# A metric for the complex plane

If $(z=x+iy,\bar z =x-iy)$ are used as coordinates for the complex plane, then

$ds^2 = dzd\bar z = dx^2+dy^2$

Thus, the 2D metric is transformed to

$\begin{array}{rcl} (\delta_{ij}) &=& \frac 1 2 \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \\ ds^2 &=& \delta_{ij} dw^i dw^j \\ (w^i) &=& \begin{pmatrix} z \\ \bar z \end{pmatrix} \end{array}$

I use $\delta_{ij}$ for the metric, since $\delta_i^j$ always evaluates to the delta tensor, for all possible metrics. In this case, $(\delta_i^j)=(2\delta_{ij})^2$.

Aside: I’ve removed an error from my post regarding the golden matrix.

# CT scans of head

Last year I got my head scanned at CitiScan, Brisbane. A GP referred me, after a blood count, in response to my ongoing seizures. I’m told there was nothing out of the ordinary. It was all bulk-billed, and the full disc can be downloaded here.

Aside: My nose looks crooked. Also, a bottom wisdom tooth is gone. Five or six cervical vertebrae are visible. My right ear looks a little more curved than the left.

# Shave soldering iron tip

Don’t solder without a clean tip, or else heat won’t conduct properly. I use scissors to shave it.

# 1 kg tomatoes ⅓ more fattening than 1 hash brown

The latter is only .6 MJ at McDonald’s ($1), while the former is .8 MJ at Coles ($4). Also, a soft serve is no more fattening than a hash brown, and less than half as fattening as regular fries (1.5 MJ). Furthermore, milk is  more fattening than cola.

# DK coffee ⅔ more fattening than a soft serve

A McDonald’s soft serve ice cream is .6 MJ ($.5), while a Donut King (DK) flat white coffee (reg) is 1 MJ ($4.50). DK have lighter coffees, but not by much. If dieting, beware coffee shops! I assume 12 MJ/day. Coles ice cream is a cheaper source of energy, at just 22 c/MJ.