4 ms·

Real science is ugly because there are a bunch of theories that kinda sorta fit, but not really well. I think Maxwell had something like 40 equations for electr

by jfoutz 11y ago

Real science is ugly because there are a bunch of theories that kinda sorta fit, but not really well. I think Maxwell had something like 40 equations for electricity. Give it a hundred years and hundreds of thousands of grad student hours, and something quite clean emerges. The unknown edges are messy, but as competing theories get winnowed out, merged and refined they become clear and concise.

AnimalMuppet 11y ago
Maxwell had 20 equations for electromagnetism, because he didn't use vector notation, so he had to do the equations component by component. But that had nothing to do with having multiple theories. The current "Maxwell's equations" are exactly the same as Maxwell's 20 equations, merely expressed in a more convenient form.
- cma 11y ago
  Wikipedia claims: "Less well known is that Heaviside's equations and Maxwell's are not exactly the same, and in fact it is easier to modify the latter to make them compatible with quantum physics.[25]"
- zardo 11y ago
  In geometric algebra it's a single equation. ∇E=∂B/∂t
  - orbifold 11y ago
    Actually you can unify E and B into a closed two-form F and get in vacuum dF = 0 d★F = ★j Where j = rho dt + jx dx + jy dy + jz dz is the charge and current density, ★ is the Hodgestar operator and d is the exterior derivative. The equations in a medium are slighly less elegant.
    - ngoldbaum 11y ago
      And if you write the electromagnetic field in terms of the 4-vector potential, it's just \Box{A_μ} = 0 (where Box is the D'Alembertian operator). Then again, this doesn't really mean anything without the context of what the notation means... Feynman has a discussion about this in Volume 2 of the Feynman Lectures: http://www.feynmanlectures.caltech.edu/II_25.html http://www.feynmanlectures.caltech.edu/II_25.html (I still can't get over how awesome it is that I can deep-link into the Feynman Lectures!!)
      - viola11 11y ago
        That's a charge that applies equally well to the standard formulation and I made this comment just to say that it IS cool you can deeplink the Feynman lectures!
  - Tycho 11y ago
    what is B?
    - carbocation 11y ago
      Amplitude of the magnetic field.
    - swombat 11y ago
      http://www.maxwells-equations.com/ http://www.maxwells-equations.com/ will answer all your questions... :-)
deciplex 11y ago
> Give it a hundred years and hundreds of thousands of grad student hours, and something quite clean emerges. Ugh, and we just had this on here the other day: https://news.ycombinator.com/item?id=9779206 https://news.ycombinator.com/item?id=9779206 :-)
- jfoutz 11y ago
  I'll defer to your expert opinion of course, but it seems like faraday discovered some odd behavior in 1821, maxwell codified it in 1861. By 1884 Heaviside reformulated them into the modern form. Perhaps 100 years is an exaggeration, but the point is it takes time to make sense of what the heck is going on. Really, pick anything. someone notices something odd, tries to explain it. there are many many experiments. Someone really clever ties them together in a nice way. Someone else really clever cleans it up. Einstein and general relativity is the only counterexample i can think of. But I'm pretty sure Poincare had a formulation of special relativity.
  - kijin 11y ago
    100 years is not an exaggeration. It took approximately 100 years after Darwin for all relevant fields of science to come to a more or less consistent understanding of the history of this planet. That's how long it took for (1) paleontologists to dig up enough fossils, sort them, categorize them, and determine the relationships between them; (2) geologists to figure out how plate tectonics have shaped Earth over long periods of time; (3) physicists to discover and refine radioisotope dating methods; and (4) astronomers to place all of that in the context of the evolution of the universe as a whole. If any of these pieces didn't come together at the right time, we might still be teaching young-Earth creationism in schools. Contrary to popular perception, science moves rather slowly. We who work in the fast-moving subfield of computer science and information technology often forget that.
    - darkmighty 11y ago
      *Worked slowly. Of course science is much faster nowawadays; although there are no more facts about the Earth to be discovered as basic as the outline of it's geologic history. Even getting a book across the globe was a major issue I suspect; you'd have to slowly accrue interest from the community around you and divulge your work a lot for it to start propagating and eventually start having effects. Nowadays cutting edge papers are often put in the arXiv even before hitting the journals (which have instant online access), and I believe even speculative theories spread much faster by email, etc. And every researcher from every field has ready access to what happens on other fields. Although I think it's not nearly as fast as it could be, and a large problem in our way are the big journal publishers. We need to restructure publishing urgently.

by jfoutz 11y ago

AnimalMuppet 11y ago

Maxwell had 20 equations for electromagnetism, because he didn't use vector notation, so he had to do the equations component by component. But that had nothing to do with having multiple theories. The current "Maxwell's equations" are exactly the same as Maxwell's 20 equations, merely expressed in a more convenient form.

cma 11y ago
Wikipedia claims: "Less well known is that Heaviside's equations and Maxwell's are not exactly the same, and in fact it is easier to modify the latter to make them compatible with quantum physics.[25]"
zardo 11y ago
In geometric algebra it's a single equation. ∇E=∂B/∂t
- orbifold 11y ago
  Actually you can unify E and B into a closed two-form F and get in vacuum dF = 0 d★F = ★j Where j = rho dt + jx dx + jy dy + jz dz is the charge and current density, ★ is the Hodgestar operator and d is the exterior derivative. The equations in a medium are slighly less elegant.
  - ngoldbaum 11y ago
    And if you write the electromagnetic field in terms of the 4-vector potential, it's just \Box{A_μ} = 0 (where Box is the D'Alembertian operator). Then again, this doesn't really mean anything without the context of what the notation means... Feynman has a discussion about this in Volume 2 of the Feynman Lectures: http://www.feynmanlectures.caltech.edu/II_25.html http://www.feynmanlectures.caltech.edu/II_25.html (I still can't get over how awesome it is that I can deep-link into the Feynman Lectures!!)
    - viola11 11y ago
      That's a charge that applies equally well to the standard formulation and I made this comment just to say that it IS cool you can deeplink the Feynman lectures!
- Tycho 11y ago
  what is B?
  - carbocation 11y ago
    Amplitude of the magnetic field.
  - swombat 11y ago
    http://www.maxwells-equations.com/ http://www.maxwells-equations.com/ will answer all your questions... :-)

deciplex 11y ago

> Give it a hundred years and hundreds of thousands of grad student hours, and something quite clean emerges. Ugh, and we just had this on here the other day: https://news.ycombinator.com/item?id=9779206 https://news.ycombinator.com/item?id=9779206 :-)

jfoutz 11y ago
I'll defer to your expert opinion of course, but it seems like faraday discovered some odd behavior in 1821, maxwell codified it in 1861. By 1884 Heaviside reformulated them into the modern form. Perhaps 100 years is an exaggeration, but the point is it takes time to make sense of what the heck is going on. Really, pick anything. someone notices something odd, tries to explain it. there are many many experiments. Someone really clever ties them together in a nice way. Someone else really clever cleans it up. Einstein and general relativity is the only counterexample i can think of. But I'm pretty sure Poincare had a formulation of special relativity.
- kijin 11y ago
  100 years is not an exaggeration. It took approximately 100 years after Darwin for all relevant fields of science to come to a more or less consistent understanding of the history of this planet. That's how long it took for (1) paleontologists to dig up enough fossils, sort them, categorize them, and determine the relationships between them; (2) geologists to figure out how plate tectonics have shaped Earth over long periods of time; (3) physicists to discover and refine radioisotope dating methods; and (4) astronomers to place all of that in the context of the evolution of the universe as a whole. If any of these pieces didn't come together at the right time, we might still be teaching young-Earth creationism in schools. Contrary to popular perception, science moves rather slowly. We who work in the fast-moving subfield of computer science and information technology often forget that.
  - darkmighty 11y ago
    *Worked slowly. Of course science is much faster nowawadays; although there are no more facts about the Earth to be discovered as basic as the outline of it's geologic history. Even getting a book across the globe was a major issue I suspect; you'd have to slowly accrue interest from the community around you and divulge your work a lot for it to start propagating and eventually start having effects. Nowadays cutting edge papers are often put in the arXiv even before hitting the journals (which have instant online access), and I believe even speculative theories spread much faster by email, etc. And every researcher from every field has ready access to what happens on other fields. Although I think it's not nearly as fast as it could be, and a large problem in our way are the big journal publishers. We need to restructure publishing urgently.