Position, Velocity, Acceleration, Jerk, Snap

The sensation of hitting your pinkie toe on the corner of a sofa may seem unrelated to the concept of derivatives, but in reality, it has everything to do with it. The reason is that our sensors are not as sensitive to familiar stimuli as they are to new ones. This phenomenon is known as sensory adaptation, which is a reduction in sensitivity to a stimulus after constant exposure to it. Sensory adaptation helps free up our attention and resources to attend to other stimuli in our environment.

A similar concept applies to the way we experience life. Our bodies are only interested in the "delta," or the rate of change that happens to us. For example, the first time you go on a plane, it is an amazing experience, but the last time, it is not as memorable. This is not the pilot's fault, but rather a result of our numbed senses, as we are not excited by anything less than 2Gs. However, a next flight on a fighter jet pulling 5Gs will be amazing again, as the delta of 3Gs makes all the difference in how we experience life.

This is the same reason why the most skilled daredevils often meet their demise while performing the very stunts that they excel at. Since anything less or equal to the last stunt doesn't feel good enough, they push for the next change in state of familiarity.

In physics, position refers to the location of an object in space and is often measured in terms of coordinates such as x, y, and z. Velocity is the rate at which an object's position changes over time and is measured in units of distance per time such as meters per second. Acceleration is the rate at which an object's velocity changes over time and is measured in units of velocity per time, such as meters per second squared. Jerk is the rate at which an object's acceleration changes over time and is measured in units of acceleration per time, such as meters per second cubed. Snap is the rate of change of Jerk over time and is measured in units of Jerk per time, such as meters per second to the fourth power.

In conclusion, hitting your toe on the sofa only hurts because you don't hit it often enough. So, practice makes perfect, it seems. Our bodies and minds react to change and the rate of change, and understanding this concept can help us understand and appreciate the world around us in a deeper way.