# How much is a mole of monkeys?

– Posted June 1, 2015 the refsmmat report · a blog at refsmmat.com

My father is an engineer. It turns out that when engineers are bored they tend to work out solutions to imaginary problems, and since I was trained as a physicist, he often forwards me the resulting email threads.

The most recent topic was this fundamental question: “If one mole of monkeys joined hands and formed a straight line, how far would the line reach?”

A mole, as you may remember from high school chemistry class, is 6.02 × 1023. This is quite a lot of monkeys, so the engineers worked out that, assuming the typical monkey has a four-foot arm span, the monkey chain would stretch for 78 million light-years.

This obviously presents an engineering challenge. How do you construct such a monkey chain? A monkey space elevator? Their arms couldn’t hold the load. A giant spacecraft full of monkeys, dispatched to start a chain in deep space, wouldn’t work—how do you plan to keep a mole of monkeys entertained and alive for the centuries it would require to transport them to distant empty space to start the chain?

Clearly, concluded one engineer, the answer is genetic engineering. We could just produce smaller monkeys, a chain of which would fit inside of Earth’s atmosphere instead of stretching into distant space, leading “to an earlier monkey chain implementation, with all of the benefits that will ensue therefrom.”1

This is when the email chain reached me, and I realized that my physics degree needed to be put to good use analyzing the problem.

## Micro-monkeys

Micro-monkeys are problematic. The smallest monkey available off the shelf, the pygmy marmoset, weighs just a few ounces but still has a four- to six-inch arm span. That means nearly ten million light-years of marmosets, still a quite impractical amount.

Clearly we need a bespoke monkey solution. How small would the monkeys have to be so that we could fit them into the atmosphere? A reasonable approach would have the monkeys encircle the equator a few times.2 If we let them go four times around, we’d have a 100,000-mile chain of monkeys, but to fit a mole of monkeys, each monkey would have to be just 10-14 inches wide. That’s 0.26 femtometers, or about a third the radius of a proton.

Now, if you used advanced biological engineering to compress a monkey (with fully-functioning organs—say, a few ounces of body parts) to a third of a proton radius, the monkey’s density would be rather extreme. A cubic meter of these engineered monkeys would weigh 1045 kilograms, or about 200 times the mass of the Milky Way galaxy. Such a density is about 1014 times the density of an Earth-mass black hole, so if the monkey production facility ever allowed enough monkeys to congregate in one place, the Earth would be consumed by a black hole.

Even if we did prevent this with basic safety precautions,3 compressing monkeys to such a density would almost certainly result in nuclear fusion. If we were to produce a 100,000-mile-long ring of superdense monkeys looping around our equator, we’d have our mole of monkeys for just an instant before the resulting nuclear explosion annihilates the Earth, probably surpassing the Sun’s energy output for one brief moment.

At least we’d get the chain of monkeys. Destroying the Earth isn’t a big problem.

Sure, the instant vaporization of an entire planet sounds unpleasant, but it’s always important to carry out a cost-benefit analysis before letting petty human emotions to get in the way of scientific progress. The United States government estimates the value of a human life to be about \$9 million, so the world population is worth about \$65 quadrillion. Throw in a few quadrillion more for accumulated land, equipment, intellectual property and so on, and we have perhaps a \$70 quadrillion (or \$7 × 1016) cost to ending every life on Earth in an enormous monkey fireball.4

On the other hand, launching our monkey chain safely to space has a considerable launch cost—the cheapest rockets cost perhaps \$4,000 to launch a single pound of payload into low Earth orbit, and a pygmy marmoset monkey chain would have to be launched much further than that to be practical. The pygmy marmosets would cost vastly more than \$1026 to launch into orbit, not counting bananas.

Assuming the cost of feeding a mole of pygmy marmosets is comparable to the cost of genetically engineering micro-marmosets—clearly a reasonable assumption—we can see that destroying the Earth is clearly the cheaper option, and hence the responsible decision by many orders of magnitude. Physics solves yet another important problem.

1. Such as the reproduction of the lost works of Shakespeare.

2. Spanning oceans is left as an exercise to the reader.

3. Consult any standard laboratory safety text for the appropriate precautions when assembling superdense genetically engineered pygmy marmosets.

4. Some of the costs could be recouped by selling the TV rights, which would undoubtedly sell for a fortune. Who doesn’t want to watch cuddly animals or enormous explosions? Why not both?