New study disproves Leonardo da Vinci's 'rule of trees'

https://phys.org/news/2023-09-leonardo-da-vinci-trees.html

by wglb • 3 years ago

72 33 3 years ago

Izkata• 3 years ago

Misleading title, the article body goes on to say that a different rule other people came up with, that was an assumption based on Leonardo da Vinci's rule, is the one that's been disproven. Says nothing about his actual rule.

zoomablemind• 3 years ago

... Says nothing about his actual rule.

Indeed! Here it is in brief from another article on the subject

"...Leonardo’s rule [for how trees branch] says that the thickness of a limb before it branches into smaller ones is the same as the combined thickness of the limbs sprouting from it."

https://www.sciencenews.org/article/leonardo-da-vinci-rule-t...

Retric• 3 years ago

That seems to again misrepresent the rule. He’s an artist drawing 2D objects not making 3D sculptures.

The connection between the surface area of branches and overall tree structure shows that it’s the living, outer layers that guide tree structure, the researchers say. “The life of a tree flows according to the laws of conservation of area in two-dimensional space,” the authors write in their study, “as if the tree were a two-dimensional object.”

Yes, a two-dimensional object like say a painting.

klyrs• 3 years ago

But now we know that most trees are living skin on a dead skeleton. If we assume a constant thickness of the vascular cambium, branches must conserve surface area, and not volume! Now, off to read the paper.

Edit: aha, my proof is correct! Only, my axiom was wrong: trees make broader capillaries for thinner branches. Well played, trees.

mcv• 3 years ago

So a rule generalised from a 500 year old art guideline does not hold up on the micro scale in 21st century science? I'm astonished it even got that far.

Terretta• 3 years ago

Right. Like the Newtonian physics of trees.

heyoni2• 3 years ago

Isn’t it also incredibly easy to prove Leonardo’s tree rule just by cutting down a few?

bgirard• 3 years ago

You can't prove something by example, you can only show that the pattern holds for the examples that you've checked.

hermanradtke• 3 years ago

Now do the same with dynamic types and unit tests.

crazygringo• 3 years ago

Biology isn't mathematics.

Yes, in math you can't prove things by example.

But in biology that's the only way you form knowledge.

Biology doesn't have axioms. In biology, proof is by induction. However philosophically unsatisfying that may be.

heyoni2• 3 years ago

Yea I misspoke. (typed)

otikik• 3 years ago

I think that's correct for some assertions.

When a statement is "this is always true", then a counterexample is all it takes to disprove it.

On the other hand, if the statement is "this is not always true" then an example of it happening is as you said - the example does not counter anything.

soferio• 3 years ago

I have been looking at trees my entire life, and never thought to even think about this “plumbing” ratio. What a lovely example of how Leonardo combined mathematics and observations.

thyrsus• 3 years ago

The body says large trees are more susceptible to drought, but the first companion article in the list below the article says large trees are less susceptible to drought. There needs to be a reconciliation.

smokel• 3 years ago

A fascinating book in this context is "The Artistic Anatomy of Trees" (1920) by Rex Vicat Cole. It made me look at trees with a lot of new insights.

The illustrations in the book are pretty crappy, but the text more than makes up for it. Highly recommended to people who like to draw or paint from their imagination.

https://openlibrary.org/books/OL23278992M/The_artistic_anato...

hdarshane• 3 years ago

Sensationalist title? Seems to me that it was just a heuristic and not really a mathematical axiom.

New study disproves Leonardo da Vinci's 'rule of trees'

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