Stars, Bubbles and Beehives – Complexity Joined

In an attempt to synthesize and to simplify, much has been said about the idea that patterns in Nature can be described with simple physical laws. This idea has appealed to mathematicians, physicists, and others who adhere to the reductionist world view. While it is true that physical laws play a very important part in pattern formation, they are only part of the story as the honey bee demonstrates.

My story begins with the stars — complex dynamic systems where the hydrogen atom hangs out. Somehow, the complex system of two hydrogen atoms and one oxygen atom joined to produce water molecules and  water drops — both  hierarchies of complex systems.

Of all the shapes in our geometric inventory, a sphere has the smallest surface area for a given volume. A common drop of water  is a naturally ordered sphere that is shaped by the influence of physical forces called surface tension.

Each water molecule interrelates with neighboring molecules by way of intermolecular forces that result in the molecules being attracted to each other. Within the liquid’s body, each molecule is pulled equally in all directions by neighboring molecules, resulting in a net force of zero. But, at the surface of the liquid, the water molecules are pulled inwards by other water molecules deeper inside the liquid. This happens because the water’s surface molecules are more strongly attracted to other water molecules in the liquid than to the molecules of  air  that surround the water drop. This net difference in attractive forces is called surface tension.

Surface tension at a water drop’s interface with its surroundings results in the formation of the smallest area for its given volume. The physical forces (patterns in themselves) associated with surface tension create a pattern — in this case a spherical water drop.

A water bubble is sustained as a result of the balance between the gas pressure inside the bubble and the forces associated with surface tension. The bubble’s internal gas pressure tends to push the sphere apart. This is counteracted by the bubble’s surface tension acting around the surface of the sphere to provide a net force that pushes inward.

Foam is a collection of bubbles. The weight or gravitational forces that act upon a collection of bubbles causes them to “pack”. A two dimensional packing of foam bubbles results in bubbles whose walls meet at 120 degree angles — forming roughly hexagonal cells. If the bubbles are of unequal diameter, the hexagons are unequal. But, if the bubbles are of equal diameter, the hexagons are of equal size — taking on the appearance of a honey comb.

What we see  is a hierarchy of interrelationships that start at the atomic level where molecules are formed. Atomic forces result in molecules interrelating in various ways. Differences in the strength of molecular forces define phenomena such as surface tension. The gravitational joining of objects created by these phenomena results in more complex systems – like foam. It is the connectivity of and interrelationships between these complex systems that result in what we see as bubbles and foam.

But, what does all of this have to do with honeycombs? As we shall see, they represent the joining of complex systems – the physical forces just described with biological patterns in Nature. With the honeycomb, we get to observe the synergistic joining of animate and inanimate patterns in Nature.

The hive and the bees within are both hierarchal complex dynamic systems. Somehow, whether through genetic, epigenetic, or cultural patterns, the bees acquire patterns of behavior. Again patterns within patterns. Somehow, the bees know to harvest the correct components from other patterns in Nature (like flowers) so as to create bees wax within their wax glands.

While constructing a honeycomb, bees use their bodies as a template. They make each close packed wax cell perfectly cylindrical, like a tube. The bees raise the temperature of the wax to 37-40 degrees Centigrade. Like glass, the beeswax becomes increasingly fluid as it is heated. The mobility of one wax particle with respect to another changes significantly at this specific transition temperature. Much like the foam forming process discussed earlier, the warmed wax cells take on their hexagonal shape due to their gravitational compression by the six closest neighbors in the packed arrangement of the cylindrical cells.

The entire process of  creating a honeycomb in a hive, therefore, comes from the joining of many different patterns in Nature – molecular structure, physical laws, bee behavior, plants, and more. All complex systems within complex systems. Everything connected in some way. All with some form of regularity.

Your comments are always welcome.

My name is Bill Graham. As a Marine Biologist who has worked in the US and Mexico for 30 years, I am a student of Nature, a teacher, a researcher, and a nature photographer. Through my work, I have acquired an ever growing passion for how everything in Nature is connected. Today, I travel extensively contemplating about, writing about, and photographing Nature’s connections. I also work with conservation projects in the USA and Mexico and mentor talented youth.

6 Responses to “Stars, Bubbles and Beehives – Complexity Joined”

  1. Sena Oran says:

    I am amazed at how nature never ceases to amaze me, thank you for sharing you wisdom! I will be using this information in my research in regards to a design project

  2. What a fascinating blog! Thanks so much for sharing your knowledge!

  3. Wonderful description of nature’s pattern of bubbles and foam. I work as a marketing director at a children’s science museum and this is very helpful as I struggle to write copy for a five year old’s level of understanding.

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