lavinia said:
It differs from the modern point of view that mathematics is not a science but is merely a "language" used for Physics.
That point of view always makes me wonder, specially when mathematicians themselves state it.(You're a mathematician, right?)
Mathematics is more than a language for anything. A language is a tool to communicate something. But mathematics does far far more than just communication. We'd have no idea how to do physics without mathematics. Of course mathematics is something much much more than merely a language.
It was sometime ago when someone asked me about applications of physics. I could start with solid state and AMO physics and all the obvious applications with lasers, semiconductors,etc. But that approach always makes me feel like I'm betraying what I love. Of course there is nothing wrong with solid state physics, AMO physics,etc. They're also beautiful physics and its good that they have those applications. But when you go in that direction, the audience may get the impression that even a student of particle physics thinks what he's studying is useless!
Instead of that, I proposed three levels of applications:
Level 1) Parts of physics that are obviously there because of the applications. like the parts I mentioned above. But of course you can see that they can't be there without the other parts of that specific field of physics which brings me to level 2.
Level 2) Physical theories that explain a wide range of phenomena and if it wasn't because of them, we couldn't harness the potentials of that range of phenomena for applications we have today. Obvious example is QM.
Level 3) Physics in the sense of trying to understand nature in its deepest levels, is a thousand years old endeavor. But in the modern sense, its only a few centuries. This long history of the efforts of millions of people have given us a wide range of tools. Now one may ask why are we limiting these tools to their original applications? Why aren't we trying to find out more areas where we can use these tools? And this is what happened in the field of complex systems. Nowadays we have physicists working on traffic, medicine, biology,etc. And these applications are not because physics is the underlying theory of biology. People who are familiar with complex systems know what I mean.
Level 1 applications are more obvious but more specific and limited. Level 2 applications are as broad as the range of phenomena the theory is supposed to work for. And level 3 applications are as broad as human's ability to come up with applications for a tool.
But there is also another point of view to answer this question. Its like asking a carpenter why should I care about your electric saw? He would say that you have no reason to care, its for me to use so that I can make for you that book shelf. So he can come back at you by asking what's the point of that book shelf? Of course you want to put your books there and if you happen to be a physicist, those will be physics and mathematics books. But why are you studying those? part of it is for applications, like that electric saw, and other parts are for more theoretical parts that are farther from applications. Now if that carpenter thinks your job is useless, his job is useless too because he is doing it for you so that you can do your job. You can follow this kind of chain reasoning for many chains of jobs and you'll end up thinking all jobs are useless. The correct way to think about this, is that mankind wants to flourish and go forward. A really critical part of this flourishing is understanding what's going on in this world. Actually most jobs out there are there to keep people alive and amused. By saying that intellectual endeavors like theoretical physics and pure mathematics are not as important as those jobs, people are actually saying that the flourishing of mankind is just by living longer and enjoying more. This is just missing the point. Of course for some people life is doing a job so that you can have money to enjoy life. That's OK, no problem with that. But if all of mankind was to think like that, we wouldn't be here. So its undeniable that a really critical part of the flourishing of mankind is by intellectual endeavors. If someone asks me this question and I have enough time and I think that the person actually listens and thinks about what I say, this'll be my answer.
And a little point at the end: People don't ask for applications of art because it wasn't supposed to have applications in the first place. But science started as people's efforts to build something they needed. So some people still think that is what it is. And so something in physics that doesn't help you build something is useless because of that definition of physics. But if you can show them that physics and mathematics are partly efforts in the direction of mankind flourishing, they may understand.
