The E calendar starts at midwinter, while the G calendar and the parallel K calendar begin with the 2nd quarter (according to our own calendar). The ancient structure of the year seems to be a division into 'summer' and 'winter'.

Maybe the Polynesians and other peoples who journeyed far and wide, sometimes crossing the equator, felt a need to construct a calendar which could function both in the north and in the south.

A step in that direction may have been to compromise as regards what half of the year was 'summer' and what was 'winter' - by way of installing a calendar that did not begin at an equinox but at a solstice.

I therefore suggest that we should not try to see what unites Mercury and midwinter but instead see what unites Mercury and spring equinox. Whatever it is we can be sure that it is ancient and complex.