### We Know You’re Out There, Spiderman

### Abstract

Using absolutely bulletproof science, we demonstrate that 35.3 spidermen are created annually and that hundreds live secretly among us.

### Introduction

Prompted by arguments about the possibility of radioactive spidermen living
among us, Mr. Harman and I decided to use a probabilistic strategy to
determine how many spidermen (if any) exist on Earth. It’s difficult to
extrapolate from the single known instance of a spiderman (hereafter the *SKI*),
but following the example of the Drake equation we’ve developed a predictive
formula. Behold the incontrovertible majesty of the *Harman-Schwartz equation*:

where:

- \(N\) : the number of radioactive spidermen created each year.
- \(P_e\) : the population of the Earth.
- \(f_s\) : the fraction of people who are bitten by a spider each year.
- \(f_r\) : the fraction of spider-bites perpetrated by irradiated spiders.
- \(f_l\) : the fraction of bitten people who survive.
- \(f_p\) : the fraction of bitten people who develop superpowers.
- \(f_g\) : the fraction of spidermen who choose to use their powers for good.

### Total Population

Note that by using the above formula we’ve only calculated the number of spidermen being generated each year and not the total number of spiderman living on earth at any given time. This can be calculated with:

\[N_{tot} = N(\langle A_d \rangle - \langle A_c \rangle)\]where:

- \(N_{tot}\) : the total number of spidermen living on earth at any given time.
- \(\langle A_d \rangle\) : the expected age at which a spiderman dies.
- \(\langle A_c \rangle\) : the expected age at which a spiderman is created.

### Plugging in the Numbers

- \(P_e\) : The population of the Earth is around 6.67 billion.
- \(f_s\) : We estimate that about \(1.66 \times 10^-3\)% of people are bitten by a spider each year.
- \(f_r\) : Between Chernobyl, Hiroshima/Nagasaki, and assorted other tests and accidents, about 2.55% of the land area of the Earth has been irradiated to some degree. We can use this as \(f_r\) if we assume an evenly distributed spider population.
- \(f_l\) : The vast majority (about 99.9%) of people survive spider bites, but obviously irradiated spiders are more deadly. Let’s set \(f_l\) to 50%.
- \(f_p\) : Working off the SKI, we’d have to assume that this is 100%. Let’s be conservative, though, and say only a tenth of people bitten by radioactive spiders develop superpowers.
- \(f_g\) : We’re totally guessing here and saying that 25% of super-powered radioactive spidermen will dedicate their lives to doing good.

Plugging those figures into the equation, we estimate that on average 35.3 spidermen are created annually.

- \(\langle A_c \rangle\) : The median age in the world’s population is 27.5 years, which is what we’re using.
- \(\langle A_d \rangle\) : This is a controversial term. For the purposes of our study, we’ve made the simplifying assumption that spidermen have an average lifespan equal to the human average (73.1 years). It could be argued for the that spidermen are especially prone to an early violent death, but following the example of the SKI we argue that the rates of violent death and cloning are approximately equal, thereby sidestepping the whole issue.

Given these estimates, we find that at any given time on Earth, on average there are 1,609 radioactive spidermen living secretly among us. \(\blacksquare\)

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