> If someone had just gotten lucky and just happened to plot mass vs velocity to recover the laws of gravity we'd still include it in all the science textbooks.
I am not so sure it would have been a hit as a stand alone formula. Newton discovered calculus and used it to lay the groundwork for almost the entire field of physics, gravity was just a minor detail in his work. Or if you are talking about General relativity, there is no way people would have discovered it from observations alone, we'd get some kind of correction term explanation similar to dark matter or dark energy since the formula is extremely complicated.
It is even possible that most physicists would have accepted those corrections as the correct solution and would be looking for the new dark particles inside of large stars for a hundred years before someone corrected them. Or the discovery of black holes would be seen as evidence of these particles, cementing our ignorance forever.
Calculus is maths. Different field, and frequently classified into the arts or astand-alone discipline as opposed to a science.
People have lonog been suspect about classifying math as a science. Mainly, I suspect, because it does not rely on data as a form of evidence instead using logical proof as a foundation.
Calculus is science if it is used to discover laws of physics which are then verified through experiments. Or in other words, Newton discovered that calculus helps explain a lot of phenomena in nature and verified that through experiments, that is the epitome of science.
The problem with the data first approach you are advocating for is that it almost never results in a good explanation, and almost all the value in science lies with the good explanations we have built up throughout history. Formulas are mostly useless, you need an intuitive explanation or people won't be able to build on top of it.
> Calculus is science if it is used to discover laws of physics
So a shower is science if the warm water inspires someone to come up with a new theory? That is a terrible place to draw the boundary; it opens up a can of semantic worms about what 'using' means. Major scientific results that are most easily expressed using calculus can be derived using processes other than calculus.
> The problem with the data first approach you are advocating for is that it almost never results in a good explanation
Science doesn't provide good explanations at the best of times. I'll willingly bet not 1 engineer in 100 can explain gravity. We just know if we measure mass we get predictive estimates of velocity. That isn't an explanation; that is reliable magic. In fact there have been a couple of centuries where even the scientists were basically just plotting data and curve fitting.
If you create new mathematics in order to properly describe a physics phenomena then you are doing science. Similarly if you create a laboratory in order to properly conduct physics experiments to verify your theories you are doing science. How the laboratory was built matters a lot for the experiment, the same as how the math language was built.
Math is a tool, yes, but it is a tool that is very useful to do science in and the act of creating and distributing a tool you use to do science is a large part of science. A shower on the other hand has no direct relationship to science, you don't need to be a physicist to make a shower, it is just a commodity. Calculus however needed to be discovered by a physicist as the math was too strange for mathematicians to find but simple enough that two different physicists found it in parallel.
I am not so sure it would have been a hit as a stand alone formula. Newton discovered calculus and used it to lay the groundwork for almost the entire field of physics, gravity was just a minor detail in his work. Or if you are talking about General relativity, there is no way people would have discovered it from observations alone, we'd get some kind of correction term explanation similar to dark matter or dark energy since the formula is extremely complicated.
It is even possible that most physicists would have accepted those corrections as the correct solution and would be looking for the new dark particles inside of large stars for a hundred years before someone corrected them. Or the discovery of black holes would be seen as evidence of these particles, cementing our ignorance forever.