6 ms·
π is not an invention, it's the relation between a circle's lenght and its radius. Not hard to understand.
by elvecinodeabajo 7y ago
π is not an invention, it's the relation between a circle's lenght and its radius.
Not hard to understand.
- n4r9 7y agoThe obvious counter-argument is that circles are an invention.
- EventH- 7y agoExcept that they're not.
- sorokod 7y agoBy humans? Do circles not exist without humans to point them out?
- n4r9 7y agoNot according to the author: > According to intuitionism, mathematical objects are products of our mind, like characters in a novel. I agree, as far as it goes... > Fictionalism holds that the mathematical universe is a collective fiction, like Star Trek or Game of Thrones.
- sorokod 7y agoWell, different characters behave differently in different novels. How is this like an idea of a circle?
- n4r9 7y ago> the Cantor set or the Borel Hierarchy is like the USS Enterprise or the Iron Throne. In fact Star Trek fans talk of the Star Trek universe and GOT fans of Westeros and they talk like these places really exist. You're right, it feels like quite a loose analogy, and only holds when discussing a "canonical" fictional universe. Still, I'm sympathetic to the idea that when we're talking about a circle we're talking about a shared abstract understanding rather than something which objectively exists.
- elvecinodeabajo 7y agoThe pupil in the eye. The sun through the clouds. The craters after an impact. The waves when you drop a rock in water. The section of a bamboo stick... And it gets more evident when you go to microscopic world. Some eggs are perfect spheres, as small bubbles in water. I think circles are a real natural shape. Not an invention. Nature brings us all kind of shapes, some of them are discovered studying living creatures, like the scutoid.
- elvecinodeabajo 7y agoThey do. http://www.hemsleyandhemsley.com/assets/Screen-Shot-2014-04-02-at-17.39.09.png http://www.hemsleyandhemsley.com/assets/Screen-Shot-2014-04-...
- elvecinodeabajo 7y agoIt's not a very heavy argument anyway. Circles are in swirls, tornadoes and even the Sun looks like a bright circle looking from the Earth. Water waves draw circles when you throw a rock in it. Circles are everywhere. Some people says "nature hates perfect shapes" but it's not true, nature creates perfect cubes in some minerals, some fish eggs are perfect spheres... And so on.
- n4r9 7y agoNone of those things are literally circles, though. If you look close enough there will be a deviation.
- elvecinodeabajo 7y agoWater waves are perfect circles as waves move at same speed in every direction, so its points are always equidistant. Let a soap bubble settle in the table and take some measurements with a ruler. They are almost always perfect circles. You can deny they're circles, but you know it's not true.
- n4r9 7y agoThey're not actually perfect circles. They're very close, but at an atomic scale there are clear imperfections.
- elvecinodeabajo 7y agoAt atomic scale sometimes there are perfect cirlces. The argumentum a silentio fallacy is bidirectional in this case.
- n4r9 7y agoEven at atomic scales there are always minor distortions due to external influences. For example, although the shape of an electron s-orbital is said to be a sphere, the only way this could theoretically be a perfect sphere is if the atom is and always has been completely isolated from all external fields and forces.