[Pete]

Just a lightning bolt hitting some primordial ooze, nothing to see here...

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.

[Soliton]

This is my final proof that Intelligent Design is real science. Clearly, the bacteria were designed by intelligent beings from outer space who, in turn, are very simple, but super intelligent silicone-based life-forms living in a superconducting sea powered by high intensity magnetic fields. They have no moving parts and are therefore simple enough to have evolved from nonliving things. It's not the creation that evolved; it was the creator.

Prove me wrong scientifically.

[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.

[Talking_Mouse]

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.

Please explain this in slightly more normal english. I think you are saying because of the point of the hexagon less volume is used so it (bee's wax) is a very efficient structure. However, I have been wrong before and I will be wrong again. So, please enlighten me.

[bert]

....Bees doing calculus just doesn't cut it for me.....

Have you ever listened to their conversations? That would be interesting and until we can understand bees, there's no hope of conversing with extraterrestials.

The other end of the wax cell is spherical and lacks the symmetry, indicating some bees have more than others in the head.

[NonZeroSum]

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.

Does water have to "do calculus" to form a sphere in a drop? Do you have to "do calculus" to throw a ball over the plate, or hit a moving target with a stone?

Bees that wasted energy making inefficient honeycombs lost out to bees that made them right.

[CDHart]

"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)."

What does this mean? I warn you, I hated geometry and algebra, but this sounds interesting.

Carolyn

[From many - one.]

Do you have a cite for that?

I'm interested iin the stimulus (or stimuli) for the transition from hexagonal prism to tetrahedral pyramid.