During last TOK lesson we were talking about mathematics in different part of the universe, and whether the mathematics of ours will be still applicable to those parts as well. I believe that in general the basic concept of math would be the same, but the values and quantities involved might be different. For example, if we take gravity (9.8ms^2) on Earth, it applies to objects on the Earth but changes even from the moon (1.6ms^2). The concept of finding the gravity is the same, which is calculating acceleration by height at which the object is dropped and time taken for it to reach the ground. But if we apply the values of gravity to calculate g.p.e or other related quantities, it would vary significantly. Also, the concept of math itself might be different. We’ve talked about a spherical plane in which the triangle’s angles add up to 270 degrees. If this kind of world does exist, then the definition of perpendicular, parallel and the properties of various shapes would be completely different from our plane geometry. If we think about it in terms of dimensions (animation flatland really helped my understanding), the concept of ‘area’ doesn’t exist in 1D world, and the concept of ‘height’ doesn’t exist in 2D world. This is the reason why we find it hard to understand the concept of 4D world with the addition of ‘time’.
Mathematics is really useful to our society and seems like an irrefutable area of knowledge on Earth. However when we enter another world with totally different concept mathematics will be redefined by their environment and concepts.