[Ichneumon]

I still haven't seen a satisfactory explantion for the pointed tetrahedral apex in the honeycomb where the displacement is approximately 35% of the length of the side of the hexagon (this results in a local minimum on the area). Bees doing calculus just doesn't cut it for me.

Local minima (or maxima, depending) occur naturally all the time, just due to the way that various forces or processes interact. For example, soap bubbles are spherical -- minimizing the surface area for the volume of air included -- because that's what happens when the surface tension at every point pulls surrounding portions of the bubble surface towards each other. Because the surface is "trying" to contract, it quickly results in a spherical shape where all the forces equalize (because the curvature is equal at all points).

A somewhat more complex manifestation of the same thing (also in soap bubbles) results in something very much like the bee's honeycombing -- whenever three soap bubbles are stuck together, there results a point between them where three planar bubble surfaces are exactly 120 degrees apart from each other (like the "joints" of a hexagonal array or honeycomb). Get enough bubbles of roughly equal size on the surface of something, and they'll naturally form a "honeycomb" configuration:

Similarly, the "dome" on each one will be the "approximately 35% of the length of the side of the hexagon", as you decribe it, which "results in a local minimum on the area". It's just the way the surface tension forces work out, the molecules don't have to "do calculus". And neither do the bees.

A lot of things that may look like "design" or "structure" often turn out to be the result of simpler processes when you take the time to learn about them. The same goes for a lot of the biological mechanisms, which is why the usual creationist method of "looks fancy to me, *must* be designed" just doesn't hold water. Especially when natural processes like evolution are *proven* producers of amazingly "clever" results, including some that are still beyond human understanding.

[Larry Lucido]

the molecules don't have to "do calculus". And neither do the bees

Back in my day they did. We didn't have any of that fancy "surface tension" kids nowadays do.

[Pete]

It's just the way the surface tension forces work out, the molecules don't have to "do calculus". And neither do the bees.

Your jump from soap bubbles to bees is missing a few steps. Where, exactly, is the surface tension force "working out", as you put it, in the bees constructing their honey combs?

[Soliton]

Truth is so boring.

[DannyTN]

If you look at your soap bubble picture, you will see numerous pentagons, especially one layer in from the edges. And if you try to visually follow the rows they don't have the same neatness as honecombs.

If it's the same force So why don't the honeycombs look more like the bubbles around the edges of the combs.

Plus don't the bees build the honeycombs one layer at a time. I don't see how the comb would have the opportunity to reorganize itself into a honeycomb shape the way you are suggesting.

[DannyTN]

If you look at your soap bubble picture, you will see numerous pentagons, especially one layer in from the edges. And if you try to visually follow the rows they don't have the same neatness as honecombs.

If it's the same force So why don't the honeycombs look more like the bubbles around the edges of the combs.

Plus don't the bees build the honeycombs one layer at a time. I don't see how the comb would have the opportunity to reorganize itself into a honeycomb shape the way you are suggesting.

[grey_whiskers]

Similarly, the "dome" on each one will be the "approximately 35% of the length of the side of the hexagon", as you decribe it, which "results in a local minimum on the area". It's just the way the surface tension forces work out, the molecules don't have to "do calculus". And neither do the bees.

Do you have a pointer to the specifics of how the honeycomb within the hive gets built? Local thermodynamic minima are all very nice, but without accounting for the energy barriers to reconfiguration (e.g. how viscous is the wax when it is first laid down? how close to the equilibrium configuration is it at that point? how quickly does it solidify?) you may be oversimplifying the picture.

Cheers!