Rain or triangle

About this video

Ana asks her brother two questions. "Is it raining in our street right now?" He goes to the window to look. "Does every triangle have three sides?" This time he doesn't move. He doesn't measure triangles, or count the sides of a hundred of them to be safe. He just says yes.

Some things you can only find out by looking at the world, with your senses or by asking someone who has: whether it is raining, how many people live in Cairo, the colour of your neighbour's car. This is knowing by looking (a posteriori). Other things you can know by thinking alone, once you understand the words: every triangle has three sides, because that is what "triangle" means; 5 + 7 is 12, which you can work out in your head. This is knowing by thinking (a priori, Latin for "from what comes before" - before looking).

The strange thing about knowing by thinking is that the world can't surprise you. Count the people in a room, and someone may walk in and change the count. But nobody will ever find a triangle with four sides: if it had four sides, it wouldn't be a triangle. That is why maths is mostly knowing by thinking.

Knowing by thinking isn't magic. You had to learn what "triangle" and "seven" mean, and everyone has added up a bill wrongly. The difference is in how you check: you check "it's raining" by looking again, and a sum by working it out again. This video goes with the Knowing by Thinking lesson of Knowledge Level 2 on Knaph.

Transcript

1. 0:00Two questions. Is it raining outside? Does every triangle have three sides?
2. 0:05For the first, he goes to the window. That's knowing by looking.
3. 0:11For the second, he doesn't move. That's knowing by thinking.
4. 0:17A new person can change a count. No triangle will ever have four sides.
5. 0:23Both can go wrong. Check a look by looking again, a sum by redoing it.
6. 0:29Some things you know by thinking. Most, you have to look.