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!

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