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This article hangs between the real and the surreal, the serious and the frivolous, propelled by an inexplicable desire to delve into the darkest corners of the human mind in the quest for answers that will probably never materialize. Wallowing in a comfortable numbness, we conveniently describe our society in terms of human intelligence, or better, in terms of the outcome of applied human intelligence, which results in everything good that we see and experience around us, from technological innovation to art masterpieces, medical achievements, civil development and scientific discoveries. Intelligence, after all, is the feature that allows a species to progress as a society. However, our world is not influenced by only this positive trait of the human kind but also by another equally potent feature that is in direct competition with Intelligence, and that is Stupidity.

Whether we like it or not, Stupidity is a potent human feature exactly as Intelligence is, and plays an equally important role in the evolution of the human race. It is, actually, the other side of the coin in a domain representing the evolutionary potential, that is the ability to make a species progress, stagnate or regress. To give an idea of the importance of this human trait and the role it plays in our evolution, we can think of this dual relation between Stupidity and Intelligence as the dichotomy of Good and Evil or the relation between matter/energy and dark matter/energy in the physical observable universe, wherein the former tries to slow down its expansion and collapse it into its original starting point, the latter tries to accelerate its growth into the future. Whichever force takes over, it will mark the destiny of our universe. So, likewise, whichever of these two human features prevails it will mark the destiny of our species.

When talking about Stupidity one common misconception is that a stupid person is someone who is lacking intellectual abilities or whose intellectual abilities do not score within a predefined range according to some specific metric in some particular test. For example, it is a common belief that a stupid person is someone with a low IQ. This is actually far from being true. A stupid person does not necessarily lack intellectual abilities of any kind and can even score high marks in many so called “intelligence tests”. As a matter of fact there are even scientists falling in such awful category, so if you think you might be stupid do not despair, you’re in good company.

Stupidity is a human feature that manifest itself into actions and there is no metric or test that can statically quantify it (actually there is no such test for Intelligence either for that matter, unless we want to scale down this very broad mental capability to fit specific needs). It obeys the Principle of Causality, wherein you can only observe and measure it in relation to the effects it produces in the surrounding environment.

An interesting classification of individuals based on specific manifested attributes, including Stupidity and Intelligence, was given by Carlo M. Cipolla, Professor Emeritus of Economic History at Berkeley. Professor Cipolla considers these human features in relation to the effects that an individual’s actions produce in a “transaction” and graphically describes them on a 2D Cartesian Plane where, depending on the negative or positive effects of the actions (benefits or damages) on the environment, which includes other individuals and ourselves, humans can be classified into four categories: Intelligent, Bandits, Stupids and Unlucky. Intelligent individuals are those whose actions produce a net positive effect on the environment, that is they realize benefits for other individuals (Eo axis in the plot) and for themselves (Es); Bandits are individuals whose actions produce benefits for themselves while damaging other individuals; Stupids are those whose actions produce a net negative effect on the environment, that is their actions damage other individuals and also themselves to some extent; Unlucky are those whose actions have positive effects on other individuals but negative or no effect at all on themselves.

Professor Cipolla formally defines a framework upon which we can build to analyze a society and its evolutionary potential. From the plot in Fig.1 we can infer that if most individuals in a society do actions that have a positive impact on the environment (half-plane above the equilibrium zone) then such society is likely to progress, while if most do actions that have a negative impact on the environment (half-plane below the equilibrium zone) then the society will probably regress and eventually extinguish itself. The Equilibrium Zone is a sort of limbo wherein the individuals’ contribution to the environment is neutral, that is the negative effects on other people caused by bandits are somehow balanced by the positive effects they produce (on themselves), while the negative effects on self caused by the unlucky ones are balanced by the positive effects on others. It is a situation where there are no Intelligent nor Stupids in which the society will stagnate. Another interesting observation is what Professor Cipolla calls the “first law”, which states that stupidity is always underestimated and any attempt to analytically quantify it fails because there will always be a greater quantity that can be observed. This intuition has already struck some of the greatest minds in history, notably Albert Einstein when he stated that there is a possibility for the universe not to be infinite but stupidity certainly is.

As an example, I used this approach to analyze the community dwelling in my small condo, where it’s easy to monitor and evaluate most of the individuals’ actions. The results are shown in Figure 2. Most individuals (indicated by the cluster of green points in the first quadrant) tend not to damage others nor themselves and to be helpful and somewhat empathetic, although none is moved by some sort of missionary spirit or world-changing ambitions (the cluster is close to the origin). The plot does not include myself for reasons that will be evident later on. There are a few bandits, mostly selfish individuals who are willing to accept some negative consequences of their actions on others as long as their gains are achieved, and an unlucky one, who is a kind person but with little patience and quite a temper which puts him easily in troubles. Unfortunately there are also a few stupid individuals. These are people whose actions damage other neighbors and also themselves, for example by damaging common services which they can use for free and that they are forced to use elsewhere upon payment as a consequence of their damage. The individual who sets himself apart in the Stupids quadrant is the most hated one (and evidently also the most stupid), a vindictive person who tends to do much more damage to others than he does to himself.

As can be seen from Figure 2, my condo can be considered, overall, a positively evolving society, although it is obvious that it doesn’t shine in this regard.

Building on these foundations, I wanted to expand a little more on this fascinating (and dangerously underestimated) subject and formally analyze some concepts to see where it all leads. Particularly, I was interested in diving deeper into the world of Stupidity to estimate its potential of influencing the destiny of our world. What follows is a theory that might intrigue, make laugh, shrug or roll eyes. Whichever the effect, the impact on the environment will be positive (it makes me happier and you more enlighted), so I’ve got peace of mind. It contains some math notation to put things formally in perspective, but you can skip the tedious stuff if it repulses you.

In the context of this theory there are some concepts apparently identical but that have different meanings. The concepts of “group” and “set” must be differentiated in that a group represents a number of individuals wherein there are strong interactions between the members, while a set (or, more generally, population) indicates a number of individuals wherein there are small or no interactions at all between the members and that can potentially give rise to groups. Note that a group does not require the individuals to be in physical proximity in order to have strong interactions, especially in today’s hyper-connected world where physical distance doesn’t matter anymore when it comes to communication.

First of all, we can, in the light of undeniable evidence, postulate the following

## First Axiom of Stupidity

“Stupidity is intrinsic to every human being”

Formally this can be written as follows:

Be $$X=\{ x_{1}, x_{2},…,x_{n} \}$$ a population of $$n$$ individuals and $$S(x_{i})$$ the stupidity of individual i-th, then for each $$n$$ we may choose it will follow that

$$S(x_{i})\neq 0~~~~~\forall x_{i}\neq 0~~~~~i=1,2,…,n$$

This axiom states that Stupidity is an irrefutable part of our reality and it is a feature of every individual belonging to the human species. Note that the term “every” must be understood exactly according to its linguistic meaning, that is all inclusive, none excluded. This may probably be considered a controvert concept and a very hard one to accept, but reality is almost always harsh and tough. Stupidity is a component found in every human being to some degree and each one of us can potentially do (or have done) some actions that can be considered as stupid according to Cipolla’s definition. However, for an individual to be categorized as Stupid his/her net contribution to the environment has to be considered.

## Second Axiom of Stupidity

“Stupidity is autonomous”

Formally,

Be $$x$$ an individual defined by its Stupidity $$S(x)$$ and by $$n$$ other features $$F_{1}(x), F_{2}(x),…,F_{n}(x)$$, then

$$S(x,F_{1}(x), F_{2}(x),…,F_{n}(x))=S(x)$$

that is, Stupidity is not affected by other personal features. It is autonomous with respect to other characteristics the individual may possess, including other skills that may make the individual appear as not stupid.

### Corollary

“Stupidity is not self-aware”

A consequence of the Second Axiom, if $$A(x)$$ is the self-awareness of individual $$x$$, then

$$S(x,A(x))=S(x)$$

that is a stupid individual does not recognize his/her actions as being stupid no matters how many times put in front of the evidence, so it is not possible to consciously control (as in increase/decrease) Stupidity. This is also the reason why I did not include myself in the example of Figure 2: if I were Stupid I wouldn’t be aware of it and I could misclassify myself.

## Principle of Non-Annullability

“Stupidity cannot be nulled without nulling the individuals affected by it”

Formally,

Be $$x$$ an individual, then

$$S(x)=0~~\Rightarrow~~x=0$$

Proof:

This is a straightforward consequence of the First and Second Axiom and states that the only possible situation in which there is no Stupidity at all is where there is no human being.

## Boosting Principle

This principle is based on a well known and widely observed human behavior, sometimes referred to as the principle of dominant opinion, and on the natural ability of human beings to improve their skills by learning. The principle of dominant opinion describes a social phenomenon wherein in a group the individuals behaviors (and opinions) are influenced by those with dominant traits. This phenomenon is present in every human sector, including (sadly) science, and is not unique to humans but can be observed in the whole animal kingdom.

Formally,

Be $$X=\{ x_{1}, x_{2},…,x_{n} \}$$ a group of $$n$$ individuals, $$S(x_{1},t_{1}),S(x_{2},t_{1}),…,S(x_{n},t_{1})$$ their respective stupidity at time $$t_{1}$$, $$[t_{1},t_{2}]$$ a time interval and $$x_{d}$$ the individual such that

$$S(x_{d},t)>S(x_{i},t) ~~~ \forall i=1,2,…,n ~~~ i \neq d ~~~ \forall t \in [t_{1},t_{2}]$$

or, in equivalent form,

$$x_{d}=argmax [S(x_{i},t)] ~~~ \forall i=1,2,…,n ~~~ \forall t \in [t_{1},t_{2}]$$

then

$$\displaystyle \lim_{t \to t_{2}} S(x_{i},t) = S(x_{d},t_{2}) ~~~~~\forall i=1,2,…,n~~~i \neq d$$

Proof:

The individuals in the group will be subject to what is known as the herd effect, wherein they will tend to improve their level of stupidity by learning from the dominant individuals, that is the most stupid in the group, until they eventually reach their level. This process, like all processes in nature, is not reversible, in that it is not possible to “unlearn” and get back to prior levels of stupidity.

## Fundamental Properties of Stupidity

1. Over-additivity (aka “Gang Reinforcement”)

This property shows that the stupidity of a group of individuals is always greater than the sum of the stupidities of the individuals taken alone.

Be $$X=\{ x_{1}, x_{2},…,x_{n} \}$$ a group of $$n$$ individuals, then

$$S(x_{1}+x_{2}+…+x_{n}) > S(x_{1})+S(x_{2})+…+S(x_{n}) ~~~ \forall n > 1$$

Proof: By applying the Boosting Principle to $$X$$ we get this property. So, if you ever wondered what a bunch of Stupids can do all together, the answer is … anything, if $$S(x)$$ is big enough.

2. Aggregation (aka “Gravitational bound”)

Stupid individuals are strongly attracted one to another and are always inclined to aggregate in groups rather quickly.

Be $$X=\{ x_{1}, x_{2},…,x_{n} \}$$ a set of $$n$$ individuals in a given region of space and $$A \subset X$$ an arbitrary subset of stupid individuals, then for any two time instants $$t_{2},t_{1}$$ we have

$$\displaystyle \lim_{t_{1} \to t_{2}} d | a_{i}(t_{1}), a_{j}(t_{2}) | =0 ~~~~ \forall a_{i},a_{j} \in A ~~~~ i \neq j ~~~~ t_{2}>t_{1}$$

Proof: This property can be proven by using the similarity-attraction theory, which explains a well known human behavior that makes individuals prefer to be in proximity to other like-minded peers. For stupid individuals, this is greatly increased by the lack of self-awareness thus increasing the likelihoods that strong bonds will be formed (on the lines: if there is something stupid to do, let’s gang up and do it regardless!).

3. Multiplicity (aka “Non-Singleton”)

Stupid individuals are never alone. In a population, if there is a stupid being then there will be at least another one.

Be $$X=\{ x_{1}, x_{2},…,x_{n} \}$$ a set of $$n$$ individuals and $$A \subset X$$ a subset of stupid individuals of $$X$$. Then

$$A \neq \emptyset ~~ \Rightarrow ~~ | A | > 1$$

Proof: Property 2) tells us that the individuals in $$A$$ will form a group. Now, suppose that $$| A | = 1$$ then the Boosting Principle applies to the only individual in A, that is the individual would be the dominant $$x_{d}$$ and it would learn from itself implying some sort of self-awareness, that is $$S(x_{d},A(x_{d}))\neq S(x_{d})$$, which is absurd as it contradicts the Second Axiom. So there must be at least another stupid individual in A, that is $$| A | > 1$$.

4. Spatial Invariance (aka “Location-independence”)

This property states that Stupidity does not depend on space, that is an individual will manifest exactly the same stupidity regardless of where it is located in the universe.

Be $$x$$ an individual defined by its stupidity $$S(x)$$ and $$z_{1}$$, $$z_{2}$$ two locations in space, then

$$S(x, z_{1})=S(x,z_{2}) ~~~~ \forall z_{1},z_{2} ~~~~ z_{1} \neq z_{2}$$

Proof: Try to have your Stupid neighbour moved elsewhere and see what happens (to the new neighbours).

While it would be interesting to analyse Stupidity independently of time, that is examine the potential of individuals to negatively affect the environment at any given point in time, we would not get the big picture. This is because technological progress gives humans increasingly powerful means to have a negative impact on the environment. In fact, intuitively one may assume that any individual nowadays has a much greater potential stupidity of any individual of the past, which in turn means that our ancestors might have been less stupid than we are now. Evolution empowers Stupidity. The two following theorems will shed some light on these aspects.

## Theorem of Conservation and Expansion

This theorem has very important implications. It states that the individual stupidity may increase with time or, at most, it remains the same. For it to remain the same, however, the individuals should be isolated, which is quite unlikely. What the theorem shows clearly is that stupidity cannot diminish, not naturally at least. The only way to decrease the level of stupidity in a society would be that of artificially interfering with its natural evolution by selection (of the least stupid) and suppression (of the most stupid). This would, however, prove difficult to achieve given the difficulty of quantifying Stupidity, aside from not being acceptable from a moral point of view.

Formally,

Be $$X$$ a population of individuals and $$S(x_{1},t_{1})$$ the stupidity of individual $$x_{1} \in X$$ at time $$t_{1}$$. Then it is always possible to find an individual $$x_{2} \in X$$ such that $$S(x_{2},t_{2})>=S(x_{1},t_{1})$$ for $$t_{2}>t_{1}$$.

Proof:

Be $$x_{1} \in A$$, then property 3 assures the existence of $$x_{2} \in A$$. We need to prove that $$S(x_{2},t_{2})>=S(x_{1},t_{1})$$. By applying property 2, at some time $$t_{2} > t_{1}$$ it will happen that $$d | x_{1} , x_{2} | = 0$$, that is they will aggregate in a group, at which point there will be three possible cases:

1. If $$S(x_{2})>S(x_{1})$$ then the thesis $$S(x_{2},t_{2})>S(x_{1},t_{1})$$ follows.
2. If $$S(x_{2})=S(x_{1})$$ then the thesis $$S(x_{2},t_{2})=S(x_{1},t_{1})$$ follows.
3. If $$S(x_{2})<S(x_{1})$$ then the Boosting Principle applies, that is $$S(x_{2}) \rightarrow S(x_{1})$$ at some point in time $$t_{2}’=t_{2} + \Delta t$$, with $$\Delta t$$ being quite small, and the thesis follows.

By iterating and extending this process we have that $$S(x_{2},t_{2}) \geq S(x_{1},t_{1}) ~~~ \forall t_{2}>t_{1} ~~~ \forall x_{1},x_{2}$$.

The Theorem of Conservation and Expansion describes how the individual stupidity potential can evolve. It is far more important, however, to understand what the stupidity potential of a group can do. Human beings are a social species and spend their lives constantly interacting with other individuals in groups. The interactions between individuals in the group give rise to behaviors that are more potent than the behaviors of the individuals taken alone. The group empowers the potential of the single units through interactions, increasing the effects that such behaviors have on the environment. This is a characteristic of complex systems, which human groups are. It is, therefore, of great interest to get a glimpse of how this sort of collective stupidity potential can impact our world.

Although human beings have always lived in groups since their inception on this planet, the ability to aggregate has constantly raised with time due to continuous technological progress. The power of interaction and the ability to connect with other individuals to form groups nowadays was not even imaginable in the past and we also cannot know how this may be in the future. While new communication tools such as instant multimedia messaging that has given birth to the social media revolution has provided individuals with enormous collective skill empowering capabilities, future technologies will probably improve this even more. It is not difficult, for example, to imagine a futuristic world where not only devices, but human beings themselves are directly interconnected one to another and are capable of sensing other individuals’ psychological state at any distance in real time. The Internet of People (IoP) or other similar technologies will likely be a reality in a not so distant future and will empower interactions and information exchange to extents that we cannot even conceive today. This, in turn, means that collective skills potential, including Stupidity, will be immensely reinforced with time.

Now, if we indicate with $$P$$ the collective skills potential empowering function for some skill $$K(x)$$, then we can most certainly state the following

$$\displaystyle \lim_{t \to \infty } P_{K(x)}(t) = \infty$$

that is, the potential of collective skills can be empowered in time without bounds, and if a bound existed it would be of so immense magnitude that it is not conceivable and can still be represented as an infinite.

## Theorem of Divergence

This theorem formally shows that Stupidity, intended as a collective skill, is unbounded and its consequences, coupled with the consequences of the expansion and conservation theorem, are quite creepy (not from the point of view of a stupid individual, obviously). The inability of humans to naturally decrease their individual stupidity and the unlimited increase of their collective stupidity potential makes Stupidity an infinite quantity.

Formally,

Be $$X=\{x_{1},x_{2},…,x_{n}\}$$ a group of $$n$$ individuals and $$S(x_{1},t_{1}),S(x_{2},t_{1}),…,S(x_{n},t_{1})$$ their respective stupidity at time $$t_{1}$$, then the stupidity potential of group $$X$$ is infinite.

Proof:

According to property 1) the collective stupidity of $$X$$ at $$t_{1}$$ can be written as follows

$$S(X,t_{1})=\alpha(t_{1}) [ S(x_{1},t_{1})+S(x_{2},t_{1})+…+S(x_{n(t_{1})},t_{1}) ] ~~~~~ \alpha(t)>1 ~~~ n(t_{1})>1$$

where $$\alpha(t)$$ is a time-variant reinforcement coefficient. Consider now the successor of $$X$$ at time $$t_{2}>t_{1}~~X=\{x_{1},x_{2},…,x_{n(t_{2})}\}$$, then we have

$$S(X,t_{2})=\alpha(t_{2}) [ S(x_{1},t_{2})+S(x_{2},t_{2})+…+S(x_{n(t_{2})},t_{2}) ]$$

and iterating

$$\displaystyle S(X,t)=\alpha(t) \sum_{i=1}^{n(t)} S(x_{i},t)$$

By setting $$\alpha (t)=P_{S(x)}(t)$$ and supposing that group $$X$$ doesn’t become extinct for other causes, that is $$n(t)\neq 0$$, we get the following

$$\displaystyle \lim_{t \to \infty } S(X,t) = \infty$$

that is, the stupidity potential of a group of individuals increases unbounded in time.

So, if we identify the above mentioned $$X$$ with the future human society, it is quite evident that there is something to be seriously worried about (Einstein warned us long ago).

## Conclusions

So, are we doomed as a species? This is a million dollar question. Despite Stupidity being unbounded, not all hopes should be considered lost. Intelligence is certainly unbounded as well, the problem is understanding which one has the fastest growth rate so that we can get a grasp of what our destiny will be. Some do believe that the future world will be a dystopia dominated by “idiocracy”, as depicted in a 2006 movie by American director Mike Judge. The feeling that many people are increasingly “dumbing down” seems to become quite widespread (among the intelligent ones, as stupid individuals are not self-aware in this respect) and much of what is depicted in the aforementioned movie is already a reality.

Another common fault of many observers, and that is probably one of the causes for overlooking the role that Stupidity plays in our world, is that of associating positive evolution to scientific and technological progress. This misconception leads to believe that we, as a species, are becoming increasingly progressed just because we can send a robotic explorer to Mars or come up with a new discovery that allows us to better understand the universe we live into. Unfortunately, scientific and technological progress alone does not give an holistic view of the situation and is no indication that we are on a positive evolutionary path. For example, a species that makes use of new knowledge to potentially destroy itself is not a progressed species by any means. And history has given us enough evidence of the potential of our species for self-destruction.

In a less apocaliptic scenario, we’ll reach a point wherein Stupidity and Intelligence will counter-balance each other preventing the counterpart to take over. It would be a world were there are only individuals whose actions will produce a net effect that is overall neutral on the environment (Unlucky that will work hard for the Bandits) or a world where the actions of the Intelligent are nullified by those of the Stupids. In this situation the society will hang in a sort of limbo where it does not progress nor regress (stagnation). This is probably the situation of the world as we see it now, at the time of this writing, and while not the best condition at least it shouldn’t lead us to extinction.

In an ideal, more optimistic scenario Intelligence will prevail, mankind will finally find its way to living in harmony, fairness and equity will be the norm, greed will turn into philantropy and humans will save themselves from self-destruction. It sounds a lot like utopia and there is not much evidence of this happening actually, but we have to be optimistic as well.

Regardless of outcome, the theory speaks clearly. Eliminating Stupidity altogether from this planet is impossible so long as human beings are present, so waiting for it to naturally subside is a dead end. Moving to extra-terrestrial environments would be a dead end as well, unless done in a very selective manner, and even so there is no guarantee we’ll live in a better world as Stupidity is non-nullable and space-invariant (poor Mars…). Nevertheless, it can probably be controlled and kept to a level wherein its negative effects on the environment are negligible or at least bearable in order to maintain the system unbalanced towards the positive effects caused by the Intelligent. One thing is for sure: if no measures are taken at all and this issue keeps being underestimated and overlooked, we risk a world overtaken by the Stupids, and such a world is certainly bound to an awful end. Now, if you’ve read up to this point, ask yourself why.

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