3 ms·

Like ∇^2 u = Δu = f? It's not really cryptic, it's taught in multivariable. And it's not done to look sophisticated, it's so that you can instantly recognize th

Like ∇^2 u = Δu = f? It's not really cryptic, it's taught in multivariable. And it's not done to look sophisticated, it's so that you can instantly recognize that it's Laplace, or Poisson, etc. If I tell you B = (dA_z/dy - dA_y/dz)i + (dA_x/dz - dA_z/dx)j + (dA_y/dx - dA_x/dy)k do you instantly see what operator is applied? That's why you just write B = ∇×A. People presenting ideas in shorter notation is not showing a lack of progress - usually it's the opposite. In old optimization papers people would write out the entire normal equations, entry by entry. Not really insightful at all, compared to A'Ax = A'b.

StandardFuture 6y ago
This seems to be presenting a false dichotomy. B = (dA_z/dy - dA_y/dz)i + (dA_x/dz - dA_z/dx)j + (dA_y/dx - dA_x/dy)k and B = ∇×A are not the only ways, out of all possible strings, to encode that information. This is the power of modern programming languages. They are mathematics with much better syntax.
vertbhrtn 6y ago
That's a trivial triangle. Modern papers go far beyond that and invent some partial diff operators, like "F.∇" which means "do the grad first, then dot product", use uncommon context-depenedent subscript and superscript indices that can mean fairly arbitrary things and so on. But my complaint is mostly about the use of unnecessary and terse formalism where a short full form is replaced by a 40% shorter form just to use a uber generic high order operator to look fancy and refer to couple mysterious (and useless in the context) theorems or other papers. This is when I have to read other similar papers and see wtf that cryptic equation really means (and often it means some mundane thing). Programmers have the same kind of mental problem: in order to look sophisticated, they intentionally use more cryptic and terse solutions to impress "less initiated" and to hide the fact that what they are doing isn't that complex.

StandardFuture 6y ago

This seems to be presenting a false dichotomy. B = (dA_z/dy - dA_y/dz)i + (dA_x/dz - dA_z/dx)j + (dA_y/dx - dA_x/dy)k and B = ∇×A are not the only ways, out of all possible strings, to encode that information. This is the power of modern programming languages. They are mathematics with much better syntax.

vertbhrtn 6y ago

That's a trivial triangle. Modern papers go far beyond that and invent some partial diff operators, like "F.∇" which means "do the grad first, then dot product", use uncommon context-depenedent subscript and superscript indices that can mean fairly arbitrary things and so on. But my complaint is mostly about the use of unnecessary and terse formalism where a short full form is replaced by a 40% shorter form just to use a uber generic high order operator to look fancy and refer to couple mysterious (and useless in the context) theorems or other papers. This is when I have to read other similar papers and see wtf that cryptic equation really means (and often it means some mundane thing). Programmers have the same kind of mental problem: in order to look sophisticated, they intentionally use more cryptic and terse solutions to impress "less initiated" and to hide the fact that what they are doing isn't that complex.