What's More Fundamental - Math or Science?
I love this webcomic.
It brings up a great debate about what is more fundamental - math or science. This is a great question to bring up to students. It sparks debate and really showcases biases that students may have. Why are mathematicians "all the way over there"? Students that love science seem to really think it is more fundamental especially if they hate math. I have had a colleague argue this case for social science. It also helps show the reasoning behind why mathematics is such an important field of thought.
Anyway, here's my take on the argument...
What is the relationship between the circumference of a circle and its diameter?
Please note, I am completely against using pi and much prefer tau for its more fundamental-ness, but for the sake of people reading this, I will stick with pi.
Anyway, back to the question.
The ratio of circumference of a circle to its diameter comes out to be roughly pi (based on the preciseness of the circle, of course).
Was pi created by man or discovered by man? This is another great question for students. It really forces them to think logically and question their own beliefs.
I don't know the exact history of pi, but I do know that pi was first thought about in the B.C.E.
Obviously, if pi was invented, then the people that made it would have supreme power over the universe. This would mean they made it so that every circle or circular object that has come into existence follows this relationship. Though highly unlikely, I'm sure some irrational people can make that claim the pi was invented.
Pi was found. We found an interesting trinket of the universe that we can/do use to make other discoveries, then use these discoveries to design stuff that can ultimately be built into something that can somehow make our lives easier. If pi wasn't found then, it still would have been there waiting to be discovered.
If it is assumed that a physical object that forms a circle always follows this ratio, then the "rule" was invented by the universe. If this "rule" was invented by the universe, then those people of the B.C.E. simply discovered it. They discovered something that is and translated it to a language that we can (hope to) understand - mathematics. So if the language that the universe "talks" to us with is mathematics, then everything in the universe can be described with mathematics (if we were clever enough). This would mean everything is quantitative in nature including anything described qualitatively. That may close the whole quantitative vs. qualitative argument too. :)
Science is simply trying to find the relationships between the different variables that exist in the universe that are detectable by us. These relationships are all quantitatively based on the universe's language, which means math would be more fundamental.
I purposely picked the easiest relationship I could think of. If one wanted to, one could replace the relationship of the circumference of a circle and its diameter with the relationship of energy and rest mass (E = mc^2) or possibly the relationship between non-relativistic force, mass, and acceleration (F = ma). Ooo... or maybe even my favorite:
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| click here for a discussion on this |
So... scientists are the discoverers (through experimentation) of relationships based on this universal language that mathematicians are trying to put together through deductive reasoning (not experimentation)?
I guess that can suffice for now.