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Nature prefers hexagons, but why?

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3d Hexagon Pattern Stock Photo Says Philip Ball at Nautilus:

The ancient Greek philosopher Pappus of Alexandria thought that the bees must be endowed with “a certain geometrical forethought.” And who could have given them this wisdom, but God? According to William Kirby in 1852, bees are “Heaven-instructed mathematicians.” Charles Darwin wasn’t so sure, and he conducted experiments to establish whether bees are able to build perfect honeycombs using nothing but evolved and inherited instincts, as his theory of evolution would imply. More.

Note how in pop science culture, a simple question like Why hexagons? turns into a hymn of praise to Darwin vs. others. You know, the author of the single greatest idea anyone ever had.

Incidentally, this kind of thing is what makes people like Prophet of Patheos sound so out of it. He avers that we need to combat naturalism, not Darwinism. On the scene of course, we observe that Darwinism comes unbidden to the lips and thoughts of naturalists, and is their primary means of communication, though subtle means, not-so-subtle means, and mere interruptions of thought as well. After a whle advanced stupidification sets in.

Okay, why hexagons? Now it gets interesting, a it appears to be a form of energy conservation:

If you blow a layer of bubbles on the surface of water—a so-called “bubble raft”—the bubbles become hexagonal, or almost so. You’ll never find a raft of square bubbles: If four bubble walls come together, they instantly rearrange into three-wall junctions with more or less equal angles of 120 degrees between them, like the center of the Mercedes-Benz symbol.

Evidently there are no agents shaping these rafts as bees do with their combs. All that’s guiding the pattern are the laws of physics. Those laws evidently have definite preferences, such as the bias toward three-way junctions of bubble walls. The same is true of more complicated foams. If you pile up bubbles in three dimensions by blowing through a straw into a bowl of soapy water you’ll see that when bubble walls meet at a vertex, it’s always a four-way union with angles between the intersecting films roughly equal to about 109 degrees—an angle related to the four-faceted geometric tetrahedron.

The rules of cell shapes in foams also control some of the patterns seen in living cells. Not only does a fly’s compound eye show the same hexagonal packing of facets as a bubble raft, but the light-sensitive cells within each of the individual lenses are also clustered in groups of four that look just like soap bubbles. In mutant flies with more than four of these cells per cluster, the arrangements are also more or less identical to those that bubbles would adopt.

The cells of many different types of organisms, from plants to lampreys to rats, contain membranes with microscopic structures like this. No one knows what they are for, but they are so widespread that it’s fair to assume they have some sort of useful role. Perhaps they isolate one biochemical process from another, avoiding crosstalk and interference. Or maybe they are just an efficient way of creating lots of “work surface,” since many biochemical processes take place at the surface of membranes, where enzymes and other active molecules may be embedded. Whatever its function, you don’t need complicated genetic instructions to create such a labyrinth: The laws of physics will do it for you. More. Cool.

The article is written as if nature in and of itself is an engineer.

Funny how, as humans come less and less to be seen as persons, nature becomes more and more so. Is there a pattern there too?

See also: Nearly 50% Americans now think humans not special What is sobering is that reduced belief in human uniqueness generally coexists with reduced interest in civil liberties, as is currently evident among millennials and especially on campuses.

See also: Nearly 50% Americans now think humans not special What is sobering is that reduced belief in human uniqueness generally coexists with reduced interest in civil liberties, as is currently evident among millennials and especially on campuses.

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This TED ED vid falls into the usual traps dicussed above: We are told that breathlessly that honeybees are “excellent mathematicians,” using hexagons.

Actually, the bees aren’t mathematicians at all, so what exactly is the source of the mathematics? As one commenter puts it, “It sounds like the bees actually choose the exagon. Do birds migrate to the south because they’ve seen some advertisement on TV??” The commenter’s point is well-taken, though mistaken by later commenters. The bees do not know why the hexagon works and did not hit on the idea after failed experiments with squares and pentagons.

Comments
EI: "And look what he and his mystic idea spawned." A strong science supported by hundreds of thousands of research papers. What has ID spawned?Indiana Effigy
April 10, 2016
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"Earthsinterface, you have just presented the ID approach to science. Something hasn’t been explained, it must be designed." No I'm affraid not. Actually your daddy Chuck holds that honor. Seriously, he perfected it. And look what he and his mystic idea spawned.earthsinterface
April 10, 2016
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Earthsinterface, you have just presented the ID approach to science. Something hasn't been explained, it must be designed.Indiana Effigy
April 10, 2016
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"For the growth of a bee, a tube would probably be more efficient from the perspective of getting necessary food to the cylindrical shaped larvae." So if there were an intelligent designer, he would have made cylindrical tubes as opposed to hexagonal compartments, therefore this is proof that evolution is true. "Cubes would be better for stacking and racking but is poor for getting food to the larvae. Hexagons are an excellent compromise." This reminds me of something Randolph Nesse said regarding doctors who mistakenly view the human body as being engineered when in reality it's just an imperfect bundles of compromises, evidently tinkered by some mysterious Nature god I suppose. Therefore evolution is true because an intelligent designer would have never done it that way. Isn't religion and faith wonderful ? Especially when it's blind faith in the face of factoidal asinine absurdities being promoted as "Truth" ?earthsinterface
April 10, 2016
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"The article is written as if nature in and of itself is an engineer." Yes, I found this in the title as well and through much of the article's stoey line. Nature has today been transformed back into some sort of animistic type of diety. Or transformed into the only acceptable scientific diety or god. It thinks, it contemplates, it tinkers etc. They leave out many other interesting natural features found in nature, like volcanic basalt hexagonal columns, hexagonal design in water molecule clusters or even snowflakes. Surely these all contain information ? *Sigh*earthsinterface
April 10, 2016
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For the growth of a bee, a tube would probably be more efficient from the perspective of getting necessary food to the cylindrical shaped larvae. But is very inefficient with respect to stacking and racking. Cubes would be better for stacking and racking but is poor for getting food to the larvae. Hexagons are an excellent compromise. Maximizing the number of larvae in a limited space, providing an effective and strong structure, and being efficient for larvae feeding. It seems to me that evolution can arrive at this solution.Indiana Effigy
April 9, 2016
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News, hexagonal close packing shows how the hex pattern and its 3d extensions tend to a minimum energy, space efficient pattern. The bucky ball pattern for geodesics is related and is a good approx to a sphere see https://en.wikipedia.org/wiki/Geodesic_dome and brings to bear triangle power in a stabilising lattice. The wax minimising while space filling argument makes sense, but how the bees hit on that is another question. BTW the geometry of hexagons is very interesting and full of irrationals. Gotta run, KFkairosfocus
April 9, 2016
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Aleta at 8, we would only know there was no design or agency if a complete account of the universe could be provided that way. Such an account (which we do not in fact have) would also explain why we mistakenly believe that there is design or agency. Which means we could never know it was true because our minds somehow randomly assembled in a particular way. We do not apprehend truth because there is no truth, not even the truth of naturalism. What we can and do have is naturalists who have discovered that there need not be truth as long as there is power. Or, as CS Lewis put it, when everything that says "I think" has been debunked, what says "I want" remains. (paraphrase) Attributing abstract intelligence to bees helps their cause.News
April 9, 2016
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re 6: News says,
Tue, Aleta at 4 but the ultimate effect is to obfuscate questions around design in nature.
Yes, but the obfuscation can go both ways, including making it sound like there is design or agency when there is not. For instance, we might informally say that sunflowers want to turn to face the sun, but we certainly don't mean that they "want to" in any conscious sense, or at least at a far end of a spectrum of what "want" can mean in respect to organisms. Avoiding anthropomorphizing non-human events, and even non-animate phenomena, is difficult because our language and perspective is so anthro-centered.Aleta
April 9, 2016
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Whatever its function, you don’t need complicated genetic instructions to create such a labyrinth: The laws of physics will do it for you.
I don't get out much these days. Have we all come to an agreement yet of where the laws of physics originated? And are they more simple than genetic instructions or more complicated? As a computer programmer, I call on a lot of functionality from the building blocks provided by the operating system and its development framework instead of coding my own basic functionality. Thus my program instructions are actually more simple, not more complicated. But it all points to an intelligent mind(s) behind both. In my case, not even close to the intelligence of those who provide the laws of basic functionality.awstar
April 9, 2016
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Tue, Aleta at 4 but the ultimate effect is to obfuscate questions around design in nature.News
April 9, 2016
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to Mung: yes, planes are mathematical ideas that are only represented imperfectly in the real world. That doesn't negate the significance of the properties I mentioned. Whether those ideas exist in some world of ideals are not is a perennial philosophical question that has been argued since the days of Plato and Aristotle, but that also doesn't affect the fact that what we understand mathematically is relevant to the actual hexagons constructed by the bees.Aleta
April 9, 2016
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to news: I mentioned anthropomorphizing separately, and I agree that is not a simplification. Rather, it is giving human characteristics to situations that they don't belong. No one should think that bees have a conscious plan, or know that what they are doing is mathematically efficient. The problem is that we see the world so much from our own point of view that people, from time immemorial, tend to want to populate the world with human characteristics. Learning that the world doesn't act as a willful being has been one of the main themes of the history of our knowledge of the natural world.Aleta
April 9, 2016
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I thought a plane was a two-dimensional mathematical idea. There are no actual planes in our world. So what we have is an ideal being represented in the real world. A Beautiful Question: Finding Nature's Deep DesignMung
April 9, 2016
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It's not a "simplification" to say that nature is an engineer or that bees are mathematicians. Such language serves the implicit purpose of obfuscating questions around design.News
April 9, 2016
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I have no comments on the actual video. I too bemoan the anthropomorphizing and other simplifications that popular science uses. But the obvious reason for hexagons, from a mathematical point of view, is that they have the best area to perimeter ratio of any figure that tiles the plane. And minimizing or maximizing various properties also characterizes many physical processes.Aleta
April 9, 2016
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