Pythagoras' Theorem. Evidence of elsewhere or our ingenuity.

[Rum]

None of the straight lines listed above are actually straight. Even light is bent by gravity.

[MiM]

None of the straight lines listed above are actually straight. Even light is bent by gravity.

Nope it isn't, at least not if Einstein is right. The universe itself is bent by gravity. Light still travels in a straight line through that universe.

[Robert_S]

None of the straight lines listed above are actually straight. Even light is bent by gravity.

I thought that light traveled along a straight line (shortest distance between two points), but that it was space that was curved.

But then again, there aren't even lines in nature. We use the word "line" to describe patterns, trajectories, and so on. But there are no actual lines when you look close enough.

[Rum]

None of the straight lines listed above are actually straight. Even light is bent by gravity.

Nope it isn't, at least not if Einstein is right. The universe itself is bent by gravity. Light still travels in a straight line through that universe.

I think you miss the point. Relative to an outside observer it does indeed bend.

[MiM]

None of the straight lines listed above are actually straight. Even light is bent by gravity.

Nope it isn't, at least not if Einstein is right. The universe itself is bent by gravity. Light still travels in a straight line through that universe.

I think you miss the point. Relative to an outside observer it does indeed bend.

Outside of what?

[MiM]

But then again, there aren't even lines in nature. We use the word "line" to describe patterns, trajectories, and so on. But there are no actual lines when you look close enough.

I think this is a kind of human hubris of which solipsism is the extreme. Obviously thoughts does not exist if nobody is thinking them, but just as obviously the cosmos doesn't give shit about us and our thoughts. If all life on earth will be annihilated tomorrow, the earth will still revolve around the sun obeying the same physical laws as always, and so will the other planets, and Pluto. And the number of bodies heavier than Pluto doing so will still be the same, even when nobody is counting, or defining "number" and "heavier".

[Svartalf]

My head hurts now.

[Sean Hayden]

It's not immediately obvious to me why a restriction on the number of possible maths would indicate that it was anything more than an invention. It's clever but I don't think it works.

Of course I'm tired and stupid so it'll take me awhile to flesh out why.

[Xamonas Chegwé]

None of the straight lines listed above are actually straight. Even light is bent by gravity.

Nope it isn't, at least not if Einstein is right. The universe itself is bent by gravity. Light still travels in a straight line through that universe.

No, quanta of light (photons) take every possible path between one point and another! It is only when they interact with another particle that their position becomes fixed - for all of the space between their creation and their destruction, they are literally everywhere at once (with varying probabilities.)

And, to take the general relativity stance instead of the quantum mechanical one, light travels in geodesics, not straight lines. It takes the shortest route, not the straightest, that route being defined by the relative positions of the matter in the universe and its associated gravitational field.

[MiM]

It's not immediately obvious to me why a restriction on the number of possible maths would indicate that it was anything more than an invention. It's clever but I don't think it works.

Of course I'm tired and stupid so it'll take me awhile to flesh out why.

If it's purely an invention, what would restrict it?

[MiM]

None of the straight lines listed above are actually straight. Even light is bent by gravity.

Nope it isn't, at least not if Einstein is right. The universe itself is bent by gravity. Light still travels in a straight line through that universe.

No, quanta of light (photons) take every possible path between one point and another! It is only when they interact with another particle that their position becomes fixed - for all of the space between their creation and their destruction, they are literally everywhere at once (with varying probabilities.)

And, to take the general relativity stance instead of the quantum mechanical one, light travels in geodesics, not straight lines. It takes the shortest route, not the straightest, that route being defined by the relative positions of the matter in the universe and its associated gravitational field.

That's why I started by saying "it's a darned good approximation"

But isn't the shortest route also the straightest? I thought that was how we define straight.

[Xamonas Chegwé]

(although, it's been a long time since i did any maffs).

You gave up checking your change then?

[Xamonas Chegwé]

None of the straight lines listed above are actually straight. Even light is bent by gravity.

Nope it isn't, at least not if Einstein is right. The universe itself is bent by gravity. Light still travels in a straight line through that universe.

No, quanta of light (photons) take every possible path between one point and another! It is only when they interact with another particle that their position becomes fixed - for all of the space between their creation and their destruction, they are literally everywhere at once (with varying probabilities.)

And, to take the general relativity stance instead of the quantum mechanical one, light travels in geodesics, not straight lines. It takes the shortest route, not the straightest, that route being defined by the relative positions of the matter in the universe and its associated gravitational field.

That's why I started by saying "it's a darned good approximation"

But isn't the shortest route also the straightest? I thought that was how we define straight.

Straightness is an ideal. As has been claimed by others, it does not exist in nature. It is a very good approximation indeed when it comes to the human scale on Earth - but it is still an approximation.

The shortest route through curved space well is not straight - and all space is curved to some degree - in 4 dimensions.

[Sean Hayden]

If it's purely an invention, what would restrict it?

My first thought is usefulness, what it describes.

[MiM]

If it's purely an invention, what would restrict it?

My first thought is usefulness, what it describes.

But that is exactly my point. If it is restricted by what it describes, then it's not purely an invention.

Obviously you can create any kind of mathematic system system by choosing arbitrary axioms, but asfaik there has been no basically different systems devised that describes our world in a useful way. That is exactly why I believe there is an element of discovery in mathematics.