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A Tale of Two Tape Measures |
Here’s
a way to check out:
1. The
NONsynchrony of menstrual cycles
whose periods are NONinteger
multiples of each other;
2. The “SYNCHRONY” of
menstrual cycles whose periods are integer
multiples of each other.
You Will Need:
* Two tape
measures capable of remaining fully extended (not just keep snapping back while
you are trying to conduct the experiment!) -- or else use cloth or plastic
tape measures.
* You will
also need a L-O-N-G table to set your tape measures on, or just a clear space
on the floor.
* Two
markers of contrasting colors (crayon, magic marker, nail polish;
red/black; you
get the idea!)
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First, let’s look at nonsynchrony
resulting from periods that are noninteger multiples of each other:
Take one of the tape measures and
place a red mark on 4 and all integer multiples of 4 (just like from a
multiplication table – 4, 8, 12, 16 and so on, until you've gotten to the end
of the tape measure). Lay this out on your L-O-N-G table
or floor...
Now take the other tape measure
and place a black mark on 5 and all integer multiples of 5 (just
like from a multiplication table - 5, 10, 15, 20, and so on, until you've
gotten to the end of the tape measure). Lay this parallel
to your first tape measure...
And start recording your data:
1. How many numbers were marked on
both tape
measures? That is, how often did “synchrony” occur, at least in the
strict mathematical sense?
2. How many numbers were marked
only on the
first tape measure? How many numbers
were marked only
on the second tape measure?
And thus, were nonsynchronous?
As the total of #2 is much greater
than #1, we conclude that a rhythm whose period has an interval of 4 days is
nonsynchronous
with a rhythm whose period has an interval of 5 days.
3. Another way of approaching this is to calculate the difference
between each “pair” of marked numbers, that is,
starting with 5 - 4 = 1, then 10 – 8 = 2, etc., calculate the difference
between marked numbers all the way to the end of your tape measures.
What kind of pattern emerges? Can you see how the numbers marked on the
two tape measures gradually diverge, and (if your tape measures are long
enough) start converging again, rather than remain in a state of synchrony?
If interested, instead of using 4
and 5 as your noninteger multiples (which are much too short to be actual
menstrual cyclces), use the actual menstrual data given by
Terry Farrah at the beginning of this MoltXibit.
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Now, let’s look at “synchrony”
resulting from periods that are integer multiples of each other:
Using the tape measure on which
you had marked integer multiples of 4, now mark
integer multiples of 10. Lay this
parallel to your second tape measure, on which you had
marked integer multiples of
5...
And start recording your data, as
follows:
1. How many numbers were marked on
both tape
measures?
2. How many numbers were marked only
on the first tape measure?
How many numbers were marked only on the
second tape measure?
As we can see, when we are
comparing two rhythms whose periods are integer multiples of each other, they
behave a bit differently than when periods of noninteger multiples are
concerned.
Namely,
ALL of the
numbers (that is, the integer multiples of 10) marked on the first tape measure
were marked on the second tape measure as well!
3. When we turn to calculating the difference between each pair of
marked numbers, that is, starting with 10 - 5 = 5, we immediately see a
problem: There “aren’t enough numbers”
marked on the first tape measure to carry out our calculations! This is because a state of synchrony exists
between these two rhythms, in a ratio of 1:2 – for every one “period” of 10
inches, we have exactly two “periods” of 5 inches.
Again, if interested, instead of
using 10 and 5 as your integer multiples, trying using 20 and 40 (granted these
are fairly short and long menstrual cycles, but still more common than 10 and
5).
Alas, we
still have a bit further to go in
understanding menstrual synchrony. And
that’s because menstrual synchrony researchers don’t just study
carefully-aligned menstrual cycles, as our two tape measures had been; for
example, try doing the above experiment with one of the tape measures 7 inches
out of alignment with the other!
As well, researchers don’t just
study pairs of women, they study the menstrual cycles of groups of women: Could be two, could be a dozen, could be
92! Just imagine how complicated the
above experiment would have been, if you were using 92 tape measures, instead
of only two!
Click here to continue – we
promise there are NOT 92 tape measures on the next screen!
X Opportunity: Rubymusyk as
Musical Genre