Conspiracy theory

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Q. How do you get four elephants in a mini?
A. Two in the front two in the back.
Q. How can you tell if there’s an elephant in the fridge?
A. Footprints in the butter.
Q. How can you tell if there are two elephants in your fridge?
A. Two sets of footprints in the butter.
Q. How can you tell if there are three elephants in your fridge?
A. Three sets of footprints in the butter.
Q. How can you tell if there are four elephants in your fridge?
A. There’s a mini parked outside.

The state of entropy of an isolated system will always increase over time.

—Newton’s second law of thermodynamics

Salient features of a good conspiracy theory: there must first be an outwardly harmless, and widely-held, view that, broadly, the things “in question” are as they seem — that the “surface explanation” is broadly true.

The conspiracy theory strikes against it. Note that, fundamentally, a conspiracy theory must not be true. It is a false explanation that purports to explain an innocent, but usually unfortunate, scenario not by reference to sod’s law, but some dark deception that is not actually there.

A theory about a conspiracy that is true — like the notorious CIA Team B operation — is not a “conspiracy theory”. That is just a plain old conspiracy. They do happen.

We can define a conspiracy as follows:

  1. Deliberate deception: The “commonsense” narrative is a deliberate deception by persons with the means and motives to obscure the truth.
  2. Secret knowledge: Conspirators may have “secret knowledge” and ulterior motives that are not available to outsiders, but may be inferred by those believing the conspiracy theory.
  3. Agents, not systems: Outcomes are caused by malice, not complexity. They are manufactured by conspirators: they do not arise through system effects, coincidence, or error.
  4. Scale: The outcome implies improbably deep, competent and effective confidential coordination among conspirators over extended periods.
  5. Sincere confabulations: Sincere believers tend to “infer”' — that is, invent — facts to fill information gaps to be consistent with the conspiracy. Over time, these flimsy inferences harden into corroborative facts.
  6. Unfalsifiability: The very lack of evidence of conspiracy is evidence of conspiracy. Evidence contradicting the conspiracy is a part of the conspiracy. Also, it is not falsifiable: evidence, whether it suggests “black” or “white”, is taken to confirm the theory. Confirmation bias is weaponised.

Conspiracy theory entropy

Bear with me while I go out on a limb for a moment. Newton’s second law of thermodynamics says that as time passes, any closed system becomes increasingly “entropic”: it goes from order to chaos. Entropic?

Entropy is a measure of the number of possible “microscopic arrangements” that could produce a given “macroscopic state” of a system. The more possible arrangements that can create a state, the higher the entropy. A random distribution has maximum entropy.

Take a tower of nine Jenga blocks, conventionally stacked, three-by three. This is a “state”. There is a countable number of ways to arrange those nine blocks to get that exact same state – by re-arranging the blocks.

The “tower” here is the “macroscopic state”, and each permutation of the nine blocks to produce it is a “microscopic arrangement”. There are 362,880 different ways to arrange nine blocks to make that one tower. [1]

By contrast, if you scatter the same nine Jenga blocks across the floor, their “macroscopic state” is simply “blocks on the floor”. There are vastly more arrangements that can create this state, including all 362,880 “tower” arrangements as they are also ways of arranging blocks on the floor. And a tower a millimetre to the left or right is a different set of arrangements of state “blocks on the floor”.

As each block can be in countless positions and orientations on the floor, and any variation in position or angle counts as a different arrangement, there are a vastly more arrangements of the “blocks on the floor” state than the “tower” state.

In the sense there are far fewer ways you can produce it, the “tower arrangement” has much less entropy than “nine blocks on the floor”. It has higher degree of order.

Since there are many more ways to be in a “high-entropy state” than a “low-entropy state”, if you upset a Jenga tower, you are likely to wind up with nine blocks scattered on the floor. If you interrupt some blocks that are already scattered on the floor, you are not likely to wind up with a Jenga tower: the blocks will just be scattered even more randomly on the floor.

Over time, therefore, any system tends strongly towards disorder. This is not because of systemic degeneracy, but because of the law of large numbers.

To increase order, you must inject energy into the system. Your fridge will not tidy itself. A careful agent can clean out the fridge, or take some scattered Jenga blocks and organise them back into a tower, by exerting effort, the byproducts of which are heat, noise and light: highly entropic forms of energy. While that agent has created some local order, overall, the system is still more disordered than it was.

Thus — and I don’t want to be too much of a downer, but hey — the heat death of the universe is our ultimate destiny.

If, per the first law of thermodynamics, energy can transformed but not created or destroyed, and if, per the second, things tend to disorder unless you inject energy into them, then since there is a finite amount of energy, it follows we are headed, long term, to a state of maximum, warm, disorder. Fear not: the heat death of the universe is a long way off just yet.

And to this end they built themselves a stupendous super-computer which was so amazingly intelligent that even before its databanks had been connected up it had started from “I think, therefore I am” and got as far as deducing the existence of rice pudding and income tax before anyone managed to turn it off.

Douglas Adams, The Hitch-Hiker’s Guide to the Galaxy

Now this being as it may, it may occur to you that, even so, we seem to be able to create more order out of less: look at us, with our rice pudding and income tax, after all. Humans are “careful agents”: we can build Jenga towers and clean out the fridge.

And there are also self-organising systems that create order, too. Indeed, we “careful agents” are a product of one: evolution by natural selection. Evolution creates more order from less.[2] Self-organising systems that can make their own “careful agents” are mindbogglingly powerful things.

Yet they are just as bound by Newton’s tyrannical laws. A bit more order here comes at the cost of a lot more disorder elsewhere.

Humans are locked in an arms race with entropic wear and tear. If things are left to themselves, they rust, mould, peel and rot. Our social systems are organised around preventing and reversing the effects of entropy. We do this in centralised, organised ways, through government, and we do this in local, ad hoc ways through social interactions and markets.

But however we do it, we need energy. Top-down “systems of control” require a lot of energy: a small executive controls a great system. The bigger the system, the more time and energy the executive must spend simply regulating it.

Their control apparatus is explicit, obvious and gets more so as the system grows — soon enough, the executive needs sirens, horsehair wigs, uniforms and jackboots keep their machine on its rails as the people in it make pragmatic personal decisions to maximise their own outcomes, regardless of the stated aims of the executive. Executive management is a diseconomy of scale.

Bottom-up systems tend to organise themselves a bit more efficiently — careful agents take the system as they find it, reacting as it changes, capitalising on opportunities it presents and as a result, the system generates order “by itself”: the invisible hand works its magic.

In a top-down system, the general rule is “no one pedals unless they are told to”. The system does not capitalise on its own momentum in quite the same way. It needs energy input from the executive command unit, in the sense of instructions, just to keep going. At the same time the executive command unit burns its own energy, just by being there.[3]

But the key difference between top down and bottom up is that since no one is there watery tidying up and controlling it, the excess entropic energy that a bottom up system throws off as the price of generating its order is plain and visible for all to see. Landfill. Smoke stacks. Acid rain. Global warming.

As a matter of fact it’s pretty difficult for top-down systems to manage entropic pollution too. But at least you control the media so you can can publicly lie about it. Eventually, though, ordinary people will notice.

And that, more or less, is the point. Entropy's gonna getcha. You can only pretend for so long.

A conspiracy theory is the hypothesis that a top-down system of control that is successfully burying entropy.

And it is a top-down system that's designed to doing something odd. It is pretending to be a bottom up system.

This takes quite a lot of effort as anyone who's ever tried to organize a surprise party will know. In thermodynamic terms, that effort is energy.

Now: let us say a careful agent is wilfully trying to create order, and at the same time conceal it. This a thermodynamic description of a “conspiracy”. That means masking the additional order, and the energy expended to create it, so everyone sees the only the regular, entropic system.

This is an eternally expanding problem.[4] The harder we try to create order the more we make chaos. Creating order to mimic chaos is also a really odd thing to do.

This is also what a criminal does. He gets away with it in the short term, because human systems for detecting energy input and dissipation are imperfect. This is a good thing. We are not yet in a perfect surveillance society, though it gets everyone nearer.

This is not just a human problem: it is the dilemma of creation itself.

So, here is an “entropic criticism” of conspiracy theories: a way of identifying them, with increasing levels of confidence.

The thermodynamic improbability of conspiracy

Conspiracies are anti-entropic: they propose that a hidden, malign order is masked by a co-ordinated, manufactured, false appearance of normality.

A conspiracy is a top-down control system that pretends to be a bottom-up system. It has to expend even more energy maintaining that charade and hiding all its visible mechanisms of control.

The energy cost of sustaining a conspiracy grows exponentially with time: each new confederate, each new obstacle, each new question requires energy to address and represents a point of potential information leakage — that is, entropy increase — that would tend to reveal the conspiracy. That risk can only be managed by more energy expenditure. All the energy expended creates its own entropic heat signature, and that too needs to be masked.

It is amazing what people won’t see when they are not looking for it, but if they do start looking for it, it will all be there, in plain view.

All the while the conspiracy “system”, which is manufactured, not evolutionary and so not naturally robust — it is almost counter-evolutionary, in fact — must respond to unpredictable external perturbations. The more elaborate the conspiracy is the less easily it will do that, and the more energy it will take. This is all tremendously wasteful and entirely defensive: none of it advances the aims of the conspiracy.

This growth of entropy, as an initially plausible small conspiracy grows, eventually becomes thermodynamically unsustainable.

At some point, conspiracies — if they are conspiracies — must run out of the energy they need to stay hidden. That an alleged conspiracy continues indefinitely to survive without being revealed should start to be evidence that it is a false allegation: that it is not a conspiracy at all. The thing about ordinary explanations is that they are naturally entropic. They create chaos, noise, light and heat. They don’t have to waste time manufacturing it.

There is therefore a kind of “Lindy effect” for conspiracy theories: the longer a system persists in an apparently random, entropic state without evidence of the hidden order emerging, the more “thermodynamically expensive” a hypothetical conspiracy to create and hide that order becomes.

Natural entropic processes that debunk the conspiracy theory become increasingly likely to be the correct explanation over time, as the energy required to maintain a deception compounds.

Human systems with anti-entropic features

Human systems create local order through information processing, but they produce waste heat and entropic byproducts. These generally leave evidence of the energy expenditure required for their ordering processes. Human system cannot perfectly control all interacting variables, there will be noise, heat, friction and externalities. You will detect their operation. This will generate observable patterns of resource consumption

Even our most sophisticated order-creating systems leave “thermodynamic fingerprints”: signs of the energy required to create and maintain order. A perfect conspiracy would need to eliminate these signatures. That would take even more energy expenditure.

When evaluating explanations, ask which requires more thermodynamic work to produce the observed outcomes, and ask where this every comes from, and how the conspirators can afford to keep feeding the beast. Conspiracies typically requiring orders of magnitude more energy to maintain than they could plausibly access.

Enter Reverend Bayes

Is there a Bayesian angle here too?

From a Bayesian perspective:

Prior probabilities: Thermodynamically likely explanations deserve higher prior probabilities. Entropic processes (things becoming more disordered naturally) should have much higher priors than anti-entropic processes requiring coordinated action and concealment.

Likelihood functions: The probability of observing our evidence given different hypotheses can be related to thermodynamic work. Evidence that would require extensive energy to fabricate should decrease the likelihood of conspiracy hypotheses.

Updating with evidence: As time passes without revealing evidence of conspiracy (despite entropy’s natural tendency to reveal hidden information), Bayesian updating should continuously shift probability mass toward natural explanations.

Complexity Penalties: Bayesian model comparison naturally penalizes complex models (conspiracy theories) through principles like the Bayesian Information Criterion, which is conceptually related to minimum description length and algorithmic complexity.

Occam’s Razor as Automatic: Bayesian inference automatically implements Occam’s razor by integrating over all possible parameter values, effectively penalising theories requiring precise coordination or specific conditions.

This provides a mathematical framework for what we intuitively understand: extraordinary claims require extraordinary evidence because they’re making claims about low-entropy arrangements that are thermodynamically unlikely to occur or persist without leaving evidence of the energy required to maintain them.

The Bayesian approach quantifies exactly how much evidence would be needed to overcome the thermodynamic implausibility of elaborate conspiracy theories - typically far more than conspiracy theorists can provide.

See also

References

  1. Assuming we ignore the possible rotation of individual blocks. This is the factorial 9! — 9*8*7*6*5*4*3*2*1. It is more than I was expecting, but it is still, relatively, a tiny number. If we factor in the possible horizontal or vertical flipping of each block, there are more than 95 billion arrangements of a 3x3 Jenga tower!
  2. But at a cost: it is a highly inefficient form of research and development. For every fitter variation, there are countless unfitter ones. Large language models are similarly wasteful in terms of their “compute”.
  3. People in executive command units, whether governmental or corporate, get to decide how much energy should be expanded on executive central command, and tend to conclude the answer is “a lot”.
  4. One approach is staying local and hoping people just don’t notice. People are attuned to see what they expect to see. Even trained experts can miss things that are significantly out of line with their expectations — the classic case is the gorilla invading the basketball court.