Math: How Many Tribbles Were Onboard the Enterprise?

In the classic Star Trek episode "The Trouble with Tribbles," the Enterprise and a space station become infested with adorable, trilling balls of fluff called tribbles. Tribbles are cute, so you may be inclined to keep one as a pet. But be warned: tribbles reproduce rapidly, so they will soon eat all of your food.


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In this scene from that episode, Spock says that there are 1,771,561 tribbles onboard the Enterprise. How does he come up with that figure? Kyle Hill, a science journalist, derived Spock's mathematical calculations.

Hill sketched the above figures and wrote:

Above, I started with what I knew. For P (population) at time 0 (when the tribbles first came aboard), there was 1 tribble. Easy enough. We also knew, thanks to Spock, that after 72 hours, P was equal to 1,771,561. Now it gets a little more complicated.

To write a useful equation, what we really want to know is what the population of tribbles will be at any one time. Therefore, I wrote Population=P(t). But we know that tribbles grow exponentially (or we are checking that assumption), so we have to include that information. To find the rate of tribble growth, we take the mathematical derivative of Population=P(t) to get P’(t). Putting those two together we get P’(t)=kP(t). (This equation says that the rate of growth is equal to some constant k times the population at some time. pops out of the normal process of taking the derivative of a function.)

The episode ended with Scotty beaming the surviving tribbles onto a nearby Klingon warship. Hill anticipates catastrophic results:

There was serious tribble trouble at 72 hours. At around 100 hours of growth, there would be a tribble occupying every cubic inch of volume on the Enterprise. Kirk and his crew would drown in pregnant, fuzzy aliens. And because the growth is exponential, it would get much worse very quickly. Less than 8 hours later, our equation tells us that Spock and Kirk would have to deal with a thousand times more tribbles — well over two billion. That’s enough to fill 1,200 Borg Cubes completely. Conclusions like that are worth all the math.

Left unchecked, the tribble birth rate equation shows an unstoppable expansion of exponential growth towards domination. That’s something the Klingons know all too well.


Comments (3)

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At some point, the advancing surface of the ball of tribbles will be traveling at the speed of light. Before the, though, the gravitational pull of all those tribbles would make the ones in the core begin to undergo nuclear fusion. The energy would cause an explosion, but if the mass of tribbles is high enough, the explosion might be contained, creating a tribble-fueled star.
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It's a food trough for goats that are on a diet. When they get too fat, their stomachs get poked by the sharp spikes and discourage over-eating.
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Hi !
It's an ancient scoop designed to pick up lost buttons in the woods.
Bad design anyway, it often picks up lots of berries and no button at all.
So, you need to throw the berries away every minute, but still no button !

Playing Schrodinger, Large, Grey, please.
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It's a shovel for encouraging five-year-olds to help with gardening. "Ye're an excavator, Harry. Now dig me a hole."

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BraveStarr, Ladies fit M, please (:
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Actual Use Guess: Might be for harvesting huckleberries, or some such.

Attempt at Humor: Industrial Size Nitpicker, every boss I've ever had possessed one.

Lesser of Two Weevils, Size XL, any color
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This is a scale model of the non-mechanized backhoe model of the 1930s, designed to give more people jobs as they did manual labor during the Great Depression.
http://www.neatoshop.com/product/Great-Vocab-Didnt-Save-The-Thesaurus-From-Extinction M
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This is the manual roto-tiller for hipsters who think using a gas-guzzling machine to make their organic gardens is too mainstream.
http://www.neatoshop.com/product/Great-Vocab-Didnt-Save-The-Thesaurus-From-Extinction M
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This is a pooper-scooper designed to spear & scoop up the turds, but let more sand & earth fall back to the ground.
http://www.neatoshop.com/product/Great-Vocab-Didnt-Save-The-Thesaurus-From-Extinction M
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It is the "Wilson Scoot Around": the deceptively simple portable rig they used to bring the animatronic head of the next door "neighbor" from the classic ABC sitcom "Home Improvement" around to boat shows and monster truck rallies for promotional purposes.
Viva Twin Peaks 2x
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It's a grooming tool for your pet Rancor!! It helps scrape off dead skin and dirt and leaves them with the healthiest of skin!

The Hound Pistols (censored) Small
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Ostrich neck basket! Their head fits through the slot on the top and it slides down their neck and rests on their chest. They can guard your valuables and no one goes near it because of the spikes, and o yea it's hanging from the neck of a big angry bird.

The Hound Pistols (censored) Small
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A fine folk art example of an Italian spaghetti harvester. Just run the serrated scoop through the spaghetti trees to remove the ripe pasta.

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Offworld Colonies -- Black -- XL
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