I’m a fervent believer in the importance of using good notation in physics expositions. Good notation can make the theory and equations in your writings look unambiguous, clear, even obvious. It can also make them easier to apply and re-use later on. On the other hand, bad notation can make exactly the same theory and equations look ambiguous, confusing, hard to understand, enigmatic, hard to re-use. Same thing with good and bad terminology.
Often, when I dislike the notation or terminology used by previous authors, I’ll change it. I just can’t resist the urge to change it if I can find something that works better. It’s a sort of obsessive compulsive behavior. Some people prefer to stick with the notational conventions laid out by previous authors, even when those conventions suck. Not me. I’m not talking about changing an “a” for an “x” or something trivial like that. I’m talking about making important changes to stamp out ambiguity and improve clarity and ease of use.
I’ve heard a famous autistic person, Temple Grandin, say on NPR that she, like many other autistics, is hypersensitive to sensory stimuli like loud sounds, the friction produced by clothing on her skin, etc. Sometimes I think I have an autistic-like sensitivity for notation. (No. I don’t think I have autism or Asperger’s although I do think I have a few loose screws.)
Some examples of my notational idiosyncracies:
One example of a case where I found the standard notation unbearable:
Quantum Circuits in the Dirac, Quayle and Bayes Conventions
- Another, more trivial example: In my papers, I underline random variables instead of following the much more common practice of using capital letters for them. I do this, not because I’m trying to be different, but simply because I want to be able to use both upper and lower case letters (and also Greek letters) as random variables.
- In my papers, I often denote a CNOT by
and a Toffoli gate (= doubly controlled NOT) by
where 1 labels the target qubit and 2,3 label control qubits. is the X Pauli matrix applied to qubit 1. is the number operator () applied to qubit 2. This notation is clear, compact, useful and unambiguous (, a matrix A raised to a power B which is itself a matrix, can be defined rigorously). Most of the quantum computing literature uses other, less convenient alternatives to this notation.