"Oh yes, that's
right." Nathan thought of his Mom
and Dad and his brother Ben. "I'll
have to wake up out of this dream pretty soon.
But I sure wish that I could come and visit you some other time and play
with you Roland - and not in a dream but in real life."

Roland and Pepper looked at him
and then at each other.

Then Pepper spoke.

"There are times when you
can come to the Other-Other Land through the Magic Mirror. The next time you
can come is when your birthday falls on a Thursday, just after a first-quarter
moon. That day you must find the Magic
Mirror and look into it and count to ten.
Then you must close your eyes and whisper the magic words. When you open them again you'll be
here."

"But I don't know any magic
words," Nathan said sadly.

"I do." Roland was grinning. "I'll whisper them into your ear."

In Helena Puumala’s

__Nathan’s Adventure in the Other-Other Land, A Children’s Story__, Prince Roland informs Nathan that there is a special day that he can come to visit his friends in the Other-Other Land, namely a birthday that falls on the Thursday just after a first-quarter moon. Just how often does this special day occur?
We can figure this out with a
little elementary statistical theory, as follows:

·
First off we know
that everyone has a birthday once per year (unless they are born on a leap-day,
but we will ignore that). So, over a
lifetime of 84 years, that gives 84 possible special days.

·
But Thursday is just
one day of the week, out of a possible 7.
So, that limits the special days to 84 divided by 7, or 12.

·
This is further
limited by the fact that only one Thursday of the month (approximately) can
come just after the quarter-moon phase has begun. That means that we should divide the 12 days
that we calculated above by 4 (there are 4 quarter phases of the moon in the month),
giving 3 of these special days in the average person’s lifetime.

·
Note that this
includes some simplifications (such as there being 4 quarter phases of the moon
in a month, which is not quite true, since a lunar month is generally a bit
shorter than a calendar month).

So, Nathan was pretty lucky to
have had a special birthday come so quickly after meeting his new friends. Of course, it may be that the mathematical
logic of our world doesn’t apply to the Other-Other Land. Or perhaps Prince Roland was just putting
Nathan on, and it was the magic words that really did the trick.

Using our own spreadsheet magic,
we can go further than this, and actually determine which are the special days
for any particular birthday. Basically,
that’s just a matter of listing a large number of days in Excel, using some
date functions to check whether any particular day is a Thursday and a birthday,
and also calculating the phases of the moon from a particular known phase and
day, to check whether that day was the first Thursday after the quarter moon. The function that calculates the modulus of
29.530589 comes in handy here, that being the length of the lunar month.

Trying this out for a few people
notable for magic gives the following years for their “Other-Other Land”
birthdays:

·
J.K. Rowling (July
31), known for writing about magic - 2014, 2025 and 2036. I hope she tried out the magic words earlier
this year.

·
Wayne Gretzky (Jan
26), known for magic around the net in hockey – 1961, 2034, 2040, 2045. That’s pretty awesome, he was born on one of
his Other-Other Land birthdays (1961).
That might explain a few things.

·
Magic Johnson (Aug
14), known for his magic in basketball (thus the name) – 1975, 1986, 1997,
2008. The last one is a bit of a
judgment call, though.

·
Prince William (June
21), since we really should have a prince in the list – 2007, 2018, 2029, 2040.

·
Katherine Middleton
(Jan 9) – since we need a princess too – 2003, 2014, 2025.

Here’s a handy lunar calculator,
where you can check what the phase of the moon was for the years 1930 to 2024.

And here’s a vaguely relevant
comic (well, it’s about the moon anyway).

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