User talk:Sintel/Conventions
Hi Sintel, I agree with most of what you say on this page except I think you meant to write "italic" where you wrote "Roman" twice. There is now a thoroughly tested proposal for mathematical notation in regular temperament theory, namely: Dave_Keenan_&_Douglas_Blumeyer's_guide_to_RTT/Conventions_for_names,_variables,_units,_and_notations
It uses standard linear algebra notation with some minor extensions designed to make RTT easier to read and learn. One of these is indeed Extended Bra-ket notation (EBK). Sure, we're not doing quantum physics. No one ever pretended we were. But we are doing physics, or at least psychophysics, as opposed to pure math. The entries in our vectors and covectors have units, whether they be cents, counts of primes or counts of generators. Our EBK notation can be distinguished from the BK of quantum mechanics because we use square brackets where quantum mechanics uses vertical bars.
The standard transpose notation you give for column vectors inside text is OK, but it doesn't allow one to distinguish between an object that is natively a vector (column vector with contravariant units) and one that is natively a covector (row vector with covariant units) but is being transposed. And EBK gives you so much more than that.
EBK has been used since the earliest days of RTT and is too useful to give up. For another thing, with nesting, it gives us a single notation that spans both linear algebra and exterior algebra, allowing us to distinguish matrices from bivectors etc. For another it lets us distinguish generator count vectors from prime count vectors by changing the shape of the non-square bracket. See Extended_bra-ket_notation#Extensions
Thanks for your help with D&D's guide, through your discussions with Douglas.
We love MathJax and use it extensively. I hope the wiki will soon be upgraded to MathJax v4.0 (released 2 days ago). I can't wait to see what it breaks. ;-) Its font control should let us use curved angle brackets that render as quite distinct from ordinary angle brackets on all platforms, as described in the above article, and thereby let us get rid of the ugly curly brackets (braces) that we've been using as a workaround.
Dave Keenan (talk) 04:11, 7 August 2025 (UTC)