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EDIT: After finally reading the text, I realized that my little rant below has little to do with the topic. --------------------------------------------------

EDIT: After finally reading the text, I realized that my little rant below has little to do with the topic. ---------------------------------------------------- The first thing I learned in my Physics undergraduate studies was Maths. Calculus. Scalar fields and vector fields, their derivatives and integrals, and differential equations of all kinds and flavours. Non-cartesian coordinate systems, transformations between them, fourier transformations. And a nice toolbox for beating the not-so friendly integrals. Even for classical mechanics, that's the foundation. If you want to talk about Quantum Physics you also need linear algebra, in particular Hilbert spaces and operators. And distributions. If you don't understand the Maths, you are left with talking about interpretations. Especially in Quantum Physics, that means you are left with basically nothing. Without Maths, you are not doing Physics. You are doing Metaphysics.

byproxy 9y ago
I almost feel that math ought to be learned through physics. At least, I remember my physics instructor explaining math concepts in a mich more terse and understandable way than my math professors.
- HumanDrivenDev 9y ago
  This is a topic I've thought about a lot. Let's forget about the pure/applied divide. That's not what I am getting at and I want to make my language very clear. Let's instead talk about "maths for its own sake" and "maths for x" (physics, computer science, what have you). Calculus is a nasty kind of maths to study for its own sake. It's not intuitive, and it's shaped by motivations that aren't at all clear until you've learned its applications. Stuff like abstract algebra or graph theory on the other hand are - to me - "quite nice". They're certainly much more intuitive than anything in calculus world. So, basically I agree with you - in high school, maths (by which we really mean geometry and calculus) should be hand in hand with physics. I mean that is its reason for being in the curriculum, to prepare future engineers. People who want to study "real maths" can learn something easier to grasp, and maybe a bit more profound.
- jeffwass 9y ago
  I have a PhD in physics, and this is exactly how I learned the material. I mean, really learned it. I did fine in plain math classes, but never quite connected with the material. Calculus and linear algebra both really only 'clicked' when applying them in my physics classes. Physics is like the "word problems" we'd have in elementary sho, but for advanced math.
  - j9461701 9y ago
    With no offense intended to mathematicians, a lot of the higher level material in my pure math courses tends to be of the "How many angels can dance on the head of a pin?" type. Debating the finer points of details that are mostly irrelevant minutia, yet which are given just as much text space as serious results that actually do things. Physics' real-world origin prevents a lot of that sort of thing, and places emphasis on a practicality I find deeply appealing. Cauchy-Riemann equations are important, here's where they come from, here's what they do, bam done.
    - nsomaru 9y ago
      Although, there have been many cases where results from Pure Mathematics have found to elegantly describe phenomena in Physics, often years after the initial result which might have been regarded as the equivalent of "angels dancing on a pinhead" by physicists of the time.
anitil 9y ago
Love your edit - rare to see that sort of honest self-criticism. On reddit it takes the form of '[deleted]' which I think is far lest honest than a retraction.
peterwwillis 9y ago
I don't know about any of that, but I know most people can understand how a computer works without understanding binary, transistors, quantum mechanics, or maths.
- happy-go-lucky 9y ago
  > most people can understand how a computer works without understanding binary, transistors, quantum mechanics, or maths. Superficial understanding :)
  - peterwwillis 9y ago
    Superficial means of the surface. The surface of a computer is made up of materials such as glass, plastics, alloys, liquid crystals and light-emitting diodes, and paints. There are many levels that make up a computer and how it functions. You can't say you only know what is on the surface if you understand how it works multiple levels down. If you meant 'they don't REALLY understand it', neither do physicists. There are many layers that make up a computer, and most physicists only understand the very bottom ones, and they can hardly use a computer as a result. Just because there are some parts you don't full grasp doesn't mean you don't know how the thing works. If that were true, all physicists would only have a 'superficial' knowledge, because even they don't completely understand how the universe works.

byproxy 9y ago

I almost feel that math ought to be learned through physics. At least, I remember my physics instructor explaining math concepts in a mich more terse and understandable way than my math professors.

HumanDrivenDev 9y ago
This is a topic I've thought about a lot. Let's forget about the pure/applied divide. That's not what I am getting at and I want to make my language very clear. Let's instead talk about "maths for its own sake" and "maths for x" (physics, computer science, what have you). Calculus is a nasty kind of maths to study for its own sake. It's not intuitive, and it's shaped by motivations that aren't at all clear until you've learned its applications. Stuff like abstract algebra or graph theory on the other hand are - to me - "quite nice". They're certainly much more intuitive than anything in calculus world. So, basically I agree with you - in high school, maths (by which we really mean geometry and calculus) should be hand in hand with physics. I mean that is its reason for being in the curriculum, to prepare future engineers. People who want to study "real maths" can learn something easier to grasp, and maybe a bit more profound.
jeffwass 9y ago
I have a PhD in physics, and this is exactly how I learned the material. I mean, really learned it. I did fine in plain math classes, but never quite connected with the material. Calculus and linear algebra both really only 'clicked' when applying them in my physics classes. Physics is like the "word problems" we'd have in elementary sho, but for advanced math.
- j9461701 9y ago
  With no offense intended to mathematicians, a lot of the higher level material in my pure math courses tends to be of the "How many angels can dance on the head of a pin?" type. Debating the finer points of details that are mostly irrelevant minutia, yet which are given just as much text space as serious results that actually do things. Physics' real-world origin prevents a lot of that sort of thing, and places emphasis on a practicality I find deeply appealing. Cauchy-Riemann equations are important, here's where they come from, here's what they do, bam done.
  - nsomaru 9y ago
    Although, there have been many cases where results from Pure Mathematics have found to elegantly describe phenomena in Physics, often years after the initial result which might have been regarded as the equivalent of "angels dancing on a pinhead" by physicists of the time.

anitil 9y ago

Love your edit - rare to see that sort of honest self-criticism. On reddit it takes the form of '[deleted]' which I think is far lest honest than a retraction.

peterwwillis 9y ago

I don't know about any of that, but I know most people can understand how a computer works without understanding binary, transistors, quantum mechanics, or maths.

happy-go-lucky 9y ago
> most people can understand how a computer works without understanding binary, transistors, quantum mechanics, or maths. Superficial understanding :)
- peterwwillis 9y ago
  Superficial means of the surface. The surface of a computer is made up of materials such as glass, plastics, alloys, liquid crystals and light-emitting diodes, and paints. There are many levels that make up a computer and how it functions. You can't say you only know what is on the surface if you understand how it works multiple levels down. If you meant 'they don't REALLY understand it', neither do physicists. There are many layers that make up a computer, and most physicists only understand the very bottom ones, and they can hardly use a computer as a result. Just because there are some parts you don't full grasp doesn't mean you don't know how the thing works. If that were true, all physicists would only have a 'superficial' knowledge, because even they don't completely understand how the universe works.