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The Accidental Astrophysicists
An anonymous reader recommends a ScienceNews story that begins: "Dmitry Khavinson and Genevra Neumann didn't know anything about astrophysics. They were just doing mathematics, like they always do, following their curiosity. But five days after they posted one of their results on a preprint server, they got an email that said 'Congratulations! You've proven Sun Hong Rhie's astrophysics conjecture on gravitational lensing!'... Turns out that when gravity causes light rays to bend, it can make one star look like many. But until Khavinson and Nuemann's work, astrophysicists weren't sure just how many. Their proof in mathematics settled the question."
Sometimes it takes decades to find the relevant uses for the math though. For example the beta function and string theory
Of course they are. They're the purist of the scientific fields.
My sci-fi novel, Ghost Thief, is now available from Amazon.com.
You're assuming that String theory is useful. It isn't even a theory. You see, to be a theory it has to do what it says it does to at least a large degree. Point of fact, there is exactly ZERO experimental evidence that it is physically correct to /any/ degree. String "Theory" is a bloody joke that has plagued Physics for decades and is now (far to late IMO) coming under significant fire for its lack of experimental evidence. Thankfully, that fire also comes in the form of much less funding so that other *far* more promising fields can get some research done.
But isn't physics still mathematics? Like, physics is a subcategory of math? along with... everything else... Hell what do I know, I'm only 16.
I really want to agree with you, but people keep finding ways that obscure, useless little pieces of purely abstract math suddenly explain something interesting about the real world. Sometimes it takes a century or two, sure. But, if you told the first people to work on imaginary numbers how useful their math would be for expressing many engineering things, and how it would be a major tool for engineering students learning to build very real things, well they'd just call you a moron. Likewise, boolean algebra, or any number of other mathematical concepts that make our current world possible and relatively comprehensible.
String Theory is more correctly a descriptive language of physical theories. Within the mathematical framework of String Theory it is possible to describe just about any configuration of the universe. In that way, it's more similar to applied math than anything else.
What String Theorists have been doing is building descriptive models of actual theories. It's a valuable exercise, but they shouldn't feel that String Theory is going to provide anything other than another modeling and analysis tool. Specifically, because String Theory is so expressive, it is impossible to make a falsifiable assertion in pure String Theory. You always need an outside theory, and it's the outside theory that provides the falsifiable assertion.
String Theory can describe just about any system, so it's impossible to prove right, and more importantly for this discussion, impossible to prove wrong. Which means that it is not science. Knowledge of this reality is gradually percolating through the physics establishment. Give it time.
Some might, but I wouldn't.
Mathematics has its own ontology - namely the axioms that it is based upon.
It has no need for a separate epistemology - it is what it is, and that's that.
Propositional calculus, on which Russell, Frege and Wittgenstein based their mathematical philosophy (which I see as applicable to all rational thought) is itself the root of mathematics - thus mathematics (or logic, however you wish to phrase it) is fundamental to philosophy, rather than philosophy being fundamental to mathematics.
You can't have an ontology without maths - epistemologies are more equal, but essentialy the whole of philosophy is based on the propositional calculus, which is only one of many possible formulations of mathematics.
One swallow does not a fellatrix make
Logic is an extension of intuition. It does not always serve us well.
Conservation of angular momentum makes the world go round.