π is not an invention, it's the relation between a circle's lenght and its radius. Not hard to understand.
The obvious counter-argument is that circles are an invention.
Where is π today? The nature of the mathematical universe
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Re: Where is π today? The nature of the mathematical universe
#22Re: Where is π today? The nature of the mathematical universe
#23Re: Where is π today? The nature of the mathematical universe
#24Earlier quoted context omitted.
The obvious counter-argument is that circles are an invention.
By humans? Do circles not exist without humans to point them out?
Not 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.
Re: Where is π today? The nature of the mathematical universe
#25Earlier quoted context omitted.
By humans? Do circles not exist without humans to point them out?
Not 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.
Well, different characters behave differently in different novels. How is this like an idea of a circle?
Re: Where is π today? The nature of the mathematical universe
#26π is not an invention, it's the relation between a circle's lenght and its radius. Not hard to understand.
The obvious counter-argument is that circles are an invention.
It'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.
Re: Where is π today? The nature of the mathematical universe
#27Earlier quoted context omitted.
Not 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.
Well, different characters behave differently in different novels. How is this like an idea of a circle?
> 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.
Re: Where is π today? The nature of the mathematical universe
#28Earlier quoted context omitted.
The obvious counter-argument is that circles are an invention.
It'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.
None of those things are literally circles, though. If you look close enough there will be a deviation.
Re: Where is π today? The nature of the mathematical universe
#29Earlier quoted context omitted.
It'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.
None of those things are literally circles, though. If you look close enough there will be a deviation.
Water 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.
Re: Where is π today? The nature of the mathematical universe
#30Earlier quoted context omitted.
Well, different characters behave differently in different novels. How is this like an idea of a circle?
> 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 abou…
The 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.