Featured image is Children on Bicycle by Ernest Zacharevic

You have, in your head, a model of a bicycle. Two wheels, a frame, handle bars, pedals. If you’re like me your model includes some extras that aren’t strictly necessary to a bike, like gears, a chain, a gear shift and brakes, but we can leave that aside. You might even have a particular bike in mind, with a particular colour, a particular number of wheel spokes, with a particular rider, in a particular place going to a particular location.

If you have some basic dynamics training you can even make a bit of an explicit model of how that person would ride a bike, using the force of the legs as applied to the pedals, the friction with the ground, the various moments of inertia of the wheels and frame, and the center mass and center of volume of the rider/bike combo. Perhaps you have even heard some stories about more exotic varieties, tandem bicycles or pennyfarthings or butcher’s bikes and the like, which follow the same basic models, though with completely different parameters.

It’s a mistake to think this has anything at all to do with the model you actually use to ride a bike. That model doesn’t have colours, or chains, or even wheels. The bike is stripped down to the most basic elements needed to control it, the handle bars and the pedals (depending on the bike there may also be a handbrake and a gear shift, but these aren’t essential). Your brain does a complex calculation on the senses available to it, of the stresses on muscles, the fluid in your inner ear and the relative angles and motion of nearby objects which it combines to form a sense of balance. Riding a bike is a complex mapping of this sense of balance to action, a negative feedback loop between your hands, the handlebars, your body’s position on the bike and the feeling of imbalance.

You may understand on some level that the handlebars are attached to the front wheel, and turning the handlebars causes the wheel to turn, which causes the bike to turn which results in a centrifugal force restoring your balance, but that kind of formal chain is utterly unnecessary to the learning. When you feel such and such and imbalance, you turn the handlebars so far, which restores the balance. You turn the bars to turn the bike, which produces a centrifugal force, and so you shift your weight to restore the sense of balance. Similarly, you are going too slow, you push harder on the pedals, you are going too fast, you ease up on the pedals.

The exact mechanics by which a bike works might be of interest, depending on what you want to do. Understanding the mechanics of angular momentum can let you build gyroscopic self balancing bikes for use by the disabled for example. Understanding gearing allows both more torque or more speed depending on the situation. Understanding how a wheel works, while non-essential to control, can help anticipate the ways in which you will be required to react to a mud puddle, or a patch of gravel. But none of these extra elements will make their way back into the riding model. What use would they be?

The vast majority of our mental models work in this way. It is thoroughly a calculation, a learned series of simultaneous equations and feedback loops that don’t produce a thought, but a feeling and (unless you can consciously suppress it) an action. The model you require to explain exactly how many degrees you would need to turn the bike handles to stay upright is fairly complex, and knowing how to perform it wouldn’t help you not fall down next time. You probably haven’t the slightest clue what the moment of inertia around the relevant axis is, and unless you’re a civil or mechanical engineer probably don’t even know how you would go about calculating it. You just felt like you were falling over and turned the handlebars until you didn’t feel that way anymore.