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.


(Video Link)

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)

Newest 3
Newest 3 Comments

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.
Abusive comment hidden. (Show it anyway.)
Yeah, I'd add a hand crank to that retrieving the kite thing. It wouldn't be that hard, so then you could repeat the process over and over. Just add cheap labor, or in the case of post-apocalypse, the young, and generate away! :)
Abusive comment hidden. (Show it anyway.)
Again, in post-apoc world, you don't want to draw attention to yourself, plus there's the potential for mobility with this design. May have to break camp and head to the mountains.
Abusive comment hidden. (Show it anyway.)
I'm having trouble grasping how this is an improvemenet over a windmill. I suppose you could let the kite out, have it collapse, and then have a wind-powered device to reel it back in; but then why not just use the wind-driven device to generate all the energy in the first place?
Abusive comment hidden. (Show it anyway.)
The advantage is that they fly "to altitudes of 2,600 feet, where wind streams are four times as strong as they are near ground-based wind turbines."
The kite collapses when it reaches the end of its tether, so it is easier to rewind.
What happens when the wind stops and the huge kite crashes at the end of a half mile tether?
Abusive comment hidden. (Show it anyway.)
A 'laddermill' would even be better: it is fully wind driven (so yes, it's a modern version of the windmill. Only much bigger and much more energy efficient.

http://www.lr.tudelft.nl/live/pagina.jsp?id=8d16d19a-e942-45aa-9b52-48deb9312e92
Abusive comment hidden. (Show it anyway.)
Commenting is closed.

We hope you like this article!
Please help us grow by sharing:

Get Updates In Your Inbox

Free weekly emails, plus get access
to subscriber-only prizes.

We won't share your email. You can cancel at any time.
Email This Post to a Friend
"Math: How Many Tribbles Were Onboard the Enterprise?"

Separate multiple emails with a comma. Limit 5.

 

Success! Your email has been sent!

close window
neat stories? Like us on Facebook!
Close: I already like you guys!