5 ms·

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

72 points by wglb 3y ago

Izkata 3y 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 3y 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-tree-branch-wrong-limb-area-thickness https://www.sciencenews.org/article/leonardo-da-vinci-rule-t...
  - Retric 3y 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 3y 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.
    - rob74 3y ago
      ...or, to quote the article: > Therefore, the plant has to reduce in its volume as it reaches its extremities, causing a higher ratio of capillary to the surrounding plant mass The way I read it: because branches at the extremities are thinner, the ratio of "living skin" to "dead skeleton" is higher. I'm just wondering why this isn't immediately obvious and why they are presenting this as a great discovery?! Also, the phrase "has to reduce in its volume as it reaches its extremities" sounds a bit backwards: sure, young branches are thinner, and as the tree grows and branches get older, they grow thicker to support the young branches that grow off them.
    - Someone 3y ago
      > If we assume a constant thickness of the vascular cambium, branches must conserve surface area. Not necessarily. Transport speed could be different depending on the diameter of the branches Also, I would think a model that has a constant flow at each distance from the roots or the leaves is incorrect. A more realistic model has water being transported up and mostly evaporating in the leaves and barely contributing to tree mass, carbon (in some form) being transported down from the leaves and gradually being accumulated, and small amounts of minerals being transported up from the roots and gradually being accumulated. That model has a constant water flow throughout the tree, but a gradient in downward flow. I wouldn’t know which is dominant. _if_ most of the transport volume is carbon being transported down to branches and roots and being accumulated, more volume would go out of the leaves than arrives at ground level. I wouldn’t know whether that’s true, though. Most of a tree’s mass comes out of CO2 in the air, but because water evaporates out of the tree, there still may be more stuff going up than going down.
- mcv 3y 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 3y ago
    Right. Like the Newtonian physics of trees.
heyoni 3y ago
Isn’t it also incredibly easy to prove Leonardo’s tree rule just by cutting down a few?
- bgirard 3y ago
  You can't prove something by example, you can only show that the pattern holds for the examples that you've checked.
  - hermanradtke 3y ago
    Now do the same with dynamic types and unit tests.
  - crazygringo 3y 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.
    - spott 3y ago
      Alternatively, you don’t “prove” things in biology, you just provide evidence for them. Proof implies a level of certainty that doesn’t exist in biology.
      - anonacct37 3y ago
        In fact you don't prove anything in science. You merely fail to disprove something.
        epgui 3y ago
        in the “natural sciences”
        3y ago
soferio 3y 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.
aaron695 3y ago
[dead]
thyrsus 3y 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 3y 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_anatomy_of_trees https://openlibrary.org/books/OL23278992M/The_artistic_anato...
hdarshane 3y ago
Sensationalist title? Seems to me that it was just a heuristic and not really a mathematical axiom.
elif 3y ago
[flagged]

72 points by wglb 3y 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 3y 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-tree-branch-wrong-limb-area-thickness https://www.sciencenews.org/article/leonardo-da-vinci-rule-t...
- Retric 3y 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 3y 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.
  - rob74 3y ago
    ...or, to quote the article: > Therefore, the plant has to reduce in its volume as it reaches its extremities, causing a higher ratio of capillary to the surrounding plant mass The way I read it: because branches at the extremities are thinner, the ratio of "living skin" to "dead skeleton" is higher. I'm just wondering why this isn't immediately obvious and why they are presenting this as a great discovery?! Also, the phrase "has to reduce in its volume as it reaches its extremities" sounds a bit backwards: sure, young branches are thinner, and as the tree grows and branches get older, they grow thicker to support the young branches that grow off them.
  - Someone 3y ago
    > If we assume a constant thickness of the vascular cambium, branches must conserve surface area. Not necessarily. Transport speed could be different depending on the diameter of the branches Also, I would think a model that has a constant flow at each distance from the roots or the leaves is incorrect. A more realistic model has water being transported up and mostly evaporating in the leaves and barely contributing to tree mass, carbon (in some form) being transported down from the leaves and gradually being accumulated, and small amounts of minerals being transported up from the roots and gradually being accumulated. That model has a constant water flow throughout the tree, but a gradient in downward flow. I wouldn’t know which is dominant. _if_ most of the transport volume is carbon being transported down to branches and roots and being accumulated, more volume would go out of the leaves than arrives at ground level. I wouldn’t know whether that’s true, though. Most of a tree’s mass comes out of CO2 in the air, but because water evaporates out of the tree, there still may be more stuff going up than going down.
mcv 3y 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 3y ago
  Right. Like the Newtonian physics of trees.

heyoni 3y ago

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

bgirard 3y ago
You can't prove something by example, you can only show that the pattern holds for the examples that you've checked.
- hermanradtke 3y ago
  Now do the same with dynamic types and unit tests.
- crazygringo 3y 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.
  - spott 3y ago
    Alternatively, you don’t “prove” things in biology, you just provide evidence for them. Proof implies a level of certainty that doesn’t exist in biology.
    - anonacct37 3y ago
      In fact you don't prove anything in science. You merely fail to disprove something.
      - epgui 3y ago
        in the “natural sciences”
        3y ago

soferio 3y 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.

aaron695 3y ago

[dead]

thyrsus 3y 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 3y 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_anatomy_of_trees https://openlibrary.org/books/OL23278992M/The_artistic_anato...

hdarshane 3y ago

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

elif 3y ago

[flagged]