As I state in my "Why studying and thinking things over is worth the effort" writeup, I firmly stand behind this metaphor. Note, in this writeup I'm linking knowledge and intelligence with memory and understanding and wisdom with experience very loosely so, my apologies if my use of the terms is confusing.

Humans have a vivid imagination, with the capability of visualizing practically anything within the limits of human experience. Yet, imagination and visualization are not the same as true understanding; one can not imagine experience.

What this means is simple: you may know exactly (neurologically and physiologically) what happens when a person sticks his/her hand on a hot oven plate but you do not understand what it really is, until you have done it yourself. If you have, it is possible to recall what it actually felt like and how you perceived the sensation, in addition to knowing everything there is to know about the event. Your understanding has grown deeper than anybody's who hasn't made the same mistake themself.

While it may be intelligent not to stick your own hand on a hot oven plate, after seeing someone else doing it, in a way it is unwise: you will be depriving yourself of an experience. The same applies to just about everything; sex, drugs, skydiving, you name it. This is where "common sense" steps in the ring - some experiences are best left unexperienced. Personally, I wish I will never have to go through - for example - any of the following: death of a child or wife, sexual abuse, long-term imprisonment, drug overdose, psychosis of any kind, becoming paralyzed etc. Some I can prevent with my own actions and decisions, some I have no power over.

To quote "Good Will Hunting" - one of my all time top-10 movies:

"So if I asked you about art, you'd probably give me the skinny on every art book ever written. Michelangelo, you know a lot about him. Life's work, political aspirations, him and the pope, sexual orientations, the whole works, right? But I'll bet you can't tell me what it smells like in the Sistine Chapel. You've never actually stood there and looked up at that beautiful ceiling; seen that."

This is exactly what I mean with the difference between knowing and understanding.

One of the obvious problems may arise from the fact that there are lots of matters that can not be fully understood as they are completely abstract. Take the mathematical point for a perfect example; an object that marks a place in space but has zero size and, thus, zero volume. There is no way for a human to fully grasp the idea of an object that is there (in mathematical sense), but isn't there (in practical sense).

The accuracy of our knowledge of the world is limited by the sensitivity of the equipment used to determine and measure.

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