortis) emerge from their nests in the heat of desert sand, which rises to 70 degrees with the rise of the morning sun, to search for the remains of other insects that were not as heat resistant as they are. They can only survive for one hour on the hot sand and under the blazing sun, which means that within an hour, they must find their food and bring it back home without getting lost. The journey is quite arduous and dangerous each day. If the slightest confusion occurs and they are not able to return to their nest in time, then it could cost them their lives.

Scientists conducted a series of research in the scorching deserts of Tunisia to find out how desert ants take their food to their nests in the shortest route possible. Researchers first determined an anthill and plotted the terrain around it to set up a coordinate plane. They observed that the ants left their nests very early in the morning to begin their daily search for food, and many of them eventually found grubs that had been planted by the scientists. However, researchers moved the ants to locations that they had not previously been to after the ant began carrying the food back to their nests. The attempt was to understand whether there was a “sign placement system” within the ants. This system would encourage the ant to find its last known location, in this instance where it had picked up, then find its way back home. However, the ant instead began heading directly to its nest. It was as if the ant determined its position concerning its nest and set off for it immediately. This experiment was repeated on many ants numerous times and with the same consistent results. The ants, as soon as they had placed on the ground, moved to the nest relative to there. With a wondrous intrinsic coding of some neurons in their nervous systems, they traveled the distance between their new location and the nest in the shortest way possible. In addition to this, the margin of error was very nominal; they found their nests with a ten percent error in the average distance of 500-meters and with an error of only two degrees in angle. Additionally, a fascinating discovery revealed that the ants could calculate errors in their navigation systems. As they approach their destination, they would make adjustments if they need to by moving back and forth in parallel lines to reach the nest with minimum error. 

Scientists determined that desert ants have about a thousand lenses in their compound eyes (remember that a human eye has only one lens) and 80 lenses in each of their eyes that can detect polarized light that comes from different points in the sky. Polarized light occurs when sunlight enters the atmosphere of Earth, hits air molecules and other particles, and then scatters in all directions. This dispersion leads to polarization, and the light that starts to vibrate in many planes begins to vibrate in only one plane. Therefore, the strongest of them is a distinct polarization that always makes a 90-degree angle towards the sun. The lens system in the eyes of desert ants uses this polarization to form a kind of Sky Map. These ants will occasionally stop and robotically move their heads while returning to their nest. This brief period allows the ants to make this sky map by surveying the sky and making a mental note of its layout. Researchers believe that ants can then calculate the direction that they need to travel to return to their nest. They repeat this movement along the way to continually update their sky maps. If they cannot find their home, then they utilize a patterned search method with a set of circular motions. It means that each ant knows how far it is from their nest at every point of their journey.

Then, how do ants find their direction to the nest? Perhaps they were guided by the position of the sun in the sky is. To test this hypothesis, researchers placed a set of mirrors to make ants perceive the sun in a different state than where it ordinarily would be. It observed that the ants changed their directions according to the new state of the sun. However, this finding raised another question; researchers wondered how the time of day would affect the ants since the sun moves across the sky during the day. However, this finding raised another question; researchers wondered how the time of day would affect the ants since the sun moves across the sky during the day.

In another part of the experiment, the researchers caught the ants after they found the bait, closed a box over them, and kept them inside the box for several hours so that they could not see the sun and its movements. It expected that the ants would have trouble finding their way back after they were released since a long time had passed, and the sun was in a drastically different position in the sky. However, they once again returned home by using the shortest distance possible. It understood that the desert ants were aware that time was passing even though they could not see the sun.

We now understand that ants determine their direction home by using the sun, but we still do not know how they figure out the distance they must travel to return to their nest. Researchers have developed three hypotheses to explore this phenomenon. The first hypothesis was the energy hypothesis. According to this hypothesis, the ants were able to know how much energy they needed on the way back by calculating it they had spent until they reached their food. The depletion of their energy meant the end of their journey. An ant loaded with extra weights to test this hypothesis as soon as it reached its food. The scientists thought that if their body weight increased, then they would not be able to strike reach the nest since they would spend more energy on the return trip. However, in this case, it did not affect the ants, and they returned home in the shortest way possible regardless of their weight.

The second hypothesis was the optical-flow hypothesis. In this hypothesis, it believed that the ants had visual memory, and this was how they remembered the way back. To prove this, scientists prevented the ants from seeing their surroundings by blindfolding the ants when they found their food source. However, the blindfold did not prevent the ants from obtaining the shortest distance back home. As a follow-up to this experiment, the researchers placed an extensive television screen in front of the ants showing an endless desert on the television screen to make the ants feel as if they had crossed the entire desert in this simulation. They used various types of simulations, but the result did not change; the ants found their way. 

The last test involved the pedometer hypothesis. It surmised that ants could be counting their steps to determine how far they had traveled. To test whether they were doing so, researchers attached stilts made of hair strands to the legs of one group of ants after they found the food. As their legs now extended, they could move with longer scale steps. Another group of ants had their legs cut below the knee, thus shortened to increase the number of steps needed to walk the required distance back. They then observed the return journey of both groups of ants. The results were astounding; the ants with shorter legs had concluded their course before reaching the nest, while the ants with longer legs ended up passing the nest. Thus, it understood that the ants counted their steps according to the distance they traveled.

The findings reveal that the ants are created with an internal system that keeps track of the steps they take and re-calibrates itself on the way back. People make these complex calculations with measuring instruments and by knowing the laws of trigonometry. However, these small creatures find their way directly back without using any tools or computer applications. They do not use their perception to find direction, and they do not use any other directional methods because they all remember direction and distance as they move forward. If you look at this situation, what would be your simplest explanation? You can only have one definition: These little creatures can measure distances and angles precisely by applying mathematical calculations and trigonometry within their conditions. Since the first day of their existence, these creatures show only a few of the shreds of evidence of the divine power created them out of nothing with wondrous systems and superior abilities in their bodies.

I have put my trust in God, my Lord, and your Lord. No living creature is there, but He holds it by its forelock and keeps it under His complete control. Undoubtedly, my Lord is on a straight path (He governs all that exists and carries out His decrees rightly and with absolute justice). (Surah Hud, 56)