Better math notation systems

[void4]

Here are Maxwell's equations:

As an absolute physics noob, this representation is worthless to me. My eyes glaze over quickly.

Yes, this notation is compact, and once an understanding of them is developed these equations can even be called beautiful. But in this form, they are just squiggles for those not familiar with them.

A million questions arise: What does the weird upside down triangle mean? Which of these letters are constants? Is one of the • or 'x's multiplication? The differential notation sucks, too.

Most of this is because the notation is incredibly implicit:

• the variables are untyped
• the names, values, types and number of parameters and outputs of functions are not given
• unknown operator precedence

At first glance, it is only obvious that these are four equations.

It is unclear how they relate to each other.

1. The second equation suggests that the output of the • operator is a scalar with no physical unit.

2. The Wikipedia page on ε_0 suggests that its datatype is a scalar, its physical unit is F*m^-1. From this, I guess that the ρ variable has to be of the same unit due to finding [1].

In SI base units, a [F]arad is s^4 * A^2 * m^-2 * kg^-1, making ε_0: s^4 * A^2 * m^-3 * kg^-1 - as would be ρ. The charge density ρ is C*m^-3, a [C]oloumb is A * s. So we get A * s * m^-3 for ρ. Which is not what we got for ε_0.

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The underspecified representation of these equations give them a great deal of generality, some of them may be applied to a varying number of dimensions - which would change the types.

https://github.com/photonlines/Intuitive-Guide-to-Maxwells-Equations/blob/master/PDF/An%20Intuitive%20Guide%20to%20Maxwell's%20Equations.pdf