Libertarians Read, Right? Then Read This

baraka wrote:

Consider Pythagoras's theorem.......Pythagoras's theorem actually fails spectacularly in spherical geometry as is easy to see. Consider a right angled triangle, the base lying on the equator and the apex at the north pole. The two sides from the apex to the base always meet the base at right angles, and they always have the same length irrespective of the length of the base, hence the Pythagorean theorem fails to hold 'in the real world.'

Here is an example of theoretical physics that has no basis in the observed data of the real world that is interesting to me, topological quantum field theory. Firstly, there is no observational data to imply that string theory is correct, and secondly a 2-d TQFT is a functor from a category whose objects are (finite) collections of circles and whose morphisms (think of this as evolution in time) are given by riemann surfaces with certain openings. None of those objects were invented to describe physical phenomena directly, and arguably they still aren't being used to describe physical phenomena.

As for other things: category theory was not developed with the intent of doing anything for the real world.

Here's another one: is there anything in the real world that is actually a continuum? We pass to the continuous because that makes our life easier.

What about groups? Groups were invented to study the roots of polynomials. Does that make them motivated by the real world? They also describe the symmetries of objects (not necessarily realizable in 3-d real space) so are they based in 'the real world?'

What about schemes? Can you clarify what is necessary for something to be considered applicable to the real world? Would you dismiss the above as math according to your definition?

Ha ha....I work very closely with mathematicians for a living and have had very interesting debates with them. I also have a strong math background myself (formal education). So I've asked these questions, of my colleagues and of my professors. There is no matter of opinion here. To suggest that maths developed with no intent (currently) of doing anything for the real world is 'an opinion' is just wrong. There are mathematical discoveries whose import was not appreciated until much later for a variety of reasons, but it was still accepted as good hard publishable mathematics at the time, then just ignored, or left alone. In fact that is one of the reasons why maths should be free to do what ever it wishes (not adhere to the 'real world') and examine seemingly useless things, (I'm sure in your eyes) since we don't know what may happen later when someone cleverer looks at it.