I did think such a calendar should really start on December 22/23, following the Winter Solstice. At this time, the tilt of the Earth is such that the days once again begin to get longer. This, of course, is a very Northern-hemisphere-biased view of the world, so maybe it is not so appropriate after all. I am fairly convinced that the calendar should be divided into four quarters, divided at each Solstice and Equinox. (Perhaps an Equinox would be a more neutral start for the year?) But how best to divide the rest of the time is more tricky.
Then we have the problem of what the year should be? It obviously cannot relate to the alleged year of Jesus' birth but what event, which must by definition occur in recorded history, is defining enough to take this place as defining Year 1.
One thing that can be modified quite easily though, is the association of days with Saints. I have therefore decided to look each day for an important non-religious scientific figure. Not sure how long this will last.
Today is the turn of Dane Agner Krarup Erlang (January 1, 1878 – February 3, 1929) who was a big man in the field of communications and is credited with the invention of Queueing Theory (used in everything from telecommunications to hospitals to computer programming) and Traffic Engineering, which is heavily used in communication network designs, including the design of this here internet. He even got a Unit of Measurement named after him - the Erlang - although my brain is not sufficiently awake to make sense of what this is. It has something to do with communication. He also has his own statistical probability distribution and a programming language named after him. That beats three miracles in my book. Well done A. K. Erlang.
Erlang shares this day with St Basil "the Great" of Caesarea who, from his Wikipedia entry, seemed to be quite a nice chap. Basil does also seem to be partially responsible for the Christianity fixing the decision that Christ was divine, which appears to have been a matter of some debate for the preceding three centuries. One cannot help but speculate what subsequent conflicts might have been resolved, and how much easier religious harmony might be, had this decision gone the other way. Oh well. I have a soft spot for people who help poor and underprivileged.