One of the reasons that the nature of mathematics has been such an enigma, is that we associate it with thought, and we tend to distinguish thought from the physical world. We do find mathematics in natural structures – some of these beautifully represented in a film you may have seen called Nature by the Numbers. We’re somewhat familiar with the efficiency of honeycomb structures built by the honey bee. Their geometry maximizes robustness while minimizing weight. Honeybees execute the building of these honeycombs with great precision. Researchers have also seen mathematics in the behavior of insects. Ants calculate the path to food which takes the least amount of time rather than the one that is the shortest distance. Huffington Post reported on a study this past April.

En route to their roach banquet, the ants did not follow the most direct travel path, the study found. Rather, they followed an angled path, traveling over more of the smoother material in order to reach the food morsels in the shortest amount of time. The findings demonstrate that Fermat’s principle of light travel also applies to living creatures, the researchers conclude.

In The Math Instinct, Keith Devlin made a nice survey of the mathematics in nature – the navigation feats of migratory birds, the logarithmic spiral of a falcon catching its prey and the mathematics of locomotion are some of his examples. Generally speaking, these observations highlight the pragmatic value of the non-symbolic mathematics. But pragmatic expectations might actually obscure the path to a new insight. Much of this blog is devoted to investigating the ubiquitous presence of mathematics, in living and non-living things, in order to raise some novel questions about the roots as well as the significance of mathematics in our human experience.

A recent story in a National Geographic blog describes the mathematical behavior of a fish, but the pragmatic motivation for the circular objects these fish create is not so obvious. Large (6.5-foot-wide) structures on the seafloor were once a mysterious feature of the underwater landscape. But these decorated circles have now been attributed to 5-inch long male pufferfish. The fish use their bodies to construct and decorate these nests, within which accepting females will lay their eggs.

The scientists aren’t sure exactly what the females are looking for when they judge a male’s nest. It could be the central patterns made of fine sand, the decorations on the outside, or the nest’s size or symmetry.

The mail fish remains in the nest to supervise the eggs’ hatching. He then looks for a new site where he starts the nest making process again. It takes a significant amount of time for this small fish to build these large geometric structures, swimming toward the center of the circle in a straight line then around the center in a circular motion. But the pragmatic value of this geometry is not obvious. It reminded me of the bowerbird. David Rothenberg described the creativity of the bowerbird’s courtship structures in his book Survival of the Beautiful.

Bowerbirds, say biologists are unique. There is perhaps no other species besides human beings that is known to create things so beautiful beyond their function, structures that we have a hard time calling anything else but art, the arrangement of objects that please us. Bowers are built to attract females, but they are far from the simplest solution to such a problem. Yet a male won’t get a female without one. And somehow, evolution has led them to build them in exact and precise ways.

I enjoy both of them because they just don’t quite fit into the functionality-driven ideas that we use to describe our world. They seem to allow the possibility that life creates for no reason. Creations become tied to what look like reasons, but the creations are not fully captured by the reasons. This is the way I sometimes think of mathematics. One of the things that gets in the way of an informed appreciation of the human development of mathematics is pragmatism.

yes, there is always a rush to find any argument that fits the dominant human narrative, that mathematics in nature must be for some practical end, that there isn’t a part of it which is aesthetic or of a higher domain. We like to think that we are the arbiters of all values, that there isn’t a partial aspect that is revealed in nature, as if we are somehow separate from nature.

its a symbiotic relationship where by value is revealed to us when we align ourselves with our intuition, just like the puffer fish. it asks no questions, and it demands no answers, it just does as it knows, and it knows maths without having to ‘think’ self-consciously as we do. it doesn’t matter if it is ‘for’ a pragmatic purpose, it is still a display of art, a construction intended to be viewed and judged. It also has perfect geometric structure which shows the fish has an unconscious understanding of mathematics. Thus do we humans n fact possess a finer understanding of maths when we re submit all our mathematical strivings through a more intuitive unconscious process there by revealing truly deeper mathematical structures.

I mean can many humans construct a pattern as the fish does in the same mental state as the fish, i.e. effectively unconscious. I am sure the fish has some degree of consciousness but compared to us it is practically in an unconscious state. thus if we were to attempt to use say zen or meditation to achieve a similar state, what could we achieve? who knows?