There is all but one science and all but one language. All scientific endeavours must bow to embodiment and measurements of the same. We label the first as physics and the latter as mathematics. Hence, describing intelligence as a physical force that maximizes the future freedom of action, adds a new aspect to intelligence that is often forgotten: the power to change the world. Intelligent systems are survival engines, that increase their chances of survival by maximizing a single quantity: the freedom of action.

TED talk “A new equation for intelligence” by Alex Wissner-Gross presents an equation he published in April 2013 in a physics journal. It may not be the most impressive talk I have ever seen. So, why did the equation blow me away? Because this very simple physical equation can guide us in our decisions and it makes intelligent behavior measurable and observable. It adds a new real physical force to the world, the force of intelligence. From the equation, we can deduce algorithms to act intelligently, as individuals, as societies, and as mankind. And we can build intelligent machines using the equation. Yes, I know, you may ask: “How can the simple equation F = T ? S? do all of that?”

Maximises the Future Freedom of Action

Before we look at the equation in more detail, let me describe its essence in everyday terms. Like many physical laws or equations the idea behind it is simple:

  • Intelligence is a force that maximizes the future freedom of action.
  • It is a force to keeps options open.
  • Intelligence doesn’t like to be trapped.

But what is necessary to keep options open and not to be trapped? Intelligence has to predict the future and change the world in a direction that leads to the “best possible future”.  In order to predict the future, an intelligent system has to observe the world and create a model of the world. Since the future is not deterministic the prediction has to be based on some heuristics. Prediction is a kind of statistical process. In order to change the world, the intelligence has to interact with the world. Just thinking about the world, without acting, is not intelligence, because it produces no measurable force  The better in can predict the future and the better a it can change the world in the desired direction, the more intelligent the system is.

The new Equation for Intelligence

Note: skip this section, if you are not interested in understanding the mathematics of the equation! This is the equation:

F = T ? S?.

Where F is the force, a directed force (therefore it is bold), T is a system temperature, S? is the entropy field of all states reachable in the time horizon ? (tau). Finally, is the nabla operator. This is the gradient operator that “points” into the direction of the state with the most freedom of action. If you are not a physicist this might sound like nonsense. Before I try to explain the equation in more detail, let’s look at a another physical equation of force.The intelligence equation very similar to the equation for potential energy F = ? Wpot. Wpot is the potential energy at each point is space. The force F pulls into the direction of lower energy. This is why gravitation pulls us in direction of the center of the earth. Or think of a landscape. At each point the force points downhill. The direction is the direction a ball would roll starting at that point. The strength of the force is determined by the steepness of the slope. The steeper the slope, the stronger the force. Like the ball is pulled downhill by the gravitational force to reach the state with the lowest energy, an intelligent system is pulled by the force of intelligence into a future with lowest number of limitations. In physics we use the ? Nabla operator or gradient to turn a “landscape” into a directed force (a force field).
Back to our equation F = T ? S?. What it says is that intelligence is a directed force F that pulls into the direction of states with more freedom of action.T is a kind of temperature, that defines the overall strength (available resources) the intelligent system has (heat can do work, think of a steam engine: the more heat the more power).  S? is the “freedom of action” of each state that can be reached by the intelligence within a time horizon ? (tau).  The time horizon is how far into future the intelligence can predict. Alex Wissner-Gross uses the notion of entropy S to express the freedom of action in the future. The force of intelligence is pointing into that direction. As we have seen, in physics the direction of the force at each state is calculated by a gradient operation (think of the direction the ball is pulled). The Nabla operator is used to assign a directional vector (the direction of the force of intelligence) to each state (in our case: all possible future states). The more freedom of action a state provides the stronger the force is pulling in that direction. So, ?S? is the pointing into the direction with the most freedom of action. The multiplication with T means the more power we have to act, the stronger the force can be.
Note: the optimal future state is the optimal state form the viewpoint of the intelligent system. It might not the optimal state for other systems or for the entire system.
If you want to understand the equation in more detail read the original paper ‘Causal Entropic Forces – by A. D. Wissner-Gross and C. E. Freer‘.

An Algorithmic Explanation of the Equation

As an intelligent system you want to get the best possible future. The best possible future is a future where you are not trapped. To get there, you try to predict possible futures. You adjust the time horizon  ? of your prediction, so that your prediction is reliable enough to make a decision. Look at all possible states and you assign a freedom of action value  S? to each state. In that map of states, you choose the state that has the highest potential for future actions, the state that gives you the most freedom and power. This requires that you have a model of how the world works and you have to be able determine the current state of the system. Now you move in that direction.
If the sate you are heading is not reachable effortless, you have imposed a force F on the world in that direction. This is the force of intelligence. Thetemperature T represents the power or “resources” you have to reach the desired state. The more power you have, the more force you can impose. As you move (in time and space), you have to constantly validate desired state and adjust the direction you move. This adjustment is needed, because your model of the future was only a vague prediction and, as you go, your internal models of the world have to be updated with the reality.

The Physical Force of Intelligence

It is Really a New Force?

This force is a real physical force. This force is not explainable with the other physical laws. If you read this, on a computer or on paper, the letters are in an order that would not exist without an intelligence imposing forces on the physical world. Intelligence influence the world. This influence is directed. The direction can be understood by looking at the formula F = T ? S?. This means some intelligent actor came to the conclusion that this is a better state to be in. Some state changes requite little force (if I type a or s does not make much of a difference). Other state changes require a lot of directed force, e.g. building a new house.

How to Measure the Force of Intelligence?

If intelligence is a physical force, it has to be observable, right? In the TED talk, Wissner-Gross gives a nice example of how alien observers could detect intelligence on earth with a telescope: Suppose alines would measure the number of asteroids hitting the earth for millions and billions of years.  But suddenly a “magic force” appears, and asteroid do not hit the earth anymore. Instead they detonate or get deflected before they hit the earth. This is when humans have learned to to prevent the impact of asteroids with some advanced technology. For the aliens, none of the “classical” forces of physics would explain this. But the Equation of Intelligence would explain this otherwise mysterious force as the Force of Intelligence

Is it a Break-Thru Like Chaos Theory?

I believe, this simple equation will change the way we see and understand the world. It may lead to a better future for mankind. I remember in the 80ies, when I studied physics, Chaos Theory emerged into physics. It provided a scientific explanation for the behaviour of complex systems. Once you understand that small differences in the initial conditions of non linear systems can yield to wildly diverging outcomes (butterfly effect),  chaos theory is simple and obvious. The Equation of Intelligence has similar qualities. Once you understand it, it is so obvious that you wonder why it was not formulated much earlier. As physicist, I really like the simplicity, beauty and generality of the equation. I also like the idea that we now can describe intelligence as a force that changes the physical world.

The Problem of Ambiguity of the Future

The biggest problem with this equations is to determine the entropic field S? and the accessible Temperature T. One might argue that this equation is useless because it is not well defined. I would agree with this critique, but the equation is a kind of approximation. The intelligence cannot know all possible future states nor can it know the freedom of action of each of the states. So, does it mean this equation is useless? I don’t think so, because it as a set of interesting implications.


Let me point out a few implications of the equation.

Intelligence Needs a Dynamic Model of the World

In order to estimate the quality (in terms of actability) of future states, the system needs a model of the world. This model is used to simulate future states and to estimate risks, cost and and freedom of action for those states. This also means that, as the intelligence moves in a certain direction in option space, it has to re-evaluate the future states and correct the predictions and the direction. Our brain is a prediction engine. It makes predictions by associations. For example, we can predict the slope of a moving body without much reflection. But sometimes we have to question the automatic prediction (as Daniel Kahneman points out) and use slow analytical thinking. For example, our intuition for probability is often wrong and depending on how a problem is described we may have a bias in our predictions. Simple intelligent systems, like a single cell following the light, have very simple ‘models’ of the world. Many systems have no explicit model of the world. Instead they have a “good enough” build-in heuristics that they find good states to move to.

Intelligence Needs Power to Act

Intelligence has to maximise the “temperature” T in the equation to increase the force (the impact to change the sate of the world). When humans learned to utilise energy (like fire) and turn it into physical forces (like with a steam engine), they increased their influence on the world. So, just observing future states is not enough. The intelligence needs to have the power to turn the knowledge about the desired future state into a force to move there. The power needed to reach the desired state is a resource that has to be taken into account when we predict the freedom of action in the future. Let’s consider an example: a cat is hunting a mouse. Instead of wasting a lot of energy running after the mouse, the cat sits still, and observes the mouse. It follows its movements and makes a prediction when there is a good moment to catch the mouse. This is a very good use of resources.

What is an Intelligent System?

Any system that creates a force into the direction of more freedom to act, is an intelligent system. This means a single cell or a single human is an intelligent system. But also communities can be seen as an intelligent systems. Animal colonies, nations, armies, religions, mankind can form intelligent systems. These systems are hold together by a set of rules that make them interpret the world in a specific way and they act (consciously or unconsciously) to give their system more (or less) freedom of action.  Some of those system do a kind of random walk in time and space, but others have internal models and rules that guides them into a direction of more freedom of action. True intelligence is revealed when the state changes and the old rules do not work anymore. In that situation, the ability to anticipate the new situation and find new solutions distinguishes really intelligent systems form just well adapted systems.

Hierarchy of Intelligent Systems

Let me point out, that intelligent systems are often hierarchical. Cells form plants, animals and humans. Humans form families, tribes, nations. The entire biotope of the earth is an intelligent system. Think about mankind. Each individual person has a model of the world, and the interaction of all humans form an implicit model of the world of mankind. Evolution, with survival of the fittest, is a form of intelligent system. Any believe system ormemes, like a religion, atheism, capitalism or communism have a build-in set of models of the world and create forces in the world. It would be really interesting to analyse how good different believe systems are in terms of maximising the future freedom of the system. In terms of force to change the world and in terms of direction. There could be memes that have a lot of force but are misguided and die out.

Competition of Intelligent Systems

Another implication of hierarchical intelligent systems is, that intelligence at one level (a single human, company, religion, nation) may undermine the intelligence of the higher level system. Or vice versa, a higher level system has to reduce freedom of actions of its subsystem in order to maximise its freedom of action. If we see mankind as the more important system that a single human, this might have implication on how we should act as individuals, companies, or nations. If mankind is pulling in too many directions at the same time, then the overall force might be zero and therefore the intelligence is reduced to the intelligence of a bare physical system.

Brute Force Versus the Force of Intelligence

If you know what the best future would be, but you cannot or do not act, brute force systems may determine your future.  It’s that simple. Thinking about a better future is not enough. The ability to act is integral part of intelligence. And that is what intelligence is actually optimising, the ability to act. The greatest idea, if not actionable, is not intelligence. Classical IQ tests measure only the future prediction part, but miss out on the power to act. Sometimes simple but strong systems rule the world and “intelligent” systems fail because they are not able to act.

Why is the Force Directed to Future Freedom of Action?

Not having any freedom of action means you are dead. Future freedom of action, essentially means to increase the probability of survival of the intelligent system. Therefore, intelligent systems increase their chance of survival by moving to states with the highest probability of survival. Because it is impossible to predict the future correctly, the best heuristic is to put yourself into a state where you are not trapped. Freedom of action means survival, which is a simple and general goal. From that, any sub goal is magically derived.

Evolution on Steroids

Because intelligent systems actively increase their chance of survival, intelligent systems are systems with an accelerated evolution. “Blind” evolution depends on random variations and the power of selection. Intelligent systems can boost the chances of survival by using force to move to states with higher chance of survival.

How to increase the force of intelligence?

There are tow ways to increase to force of intelligence:

  1. Make better predictions of the future, which means detect sates of maximum freedom of action
  2. Increase the power to move in the desired direction. By adding more energy or being clever in finding paths that require less resources.

Other Implications

The last few days, I did not sleep well, because my mind was overwhelmed by thinking about the implications of that simple equation. Here are just a few thoughts and each of them needs further exploration and refinement:
  • I read about claims that say, artificial intelligence needs senses and a body to interact with the world. I think this is true, because in oder to change the future, intelligence has to interact with the world (apply forces). In order to make predictions it has to sense the world. So, AI without a body and senses is no intelligence because it cannot understand and interact with the world and therefore cannot apply any directed force.
  • Intelligence based on that definition might not have a “moral” in the sense we use moral. The only goal it has is to maximise its future ability to act. The moral emerges from what has to be done in order to get to the best future. E.g. if you own a company and you treat you employees badly, it might fire back in the future because they may leave or they revolt against you.
  • Intelligence may flow with the laws of physics but occasionally use force to change the world in a way that opens changes in the future.
  • As Wissner-Gross shows in his video on the Entropica webpage (which is also shown in the TED talk), a AI system that is build to maximise future options automatically chooses “intelligent” goals. For example a trading robot that maximises the portfolio, because it gives the system more freedom of action in the future within that game.
  • Politics is often not very good at maximising the future freedom of action of the nation. Instead they are focused on maximising their own power.
  • It would be interesting to analyse the way we manage software development with the question of how we can  maximising the future freedom of action….


The simple formula
    F = T ? S?
explains how intelligence applies forces to the world that maximises its future freedom action. If we understand and apply it, we might be able to act more intelligently, which means we may put us in a better state for the future. It might provides us with cues on how to act more intelligently as individuals, as families, as communities, as companies, as countries and as mankind.