
Leonardo da Vinci's tree rule may be explained by wind - ColinWright
https://phys.org/news/2012-01-leonardo-da-vinci-tree.html
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chicob
Also pertinent to wind resistance is whether or not the tree is deciduous, the
shape of the leaves' margin, the texture of bark and how they interact as a
group in forests.

Another aspect that explains why the vascular explanation is not enough is the
resistance of the trunk in supporting the wood's weight. Also important here
is the roots' structure.

When I imagine a situation where wind resistance is fundamental, I think of
palm trees being subject to seasonal tropical storms, and these look nothing
like the diagram in the article.

Underwater, where vascularization and weight are not as important to many
branching structures like corals or algae, there is still the problem of
resistance against a moving fluid. But the branching/girth/length/angle rules
seem to be different.

So I'm still with team "branching optimized for sun/air exposure and
constrained by vascularization, weight and root structure".

~~~
dsnuh
Just a note - palm trees are part of the grass family, and have more in common
with bamboo and turf grass than they do with trees. It doesn't surprise me
that they would be different.

~~~
chicob
Exactly. And here is the point: what exactly does 'tree' mean here?

Palm trees, bamboo, corn, reeds and such are all of them quite different from
the schema presented in the article. This schema seems to be some specific
subset of large Eudicots, like magnolias, oaks, shrubs and such, or at any
rate some paraphyletic family of plants.

In taxonomical terms, Pinophyta are even more distant from the aforementioned
plants, all of them Magnoliophyta. Pine trees, cypresses and other Pinophyta
branch as well, but their branching does not fit the schema in the article.

Why wasn't the hypothesis tested against the Pinophytae' specific (and quite
common) kind of branching? Is surrounding fluid resistance only important for
that arbitrary set of plants?

If fluid resistance, ubiquitous in plant evolution, were of such an importance
in explaining a difference between what is predicted by the vascular
hypothesis and what is actually observed in branching trees, the same could be
said for _all trees that branch_ , and this theory should be able to do some
predictions for other branching (and non-branching) plants.

This hypothesis should have been tested for other structures right from the
start, and not just for an idealized form of unwarranted generality.

But don't get me wrong: I think that it's very good to have aerospace
engineers putting forth this idea, and this article adds to our understanding
of tree growth and evolution. I just find it incomplete.

~~~
posterboy
Most plants would be protected by trees, so trees kinda ... stand out.

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hyperpallium
> the combined cross-sectional areas of a tree’s daughter branches are equal
> to the cross-sectional area of the mother branch.

Seems so logical, for a flow in the daughter pipes to match the mother pipe...
except that the wood of a tree is dead, and the flow happens in the bark...
leading to a sum-rule for circumference, proportional to radii and diameter.

However, the point of a tree is structural, to get higher than other trees,
higher than herbivores. Is the strength of wood proportional to cross-
sectional area (required to resist gravity - the essential problem of height)?
If so, that would explain the rule. Similar reasoning to wind in the article.

EDIT it also means the weight per height remains constant through branching...
this doesn't seem sustainable; you'd want it to taper.

~~~
oasisbob
I like your train of thought. You absolutely want the right amount of taper.

Regarding wood strength being proportional to area: it can't be as simple as
that - wood is a strongly anisotropic material, so direction of loading
becomes critical to understanding what's going on.

Natural trees have defects, and they "know" it. Limb attachment is messy
business - in many species they are frequently defective. Doesn't reduce well
to modeling actual limbs as simple beams or whatnot.

Starting to understand thigmomorphogenesis and how trees deal with it in terms
of load shedding, compartmentalization, and reaction wood growth was one of my
favorite "ahhh ha" moments.

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SNACKeR99
It occurs to me this could be a metaphor for code complexity at various levels
of abstraction. I'm picturing a recursive method that:

\- calculates LOC of a top-level method \- calculates lines of code for each
method called within that \- builds an hourglass visualization showing as you
go up or down the abstraction layers how the LOC changes

It seems like this might be useful for seeing \- where in the abstraction
layers there are major changes in density of functions \- where there is over-
abstraction (many, many tiny functions) \- where there is not enough
abstraction (a bulge in LOC, or overall large numbers)

Combining this with cyclomatic complexity may provide a more nuanced view for
code analysis. It would allow you to quickly hone in on parts of the code-base
that have too much density.

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scotty79
It's surprising for me that this is new idea. Wind is the main thing trees
oppose (besides gravity and each other). It should be first idea that this is
the thing that shapes them.

This might be one of the cases when weird experimental "law" drives people
away from the actual cause.

I always felt the same way about Kepler's laws. While they are true, you can't
find in them any trace of actual reason why things are the way they are
(conservation of energy and angular momentum in gravity field).

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n4r9
> While they are true, you can't find in them any trace of actual reason why
> things are the way they are (conservation of energy and angular momentum in
> gravity field).

Your so-called "causes" seem just to be more general "experimental laws". Does
conservation of energy really make you feel like you understand the reason why
things are the way they are?

~~~
whatshisface
If I told you that your car was propelled by an engine that ran on gasoline,
would you feel any closer to understanding it?

~~~
posterboy
No, because that's profoundly misleading. The car is propelled by the wheels.
Those may be moved by a motor directly or indirectly, but the car is not moved
forward by the explosion of gas directly, there needs to be a transformation
of the energy into circular motion. There are many many different types of
motor, so the specifics may be detailed. But for a naive explanation, you
could just say "fire".

I wonder how difficult it is to build wooden axis and hinges that overcome the
force of friction in old carts.

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diroussel
Why should this have anything to do with wind. It would seem to me that he
conservation of cross sectional area is because all the capillaries need to go
from root to leaf.

If the area above a branching point was more than below then how would those
capillaries going up to the leaves be fed?

If the area above a branching point were less than blow then how would the
capillaries going down to the roots be fed?

Remember the roots fees the leaves and the leaves feed the roots. So it needs
to be a balanced system.

~~~
conscion
From the article

 _Although researchers have previously proposed explanations for the rule
based on hydraulics or structure, none of these explanations have been fully
convincing. For instance, the hydraulic explanation called the “pipe model”
proposes that the branching proportions have to do with the way that vascular
vessels connect the tree’s roots to its leaves to provide water and nutrients.
But since vascular vessels account for as little as 5% of the branch cross
section (for large trunks in some tree species), it seems unlikely that they
would govern the tree’s entire architecture._

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coldcode
Amazing that someone 500 years ago was both interested in and had the
analytical skills to propose a rule we are still trying to understand today.

~~~
Tor3
.. and that "Someone" was nearly always the same guy: Leonardo da Vinci. He
must have been maybe the most curious man ever.

~~~
jacobolus
A few notes:

* 500 years ago there hadn’t been intensive centuries-long studies of many of these phenomena, so if you wanted to know something about it the only way was to do independent investigation.

* Even for subjects which had been studied, books were rare/expensive, poorly indexed, often contained a mishmash of disorganized material, hard to track down, and often flagrantly wrong but remaining uncorrected for centuries.

* Leonardo was notoriously bad at sticking with any project, from his childhood on, easily abandoning his work and jumping to another topic, including leaving many of his paid projects unfinished. Probably serious ADHD.

* There have been many intensely curious polymaths, but in many cases they didn’t take proper notes, the notes were lost/destroyed, the notes are buried in an archive somewhere where nobody reads about them, ...

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dhimes
Is there variation in areas where the winds are low compared to where they are
high?

~~~
kevin_thibedeau
Monterrey pine grown in it's natural costal habitat is gnarly and unsuitable
for lumber. The same tree grown on plantations outside the US produces
straight grained "radiata" pine lumber.

~~~
dhimes
Am I correct in assuming that the natural coastal habitat is windier than the
plantations?

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oasisbob
I find the article and paper somewhat frustrating.

It doesn't say anything new about da Vinci, and it sure doesn't seem to add
anything which isn't already an accepted idea in biomechanics. The article
revives vascular constraints as a strawman before beating it down again, as if
it's still a theory of limb structure thats taken seriously.

My takeaway: da Vinci's rule is easily explained by modern foundational
biomechanics.

~~~
zwischenzug
What's the beat-down?

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arketyp
If you'd imagine the growth somewhat like a material paste, if the material
flow is constant and if the branches grow with equal length, then da Vincis
rule follows, no matter the individual branch girth. I suspect da Vinci wasn't
observing this as much as arriving how it ought to be.

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lcnmrn
Gravity and wind. Wind alone doesn't explain it.

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gameswithgo
I would have just assumed 'divide by two' was the most likely genetic accident
to fall into place and it worked fine.

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zwischenzug
I thought this had been explained by how this setup maximizes the efficiency
of the respiratory system.

This was discussed in a great book I read called Scale:

[https://www.amazon.com/Scale-Universal-Growth-Organisms-
Comp...](https://www.amazon.com/Scale-Universal-Growth-Organisms-
Companies/dp/014311090X)

the human vascular system follows the same rule iirc.

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deytempo
Shouldn’t that be in reverse? I’m pretty sure Wind came before da Vinci

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anc84
That website almost freezes Firefox for me after a couple of seconds.

And I cannot do a JavaScript profile as it just locks everything...

~~~
syoc
I experience the same on FF 62.0.3 MacOS. Running uBlock and uMatrix and some
other add-ons so I think there might be some less then stellar first party js
to blame.

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anc84
Also using those. Weird!

