Understanding Thought part 2

Idea: Truth Projection

Let us start wth an example:

1. You have 2 apples and 3 pears
2. Someone asks you "How many apples do you have?"
3. You are only allowed to give a number in your answer.
4. What will you respond?

My answer here would be "3 apples" I think. Why?

Let us first agree on some things. If the rule in 3 wasn't there, you'd say "I have only 2 apples, but I do have 3 pears also". Perhaps someone is hungry, baking an apple cake, making apple juice or something else. Here it would be interesting to know about the pears.

The other thing we should easily agree on is that some answers are plain wrong: If you answer "1" or "0" that is (for all possible intents) wrong. If you answer "6 apples", "7 apples", or more, that is also wrong (for all possible intents of the question).

So why "3 apples"? I can picture a range of different scenarios (intents of the question). If the person asking only could eat apples and was hungry (think Death Note), then you would be slightly wrong. The same goes if the one posing the question was in the store and could easily have bought 1 more apple.

What if the one who asked wanted to make apple juice, and he thinks that pears are good too. Well, then 2 apples and 3 pears would make a lot more apple/pear juice than would 2 apples (150% more). On the other hand, 2 apples and 3 pears would make a bit more juice than 3 apples (67%).

In day-to-day life, this doesn't happen with apples and pears, as it is simple to give all the information. But you can never give all possible information, so we try to say what's relevant, and to not say stuff we think is irrelevant

This phenomenon appears clearly in the teaching of mathematics and physics.

Mathematics example: We normally teach that all (positive) functions can be integrated. Some teachers tell the students that there are some (positive) functions that cannot be integrated, but you would never teach what kind of functions these are, so in essence you say "Any function you will ever encounter is integrable". Then when you study some more you learn that there are lots of functions that cannot be integrated. Then you learn that these can actually be integrated, we just have to expand our method of integration a bit. Then you learn that even with this new kind of integration there are some super-strange functions that cannot be integrated.

Physics example: When you learn about electrons on a small scale (quantum mechanics), you learn that they work the way waves on the water works. You can have one big "up" wave meeting a big "down" wards wave, and cancel out. When a wave hits a small opening, it expands out after this opening. But electrons do not work as waves on the ocean; they can be collapsed, they have more directions than just "up" and "down" (they have a kind of imaginary "left" and "right" also).

Often the whole point of being pedagogical is to be able to give the best possible Projection of what you considers to be True, down onto the 'plane' of the listeners understanding.