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Applying the Design Filter to Hexagons

Photo: Saturn’s North Pole hexagon, via NASA/JPL-Caltech, Attribution, via Wikimedia Commons.

Hexagons (at least macroscopic ones) are relatively rare in nature. The most common place we see them is in beehives. It could be argued that if bees are intelligently designed, for which there is ample independent evidence, then the structures they create are also intelligently designed. We might argue that hexagons are the most efficient packing spaces for the least amount of material. We might point out that the design also provides more robust protection against stress than square-shaped cells. We can see that the structural design performs a function.

Our propensity to infer design, though, has to face up to other examples of hexagons in the non-living world. Some have been difficult to explain by natural law.

Columnar Basalt

When lava cools, it often forms polygonal-shaped columns, and hexagons are the most common shape. Many physicists have tried to understand how this occurs. There have been partial solutions, but nothing fully satisfying. A paper in Physical Review Letters reproduces the hexagonal columns with a mathematical model. The basic idea is summarized in a news release at APS Physics, along with a stunning photo of a pyramid of hexagonal basalt columns at the Giant’s Causeway in Ireland. It sure looks designed. How do we make a proper inference?

The surface of cooling lava contracts more quickly than the still-warm liquid underneath, creating a stress that is relieved by the formation of cracks. Martin Hofmann from the Dresden University of Technology, Germany, and colleagues considered a uniform lava layer and calculated the energy released from different crack patterns. They found that, in the initial stages of cooling, when the cracks start to appear at random places on the surface, the energy release is greatest if the cracks intersect at 90-degree angles. Butas the lava continues to cool and shrink, and the cracks collectively start to penetrate into the bulk, more energy is released per crack if they intersect at 120-degree angles. This transition from individual to collective growth of the cracks drives the pattern from rectangular to hexagonal. The hexagonal pattern is then maintained as the lava cools further, eventually leading to an array of hexagonal columns, similar to those seen in nature. [Emphasis added.]

One can find columnar basalt in many locations: in the Grand Canyon, in Yellowstone Canyon, in Utah’s Zion National Park, in the Rocky Mountains, at Devil’s Postpile in the Sierra Nevada, and of course at the Giant’s Causeway, along with other places around the world. The uniformity of the columns can be impressive, but they are rarely perfect. Many times other polygons are mixed in with the hexagons. 

Saturn’s North Pole Hexagon

A giant hexagon made up of clouds has persisted for decades on Saturn’s north pole. This formation has baffled scientists since it was first discovered by the Voyager spacecraft in 1981. It appears to be unique in the Solar System, and it’s huge: 20,000 miles across and 60 miles deep. Saturn’s south pole also has a giant vortex, but not this polygonal shape. describes attempts to explain the feature:

Scientists have bandied about a number of explanations for the hexagon’s origin. For instance, water swirling inside a bucket can generate whirlpools possessing holes with geometric shapes. However, there is of course no giant bucket on Saturn holding this gargantuan hexagon.

Voyager and Cassini did identify many features of this strange hexagon that could help explain how it formed. For example, the points of the hexagon rotate around its center at almost exactly the same rate Saturn rotates on its axis. Moreover, a jet stream air current, much like the ones seen on Earth, flows eastward at up to about 220 mph (360 km/h) on Saturn, on a path that appears to follow the hexagon’s outline.

We know that standing waves can maintain nodes that are stationary with respect to their reference frame. Something like that appears to be at work in Saturn’s polar winds. The article says that the “bizarre giant hexagon on Saturn may finally be explained.” A model by a planetary scientist from New Mexico reproduces many of the observed properties of the hexagon.

The scientists ran computer simulations of an eastward jet flowing in a curving path near Saturn’s north pole. Small perturbations in the jet — the kind one might expect from jostling with other air currents — made it meander into a hexagonal shape. Moreover, this simulated hexagon spun around its center at speeds close to that of the real one.

The scenario that best fits Saturn’s hexagon involves shallow jets at the cloud level, study team members said. Winds below the cloud level apparently help keep the shape of the hexagon sharp and control the rate at which the hexagon drifts.

This hexagon may not be permanent, since it is subject to perturbations by processes that have no particular reason to maintain it. A simpler case is seen in Jupiter’s Great Red Spot that appears to be shrinking after three hundred years since it was first observed.

Tiny Non-Living Hexagons

Snowflakes are classic examples of orderly structures with a hexagonal shape. Other non-living hexagons include the ring structures of many organic molecules (at least the way they are diagrammed by chemists). Some minerals also display hexagonal packing. Most of us have seen soap bubbles form hexagonal interfaces when they are packed together. An occasional hexagon can be found in mud cracks on a dry creek bed.

Life-Produced Hexagons

Bees are not the only hexagon-makers in the living world. We find hexagons on tortoise shells and in the ommatidia of insects’ compound eyes. Some diatom species form free-standing hexagons in addition to the more common circles, triangles, squares, and pentagons. We humans, of course, are great hexagon-makers. Understanding their ideal packing geometry, we make them in telescope mirrors, geodesic domes, and soccer ball covers. Sometimes we create them just for their artistic value.

Proper Inferences

If humans create hexagons by intelligent design, is that true for other living things that make them? And how should we distinguish the design inference in life from the natural hexagons on Saturn or in columnar basalt? These questions provide an opportunity to understand William Dembski’s Design Filter.

It’s not enough that something be orderly. Casey Luskin has discussed columnar basalt, answering ID critics’ accusations that the Design Filter would generate a false positive. We’ve also explained why snowflakes do not pass the design filter, despite their elegance and beauty. It’s not enough, further, that something be rare or unique, like the Saturn hexagon. The Design Filter prefers a natural-law explanation if one can be found, or if the probability of the phenomenon’s occurrence by chance is sufficiently high.

But do we wait forever for a natural explanation? Planetary scientists struggled for 35 years to explain Saturn’s hexagon. Shouldn’t we wait to explain beehives and compound eyes without reference to intelligent design? Isn’t natural selection a natural law? (Actually, it’s more like magic than a law of nature, but we’ll entertain the question for the sake of argument.) 

Intelligent design is not a gaps argument. It’s a positive argument based on uniform experience. We have experience watching melting lava or drying mud forming geometric patterns. We have no other experience with hexagons forming on gas giants like Saturn, though. What do we do?

The Information Enigma

The short answer involves information. The hexagon on Saturn performs no function. Columnar basalt doesn’t say anything. Snowflakes don’t carry a message. They are mere emergent phenomena that are not that improbable, given laws of nature with which we are familiar. The Design Filter works properly by rejecting a design inference for these on the basis of probability and natural law. 

All the living examples of hexagons, by contrast, are produced by codes. Beeswax will not form into hexagon cells on its own, nor will silica arrange itself into the geometric shells of diatoms. A digital code made of DNA dictates the placement of ommatidia in the insect eye and patterns in the turtle shell. Each of these structures performs a function and is the outcome of processes directed by a code. 

The coded information makes use of natural laws, to be sure, but it arranges the parts into hexagons for a functional purpose. In our uniform experience, we know of one cause that can generate codes or instructions that lead to functional geometries — intelligence.

There is one sense, though, in which we could make a design inference for the nonliving hexagons like snowflakes, basalt columns, and planetary atmospheres. Certain features of the universe are so finely tuned that without them, water, atoms, stars, and planets would not exist. It takes a higher-order design to have a universe at all. 

You might even say that the elegant mathematics that allows us to describe hexagons is conceptual, not material, as are the aesthetic values that allow us to appreciate them. So even if the Design Filter rejects a design inference for some of the hexagons at one level, the mere existence of atoms, natural laws, and beauty warrants a design inference in a broader context for all of them. Without minds, we wouldn’t even be debating these questions.

This article was originally published in 2015.