In nature, I have rarely seen 90 degree angles (a few exceptions are the plants and trees coming straight out of the ground) I suppose this angle provides the path of equal lateral stress on the organism during growth while reaching for the sun, but beyond the main trunk or stem... obtuse or acute angles of every sort. At bifurcations, almost always acute angles to maintain upward trajectory. With spacing angles between lateral branches taking obtuse angles to set up solar panels without self-interference.
With my puppy, similarly, acute and obtuse angles: corners of eyes, outlines of ears, angles ears make with each other, folds of skin/fur. Also, a commonality in nature are smooth flowing lines, graceful like a dancer. Even the gnarled tree branches resemble the twining eagle arms yoga pose. The structural pieces vary from curved lines to straight lines, but still they have flow. For example, a blackberry stem - strong, thick, flowing and supportive of the intricate blackberry leaves with its acute and obtuse angles, and curved lines of the blackberry itself. Is there a more general pattern at large here?
Generally straight bones --> Obtuse/Acute flowing Musculo-vascular system --> generally curved lines of adipose tissue & skin/fur/feathers/scales.
Generally straight bones --> Obtuse/Acute flowing Musculo-vascular system --> generally curved lines of adipose tissue & skin/fur/feathers/scales.
Generally straight stems --> Obtuse/Acute flowing branches/leaf shapes --> generally curved lines of fruits.
How interesting!
Human-made objects are a different creature: I've noticed many more 90 degree angles. I suppose this pattern probably plays a functional role for efficiency as well as strength. Take the stone table top on this bench at school. To get from the top of this shape to the bottom is 180 degrees total: Let's imagine the edges would be more decorative with a nice 45 degree slope (instead of 90). Now, it's less aggressive on top, but more aggressive (sharper? more dangerous?) on the bottom angle with it now being a 135 degree turn to reach the bottom side (or counting the interior angle - a sharp 45). Perhaps this means we want to make a second cut to lessen the sharpness of the bottom edge with another 45 degree angle cut. Well, now it's less aggressive, but required two cuts - also, if you lean on the edge, you'll have a single line of pressure across your abdomen. Instead, bringing back the single 90 degree cut means less processing and functionally more comfortable to lean against.
90 degrees seems like a good trade for efficiency of tool power while maintaining structural strength whether it is with compressive...
If we did not need to use tools (or weren't given the luxury), would our human-made world look vastly different in terms of construction? Would we be constrained to the grid? I imagine I could research the first structures made by ancient cultures for shelter and witness the angles and lines used.
Oh! A thought occurred: when constructing survival shelters (ie. lean-to) the angles do look quite different. There is a uniformity to stacking and laying logs and detritus, but in terms of support, unless you're driving support columns into the ground (like a tree would grow naturally), everything more resembles natures angles of acute and obtuse angles. Huh! That's funny!
Oh! A thought occurred: when constructing survival shelters (ie. lean-to) the angles do look quite different. There is a uniformity to stacking and laying logs and detritus, but in terms of support, unless you're driving support columns into the ground (like a tree would grow naturally), everything more resembles natures angles of acute and obtuse angles. Huh! That's funny!
Source: https://www.outdoorlife.com/wp-content/uploads/2019/01/23/IOT7YTOGKMQYAD2HOAQNDQDML4.jpg?strip=all&quality=85
At what point does the pattern switch?
At which point does human-creation want to demonstrate otherness in construction?
In history, tool-use is considered advanced... so does that mean 90 degree angles are more advanced than nature?
With even more advanced tool use, we construct complex structures that yet again resemble nature as inspired by nature (ie. Science world in Vancouver, Bird's nest stadium in Beijing by Ai Weiwei, etc). At what point does it (tool use, building techniques, human-mentality of otherness to nature) come full circle and witness nature as inspiration as master-builder again?
Source: https://images.spaicelabs.com/images/flus6j8v/production/83ae119450b402c12531174975b44cab84b26d1e-1920x1438.jpg?rect=241%2C0%2C1438%2C1438&w=3840&fm=webp&q=75&fit=max
Source: https://www.re-thinkingthefuture.com/wp-content/uploads/2024/01/3.-Beijing-National-Stadium-Beijing-cover_900_584.jpg?w=999
Perhaps I could teach my students to learn about lines and angles in a hand-out using these same guiding questions provided by Dr. Gerofsky as they led me to some interesting conclusions with good reflection:
- What kinds of lines and angles did you see in most living things?
- What kinds of lines and angles did you see in human-made things?
- Are there typical lines and patterns that show up in living things vs. human-made things?
- Are there exceptions to your pattern or trend?
- Why do you think these trends exist in nature?
- Why do you think these trends exist in human-made things?
- Have you seen human-made things inspired by nature? If so, what makes them "different" than typically human-made things? If not, google it and report back!
Source: https://pyxis.nymag.com/v1/imgs/93a/6e1/da8f39123264bbe2d28b10fa84d6b18278-strat-investigates-snail-mucin-01.rsquare.w400.jpg
Thinking about ways to experience lines and angles through whole-body movement or large body motions outdoors, the first thought that came to mind was to create an interactive lesson hook involving full body yoga. Here's a potential framework for the lesson:
1) Warm-up with yoga in a large space.
2) Afterwards, breakout into small groups with the new repertoire of yoga flow and analyze the movements that they attempted to perform.
Perhaps a categorization of movements with a question set like this:
- Which positions would you associate with acute angles?
- Which positions would you associate with obtuse angles?
- Are there any positions that resemble human-made things as discussed previously?
3) Construct their own positions/movements inspired by nature's creations. Chain-them into a flow.
Or using the poses from the example flow, create themed flow sets for exploring angles from smallest to largest.
Or using the poses from the example flow, create themed flow sets for exploring angles from smallest to largest.
That's all for now!
Hi Oliver!
ReplyDeleteYour sketch is amazing! You are such a talented artist! I like the idea of comparing angles between human-made things and natural things. Indeed, there are more right angles in human-made things --- I’ve never realized this, but it makes so much sense! As you said, 90 degree angle is a good trade for the efficiency of the tool power so people intentionally use right angles in building things. By looking at those comparisons, I also started to wonder if some of the human-made things are influenced by nature. Depending on the local geographic structure and land, people have to optimize a way to construct something that fits the environment best, which means humans can never be isolated from nature.