Qualitative definitions for physical quantities are mere hypotheses. For instance when I say that momentum is a measure of the quantity of motion in a body it makes no sense. Such definitions are retrospective at best and do not truly contain the meaning of the mathematical expressions. The same goes for even more obscure definitions such as mass of a body being a measure of the amount of matter contained in it. It makes much more sense to simply provide a mathematical expression and A measurement methodology. The method of measurement indicates its physicality and the mathematical expression is usually a law of physics. It could be that the means of measurement itself is based out of a law that helps to relate the mathematical quantity in question to other measurable quantities.
Honesty in science ends there. Hypotheses must be seen and recognised for what they are especially by those who do not belong to the scientific community. The world imagines that science is absolute. It is true that the scientist the best we have that the scientific approach lends a flexibility that is absolutely necessary if we have to truly understand the universe.
I have always wondered about mirrors. We speak of lateral inversion but when you stand on a mirror you are seen upside down what would you call that
I have always struggled with having a coordinate system with the three Axis not being at 90 degrees with each other. In such a case how would equations of lines planes and surfaces be
How would you define cos theta
I needed to clarify to myself that even cells are made up of atoms
Organised thought is intelligence
I have always looked for a link between the equations we write and the actual behaviour of bodies in classical physics. We write down some equations and then jump directly into looking for reasons why there are sources of error and deviations between calculator results and actual measurements. I felt that we never stop to think why this even works in the first place.
If I write a textbook or create a video course it will always have a retrospection section. Which would question the shuttle assumptions we have made along the way.
To answer this specific question on why this works it is the law of physics that binds physical behaviour to the medium of mathematics. They so easily say that mathematics is a language in which laws are expressed. In truth mathematics is way more than that.
Mathematics is the intrinsic continuity of reality that allows us to even have a conversation. It is the glue of consistency across reality whose smallest failure can completely break understanding. A language is just a medium of communication. Ideas still exist even if there isn't a common medium to exchange them. Even if there is no language at all an idea can exist in an obscure for that still understood by thought in its own inexplicable way.
However, in the absence of mathematics ideas cannot exist.
I once wrote down a statement that I call Raam's law which simply states simply "mathematics works".
This is not a means for me to feed my own vanity but an opportunity to acknowledge the level of sophistication we are able to go to because of the internship consistency of mathematics. It is to pay respect to a fat that we have overlapped for a very long time and have taken for granted so easily.
