In Cartesian coordinates the mathematical operators such as grad, div and curl all have simple/beautiful forms.

Therefore, is it natural to conclude that space is in some way inherently Cartesian? An image at any scale from atomic to galactic would not support this suggestion.

Is there any other coordinate system in which each of the three coordinates (e.g. x,y,z) have identical properties to each other?


Let's assume that the parallel postulate holds!

It is natural to do lots of foolish things. Why should we do them after we realize our error?

These things you have mentioned are models or tools. Sometimes they are motivated by or used to approximate nature. Sometimes, they were originally just mathematical and have been adapted to some natural phemomenon. Sometimes they do a good job helping us to explain something or to build something or to get somewhere. None of this means we should get ahead of ourselves and start to think we understand the universe. Models and theories come and go.

My views. I welcome others'.

Such operators have "nice" form because Cartesian coordinates are based on straight lines at right angles and our basic calculus formulas are them selves based on Euclidean geometry which makes straight lines and right angles nice. That has nothing to do with "space". In fact, space itself, in the large or near massive bodies is NOT Euclidean nor Cartesian. According to the theory of general relativity, the nature of space changes according to the mass-energy in the region.

Forgive me if I'm wrong, but I think nature is "ugly" in Cartesian coordinates. Take a look at atoms, for example, even the simplest of them are very messy or even impossible to solve in x,y,z. Spherical coordinates, on the other hand, are much more useful in these situation. Electron orbitals are just spherical harmonics. And when we bring in spin, we must throw Cartesian out the window. When we look at a cosmology, cartesian coordinates is once again not useful since space is curved at such scale. I think that nature is not cartesian; however, we do live on a scale that is best describe with such a system. Therefore, many of the equation we use looks nice in this coordinate system. If we were any bigger or smaller, things would look much different.

Thread closed, since this is all nonsense (in that nature knows nothing of coordinates, they are used by sentient being when and if the are useful)

CB

Since I have had a complaint about closing this thread I will amplify my reasons.

This thread is either a category error or a variant of "The Unreasonable Effectivness of Mathematics" question raised by Eugene Wigner (which itself may be the same type of error, but never mind).

For arguments over the Wigner question just google "unreasonable effectivness mathematics", you will find more argument than you can shake a stick at.

CB