If anyone from Marvel/Sony is reading, feel free to shoot me a message—I’ve got some ideas for the next Spiderman movie. 6/6

And, finally, if all of that wasn’t enough, it turns out that many insects accumulate static electric charge in the course of their daily activities. Spiderweb, being conductive, *can reach out to meet a passing insect.* (Ortega-Jimenez and Dudley, 2020, www.nature.com/articles/sre...) 5/6

The stickiness can come from one of two places. Most spiders coat their webs with a glue-like adhesive to hold prey in place. But some spiders fray parts of their web silk to take advantage of van der Waals forces—tiny electrostatic attractive forces—over a wide area of their prey’s bodies. 4/6

You may have heard that spiderwebs are stronger than steel, but that’s not quite correct. Spiderwebs combine strength (how much can I push on it) with extensibility (how much can I stretch it) for extreme *toughness* (how much energy can it absorb). Steel is stronger, but spiderwebs are tougher 3/6

Spiderwebs are made of silk, which should already raise some questions because silk is not famous for its stickiness. Spiders can produce different kinds of silk (seven varieties are known to science!) with properties adapted to various components of their webs. 2/6

Today I am very grateful I am not an insect, because today I learned how spiderwebs work. Did y’all know they conduct electricity 1/6 ⚛️🧪

update on progress for today's explainer

But when mosquitos sense elevated CO2, they pay increased attention to other cues, like heat or chemicals that waft off of human skin. They even have pretty decent eyesight, taking a special interest in dark colors, and even without CO2 mosquitoes can use these other cues to find us. 3/5

Mosquitoes do undeniably sense your CO2 exhalations, in a critical component of their sensory arsenal. They have a specialized type of neuron on the organs near their mouths that is specifically triggered by CO2: 2/5

I once heard that insects like mosquitoes track you through the CO2 you exhale, and so holding your breath can help you avoid bites in a swarm. Today I am disheartened to report that the sensory tour de force packed into these 2.5 milligram bodies can still counter tricks like these. 1/5 ⚛️🧪

This gives us a new contact condition. At one value of G, all three distances are the same, but as G continues to shrink the distance to organ m+n actually becomes smaller than the distance to organ m! So we’ve updated from (m,n) parastichies to (n, m+n)—exactly the Fibonacci sequence.

This defines a circle, a constraint alpha and G must satisfy. But m and n cannot take any value. Let G evolve towards 0. As this occurs, the lattice shifts, until organ 0 has three contacts; the new contact is with the fourth corner of its rhombus, which is organ m + n.

This contact can be expressed as the requirement that the distance d from organ 0 to organs m and n in are equal, if 0 is in contact with m and n. Defining a growth rate G (roughly, the rate at which organs move out), divergence angle alpha, and winding numbers r and s, we find

Math nerd afterparty: why do rhombic lattices approximate the golden angle? The constraint that the new organ touches at least two members of an older row defines a “rhombic lattice”, because, well, little rhombuses are evident in them:

Pinecones have some of the easiest parastichies to identify. If you can find a large, slow-growing pinecone, and you take a ratio of clockwise and counterclockwise the parastichy numbers, you’ll have arrived at a contrived but well-earned approximation of the golden ratio. 16/16

This constraint defines an equation relating the angle at which a new organ appears to the rate at which new organs move away. I’ll include the full calculation below the references; as that rate drops to 0, the angle is constrained to be a better and better approximation of the golden angle. 15/16

We can understand that constraint—"as soon as there is enough space”—as a requirement that the new organ will touch at least two older leaves in an older row (not necessarily side-to-side). This connects the rate at which organs move away from the stem and the location where new organs form. 14/16

These numbers of spirals are Fibonacci numbers! This shouldn’t surprise you—remember that as we take ratios of larger and larger Fibonacci numbers, we get closer and closer to the golden ratio, and by extension the golden angle. 11/16

What if the leaves are 137.51° apart, or 0.3819… of a circle apart? Then I expect 2 spirals (successive members separated by 0.236 of a circle), 3 spirals (0.146 separation), 5 spirals (0.09 separation), 8 spirals (0.056 separation), 13 spirals (0.034 separation), etc. 10/16

For leaves 7/30ths of a circle apart, this means I expect 4 spirals (4 x 7 = 28, 2/30ths separation), or 9 spirals (9 x 7 = 63, 3/30ths separation), or 13 spirals (13 x 7 = 91, 1/30ths separation), etc. The exact number(s) of spirals will be set by how quickly leaves move out from the center. 9/16

But if the angle between leaves is, say, 84° (or 7/30ths of a circle), I see spirals instead. This is because an angle of 84° wants 30 straight files of leaves, but old leaves are pushed out of the center before 30 new leaves form. Only every 30 leaves will be exactly in line with one another 7/16

So what’s this got to do with pinecones? Think for a second about how a plant grows. New organs form in the center of the plant, while old organs get pushed outwards at some rate. If new organs appear at, say, 180° from each other, I get straight files like this: 6/16

That number, it turns out, is 1.618033988749… which is the golden ratio. If you take two line segments whose ratio of lengths is the golden ratio, wrap them into a circle, and compute the angle spanned by the smaller segment, you get the golden angle, ~137.51°. 5/16

Each spiral arm is called a parastichy (“puh-RASS-ti-kee”). As early as the 1830s, biologists noticed that the overwhelming majority of parastichy numbers were successive Fibonacci numbers. Darwin wrote that this pattern could “drive the sanest man mad.” 3/16

If you look at plants with tightly packed organs, you may notice spiral patterns. Some plants, like this aloe, have distinct spirals in one direction, while in others, like this cactus, it’s easier to see that there are both clockwise and counterclockwise spirals. 2/16

The golden ratio is an irrational number; if you divide a line according to the golden ratio, the smaller part relates to the larger part the same way the larger part relates to the whole. And you can compute the golden ratio yourself, with a pinecone. 1/16 ⚛️🧪

Pretty standard stuff

Just a normal day at Berkeley Lab

new black banner on arXiv hits different ⚛️

lol for a second I thought there were actually 0 new listings on astro-ph.CO today, seems to be sitewide though