Libertarians Read, Right? Then Read This

farfromglorified

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.'

Why would you ever apply a Euclidian theorem in spherical geometry, if you want precise results?

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.

Absolutely. Now, would you say that string theory is correct physics if and when it is shown that it does not describe physical phenomena?

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

Yet it was developed precisely on "real world" concepts, yes? And by real world, again, I'm referring to a given set of rules and structures.

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?

I'm not dismissing any math that is based on defined constants and operations.

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.

I don't think you're understanding me. I'm not questioning theoretical math, nor am I impugning math's uses for hyperbole. What I am impugning is the concept of subjective mathematics -- a mathematical system whose proof lies not in logic but rather in opinion.

baraka

farfromglorified wrote:

Why would you ever apply a Euclidian theorem in spherical geometry, if you want precise results?

I'm sure there is a point here?

farfromglorified wrote:

Absolutely. Now, would you say that string theory is correct physics if and when it is shown that it does not describe physical phenomena?

You mean if it is falsified? If it is proven false, then it is false. My point is a lot of math comes into fruition without recourse to the real world. A mathematician does not consider 'he real world' when doing math, period.

farfromglorified wrote:

Yet it was developed precisely on "real world" concepts, yes? And by real world, again, I'm referring to a given set of rules and structures.

'Real world' concepts do not mean jack to a mathematician, that is my point. It has no bearing on how they perform math.

farfromglorified wrote:

I'm not dismissing any math that is based on defined constants and operations.

Yet you are insisting that it has to apply to the 'real world' and that is simply not the case.

farfromglorified wrote:

I don't think you're understanding me.

And I don't think you understand mathematics But you are right, I don't understand how you can compare how a mathematician does math to your philosophy.

farfromglorified wrote:

I'm not questioning theoretical math, nor am I impugning math's uses for hyperbole. What I am impugning is the concept of subjective mathematics -- a mathematical system whose proof lies not in logic but rather in opinion.

Who said anything about 'subjective math' other than yourself when you first made the shoddy analogy. What I am telling you is that higher mathematics is not as black and white as you wish it to be. There is the concept of 'undefined terms', and you give meaning to those 'undefined terms' using terms of your APPLICATION.