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> A bicycle is an incredibly simple visual form

I disagree, compared with most objects a human daily interacts with - doors, furniture, lifts, cars - a bicycle is one of the most complex visible forms. I'm talking about what can be seen from outside, since obviously a car is much more complex on the inside.

Most of the stuff we deal with is composed of square/boxes and circle/tubes. Triangular shapes are quite rare in human spaces (I don't have any in my house), and the bicycle critically has two triangles at it's core. Chains are also very rare. So I don't think it's a surprise that many struggle with the core - two triangles and a chain.

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Clench your fist. Take a moment to notice the complexity of the geometry. Consider how you might reduce that shape to simple geometric forms. Consider how you might represent the three-dimensional form as a set of two-dimensional lines. Turn your hand around and look at it from a different angle. Open your fist and make an "OK" or a "peace" sign.

Go to your refrigerator and take out a lettuce leaf or a piece of broccoli. Look out of your window at a tree or a bush. Go to your bathroom and look at the toilet or the faucet. Look in the mirror and make a funny face.

A bicycle is more complicated than many rectilinear man-made objects, but it's a relatively straightforward collection of lines. Even the drawings in the linked article with their horribly mangled geometry are immediately recognisable as a bicycle. It's not a difficult thing to draw, relatively speaking.

You conflate geometry and topology * . The topology of the human hand is right in front of you to examine. A lettuce leaf is like a disk plus a wavy boundary and noise. Broccoli is a tree. A bicycle is topologically complex object with high genus. A bad drawing of a hand can still has the right connectivity, it could be smoothly deformed into a realistic hand. Not true for most of these bicycle drawings.

* using "topology" to refer to the graph structure of the skeleton of the solid, not the typical mathematical meaning.

> it could be smoothly deformed into a realistic hand.

It's probably a good thing that this isn't what defines a drawing as good. A bicycle frame has a couple straight lines and that's about it. A hand, or broccoli, has complex compound curves all over the place.

Ask any artist to draw a bicycle and it'll probably end up pretty good. Ask any artist to draw a hand and there's a good chance it'll not end up good, even when using reference material.

There's a reason a lot of artists have problems drawing hands.

Hands aren't hard to draw because hands are super complicated; hands are hard to draw because humans are evolutionarily finely tuned to recognize and be disgusted by distorted human bodies, which in nature is a signal of disease. Look at the diversity of broccoli proportion at the grocery, then imagine hands with the same diversity -- grotesquely long or lumpy or twisted, which too few or too many fingers. OTOH, cartoon hands, outside the uncanny valley, look fine, even when (as is common) missing a finger.

They just need to pull the Escher trick and draw a hand that can draw hands.

That maybe because hands have a dynamic form/shape while a bicycle has a static form and is thus easier to remember or draw.

> Look out of your window at a tree ...

> Even the drawings in the linked article with their horribly mangled geometry are immediately recognisable as a bicycle. It's not a difficult thing to draw, relatively speaking.

I guess, the point is that a bike is easier to draw that natural objects.

I bet if people had been asked to draw a tree, 100% of the pictures would be recognisable as proper tree. Conversion from reality to visual representation is not only a function of object complexity it is much more complex (pun intended).

Ah, this is where it gets interesting.

I suspect the author of the (wonderful) book linked above would suggest that 100% of the pictures would be recognizable as a _picture of a tree_ -- a form which we all learn by age 5 but which does not actually correspond to a physical tree much, if at all.

Exactly. We don't learn to draw the tree we see out of the window, but the idea of a tree. Children don't really draw - they write in pictograms. We teach them icons that represent things, but we don't teach them how to translate seeing into drawing. The bicycle drawings show how quickly that habit of drawing the idea of a thing breaks down.

We falter when we try to draw something that we haven't learned the "correct" pictogram for, because our mental concept of the thing is completely divorced from the appearance of the thing. Most adults can just about draw a chair isometric projection, because they learned how to draw a cube. That crude model of perspective usually falls apart when they try to draw a dog - they know that it's supposed to have four legs, but they can't work out where to put them. You end up with a drawing like this:

https://ellenhenderson.files.wordpress.com/2011/11/dog_new1....

> The bicycle drawings show how quickly that habit of drawing the idea of a thing breaks down.

That's because the idea is vague in most people's mind. The don't really care (and they shouldn't need to of course). Ask a bike engineering to draw it, and they will be pretty accurate. However, the people whose idea is vague doesn't know it's vague, which is interesting, and I guess that's the point of the article.

In fact, this translates to much more than drawings, but for all facets of any complexity. You often hear people claim that a particular problem is easy, "just" do X!

That dog's legs seem fine, once you consider the (over-constraining) constraints of drawing using a single outline with no 3-D / z-layer structure.

If your goal was to point out how much more complex a hand is than a bicycle, I don't think that logic follows. Drawing hands are hard too!

Drawling lettuce? Lettuce doesn't have obvious structural flaws if you get the veins wrong. A green blob with a few lines will pass the test a lot easier than these bicycles.

If you want to draw a line-drawing of a hand vs a bicycle, the hand is much easier - four parallel fingers off a palm, with a thumb off at an angle.

The bicycle is much more complex geometrically - wheels in tandem, triangular frame, relationship with seat, handlebars, tire forks, sprockets and chain, pedals, brakes & brake handles if you're picky...

A photorealistic hand is hard to draw/render because of the complexity of the materials and curves, fine texture like hairs, freckles, pores, fingernails, etc., but you wouldn't expect or get those asking your 30 people to take two minutes and draw a hand.

> Triangular shapes are quite rare in human spaces (I don't have any in my house)

Triangles are essential in low-weight rigid structures. Look at any exposed steel construction around you (a bridge, perhaps) and you will see many triangles. The utility poles and streetlights in my neighbourhood use triangles. Unless your house has a flat root, the upper most floor is likely composed of triangles (called trusses) that you can't see because they are hidden. (They would be easy to spot in barn.) Even the desk I am sitting at now has triangles to ensure the legs don't collapse if the desk is shoved sideways. If you happen to live in a seismically active place, you would likely see triangular bracing on many buildings. And finally if you (or your kids) have even done one of those engineering challenges in school where you have to make a tall, load-bearing and light-weight structure on a budget you likely used triangles. Triangles are everywhere, if you learn to see them.

And as for the main point of this post - one reason to learn to draw is that it forces you to really see what you are drawing. Drawing from your imagination is no substitute.

> Triangular shapes are quite rare in human spaces Not a football fan, eh? Triangles are the essential building block for breaking down defenses. </bad_joke>

As for what you actually meant, triangles (and other variations of 3) play a very import role in visual design. Admittedly, these might not be obvious to most. I know you really meant physical items. However, it might be a style of design of a more modern era. I have a glass coffee table that has a triangular raised extension, from the 50s I believe. I also have a round two tier table, built by my grandfather in the 50s as well. The top tier sits on an X shaped pier with 90 degree notches cut out of the verticals leaving a very distinct triangular shape, plus the gaps of the X shape as well. Just from memory, the cars from the 50s had lots of triangular shapes/markings, specifically thinking of the fins. I wonder why the triangle seems to have fallen out of favor?

Even for cars, it's hard to get the relative positions of wheels and windows and the hood right on the first try.

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