Tag Archives: mathematics

The Fibonacci Cat Sequence


Here’s a guest post full of awesome from The Man (illustrated by ME!):

Today I will share with you a discovery I have made in the field of Cat Mathematics which I have entitled the Fibonacci Cat Sequence.  I will also describe the risks of the Fibonacci Cat-scade Scenario and attempt to determine the COCL Limit.

Just as a brush-up, the Fibonacci Sequence is that neat little pattern of numbers where you add the last two elements to get the next one.  If (1,1,2,3,5,8,13,21,34,55,…) rings a bell, good for you.  If not, don’t worry– the maths will make sense soon.

teacher man

First we must seed the sequence with the values F(0) = 0 and F(1) = 1.  Imagine as follows:

I start out with no cats.  [F(0) = 0]

But someone gives me a cat.  [F(1) = 1]

For a while, I am happy with one cat.  [0 + 1 = 1, so F(2) = 1]

REAL WORLD EXAMPLE #1
The Wife and I had no cat.  Then we adopted Mehitabel, and we are happy with her.  So far, so good.

Hitty to the world

After a while of having one cat, many people decide to get a second kitty as a playmate.  [1 + 1 = 2, so F(3) = 2]  And after getting a second cat, a third little kitty would be so cute in the mix, no?  [1 + 2 = 3, so F(4) = 3]

REAL WORLD EXAMPLE #2:
My Honored Grandmother had two cats, meek little Tabby and a big black Maine coon cat named Pharaoh.  When my father moved up there to Massachusetts with her, he brought along our old cat Tom.  (The fifteen-hour car ride from Indiana to Massachusetts with an ill-tempered, half-drugged part-Siamese is a tale better left for another time.)  So by adding a third cat to the mix, we were a stable position.  And when poor Tabby passed away, Honored Grandmother adopted spritely Henry.

3 kitties

So far the Fibonacci Cat Sequence is fairly linear, except for a little dawdling there at the beginning. But here’s where things start to take off.  Once a person has three cats, they may not simply get a fourth cat.  They will immediately get a fifth cat.  [2 + 3 = 5, so F(5) = 5]

REAL WORLD EXAMPLE #3:
My aunt passed away a bit ago, and she had two cats, Sassy and Ginger.  So those two cats came to live with my father and Honored Grandmother.  And then they had five cats.  Not too long ago, Pharaoh fell ill and passed away as well, and then there were four.

BUT FOUR IS AN UNSTABLE POSITION IN THE FIBONACCI CAT SEQUENCE.  NATURE WILL NOT ABIDE IT.

Just recently, one of Stockbridge’s most celebrated residents, Mary Flynn, passed away, leaving behind her cat Andy.  Andy has come into Honored Grandmother’s care, and now they once again have five cats.

From here, the sequence really starts to take off.  [3 + 5 = 8, so F(6) is 8; 5 + 8 = 13, so F(7) is 13; 8 + 13 = 21, so F(8) is 21, etc.]

cats cats cats

And this is where the danger really begins, in a phenomenon I would like to tentatively call the Fibonacci Cat-scade Scenario.  The further you go past three cats, or F(4), the more out of control your cat-hoarding tendencies get, until you suddenly are up to your eyeballs in fur-buckets.  Once you have five cats, you cannot simply get a sixth or seventh– you must get an eighth.  Once you have eight cats, you cannot simply get a ninth, tenth, eleventh, or twelfth– you must get a thirteenth.

We must now examine the risks of becoming a Crazy Old Cat Lady (COCL).  [I use the term COCL in a gender-neutral sense: both men and women can become Crazy Old Cat Ladies, and the term is simply being used out of respect for tradition.]  Estimates vary as to when precisely a person becomes a COCL, and future research will need to investigate how age, gender, and actual insanity modify this number.  My work here is primarily to create a mathematical backbone of sorts for those future investigations.

For now, I will postulate that the divergence point between a strict linear model and the Fibonacci model at F(4) is the COCL Limit.  Once you have more than three cats, you are in danger of being a Crazy Old Cat Lady.

cat graph

In the case of Honored Grandmother, I’ll give her a pass, partially because my father lives there in the house with her (so two of the cats could be his, and three of the cats could be hers), and partially because she’s the most awesome, tough-as-nails octogenarian I know.  But for others tempted to expand their cat-families to F(5) and beyond… beware.

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Memory


I have never been very rebellious.

I think I’m living on the edge when I choose to buy a different entree at a restaurant or decide to buy a new pair of shoes. There was one Kindergarten day, however, that I tasted rebellion. I saw the edge, and I ran to it. I danced on it. I made it mine.

It was free-time, and the teacher had turned her back. My boyfriend-of-that-week and I had finished up our very romantic activity of disecting ant brains in the corner and decided it was time to join in a little more socially acceptable fun. We went over to our friend who was playing with the memory cards, and he was nice enough to instruct us in an innovative and quite cool way to use the memory cards in another game. This was ingeniously titled “Flick the Memory Cards Across the Room.”

It was obvious that this game was an ageless classic before we even began playing. Thus with euphoria we began to flick all the cards, one by one, in large arcs across the classroom to the awe of our peers. We were heroes! We were awesome! I began to understand why people crossed socially acceptable norms! I began to see the possibilities of a life truly on the edge, the edge where games were played with the pieces of other games.

It took about 5 cards flying at break-neck speed through the kinder-air-space for the teacher to approach our table with a face that could only mean the worst punishment known to 5 year olds world-wide. Time Out. And for the first time in my life I was sentenced  to engage in the shameful, silent solitude.

We were forced to sit at a table, facing away from the other kids, only able to look at the wall of times tables in shame – a public, mathematical doom. I felt I had no choice but to begin planning my funeral in my tiny, plastic chair. I knew that once the adults of my young life found out of my unforgivable sin that I would certainly pay. What would my friends think? What would my mother think? What on earth would my punishment be?

That afternoon my friend’s mom picked me up, and I swore she knew. I walked begrudgingly to my decided fate of hours hung upside-down, perhaps a brief session of water boarding, and then the worst possible option I could think of – incurable diarrhea. She must have known that I would be forever marred by my time out experience. Yet she didn’t say anything.

I wasn’t fooled, though. I knew she was taunting me in her head. Reading into every silence and jumping at every sound I began to deflate. I soon became the blubbering mess of paranoia and guilt that my mother picked up when she got off work.

I sloshed around in the car feeling sorry for myself waiting for the news of my social blunder to come forth. What kind of mother was she? She should have unleashed indescribable wrath by this point! The teacher must have contacted her of my transgressions! I then decided that if she wasn’t going to be the adult she should be that I needed to take over. I needed to tell the world what I had done!

She then began to laugh! Laugh I tell you! Here I was dying of guilt and shame, and she found it humorous.

I was dumbfounded.

My mother later took pity and explained that she was entirely pleased with herself for having trained me to punish myself like a very simple dog. (It still works. I haven’t lived with her for years and still call to randomly confess wrong-doings.)

And as for the time out? She didn’t care at all.

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