Good morning.
If you’re reading from faraway, and you’ve awakened to a day of sunny skies and seventy-five degrees, then you’ve missed out on a crisp Whitewater day with a high temperature of thirty-eight. Our November is as November should be.
It’s a grand opening for Whitewater’s new, expanded Walmart today. I walked through last night, and I’ll write more about Walmart later tonight. It’s an inviting sight to walk into the store and see — as one walks in — so much produce on display. Walmart may do a hundred small things wrong, but they do one thing very well (as well as any retailer on Earth: they offer lots of products to people in lots of places.
The New York TImes recalls that on this day in 1933, The United States and the Soviet Union established diplomatic relations:
On Nov. 16, 1933, the United States and the Soviet Union established diplomatic relations. President Roosevelt sent a telegram to Soviet leader Maxim Litvinov, expressing hope that United States-Soviet relations would “forever remain normal and friendly.”
It was the right practical step to establish relations, but ‘normal and friendly’ (or at least their approximation) were only possible with Russia after the collapse of the Soviet Union.
There’s a story at Wired that describes, and offers an explanation, for da Vinci’s observation that a tree typically grows so that the total thickness of the branches at a given height is equal to the thickness of the trunk. Kim Kreiger writes that
The rule says that when a tree’s trunk splits into two branches, the total cross section of those secondary branches will equal the cross section of the trunk. If those two branches in turn each split into two branches, the area of the cross sections of the four additional branches together will equal the area of the cross section of the trunk. And so on.
Expressed mathematically, Leonardo’s rule says that if a branch with diameter (D) splits into an arbitrary number (n) of secondary branches of diameters (d1, d2, et cetera), the sum of the secondary branches’ diameters squared equals the square of the original branch’s diameter. Or, in formula terms: D2 =Sigma di2, where i = 1, 2, … n.
But, why? Botanists had speculated that trees’ shapes followed the rule to allow for the pumping of water from the ground. There’s likely a very different reason:
But this didn’t sound right to Christophe Eloy, a visiting physicist at the University of California, San Diego, who is also affiliated with University of Provence in France. Eloy, a specialist in fluid mechanics, agreed that the equation had something to do with a tree’s leaves, not in how they took up water, and the force of the wind caught by the leaves as it blew.
Eloy used some insightful mathematics to find the wind-force connection. He modeled a tree as cantilevered beams assembled to form a fractal network. A cantilevered beam is anchored at only one end; a fractal is a shape that can be split into parts, each of which is a smaller, though sometimes not exact, copy of the larger structure. For Eloy’s model, this meant that every time a larger branch split into smaller branches, it split into the same number of branches, at approximately the same angles and orientations. Most natural trees grow in a fairly fractal fashion.
Leonardo was right about the relationship of branches to trunk, and now centuries later we know why: it’s all about endurance and resistance.