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In order to quantify beauty we first need to come up with a scientific measure of attractiveness. Why are some things ugly and other things attractive? Attractive means appealing and why do some things cause pleasure visually while others don’t. You can compare attractive objects to find the answer! Some pretty things have an organization to them, a structure to them like a messy room wouldn’t be pretty because there isn’t any structure. With structure it’s easier to separate the objects in your head so it’s not confusing and it’s easy and pleasurable to “think” about (maybe you see confusion so the emotion is created in your mind, and you become confused). What about a star versus a circle? The star is more complicated than the circle. That is why it is more beautiful (a simple circle is clearly very plain compared to a star, so maybe because there is more think about with the star it is stimulating and therefore beautiful. Just think of your mind as a computer, the star would take more processing power to analyze. So what about a circle versus a square? The circle is one line but the square is 4 lines that’s why the circle is more appealing, it isn’t as jagged or rough so feel more cozy with the circle. A square looks flat and that’s unattractive for similar reasons. Rough things might seem unattractive because when you touch them they feel bad (or you could say they are less wholesome in your mind causing them to generate more pain because people want to feel comforted). So your opinion is biased. A circle is easy to think about because you only have to think about one line. Since the star has more lines than the square and it’s more beautiful, so maybe a triangle is prettier than a square (because a triangle looks like a star)? But a triangle is prettier than the circle because it is more complicated. So a square is too complicated, a star is just complicated enough, a triangle is a little less complicated than that, and the circle is too simple. So in order of prettiness there is star, triangle, circle, then square.
You can take that analysis of basic shapes and apply it to all other objects because all objects consist of some pattern of those basic shapes or shapes similar to them. Like the cushions of a couch might be pleasant because they are round and we described the circle as more pleasant than a square because it is round.
More Examples:
A dog would prettier (or cuter, more appealing) than a circle because it’s more complicated than the circle, the circle is too easy to think about. A dog is much more interesting because it has many more lines that flow nicely and is cute. The star, however, is more pretty than the dog because it’s more complicated, the dog might be cuter but since the triangle is structured it is more perfect and therefore more appealing in a pretty way, instead of a cute way like the dog. The dog is one wandering line but a triangle is more structured and structure is going to generally be considered to be more pretty and appealing. The star/triangles however with its structure is harsher to look at with the sharp edges, a dog doesn’t have any sharp edges. Like wrinkles might be considered to be uglier than a plain face because the plain straight face is cleaner and more structured.
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