>>>     As for math, would you say that, for example, the branch of mathematics
>>> called geometry studies how the real world works or not?
>
>> Which geometry? Euclidean geometry? Elliptic geometry? Hyperbolic
>> geometry? Some sort of non-homogeneous geometry?
>
>> Pure mathematics studies these geometries purely for their own sake. One
>> or other of them /may/ correspond to the real world.
>
>    The very word "geometry" means "measuring land" (from ancient greek
> geo = earth/land, metri = measurement).

And the very word "atom" means "cannot be cut". Not without a particle 
accelerator, anyway...

(For that matter, "electron" means "amber". Science and technology is 
littered with terms made up of Greek or Latin words, the literal meaning 
of which are utterly inappropriate considering what the term means today.)

> Geometry is one of the oldest
> branches of mathematics (probably only preceded by elementary arithmetic)
> and was, indeed, motivated by real-world applications (such as measuring
> the area of a piece of land and dividing land into equal parts by area).
>
>    If that's not science, I don't know what is.

Personally, I would make the separation that "Euclidean geometry" is a 
mathematical theory, while "the real world conforms to Euclidean 
geometry" is a scientific theory.

(And, for that matter, a scientific theory which has been falsified as 
thoroughly as Newton's laws of of motion have been falsified. In other 
words, it's incorrect, but it's close enough to being correct as to be a 
useful simplification, most of the time...)

Mathematical theories exist independent of the physical world. For 
example, the Manhattan geometry surely doesn't describe any real-world 
situation (except something really abstract like network topology). 
Certainly it doesn't describe the physical shapes we see with our eyes. 
And yet, it is a perfectly valid and self-consistent mathematical theory.

Post a reply to this message