User:Quondum

From Wikipedia, the free encyclopedia
Jump to: navigation, search


I welcome all comment and suggestions from other Wikipedians. If I am ever uncivil or illogical, I may just need some guidance or sleep. If I make some changes that are counter to a dominant convention within Wikipedia, please do not hesitate to mention this. I tend to focus on what I perceive as inconsistencies, whether logical or typographical.

I am an electronic engineer, and enjoy areas such as cryptography and side-channel analysis (and countermeasures). I have an interest in mathematics and physics. I like rigour, simplicity, regularity, and (dare I mention it) terseness/compactness of exposition.

Quirkinesses[edit]

Units[edit]

My preferred set of units:[1] SI (with reservations[2]), and IEC binary prefixes.

My preferred set of natural units could be termed reduced Planck units defined by base units equal to products of powers of the constants c0[3], ħ, ε0, kB, G0 = −1/(4πG)[4], rad, sr, nat.[5]

Symmetry[edit]

I'll generally prefer a presentation that makes an underlying symmetry salient. For example, I prefer Maxwell's equations expressed in terms of E and H rather than E and B – to emphasise the symmetry of E–M duality. Also manifestly coordinate-free formulations in physics.

Triviality[edit]

Exclusion of trivial cases to avoid awkward phrasing of theorems at the expense of mathematical regularity is something I find ugly. Every class of mathematical object should be defined such that a homomorphism onto the trivial terminal object is well-defined. First-order logic should not axiomatically exclude the empty universe of discourse. This excludes, for example, the axiom 0 ≠ 1 normally used in defining fields.

Utility[edit]

Wikilinks[edit]

Notes[edit]

  1. ^ One should start with quantities (such as in the ISQ). These would include a locally orthogonal set of four separate geometric dimensions (time, x-distance, y-distance, z-distance), plane angle, solid angle and higher angles (including hyperbolic angles), speed, mass, energy, entropy (negative of information), electric charge, magnetic charge, colour charge (triple), temperature, luminance, and many more.
  2. ^ The use of the prefixed unit kg as a base unit is awkward; also, considering that Hz = 2π rad⋅s−1, the SI premise that Hz = s−1 forces the unnatural conclusion that considered as a dimensionless constant, 1 rad = 1/(2π). Also, treating rad, sr and nat as dimensional constants instead will help with clearer thinking.
  3. ^ An interesting choice of normalization would be to put 1 = −c02. This does not imply that the imaginary unit is used but only that a velocity 3-vector squares to a negative value; a neat choice would be to have in place of c0 a constant with the value c02. This embodies the inescapable result of special relativity that because the square of a timelike vector delta has the opposite sign of the square of a spacelike vector delta, the ratio of the two squares is negative. This does not in general change the standard form of equations in natural units, but rather how an equation is expressed in SI units.
  4. ^ The unusual choice of normalization for a gravitational constant results from two considerations: that the reference direction for force be consistent (independent of the type of force, for example when matched with Coulomb's law), and that the equations be rationalized. Forgive the pun, but I consider this to be the only rational choice, especially when considering other symmetries and dimensions.
  5. ^ Derived units would equal the constants μ0 = 1/(ε0c02), Z02 = μ0/ε0, q02 = c0ε0ħ. The electromagnetic coupling constant would be e = 4παq0 ≃ 0.30282212⋅q0.