Drake’s Equation vs. the Fermi Paradox

Or: Modifying Drake’s equation to account for the Fermi paradox

Drake’s equation

Drake’s equation is an attempt to approximate the number of intelligent civilizations in the Milky Way galaxy that are broadcasting signals at a particular point in time:

N = R * fp * ne * fl * fi * fc * L

As per Wikipedia:

R = the average rate of star formation in our galaxy
fp = the fraction of those stars that have planets
ne = the average number of planets that can potentially support life per star that has planets
fl = the fraction of planets that could support life that actually develop life at some point
fi = the fraction of planets with life that actually go on to develop intelligent life (civilizations)
fc = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space
L = the length of time for which such civilizations release detectable signals into space

More about the Drake equation: https://en.wikipedia.org/wiki/Drake_equation

Fermi paradox

The Fermi paradox is the apparent contradiction between:

  • the high probability that life exists in multiple places throughout the Universe,
  • the lack of evidence for the existence of extraterrestrial civilizations.

More about Fermi’s paradox: https://en.wikipedia.org/wiki/Fermi_paradox

Modified version of Drake’s equation to account for Fermi’s paradox

My proposal is that Fermi’s paradox constitutes what is generally perceived as a paradox because it incorporates two implied pre-conditions: When one claims “lack of evidence”, it can only be claimed:

  • from a perspective,
  • at a point in time.

If a certain observer, with a limited perspective, does not detect or acknowledge evidence on something, it doesn’t mean evidence doesn’t exist. Which is followed, logically, by the idea that, in case an observer lacks evidence but evidence might indeed exist, it’s a distinct possibility that the observer hasn’t detected (or acknowledged) that evidence yet.

Mathematically, then: D(o, N(t))=f(o,t)

Meaning: N, the number of civilizations that is broadcasting some kind of signal, at a certain point in time, AND end up being detected by us is, indeed, not only a function of time but also a function of the observer. D(o, N(t)) is the number of civilizations detected by observer o from those N(t) that are emitting.

If we are to study the nature of this function f, we should assume both:

  • random/accidental components — such as the distance between the observer and the closest signal; this does indeed allow for the statistical anomaly that an observer might be very far from any detectable signal for a very long time.
  • artificial components — the occurrence of the signal depends on the observer’s readiness and capacity to detect it.

I believe random/accidental components have already been covered by Drake’s equation. It covers this statistical distribution by defining certain factors as averages, e.g.:

R = the average rate of star formation in our galaxy
ne = the average number of planets that can potentially support life per star that has planets

What is not covered by Drake’s equation is:

  • intelligent design that times the signal precisely so that it reaches the observer only under some circumstances: as i defined it above, readiness and capacity, or, we can use the notation rc;
  • reduced capacity to detect signals — again, quantified by: readiness and capacity, or rc (i.e. perhaps we simply lack the technology, at the moment, to detect those signals that are emitted).

It’s not my purpose, in this article, to define or describe our readiness and capacity to detect a signal coming from an extraterrestrial civilization — i will leave this to the reader. However, the purpose of this article is to generalize Drake’s equation to a point where it’s more likely to explain away Fermi’s paradox:

D(o, N(t)) = N(t) * rc(o,t)

or, in more Drake-like terms:

D(o, N) = R * fp * ne * fl * fi * fc * L * rc(o, t),

where:

  • rc is the readiness and capacity of observer o to detect a signal at time t
  • o is humanity in the case of Fermi’s paradox.

One could also approximate rc as a product of the two components, readiness and capacity:

rc(o, t) = r(o, t) * c(o, t)

Conclusion

My conclusion is: the Fermi paradox is highly dependent on 2 variables: the observers (in this case, humanity) and the point in time when the observations are made. In other words, the Fermi paradox is only a paradox to us, right now. I submit that, in a quantum / probabilistic world with changing variables, the Fermi paradox itself will be contradicted by reality in the perception of an ever-growing* percentage of humanity.

* The rate of this growth is, as of yet, undetermined and subject to future observation :) But the point of the readiness and capacity factor (rc) is to make us realize that the process of getting in contact with an alien signal/civilization can depend on us (humanity) and our state to the same degree that it depends on other statistical, cosmological factors.

Photo by Greg Rakozy on Unsplash