I would like to create a formula that tackles the question of how likely a civilization is to commit self-annihilation. At first glance it doesn't sound possible or practical for that matter. I concede it's difficult to formulate and is likely to not be 100% accurate. However, I think it has merit nonetheless. To quote one of my favorite statisticians George Box:

All models are wrong, but some are useful.

This mind-set is useful when discussing the self-annihilation of civilizations. For instance, Frank Drake didn't have the audacity to think he could actually quantify how many intelligent civilizations are in our galaxy when he formulated the Drake Equation:

$N=R_*\cdot f_p\cdot n_e\cdot f_l\cdot f_i\cdot f_c\cdot L$

Rather, the point was to generate scientific discussion and apply concepts as currently understood (Fermi paradox, ect). Another cool thing about the drake equation is that although it tries to model something ambitious like the number of intelligent civilizations, the right-hand side variables are mostly able to be objectively quantified. Then there is $f_i$, which is the fraction of civilizations that actually develop intelligence. It's unlikely that $f_i$ can ever be measured or guessed at accurately, but Drake put it in the model nonetheless. From this perspective, the Drake equation shows how much we know and can quantify and what remains purely conjecture.

Similarly, I hope that an equation formulating the likelihood of a civilization to commit self-annihilation can be informative and useful.


In a similar spirit to the Drake equation, how can I create an equation that tries to model the likelihood of a civilization to commit weapons-based self-annihilation using as few purely conjectural variables (like $f_i$) as possible? The left hand side variable is $P$ (probability of self-annhilation). So the output is a probability between 0 and 1. To further make things more manageable, let's limit the specification to at most 7 right-hand variables only (7 is the number for the Drake equation, and it's a lucky number). This way we don't have to model a chaotic outcome that could have very high $k$ (right-hand variables).

  • 1 meaning inescapable self-annihilation
  • 0 meaning totally safe.

$P= ?$

Further Clarifications:

  • Answer should fill in the right-hand side variables, $P=?$
  • Answer doesn't have be an explicit formula, a list of right-hand variables is acceptable
  • No worked out examples are required; I have one provided below for clarity, but I'm not trying to crunch any numbers yet.
  • non-weapon related notions are out of scope; that's not to say they are not important, we're just simplifying things a bit.
  • Priority is given to variables that are quantifiable
  • Regarding model specification, you may want to consider if there are certain components of the model worth mentioning, interaction terms, quadratics (capturing diminishing effects), ect
  • Up to 7 right-hand variables are permitted. We would want the variables with the most(dangerous word choice, I know) explanatory power, and other variables will be assumed to be zero.

Example These are strictly for illustration purposes; please do not over analyze them. That said, suppose a caveman civilization that is mostly peaceful but has a few marauding gangs, all with very primitive technology like wooden clubs and rocks. The probability of the few gangs wiping out the entire civilization should be low. Say: .000000001. In another world where everyone has access to nuclear bombs, John Doe is fired from his job and takes down the whole city with him -- such a world should have a higher $P$, say: .95.

I have included the , and tags accordingly. This is the extent of my research and thought-experiments; if you feel it necessary to broaden the scope beyond these fields, you may. Just explain in your answer.

Disclaimer: I realize there is a subjective nature to this question, but much in the same way that the Drake equation is criticized by some, it is still respected by many. I'm hoping that the tag will allow us to evaluate answers in a qualitative, constructive yet still fun manner.

  • $\begingroup$ Everyone is going to differ on what does and doesn't constitute a meaningful variable in such an equation, as such I've VTC'd as POB. $\endgroup$
    – Ash
    Aug 5, 2018 at 14:30
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    $\begingroup$ @Ash I think that's a reasonable position to take, but I also think that goes against the spirit of the Drake Equation. I still assert that the line in the sand is clear enough for meaningful and constructive answers. There is a kind of paradoxical conflict in terms regarding POB and the hard science tag. There is a saying in statistics that we can always torture the numbers to confess to whatever we want. Indeed, I already conceded in the post about subjectivity, but I take issue with the "P" in POB. There is enough here to avoid pure opinion spouting. $\endgroup$ Aug 5, 2018 at 14:55
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    $\begingroup$ The hard-science tag is particularly inappropriate here, as it's this is wildly speculative stuff. The likelihood for a civilization to "self-destruct" is dependent entirely on the nature of that civilization - something way beyond our ability to model, otherwise politics on Earth would be modeled and predictable by computer, which is not the case. We don't have hard science for this. $\endgroup$ Aug 5, 2018 at 15:52
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    $\begingroup$ This qustion is desperate for the sandbox. Are you asking for the equation? The list of potential variables? The interaction between the variables? A first-order approximation? Note that a PhD thesis could be won with this answer, if the answer is thorough, but by definition that's too broad for the intent of this site. Sandbox. $\endgroup$
    – JBH
    Aug 5, 2018 at 16:48
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    $\begingroup$ Similar to the Drake equation, the variables themselves can be primarily opinion based. You can discuss the likelyhood of a civilization occurring. BUT YOU CANNOT ARGUE THAT THE VALUE CANNOT EXIST IN THE EQUATION. The variable of how likely a civilization appears HAS to be somewhere in the Drake equation, there is no opinion that can disqualify that. Therefore the question above is ANYTHING BUT opinion-based: it asks which variables are necessary to calculate a civilizations chance to annihilate itself with weapons. Not how likely the variables themselves are. $\endgroup$
    – Demigan
    Aug 5, 2018 at 16:49

1 Answer 1


As a nerd that loves a good formula, I'd love to take a shot at this.

In the Beginning

I would like to start with a formula I first heard mentioned in a TED talk by Hannah Fry, "The Mathematics of Love". At one point, she shows a formula that is used to model likely that a couple would get a divorce. The two formulas were as follows:

$$ W_{t+1} = w +r_w*W_t + I_{HW}(H_t) $$ $$ H_{t+1} = h + r_h*H_t + I_{WH}(W_t) $$

Allow me to offer some explanations for the equations. To calculate the wife's reaction, $W_{t+1}$, consider the wife's mood when alone, $w$, plus wife's mood when with husband, $r_w*W_t$, plus the husband's influence on wife, $I_{HW}(H_t)$. The same is true of the husband, taking into consideration his mood when alone, his mood with wife, and the wife's influence on husband.

Hannah makes a throw away comment after showing this formula, mentioning that it also accurately models two countries escalating towards nuclear war (or any other type, I guess). When the two countries or two factions of society or whatever two groups are in conflict and both have procured means of mutually assured destruction, these formulas are a pretty good indicator of a civilization destroying themselves.

But it isn't a probability. So...

There Goes the Neighborhood

I know that the original poster said 0 should be gaurenteed destruction and 1 is no worries whatsoever, but if the equation is predicting how likely a civilization is to self destruct, then we need to flip those values. For this formula, 0 means no chance of societal collapse and 1 is guaranteed destruction.

$P = S_T * W_a * D(I_{AB} + I_{BA})$

Here is the explanation for the variables I used.

$S_T$: Does this society have sufficiently advanced technology to destroy themselves? A caveman society that uses rocks and big sticks would have a low technological factor.

$W_a$: How accessible are the weapons? A caveman society would have readily available weapons, but they aren't very advanced.

$D(I_{AB} + I_{BA})$: This is a function of desire to use the weapons, based on two factions' influence and opinions of each other. Pick any two groups for $A$ and $B$: John Doe and the rest of the world, husband and wife, USA and Russia, etc.

Of course this formula focuses primarily on weapons and people's desire to use them. There are other ways for a civilization to crumble, through political, economic, or cultural means. I'm not a politician, and economist, or a anthropologist so I didn't address those methods. Also, it seemed like the question was leaning more towards a weapons-based destruction.

  • $\begingroup$ very interesting approach. I agree with flipping 0 and 1 for P. I also limited the scope to weapons-based self destruction; seeing how much effort going in to just one facet of the equation made me realize just how broad it was. $\endgroup$ Aug 5, 2018 at 16:02
  • $\begingroup$ Conceptually interesting, but this would apply to the equivalent of a Cold War. A multipolar world with many powerful actors (nations, organizations, even individuals) with sufficiently powerful weapons would make a more complex equation. Also, multiple classes of weapons of mass destruction could further complicate the matter. Brilliant concept of adapting the mathematics of love into an equation for self-annihilation. $\endgroup$
    – a4android
    Aug 6, 2018 at 5:30
  • $\begingroup$ @ aAndroid4, I respectfully disagree. Anyone desiring to destroy the world can be classified as themselves and everyone else. Any single person or group can be modeled (within this equations accuracy) by letting A represent those wanting to destroy the world and B is everyone opposing them. $\endgroup$ Aug 8, 2018 at 19:59

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