arachnomatics (the mathematics of spiders)

ARACHNOMATICS drawn in 2012 using ballpoint pen, roughly 21 cm x 29cmSpiders have a deep understanding of mathematics, logistics, economics, finance and engineering. In my backyard lives a species that constructs circular webs based on the value of π (pi), the mathematical ratio of a circle's circumference to its diameter.

My backyard spiders seem pretty clued up on geometry and calculus as well: they know how to approximate a circle using straight lines only, ie they spin tangents not arcs! There are no curved strands of silk in these spiderwebs, only straight.

Logistics, economics and finance? Spinning a web comes at a cost: the spider creates the building materials (web-silk) from the substance of its own body. If we were to construct our dwellings out of our own bones, we'd presumably want to minimise the amount of building materials in the construction.

There's a cost/benefit analysis involved. Without a decent web the spider starves to death. If the spider under-invests, ie builds a smaller web, there's a risk that the web will not capture enough food for the spider to live on. But if the spider over-capitilises -- builds a larger, fancier web -- there's a risk that the return on the web-building investment will never be enough to recoup the initial investment, and the spider will ultimately starve to death.

How can you tell when a spider calculates correctly? That's easy. Every living spider has calculated correctly, has figured out the optimum cost/benefit ratio.

It's a complicated calculation, involving several variables including the circumference of the outermost circle, the number of inner concentric circles, the number of "spokes" in the wheel, the distance between each of the circles, and the dimensions of the species on which the spider preys.

If the distance between the concentric circles of the web is too large, prey can slip through the web without touching any of the sticky strands. But if the distance is much smaller than needed to catch the prey species, the spider will have over-invested, over-engineered the web, and may end up making too small a profit to survive. The spider may end up being liquidated!

Where did the spiders learn all this economics, maths and such? At the School of Natural Selection in the University of Evolution.

I'm not a biologist and I've never studied biology. So the questions below reflect my ignorance. I'm not asking them because I'm trying to be clever. I'm asking them because I don't know the answers, and I couldn't be bothered to look them up. So here goes.

The spider builds its web by virtue of instinct, not knowledge. But what is instinct made of, what substance? Of what is it comprised? (Similar questions can be asked about knowledge, thought, consciousness, memory, self etc.) Is it possible that instinct and knowledge are made of the same stuff?

Where can instinct (knowledge, thought etc) be found, at what location/address? (And BTW those things haven't yet been found anywhere in the human brain.)

To say that web-spinning and other "instinctive" behaviours are hereditary, ie passed on genetically from progenitor to offspring, doesn't clear anything up for me. What specifically is the mechanism that tells the spider step-by-step, strand-by-strand how to build a good web (incorporating all the maths and other technical aspects discussed above)? What is saying to the spider: "Stop. Rotate your body 180 degrees. Advance until you get to the next junction. Change the angle of the silk by 5 degrees. Move inward toward the centre of the web by 4 millimetres..."?

If a spider builds a bad web, death tells the spider that the web's bad. But what death doesn't tell the spider is specifically and exactly HOW to build a good web.

Choreography is a way of specifying human body movements. What is the choreography of web-spinning? Who is the choreographer? Where is the choreography? In what language is it written? Is the value of pi specified in the spider's genetic code? Is the optimum number of spokes specified? The optimum distance between the concentric circles? The optimum number of concentric circles? The optimum overall granularity of the web in relation to the dimensions of the preferred prey species? Not one of those things, to the extent of my limited knowledge, is specified by or is carried by the genetic code.

Does the spider know how to build a good web, using "know" in the broadest sense of the word (= has access to the data)? How does the spider know? Help!


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Anonymous said...

It is common sense. It is knowing innately what to do. It comes from your subconscious. Parasympathetic. Medulla Oblongata.

Anonymous said...

The proprioceptors spiders use to the greatest extent are those associated with the leg joints. These allow them to know the extent of flexion or extension that exists at each joint at a given moment. Some extensive neurophysiological studies have been performed on the overseas ctenid species, Cupiennius salei, and we now know that this species has numerous hairs (or sometimes whole hair plates) of different sizes around each of its joints and that the extent of deformation of these as flexion or extension occurs at that joint is used by the spider's nervous system to monitor the posture of that leg.

Anonymous said...

Also Sympathetic. Not sure what the equivalent to the Medulla Oblongata would be in spiders?

masterymistery said...

Anonymous, thank you for your comments, which I found highly insightful and informative. You've added much to this post. I wouldn't have a clue about the MO equivalent in spiders. But from my limited biology, spiders don't have a spine, therefore they could not have an MO or MO equivalent, I think... Maybe...

masterymistery said...

Ignore previous comment re MO in spiders. After having done 43 seconds of basic research via google, I see my previous comments were totally wrong...