Cat Food Randomization:
The World Conspires Against Me
Contributed 3 November 2006 by a human "Provider For The Cat"

There are at least two constants in my life: 1) I love cats, and 2) I dislike the process of shopping. I make no excuses for the first (most men claim to be dog lovers), it is simply a preference of personality. As for the second, although I love SafeWay (often having referred to such locales as similar to DisneyLand), the process of shopping proves to be far too time-consuming and entirely inconvenient. Perhaps if I worked less, or if those who control the outer bounds of our Earthly existence would extend the Terran rotation another six hours, shopping would be less annoying. Alas, neither scenario seems possible at this time, and so I do what I can to reduce the anchor-like drag on my limited time:

I buy fifty-one cans of cat-food.

Why do I buy fifty-one cans of cat-food, you ask? Well, the answer is simple: The cat-food is on sale. And when the conditions are ideal, one must take advantage of a situation, jumping in with both feet. The conditions are as follows: 1) An item is on sale; 2) The sale-price is acceptably low (as opposed to "SAVE 5 CENTS PER CAN!!"); and 3) The item is something I actually use. I do not use dark-rye bread, and so despite the undoubtedly excellent sale price on dark-rye bread, I do not buy such. If you enjoy dark-rye bread, SafeWay is probably having a sale. Hurry up now, before all of the dark-rye bread is sold out. I also do not use certain varieties of squishy-cheese, hair products, canned beans or feminine hygiene devices. Despite the sale prices ... I'm sure you get the point.

What about the cat-food? What about this randomization? And where is the conspiracy? I hear your questions. No doubt I digress. But such digression is necessary at this time to prove my sanity, despite such insane circumstances. Please, Dear Reader, make with the patience and read on.

At this time in my life, I live with a cat. Anyone who has experieced such will understand my statement is completely accurate, as the cat does not live with me. The household belongs to and is controlled by the cat. I am merely a small subservient part of the cat-empire which has chosen to set up a base in the hills of San Rafael and allows me to find shelter under its roof. I have signed and agreed to the "Terms Of Co-Habitation" as described under contract by the World Cat Federation. They own me.

(Check out The truth is out there.)

No, I am not mentally unstable. I just buy fifty-one cans of cat food because it is on sale.

Intellectually speaking, cat-food is a difficult item to purchase. It's the variety! First, how can any person who cares for a cat expect said cat to find enjoyment in food when eating the same thing day after day? Second, who in the world knows what food a cat ultimately desires from one moment to the next? Chicken, beef, sea-food, gravy, medley, sliced, aspic, bits of cheese, senior, organs, no-gravy, ground, dinner ... the list goes on. Some cats will meow continuously until fed and then immediately begin hoovering up what ever food is placed in front of them. Some cats will act entirely aloof, not even appearing for the ceremonial "Opening Of The Can", and then forgoing the hoovering process in favor of turning up their pink little noses at a loving offer. And then other cats will act enthusiastic about the food but walk away when the bowl touches the floor. Odd behavior from these cats. I suppose it's one reason I love them.

And what in Hell is aspic? Ugh.

Again, I digress. On to the topic at hand. Fifty-one cans of cat-food, two different manufacturers, at least nine varieties, five or six cans of each variety, and an absolute necessity that no variety of food is served to the reigning cat two days in a row. One widely held belief is that no cat can remember the food it is served two days in a row and thus nobody should care. If "Sliced Chicken And Beef Medley In Aspic For Seniors" is on sale, many humans would have Kitty being served that very brassez du mal every single day, day-in and day-out, for ever more, without end, until it runs out.

"Here you go Kitty, now hoover down your nice brassez du mal like a good kitty. Oh, poor Kitty! Why are you so sad? I've been feeding you the "Sliced Chicken And Beef Medley In Aspic For Seniors" every day now for twenty-seven days. Can I spoon some more aspic on it for you?"

(The police would later find a partially shredded, decomposing body wedged thoroughly between the refrigerator and the wall, small bits of litter and fur clinging to the skin, thus betraying the mysterious attacker. No doubt the quiet neighbor living two doors up the street, whom everybody thought was a nice guy, had performed the grisly task. After all, he does own a BB-gun. Said neighbor would be unceremoniously hauled away to a dank cell somewhere far beneath ground never again to see the light of day. The house in which the grisly task had been completed would be sold and nice new neighbors would move in. The nice new neighbors would find Kitty flitting amongst the bushes in the back yard, install a PetCo-approved cat-collar and assume the duties of "Providers To The Cat". And then one day SafeWay would have a great sale on "Ground Sea-food And Beef With Organs And Bits Of Cheese AND Gravy In Aspic". The Providers For The Cat, spying such a great sale and carefully weighing their financial options, would buy about thirty-twelve cans of this melange de vomi. And exactly twenty-three days later the grisly task would be repeated, this time the police finding partially shredded and decomposing bodies buried under an enormous avelanche of canned "Ground Sea-Food And Beef With Organs And Bits Of Cheese AND Gravy In Aspic". The house would be cleaned, the cat-food sold to pay off the mortgage, and nice new neighbors would move in. This time, however, in an effort to escape the insanity, Kitty would pack his bags and jump the first freight to anywhere out of town. Although known for their occasional viscious behavior, cats are certainly not merely cold-blooded killers. End of story, please drop the curtain.)

I desire not to be shredded and stuffed between large kitchen appliances, or buried under an avelanche of cat-food. I desire only that the cat for whom I care is as happy as an overly-fuzzy house cat and agent of the World Cat Federation can be (, and that said cat is not subjected to a continuous flow of the same meal.

(Oh damn the lack of opposable thumbs! I long to see the day that the Cat may rise up against the oppressive Can-Opener and triumph once again over his or her choice of food! If only I may last...)

So after careful thought, I devised the Cat-Food Randomization Algorithm.

Some of you may exclaim "I know what an algorithm is!" Some of you may utter "Hmmm. I think I heard that word 'algorithm' back in high-school." And some of you may grunt "Urph?" while hoovering down your own pile of "Mashed Chicken And Imitation Crab Guts In Aspic For Seniors". (Yep, there's that 'aspic' again.) And so for all of you, I provide the following: An algorithm is a step-by-step problem-solving procedure, especially an established recursive computational procedure for solving a problem in a finite number of steps. And thank "God" for that finite number of steps Ladies and Gentlemen, for my Co-Provider For The Cat, with whom I also co-habitate, had listened to just about enough of my seemingly inane ramblings on the topic of cat-food randomization and was soon going to begin beaning me with vegetables if I did not immediately step to the task of properly installing the newly-purchased cat-food in our pantry.

The algorithm as I designed it followed thusly:

1) Carry the two shopping bags, filled with a total of fifty-one cans of newly-purchased cat-food, in to the living room.

2) Dump out all of the cat-food on to the living room rug. (We wouldn't want to dent the nice floor.)

3) Sit down and stir about the cans of cat-food, all the while intentionally paying no attention to the can labels.

4) Haphazardly place the cat-food back in to the grocery bags to ensure no order was formed.

5) Carry the two grocery bags of cat-food back in to the kitchen and properly install the cat-food in the pantry, without ever looking down in to the grocery bags, thus further ensuring the random selection of Kitty's breakfast and dinner.

It seems simple enough. It involves a finite number of steps. It involves a recursive, somewhat mathematical procedure. (Okay, so I'm stretching a little here.) It is designed to solve a problem.

How on Earth could something so simple and beautifully benevolent go so horribly awry?

I dumped out the cat-food. I mixed the cat-food. Then I mixed the cat-food again. I tossed it back in to the grocery bags, paying careful attention to the degree of my haphazardness. And when I stacked the cat-food, I did not look down.

And here, HERE, is the point at which the conspiracy is EXPOSED! For the LAST TWO CANS of the fifty-one cans of thoroughly mixed cat-food WERE OF THE SAME BRAND AND VARIETY!!

How could this be? With all of the forethought, the analysis, the loving feeling and the absolutely flawless execution, HOW COULD THE CAT-FOOD BE PROPERLY INSTALLED IN THE PANTRY AND THE LAST TWO CANS BE OF THE SAME MANUFACTURER AND VARIETY? HOW? I ASK YOU!

At this time, let us calmly back away from the precipice of intellectual disaster. Let us straighten our shirts, smooth down our hair, and pick up all those pens and pencils from the floor. Let us enter the realm of mathematics.

(I am not insane. I tell you: I am not insane!)

We have the following: fifty-one cans of cat-food in nine different varieties with no less than five but no more than six cans in each variety. We shall not, for this analysis, consider the two different manufacturers of said cat-food as this variable will be absorbed in the analysis of the nine varieties. Let us label a sample set of cat-food thusly:

5 cans of variety A

5 cans of variety B

5 cans of variety C

6 cans of variety D

6 cans of variety E

6 cans of variety F

6 cans of variety G

6 cans of variety H

6 cans of variety I

(I am not using actual cat-food varieties for the sake of simplicity and so I do not have to consider the gut-wrenchingly disgusting cat-food blends typically seen on store-shelves. Who makes this stuff up, anyway?)

Further, let us assume that the two identical cans were picked from a set of six cans. They actually weren't, but let's just say, so that the chances of a conspiracy are reduced. On first pick, the chances of picking a can from one of the sets of six cans are six in fifty-one, or 11.76%. But this doesn't matter because we're not yet specifying one particular variety. (I'm just keeping you on your toes.) Now let us pick another identical can. Because we have removed a can from the overall set (and the target variety), our chances of immediately picking another can of the same variety are reduced to five in fifty, or 10%. Simply put, that's a 1 in 10 chance of picking two identical cans of cat-food from an overall set of 51 cans.

Now let us sit quietly and contemplate those odds. 1 in 10. That's pretty low. I once bet on a horse with odds similar to this. The ticket was not a winner. And although I had a lot of fun rooting and shouting for the horse (whose name I remember to be "Fantastic-Lead-Ass"), I did indeed learn my lesson. But this is not lesson enough to remove all reasonable doubt of a conspiracy.

So now ... now I shall deliver the coup de grace (that's not a variety of cat-food): What are the odds that the two similar cans WOULD APPEAR ONLY AT THE VERY END OF THE SERIES? We are not merely rolling a set of dice here, Ladies and Gentlemen. Oh no. That would be far too simple. This is a conspiracy we're dealing with and I intend to annhiliate all reasonable doubt of its existence.

Why is this further analysis of the order in which the cat-food was stacked of any importance, you ask? Well, it's like this: There are two basic components to any statement: 1) The content of the statement, and 2) The delivery of the statement. (Heh. I just used a double-colon in a syntactically correct manner.) In this case, the content is obvious: Someone, somewhere is trying to tell me that he or she is firmly in control of the realm in which I exist, even in control of my very being, and there is nothing I can do about it. Oh, so obvious. Oh, so easy.

But the delivery!

And this is where the entire idea of this treatise (now far more lengthy and deep than I had originally intended) comes right on home. Barring a terrible fear of stage-fright, any person can stand on a stage and tell jokes. Only those who master the delivery of those jokes can properly be called comedians and avoid being coated with vegetable matter. The delivery of a joke (or speech or sermon or statement) is what causes an audience to sit up and take notice of exactly what is going on.

In the "Case Of The Mysteriously Stacked Cat-Food", if two identical cans were picked and stacked next to each other somewhere in the middle of the stacking, they may never have been noticed, no conspiracy would have been suspected and all of this writing may never have taken place. But after experiencing this perplexing set of events, I went back and inspected the stacks of cat food (all seven of them) and THERE ARE NO TWO IDENTICAL CANS STACKED IN SEQUENCE. Oh my, what are the odds of THAT? The delivery of this statement seems to have found its mark.

So at this time we consider two further sets of odds. First, we consider the odds that the last two cans are identical. Second we consider the odds that no other two identical cans in the set are stacked next to each other. As you will see at the end, the odds of the cans of cat-food being stacked as they were are pretty darned slim.

As astutely pointed out earlier, the odds of picking any two identical cans from the entire set of fifty-one are about 1 in 10. But when forty-nine cans have been picked and stacked, what are the odds that the last two cans are identical? If any one variety has a 6 in 51 chance of being picked, we have to consider the odds of two cans, and multiply those odds. 6 in 51 is about 11.76%. So the chance that the last two cans are of the same variety is (11.76% x 11.76%) or 1.38%. For you gamblers, that's less than 1 in 72. Are we getting somewhere yet?

In order to compute the odds that no two identical cans in the first forty-nine of the set are stacked next to each other, we must first start with the odds that any two identical cans WILL be stacked next to each other. And the odds of this are pretty good. If two random cans are selected from the fifty-one and they are not identical and they are both from sets of six cans, then the average number of cans per set is 5.44. This means that any variety has a 5.44 in 49 (or 11.1%) chance of being picked. And since there are nine varieties, we multiply the 11.1% times 9 to find the odds of any two cans of the same variety in the first forty-nine being stacked next to each other. The result is a 99.9% chance that any two cans in the first forty-nine will be identical and stacked next to each other.

"But wait!", you protest, "As the cans are picked, the odds of two identical cans coming up next to each other decreases!" To which I reply, "Ah, but you have not considered the uniform decrease in not only the varieties, but also the total available set." And I explain. Let us assume we have picked exactly half of the forty-nine cans. I know this is impossible, for how can one select half of a can? But in this case, for the sake of the mathematics, we are going to assume. And then let us assume there are exactly half of the cans in each variety remaining (I know, more fractions). At this point, we would have a total of 24.5 cans and 2.72 cans in each variety. At the half way point, the odds of picking any one variety are 2.72 in 24.5, or 11.1%.

So it is settled. If stacking a set of forty-nine cans of cat-food, the varieties and quantities of each being described as above, there is a 99.9% chance that at least two identical cans in the set will be stacked next to each other.

This means there is a .1% chance that NO identical cans will be stacked next to each other. Are you a gambler? How do those odds of 1 in 1000 sound? Oh this is definitely going somewhere.

And now, I will blow your mind. If there is only a .1% chance that no identical cans in the first forty-nine will be stacked together, and there is a 1.38% chance that the last two cans will be identical, then the odds of both of these circumstances occurring is only .00138%. How much would you bet on odds of less than 1 in 72,463?

I believe this eliminates any resonable doubt. If you believe in evolution, there were better odds than this for not only life developing on this planet, but on the specific development of human beings such as we are.

My cat-food randomization algorithm did not fail. Most random studies succeed with far less work than being twice randomized under double-blind circumstances. I do not believe many people would consider odds of less than 1 in 72,463 as an indicator of any predictability.

The statement has been well-received. There is a conspiracy afoot. Some one, or some thing, believes he, she or it is in control, and appears to be flexing some muscles. Well, I flex back. And I say to this being, this thing: Step out! Step out in to the light of truth! Show your self to me and to the others you would daily torment with such audacity! Do not hide behind the human frailty of our invented "coincidence".

I dare you to show your self.

And if you choose to remain a coward, then let loose of my life. Let the cat-food naturally randomize in a way only such a well thought out and executed algorithm would allow. Let the kitties of the world not be tormented by an undeviating diet. Allow those who live on this small rock a life of surprise and delight.

You would not want to incur the wrath of the World Cat Federation ( Nor would you want to incur mine.

And now I shall go forth, spreading my message of unbelievable circumstance, and improving the cat-food randomization algorithm. I seek not only to help the kitties of the world (in my servitude to the World Cat Federation; see The truth is out there), I seek also to better the human existence. So many of us humans have been misled, placing all of our faith in false leaders; I shall seek to spread the word of the imperfections in those who would seek control.

I see you out there. Oh yes I do. Numbers do not lie. I caught you this time. Will the next advantage be mine?

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