HWC Tutorial - Page 3 - Months

The Months

So far, all well and good. I trust that by now you can find any day in a month by starting from any other day in the month, and move no more than three times to the elevator, shift mentally, and move no more than three more days to the target date. But what what about the other months? Maybe you know the weekday of a date in one month, but you'd like to find the weekday of a date in another month. How can we do that?

Let's stay with the same starting date of Wednesday, August 2. What weekday is Christmas in that same year? If you don't mind a lot of drudgery, you could move to the last day of August, call that the 0 of September, move to the last day of September, rename it the 0 of October, and so forth, to bridge your way a month at a time to December, and from there on to the 25th. It would work. But is that how we're going to do it? Of course not. There's a much faster way if you don't mind just a tiny bit of memorization. (Gasp! Did I say the "M" word? Don't panic. I wouldn't suggest it if it weren't easy.)

Let me finish off the example I started just for a little introductory flavor. Then afterwards I'll lay out the whole year for you. But first, let's go from August 2 to August 8: "2, 1, 0...7...8", middle, index, thumb...thumb...index. August 8 is Tuesday. Because I have learned the specially identified dates in this system, I happen to know that August 8 always falls on the same weekday as December 12. I haven't told you why just yet. But trust me for a moment. If August 8 is an "index finger" day (see how I'm still avoiding weekday names because we're in the middle of an example?) then December 12 is also an "index finger" day during the same year. From here we can go "12, 13, 14...28...27, 26, 25," touching index, middle, ring...stay on ring...middle, index, thumb. December 25 is a Monday (because we ended on the thumb). Now that's much easier than bridging your way from August to December, isn't it? Let's review that whole sequence: "August 2, 1, 0, 7, 8...December 12, 13, 14, 28, 27, 26, 25" while touching middle, index, thumb, (thumb), index, (index), middle, ring, (ring), middle, index, thumb. Try making the HWC moves while looking at just the numbers, and counting them off in the correct direction on the hand, pausing where you shift mentally without moving.

Doomsday

Some of you may already know the system I'm about to describe. Though the HWC system of hand positions is my own invention, the list of memorized dates for months is borrowed from a widely used weekday method known as Doomsday by Dr. John Horton Conway of Princeton University. The Doomsday method is a very popular system among calendar enthusiasts, and is addressed many places on the web, so I'll be as brief as I can here. If you'd like to see the whole Doomsday method with its math-oriented approach to the other components of the date, search for calendar doomsday on the web. Want to know why it's popular? Because it's easy. The memorized months are easy, anyway. If you're not handy at multiplying and dividing, the HWC counting techniques may be easier for you than Conway's math methods for the years.

The word "Doomsday" is simply a variable name standing in for one of the seven days of the week. In any year, Doomsday is equated to one and only one weekday during the course of a year, but the specific weekday equated to Doomsday changes from year to year. The value of Doomsday is based on the weekday that corresponds to the last day of February. Whenever August 8 falls on a Tuesday, such as in our example, the last day of February also falls on a Tuesday that year, as do all the other dates we will commit to memory. So we say that, in this year, Doomsday is Tuesday. Dr. Conway refers to the last day of February as "March 0," the date-of-origin for Doomsday in the year. See? That 0 day comes in handy again. You already know what I mean by March 0, because we used the 0 day in our Elevator Method. March 0's real date might be February 28, or it might be February 29, depending on whether the year is a common year or a leap year. ("Common" just means "non-leap.") Now we just need a date in each month which falls on Doomsday, and we can jump directly from one Doomsday date to any other during the same year. They all have the same weekday. If we're lucky, we can find dates which are easy to remember. And guess what? The list of dates Dr. Conway has picked out can be recalled by just remembering four fun facts. Easy! (The dates are Dr. Conway's idea, but the group names such as "Even Steven" are my own.)

• Last or Leap: January 31 or 32, February 28 or 29
  (for January and February, use the first date in a common year, second date in leap year.)
• Elevator of March: March 0
• Even Steven: April 4, June 6, August 8, October 10, December 12
• Odd Job: May 9, July 11, September 5, November 7

Even Steven: Let's start with the easiest grouping. In the five even-numbered months after March, the day of the month which equals the number of the month falls on Doomsday. These dates can be written 4/4, 6/6, 8/8, 10/10, and 12/12. The day is "Even Steven" with the month.

Odd Job: These four odd-numbered months are almost as easy, if you remember this "job related" mnemonic: "I work 9-5 at the 7-11." This simply means that 9 and 5 go together, while 7 and 11 go together, in either order. The dates can be written 5/9, 7/11, 9/5, and 11/7.

Elevator of March: March 0 is an Elevator date as we've already seen. When you find Doomsday for the year, you can immediately "ride the elevator" in March. You don't have to step in from some other date. March 0 is Dr. Conway's date-of-origin for Doomsday. It's a helpful reminder that it's already on the elevator.

Last or Leap: Since the last day of February is Doomsday, we use that as our Doomsday starting date for that month. This date is the 28th in a common year, and the 29th in leap year. The rule here is, "Use the normal last day of the month in a common year. Add one day more in leap year." For January, we simply apply the same rule, giving us January 31 in a common year, and January 32 in leap year. Though January 32 is a fictional renaming of February 1 (we don't really add a leap day to January), we can pretend to add 32 as a "leap day" just to use it as a numeric starting point for counting down to the real days in January. And now you see why we included 35 as a multiple of seven. If you want a January date in leap year, you can start on 32, count forward to 35, then ride down to the other multiples of seven in the actual date range of the month.

Leap Year Rule: At this point, we need to know which years are leap years so that we know which dates to use for January and February. Years which are multiples of 100 are not leap years unless they are also multiples of 400. For all other years, multiples of 4 are leap years. So the full Gregorian Leap Year Rule can be stated like this:

• All multiples of 400 are leap years.
• All other multiples of 100 are common years.
• All other multiples of 4 are leap years.
• All other years are common years.

In summary, here are the Doomsday entry dates in order:

• January 31 or 32
• February 28 or 29
• March 0
• April 4
• May 9
• June 6
• July 11
• August 8
• September 5
• October 10
• November 7
• December 12

Now you should be able to start from any known date and weekday combinaton in the year, find Doomsday during that month, change directly to the Doomsday date in the target month, and find the target day, moving from any month to any month in the year. If you know the weekday of any date in the year, then you've got the whole year laid out at your fingertips. (Okay, that's the last "fingertips" remark, I promise.)