Geniuses Determine How Long It Would Take for Star Trek’s Tribbles to Completely Fill the Enterprise

A new paper guesstimates how long it would take for tribbles to fill the USS Enterprise on Star Trek.The math of population growth is more than just exponential.Spock calculates the population of tribbles in the classic episode, “The Trouble with Tribbles.”

Physics undergrads at the University of Leicester have made a growth equation for the Star Trek universe’s infamous troubling tribbles—purring balls of fluff that rapidly multiplied aboard the USS Enterprise in a classic 1967 episode. The students did this research for publication in Leicester’s undergraduate journal Physics Special Topics.

The “Trouble with Tribbles” application is novel, but this fits into an old math problem that many of us learned about squirrels. Population is funny when it’s tribbles multiplying the Enterprise into oblivion, but real populations don’t increase exponentially forever—it’s never that simple by a long stretch. So the ideas at play are exponential growth and then logistic growth, which can be gathered together as population or demographic formulae.

Tribbles are taking over, but at some point, the ship would be saturated enough with tribbles that there’s no room for new tribbles. That’s the carrying capacity of tribbles for this specific area, which is the inside of a spaceship instead of, say, a city park. Growth does not continue at exponential pace.

It’s here that our friends in Leicester begin to go wrong. They use an exponential equation instead of including the natural logarithm that better represents how a population approaches carrying capacity. As Khan Academy puts it, “Exponential growth produces a J-shaped curve, while logistic growth produces an S-shaped curve.”

Indeed, the students acknowledge this in their paper. Even within the utopian environment of the Enterprise, where every atom is recycled and made accessible again via the replicators, the tribbles can’t just reproduce forever; this isn’t the Library of Tribabel. Where squirrels or rabbits end up competing with each other for increasingly scarce food and other resources, the tribbles are being fed poison in an effort to control them.

“Luckily, in the crew’s case, the tribbles are feeding on toxic grain and begin to die out, so the population of tribbles does not end up filling the entire ship,” the students explain. “In this case, the assumption that the tribbles remain alive is incorrect. This means that the tribbles would not fill the USS Enterprise in the short time of 4.5 days.”

Examining your assumptions is a very . . . logical thing to do.

But how did they arrive at the estimate of 4.5 days to begin with? First, the students used an existing estimate of the volume of the Enterprise, which they sourced from a Wired article titled simply, “How Much Does the Enterprise Weigh?” Then they measured a “replica tribble” that they assume, intriguingly, “is roughly cylindrical.”

Each tribble has a litter of 10 young per 12 hours. By using the known population over time, they found an equation to represent the unknown “growth constant” of the tribble population:

“T is the number of tribbles after time t, T₀ is the initial number of tribbles at time t = 0, k is the growth constant of the tribbles (to be determined) and t is the time in hours,” the students explain. Using their estimates of the volume of the Enterprise and the volume of a tribble, “we found that the number of tribbles required to fill the USS Enterprise is 18.4 ×10⁹ tribbles.” From there, they calculate out the total required time of 4.5 days.

To really get into the nitty gritty of where and how the tribble population would reach carrying capacity, we’d need to add a lot more parameters. The Enterprise isn’t one giant open space inside, and tribbles need air to breathe, for example. Indeed, the future is bright for tribble-based math for these undergrads, with nowhere to go but up—just slowing more as they reach the carrying capacity.

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