The daft idea of the world coming to an end when the Mayan calendar ticks over got me thinking. What if we could start again with our calendar. Would it have 7 days and 12 months?

13 Months

Given a lunar cycle of ~29.5 days, it seems to me that we could keep our current 7 days in a week and have a standard four week month. This would mean that the phases of the moon would slowly drift from our month, much like they do now.

28 x 13 = 364 days. This means that we have an extra month that we have to accommodate and name.

Rearrange the months

While we're changing the months, it might be worth rearranging them a little. It would make sense to have the months of September through to December relate to months seven through to ten, given their roots. If we move July and August, which caused the problem in the first place, we'd end up with the following months:

• January
• February
• March
• April
• May
• June
• September
• October
• November
• December
• July
• August
• Month Thirteen

Extra days

With the one or two days left over, these should not be a normal weekday. By doing this, we can ensure that the same day of the year falls on the same day of the week every year.

January the first would start on a Monday, and after thirteen months we would end up on the end of the fourth week of the thirteenth month on a Sunday. The next day or two days (depending on whether it was a leap year) would be days with unique names, rather than any of our current names for days of the week.

Predictability

With our predictable days, we can now figure out what day of the week certain events happen. However, most of the year comes after the end of Februrary, so calculating where in the year the dates come in the new calendar dependent on whether it's a leap year or not. Given that approximately three out of four years are not leap years, we'll work from the perspective of a non leap year.

As an example, let's look at ANZAC Day, which falls on the 25th of April. With a 28 day February, we can calculate which day of the year ANZAC Day falls on:

31 + 28 + 31 + 25 = 115

In our new calendar, ANZAC Day would fall on the third day of the fifth month:

28 + 28 + 28 + 28 + 3 = 115

So ANZAC Day would be on the third of May, which would always be a Wednesday - as all months start on a Monday and end on a Sunday.

Of course, if for any particular day the month and day are more important than the time of year, they can be kept where they are and still have a predictable day of the week. For ANZAC Day, if we keep it on April the 25th, it's going to always be on a Thursday.

Time

A day has 60x60x24 = 86,400 seconds. I wonder if there's a way to simplify time, while keeping the second as the basic unit of time.