If you stand outdoors on a clear starry night with a compass and a protractor you can identify any star. [Polar angle] How far do you have to turn clockwise from North to see the star directly in front of you? [Azimuthal angle] How far above the horizon do you have to lift your head to see it head on. [Radial distance] How far away is it? Wikipedia will show you a lot of Greek symbols and calculus equations but what I just said says the same thing in ordinary language.
Remembering what I said yesterday that qualities can be measured in the same way. Which direction is it and how much of it? Take a baseball and cut it in half. Glue one piece to a thin piece of glass and the other piece on the other side of the glass directly adjacent to the first piece. 360 degrees marked on the glass around the baseball. The angle above or below the class on a protractor. The magnitude measured with a ruler.
Any point on that baseball becomes an object of interest. Chocolate ice cream. If you like it there will be an arrow shooting out from the center of the baseball in the chocolate ice cream direction with a magnitude directly proportional to the amount you like or dislike it. Vanilla ice cream might be right next to it. If you like vanilla it will be longer or shorter than chocolate by the amount you prefer it. If, on the other hand, you don't like vanilla the arrow will shoot out of the baseball on the other side of the glass.
Why does this matter? By the time all the likes and dislikes are aggregated the surface of all the arrow points will appear as a lumpy potato rather than a smooth baseball. That lumpiness defines us in more ways than a simple statistical summation.
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will follow up tomorrow with an interesting algorithm about lumpy potatoes and human personalities.
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