THIS PART IS KIND OF A RANT, NO NEED TO READ, JUST STUFF I DIDN’T SAY IN CLASS (feel free to stumble through my rant if you want to though)
We’re supposed to describe the ‘Mathematical Method’, but I’m not even sure what math is. There’s a part of me that thinks that it’s simply a social construct. One could counter that thought rather easily, because if you thought about math in an extremely one dimensional fashion, math exists, numbers work, and they repeat. Therefore math can’t be a social construct because it exists and developed separately in different cultures. However, we only experience the world in three dimensions, four if you count time, or more because I’m not exactly smart. The thing is, we don’t really understand our world, and it could all be coincidence that math works for us the way it does. That does mean it’s right or true. We could learn one more simple thing about the world, we could learn something about the way math works considering higher dimensions, and our entire system of math going down to one plus one could be wrong.
In class we discussed how in math, things can be proven mathematically and physically. However, we had an extremely flawed discussion about it that really annoyed me. We discussed the idea that triangles can have different sums of angles based on the shape of the plane they’re on. For example, we discussed triangles on spheres. I think the problem was that the people in the class didn’t understand that mathematically, spheres are two-dimensional objects, balls are the ones that are three-dimensional. Someone in class used the idea that if you cut out a triangular piece of pie crust from a curved pie, it’s a three dimensional object and therefore not a triangle, and rather a prism. Therefore, continually proving that the sum of angles on all triangles is 180 degrees? That got me extremely frustrated but I’ve been working on holding my tongue. Anyways, the entire basis of that argument is wrong because the pie crust is three-dimensional, not two dimensional. Also, the idea that a plane must be perfectly flat is kind of frustrating. However, this was a good introduction into the idea of whether there are mathematical ideas that can’t be proven physically, only mathematically.
THIS IS WHERE I ACTUALLY DO MY HOMEWORK
I guess the mathematical method is Euclidean logic, as in the seven books of Euclid that Lincoln took off five years to read and ponder. Based on that assumption (I’m using Euclidean logic here), the mathematical method is the use of known facts, to extrapolate new facts. For example, I know the sky is blue, because my mother told me so, therefore, anything that looks like the sky is also blue. It’s annoying that I never got to study logic in math class in school, we should really put it into the curriculum. However, I still use this in school, it’s how we learn every single subject. Take science, if mixing water and acid results in an exothermic reaction, and I know that exothermic reactions give off energy. We constantly learn things, and put them together to realize new things. In a way, that’s all learning is, and therefore, everything is the mathematical method.
In that way, one could say that the scientific method, is part of the mathematical method. In the way that people argue the natural sciences are branches of math, simply with dimensions, the scientific method is a branch of the mathematical method. The scientific method involved the use of prior knowledge to gain further knowledge. However, at its’ very base the mathematical method doesn’t have an empirical element. Whereas is science, you test theories, making science seem very different than math, and in my opinion, much less concrete. Because of the empirical nature of science, the use of the scientific method involves degrees of certainty, whereas math doesn’t. However, I’m not completely sure where the line between science and math is. Depending on your definition of math, it does have degrees of certainty. In fact the mathematical method could also be something within the scientific method. Often times you have prior knowledge on a subject (knowledge + observation), which leads to a question, which leads to an experiment, data collection, and conclusion. Math also has all of these elements, except the experiment part is usually the process of solving an equation, and the data and conclusion are the answers. That mostly assumes that math is equations and it’s definitely more than that. Still, this illustrates the fact that math and science are so intertwined it’d be impossible to find a proper difference for “strengths and weaknesses”.
The “strengths and weaknesses” of the mathematical and scientific methods boil down to one main thing, truth. They both attempt to find truth in slightly different ways. One could say that the mathematical method is flawed because it makes assumptions, such as “the sky is blue”. However, the scientific method also makes assumptions, if you’re testing the density of two different balls, you don’t question whether they’re balls, or that they’re what you’re actually measuring. In that sense, they’re equal. One could argue that a strength of the scientific method is trials, however it can never find a perfect truth, and it’s always based off of flawed fact, just like the mathematical method. On the other hand, a strength of the mathematical method is that it doesn’t have degrees of certainty and therefore can have perfect truths if you don’t take into account the degrees of certainty of the original truths.