Wednesday, February 12, 2014

A new Equation for Intelligence F = T ∇ Sτ - a Force that Maximises the Future Freedom of Action

Intelligence is a Force with the Power to Change the World

Describing intelligence as a physical force that maximises the future freedom of action, adds a new aspect to intelligence that is often forgotten: the power to change the world. This, I think, was the biggest revelation for me, when I started thinking about the the new equation for intelligence. The second revelation was, that intelligent systems are survival engines, that increase their chances of survival by maximising a single quantity: the freedom of action. Both insights may sound trivial or obvious, but I don't think they are.

A few days ago a saw the TED talk "A new equation for intelligence" by Alex Wissner-Gross. He presents an equation he published in April 2013 in a physics journal. It may not be the most impressive talk I have ever seen. And I had to watch it twice to fully understand it. But the message excites me so much, that I don't sleep well since a few days. I thought everybody must be excited about this equation. But, it seems that this is not the case. Either I am not understanding it correctly or others don't get it. Or maybe it resonates with me, because I am physicist, with a strong background in computing, who has done research in computational biology. To find this out, let me explain my understanding of the equation. Please tell what your think and what's wrong with my excitement (I need sleep)....

So, why did the equation blow me away? Because this very simple physical equation can guide us in our decisions and it makes intelligent behaviour 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  Sτ do all of that?"

Intelligence is a Force that Maximises the Future Freedom of Action

Before we look at the equation in more detail, let me describe its essence in every day terms. Like many physical laws or equations the idea behind it is simple:
  • Intelligence is a force that maximises 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 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 (well, sometimes it is intelligent not to act, because the physical forces drive you already in the right direction, but that is a way of optimising resources). The better in can predicted 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 F = T ∇ Sτ

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

This is the equation:

   F = T

Where F is the force, a directed force (therefore it is bold), T is a system temperature, Sτ is the entropy field of all states reachable in the time horizon τ (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  Sτ. 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).   is the "freedom of action" of each state that can be reached by the intelligence within a time horizon τ (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, Sτ 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  τ 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   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. The temperature 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 ∇ Sτ. 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 Sτ 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 or memes, 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

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. 


  1. Nice, I saw the TED talk ... I just wonder what this got to do in Eclipse and Java, resp.

    1. It is only indirectly related to eclipse. If you look at some of my previous posts, I am very concerned about the future of eclipse and especially about the problem of the tragedy of the commons. I have a half-finised post that applies the formula of intelligence to the eclipse eco system.

      If we assume eclipse is an "intelligent system", the question for me is: is the sum of many intelligent subsystems (individuals and companies) driving eclipse into a direction of survival. Or the sum of forces (each one intelligent for the subsystem) not good for eclipse as a system.

  2. You might want to explore the concepts of intelligence, freedom and commerce. Intelligence requires increased freedom, for the system that contains it. An intelligent system can increase it's freedom, by restricting the freedom of other systems. Commerce increases the freedom of companies, by decreasing the freedom of individuals, and individual companies can easily get locked into their own restrictions, ultimately decreasing their freedoms. Laws that restrict commerce ultimately restrict freedoms, and thus restrict intelligence. But companies prefer these laws because they facilitate increased freedom for individual companies in the short term. The goals of companies to produce quarterly and annual results ultimately decreases freedom and intelligence of the entire system.

    1. This deserves a response :-). I agree with these comments, Tracy. Watching the TED talk it excited me too for several reasons. One part is about what is inside the equation, the other part about what is left out of the equation. The systemic view can easily lead to an orientation towards the "brain". But from a human perspective more is needed. It is noteworthy that nobody comments on this. The comments below are mostly about the inside of the equation (which is also interesting b.t.w.)

  3. Thanks Michael. This is a great explanation.

  4. I found an article that describes the force of intelligence in a really nice way

  5. I am probably missing the point, so help me with this:
    >Any system that creates a force into the direction of more freedom to act, is an intelligent system.

    but once an action is taken, your choices are reduced.
    To me this equation says inertia= infinite intelligence since all your possibilities are open.
    Isn't observable 'intelligence' about making optimal choices to obtain a 'better' future state?
    but... maybe i'm missing the point.

    1. If you chose to open a box, the diffenrent futures you can face in a 5 seconds horizont increase a lot compared with not oppening it, so once a decision is taken, another set of options opens in front of you, wider or narrower, who knows... and the goal here is to get the widest possible set of options in a near future.

    2. Agreed. Also, Baroquenhorse, I believe your equation is true if you substitute "entropy" for "inertia", and the author states that the ability to achieve entropy is a requirement for developing intelligent systems - though why, I don't understand.

    3. I think the point is that the future states are vague/approximations, and the system also knows that so it always acts in anticipation of more favorable future options.

  6. > but once an action is taken, your choices are reduced

    True! But not acting is also a choice. But is it the best choice for the future? Sometimes yes, but sometimes no. If you are only floating into the direction you are pulled you may miss an opportunity to invest a bit (by acting) to get more in the future.

    Do you know the famous Marshmallow Experiment ( The children who were able to resist an immediate attraction (eat a marshmallow) in order to receive a reward in the future (two marshmallows) have been more successful in their adult live. This is the "act" part.

    For use humans it is a balance between enjoying life now and being prepared for the future. If you do not enjoy your life now you might suffer and get sick. If you use all your resources immediately, you may not have the power to overcome a crisis or you cannot take an opportunity.

    1. Thank you Michael for responding. I do agree with all you've said. I am not familiar with the marshmallow experiment, but i do know of a similar one with a Hersey bar :)... and i wish i could get my boss to agree that often the best decision is no decision. I think my trouble here is i didn't understand the notion of 'best choice' to be in the equation... action appears to be missing.

  7. If you choose not to decide you still have made a choice. Until you consider 4 things 6 different ways you have not had a thought. If it is a force it acts upon a field. What does the fact that parity is not conserved say about this new field? Intelligence is a property of entities or an intelligent field creates entities more reseach is needed

    1. It is not a real force, it is an "entropic force", in the same way a gas tendency to the equilibrium can be thougt as the sum of its particles momentums or a single "entropic force" applied to the gas as a whole.

      The second is not true, and there is no field that correspond to such a "force", in the same way no field exists to "force" you to change channel when a bad commedy starts on your TV.

  8. Can this be related to things like 'restricted Bolzman machines' (RBM) and auto-encoders in deep learning neural networks (NN)

    1. Yes, but not as part of the idea itself, but as a general way to "simulate" the future of a system: if you use a neuronal network to simulate the future of the system, your algorithm will learn and will be usable with systems you can't deterministically simulate.

      But once the simulation have been replaced with a neuronal network, the "decision taking" algorithm is the same one: use the simulation to calculate the entropy at a given time horizont for each option you are considering, average all the options with its entropy as a weigth, and you get your "intelligent force".

  9. I found your blog entry to be quite interesting and useful. I wonder what your thoughts might be on the following formulation?

    From cybernetics (which has been around since the 1940s
    VO = VD + U – (VB + VR)

    V represents variety of system states.
    VO is the outcome or goal state. Variety is reduced to obtain the desired outcome.
    VD is the variety of disturbance (states other than the goal state).
    VB is passive regulation.
    VR is active regulation – behavior
    In active regulation, only variety (VR) can reduce variety (VO)
    U is uncertainty.

    We can reduce variety (states other then the goal state) three ways driving the system to its goal state:
    1. Active regulation (VR) – think of a thermostat controlling room temperature
    2. Passive regulation (VB) – think of the insulation in the room’s walls
    3. Reducing uncertainty - (U).
    Through knowledge via learning (model of the world)
    By placing the system in approximately the same initial state
    By improving awareness of the current state of the system

    Relating cybernetics to the equation for intelligence
    How is VO = VD + U – (VB + VR) related to F = T ∇Sτ?
    ∇Sτ points in the direction of the most flexible state.
    • For an intelligent system, ∇Sτ represents the goal state
    • From cybernetics, VO is the goal state
    • Therefore, VO = ∇Sτ, since both represent the goal state
    • Sτ is the entropy field of all the reachable states in the time horizon τ (tau), a freedom of action value for every possible state.
    • VD is the variety of disturbance (states other than the goal state).
    • Therefore, Sτ = VD, SτB = VB, SτR = VB
    • Therefore, ∇Sτ = Sτ + U – (SτB + SτR)
    • Factoring in the power to act, T:
    F = T [Sτ + U – (SτB + SτR)]

    Introducing U from cybernetics explicitly accounts for the intelligent system’s model of the world as well as awareness.
    This formulation also makes explicit the value of passive regulation, which conserves T.

    Does the above formulation hold water? If so, it seems to support your argument, especially your assertions about the systems model of the world.

    1. Not sure if it holds water, but it makes a lot of sense to me!

    2. In this approach there is no "goal state", instead, you take the decision (in this present) that gives you a wider set of futures, or a bigger entropy gain in a given elapsed time.

      If the best possible future start by taking a decision that is also taken in a big number of "not so good" futures, it may be better for this algortihm to take a course with not so bright futures, but a bigger number of them.

      What you really use here is: take now the decision that opens more different futures to you (instead of take the decision that could drive you to the brightest future).

      It is the idea of "entropy" what makes different one approach form the other.

  10. Thank you Michael for this explanation. Your not the only one who's really excited about this revelation :-) Whilst my mind is still reeling I think it may show that morals are a result of intelligence. We give blood not necessarily for any altruistic reason, just that it is a good thing to do that may come back and help us later, increasing our possible future actions for little effort now.

    1. Agreed.

      If you think with a 5 seconds horizont, give blood is a non sense, but when you think with a 5 years horizont, it makes perfect sense.

      The longer you can predict your futures, the smarter you are, or the more "sublime" or "moral" your decisions look.

      Also, the better you get predicting the good or bad a future will be for you, the more "moral" you get: helping others open more future possibilities to you than any other thing could do, but not all the people can "predict" this, so it is very common to ear people say "I helped people in that or this way and I never imagined how good it made me feel until I tried"... that is not being too good at calculating a future "goodness".

  11. You do realize that this equation inherently makes the universe intelligent as the evolution suggest that the survival intsinct is a driving force in the universe.

    1. Yes, according to this definition intelligence is an inherent part of the universe that somehow "unfolds". Higher forms of intelligence have are better in predicting the future freedom of action and are better able to move into preferred states.

    2. Agreed, but maybe with reservations. What I take away, at least now, is the conclusion that evolution necessarily creates intelligence, because those systems that persist are ones that have created, or inherently possess, freedom of action. I have difficulty with this thought, because one would suppose, as has been said above, that the ability to 'see' the future is required - but I don't think that's part of the original theory. Rather, I think evolution selects for those systems with the greatest freedom of action, simply because freedom of action = variation. So knowing the future isn't required - all that's required is the ability to generate, reliably, enough options that one or many will persist. To put this another way, there seems to be a 'meta' level to evolution.

    3. I agree that 'seeing' the future is not required. However, if you look at 'intelligent' systems, in retrospect, you will see that they 'predicted' the future better. Instead of predicting the future one could say they have a better internal model of the world. And this model is detecting the direction of the gradient of future freedom of action. Here, the time horizon τ (tau) plays an important role. Sometimes following the short term best direction is not the best in the long term. A classical example form human intelligence is the marshmallow experiment: Children that could delay gratification are more successful in life.

      If a system evaluates the future within a short time horizon, it may burn all its resources immediately because this will maximize freedom within that time horizon, but it may freeze the system in the long run.

      In some way 'survival of the fittest' and 'maximizing future freedom of action' are equivalent. But the equation of intelligence gives a measure what the 'fittest' is: the fittest systems are the ones that do keep the freedom of action.

      Note that the equation of intelligence applies to systems at all levels: from abiotic adaptive systems to societies.

    4. More intelligence means improved ability to predict future states (Sτ) and power or ability to act (T), which should accelerate exponentially based on the equation until it approaches infinity. To me the presence of intelligence explains the acceleration in the expansion of the universe much better than dark matter.

  12. Thanks for the very intelligent (pun intended) explanation, Michael!

  13. All you did was describe "Systems Analysis"

  14. Hi Michael, I read the article just when it came out, I couldn't really sleep well until some months a go, when (I hope) I understood the implications completely (well, in the basic implications).

    I have a blog about it ( with videos, a working exe and source code (for delphi7, object pascal, but may be I will por it to java some day to use it on some android games with intelligent bad guys).

    I LOVED to read your post as it sound quite like me talking of it to everyone around me! (btwe, I am mathematician but love physic, the weirdest the best).

    Most of your thoughts are shared by me, but I find it not appropiate to talk about "freedom of action", it really uses "entropy at a future horizont", where microstates (in the present) are switched to macrostates but measured in a future time.

    I also managed to "implant" goals to the intelligence, make some agents to cooperate or compite, and some other goodies just by manipulating the metric in the states space (entropy gained from state A to B is a metric, so I changed it to test and... ops, it worked nicely).

    If you want to play around with the exe and the code, I will be delighted to hear from you, really, so feel free to... anything.

    1. I looked at your site, it is really impressive what you have done! Very interesting that you have successfully used the equation to model intelligence :-)

    2. > I find it not appropiate to talk about "freedom of action", it really uses "entropy at a future horizont"

      I would agree that his is way more precise, but "freedom of action" is easier to understand in in real life. Or do you think that "entropy at a future horizont" is very different form "freedom of action" ?

  15. It definitely is an interesting way to look at intelligent behavior in animals and in humans. In fact, the behavior of all species is driven toward positions of safety and security for survival.

    In human societies and in martial traditions you see this same principle of moving toward the most strategic or best tactical position. Within society this usually is measured in terms of positions of greater status, wealth or power that translates generally into greater freedom of action. However, a narrow materialistic view on the individual level does not automatically produce greater collective freedom of action.

    Thus, larger values that aren't utopian tend to work out better for everyone.

    Another concept that is different and yet similar is the following formulation: Philosophical Assumptions define Theoretical Models determining Practical Applications.

    So, that intelligence is not merely a force seeking greater freedom of action but also is a set of reality constructs whereby one relates with the environment. These constructs can be more or less effective in terms of greater freedom of action.

    Interesting stuff...

  16. attention intelligence a sub system related to our senses as variables?

  17. fascinating observation and formula, but I think you ignored a point in the "How to increase the force of intelligence?
    There are tow ways to increase to force of intelligence:

    Make better predictions of the future, which means detect sates of maximum freedom of action
    Increase the power to move in the desired direction. By adding more energy or being clever in finding paths that require less resources." paragraph;
    our world has many imperfection and unpredictability, and blind evolution comes in here:

    3. Making imperfect variations to cope with unpredictability
    I enjoyed your post.

  18. Great stuff! I’m in the process of codifying evolution for practical use. The current reference point is "increasing ROI" (in general, not just a near term bottom line). This is a past to present measure. Maximizing future freedom within a scope seems like a present to future measure. I am struggling to define future options when choices are like “hire 5 people”, "hire 9 people”.

    You ask, "It would be really interesting to analyse how good different believe systems are in terms of maximising the future freedom of the system" If you have a classification that holds each belief system (within an economic context) that tracks costs, that’s easy to display. That's a big part of my project.

    1. When maximizing Return Of Investment, the question is, what is the Return. The answer of the equation for intelligence is that the "Return" is to not be trapped.

      The difficulty with the equation comes form the unpredictability of the future. Since we live in a world where at any time unpredictable events can happen (heart attack, earthquake, impact of an asteroid...) and even the "predictable" is not so predictable. But, if you make many decisions and if your decisions are a bit better on average than the predictions of other systems, you may gain more freedom of action in the long run. So, “hire 5 people” or "hire 9 people” is just one on the many decisions that add up. Maybe it's not the quantity of people you hire that matters, but the quality.

      When it comes to "believe systems", I think the ones that best observe "reality" and drive the best conclusions will win. In some cases, humans are driven by an utopia or by a believe that is no based on the reality. On the other hand, some religions seem to be very successful, even if its believes are not based on "reality".

      As individual you might come to the conclusion that not following the rules of the society (or the religion) gives you an advantage. But if you look at the society as a whole as an intelligent system, individual freedom might undermine the future freedom of action of the entire system. Take birth rates: for an individual a child might reduce the future freedom of action. So, if all intelligent individual decide not to get children, it might be bad for the system. Likewise, if everybody believes having many children is good, then the system might starve form overpopulation.

      "The tragedy of the commons" is a classical problem where the interest of individual members of the system in undermining the interest of the entire system.

  19. i just want to add my cent into this whole topic. From reading the above posts, I see the words force and freedom and this reminds me immediately to Friedrich Nietzsche's concept of "The Will To Power". Also, a poker game algorithm might also be closely related to this whole thing since acquiring a huge stack allows one more freedom of action in the game.

    1. Good point! It did not occur to me that 'force' and 'freedom' are used together in this context and that freedom and force are are often seen as opponents.

      I think, freedom in general requires the power/force to defend itself, else its options may be reduced (by other powers) and at the end the freedom of choice is gone. Using force to defend freedom takes resources. Therefore intelligent systems minimizes the power used to defend its freedom but it does not neglect it.

      So I think it may well be related to Nietzsches "Will to Power" ("Wille zur Macht").

  20. I'm the Anonymous who posted replies above on today's date, and I wanted to make some general comments too. First, the equation seems to indicate a direction to evolution, which I have supposed was impossible - but on later thought, evolution already seems directed toward reducing resource demand. Second, there also seems to be a general law, not stated yet AFAIK, that networks tend to concentrate over time - but in some way this tendency must oppose entropy. So third, there seems to me to be a need for a reconciliation between these ideas - evolution, intelligence, concentration and entropy.

  21. Interesting - some work done by Colonel John Boyd to form the OODA loop might be a decision system framework to test the rigor of this equation within the context of all known tactical flight patterns - as documented to date. Entropy & time distortion being the crux of Boyd's strategic approach to winning ... some parallels here.

  22. I think Colonel John Boyd to form the OODA loop was the missing piece for me. The motivational structure behind an active AI. It answers the WHY question for me. We may have goals and the means to move toward our goals but WHY do we do it. We are forever in the OODA loop and the WHY of it is a self-proof.

  23. This article blow my mind away too. I was wondering if is it possible to know the algorithm that were used to produce the simulations? Did you get it?

    1. Not really, but take a look at by Sergio Hernandez. He has some code running using the equation.

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  27. The equation is based on "entropic force" which is a real physical force that results from a system that is not in it's highest-probability state. For example, if you have a box with all the gas molecules in 1/2 of it with a partition in the middle, you remove the partition and then there is an entropic force that will result in them spreading evenly in the box. This force has the same equation in Wikipedia as this one, with subtle changes. In this idea, he wants says the system takes a path in which entropy production over any time period has maximized entropy production. This is like doing dynamics with least action instead of Hamiltonian. He restricts T to being a "casual path" which "that parametrizes the system’s bias toward macrostates that maximize causal entropy". I do not know what that means, but in the video he refers to it as a "strength", which is not a respectable or clear description. He says in the video it drive "forced degrees of freedom. It seems like he is setting up systems with constraints that result in entropic forces that result in certain outcomes, as you would expect. For example, he gets a gas particle to "spontaneously" go to the middle of a 2D box when there are 2D forces being applied. Why would anyone be surprised or expect a different outcome? I am not able to see how this is interesting. Here is a more professional review that agrees:

    1. Scott,

      one of the quotes in the article ( you refer to is:

      > "when you get married, you are deliberately restricting the options available to you; but that does not mean that it is irrational or unintelligent to get married"

      Indeed, at an individual level this may restrict the options available. But does it for the human population as a system? Not sure what the answer is.

      As I understand the equation, it is about systems that can observe their environment, make predictions about the future and then act accordingly. It’s about systems that can "simulate" the future and evaluate the outcome. As a general rule, which potential future states should the system choose? The answer is "the state with the most freedom of action".

      Complex intelligent systems like humans have many more constraints that drive the decisions.

      Honestly, I am not sure if the equation makes really sense or not.

  28. He does not explain the variables clear enough for me to understand or use. Your summary of it, which he states in a similar way, is a common tactic in competition against others or nature when the future is less predictable. But in well defined problems that you can model completely, there is a specific path chosen that can greatly violate this rule (as viewed from the perspective of someone with less knowledge). But from an omniscient view, knowing the best path is like never having an option except to choose that path. Not knowing or being able to control the future is intrinsic to wanting to keep options open. "Options" depends on amount of knowledge like "order" and entropy. "Entropy" is a measurable thing not subject to opinion, but it is a willful blinding of the most of the data: it throws out the details of the exact momentum and position of each particle and relies only on the bulk measurements of T, P, N, and V.

    I believe "keeping options open" is equal to not spending Gibbs free energy which a combination of potential energy and pre-existing order. He shows a weight on a stick that automatically balances. I do not know how he got from his equation to that, but maintaining potential energy achieves the same thing. It is also the lowest-entropy state: we can see it is straight up which is a defined position, but it may fall in many different directions. It is keeping options open, and yet it is preventing entropy from being increased. As you've listed the equation, the standard entropy force, it should immediately fall. This is not exactly the equation he uses. His subscripts are saying max entropy gradient over a certain time, or something like that. It seems his equation is maintaining the gradient at a max which is right before it "decides" which way to fall.

    We keep assets (potential energy in a low entropy state) that we believe will maintain value (be convertible to work energy with minimal entropy production, aka efficient) in times of turmoil. It could be dollars, gold, bitcoin, skill, or social contacts. But if we know the future, we spend it on other things that will result in the most long term profit (acquisition of other low entropy potential energy assets like a stock that may fluctuate wildly in this value. The end goal is supposedly to transfer the potential energy gains to our offspring so they can survive in the future, where "offspring" could be children, ideas, machines, or the greater community.

  29. You have cast this physics idea as under the control of intelligence, but I believe the physics of matter causes intelligence to occur. I believe the "meaning of life" (the goal of godless, mindless dynamics) is to emit entropy to the universe while decreasing it locally and increasing local potential energy. For example, biology seems to be replacing itself with more efficient machines that depend on very strong bonds in order to acquire sunlight energy and to use that energy to move matter, make structures, and to think about how to do it most efficiently and profitably (more potential energy and lower entropy in the end). These very strong bonds in today's society depend on oxygen atoms being removed from carbon (nanotubes, graphite, carbon fiber), metal ores, and silicon (CPUs and Solar cells). I do not know the chemistry of cement well enough to include it. Imagine society if the silicon, metals, and carbons did not exist (or they still had their natural oxygens attached). Look at the exponential trends of these increasing as biology decreases in relevance to the economic (economizing) machine. Economizing means spending energy and order (ores in a vien is pre-existing low entropy) effieicntly, but what is economics efficiently trying to do? The will of people? No. That assumes mind controls matter, but mind is not seperable from body, and mind has no rpe-existing force dynamics did not give it. Believing mind controls us is like believing in a soul. It's a handy but false model like a "selfish" gene. Mind and genes are implementing physical dynamics. Genes are the physical memory of past dynamics. Mind is a chemical reaction, not a pre-existing or fundamental force.

    Evolution is the result of the dynamics of matter. Matter moves as a result of energy potentials (F=-dU) and low entropy (F=TdS). We think mind controls, but it is the expression of past dynamics under these two forces. Schrodinger initially said "negative entropy" was key to life, but in an update he corrected himself to say it was Gibb's free energy, dG=dU+pdV-TdS. For Earth's surface, p, V, and T are kind of constant, and the remaining dU and dS are the two forces I've just mentioned. The minus sign works out because here we have F=T*dS and all other forces are the result of F=-dU. F=ma implies an intelligence behind the F to move the m, but there it is ultimately sourced from a -dU and TdS. -dU+TdS=F=ma, not Mind+genes=F=ma.

    I view evolution as dynamics creating memory/computation systems that catalyze matter into forming more memory/computational systems. Structures and bodies are the support structures for minds to create more minds, so it is easy to see why we think of mind as a primary force. But the primary source is dynamics. "We" (dynamics) cash in on the environment's dU and -dS to replenish and add more of them to our own systems (energy is released if we put the oxygen back into our silicon, metals, and carbon, as well as entropy increasing back to where it was). The dynamics trend is to create local order and increased potential energy, cashing in on energy from the sun. Fossil fuels are being depleted, but there's potential energy in the new bonds we are creating and they are harder to get started in burning. Entropy does not increase on Earth because it is an open system.

  30. When oxygen is removed, the refined solids have 1/5 as much entropy. The waste heat and entropy emitted in the refining is released to the Universe, leaving a much lower entropy in the solids that make up society. They also acquire a large amount of potential energy like fossil fuels compared to the previous ores. Denser materials result in lower entropy because less flexibility means fewer position*momentum states that can be occupied at a given temperature. This also means the materials are more predictable and controllable in a deep sense that makes them more efficient in structures, thinking machines, energy acquisition, and movement of matter.

  31. Thank you very much for this article. When I originally saw that TED talk a few years ago I got very excited too because it helped me understand intelligence much better.

    I also started taking decisions based on how much freedom I would get from their predicted outcomes. In general it helped me understand the model of the world that I currently have. I really liked your article and I think that it explains the subject really well.

    There were two concepts in this article that were particularly eye opening to me: The fact that you define intelligence as a real force in the world and also the section where you explain "How to increase the force of intelligence".

    I found it really useful to know that intelligence depends on power to make a change in the system. It gives me a clear way of increasing the chances of change. Also, the fact that making better predictions will increase intelligence. I would add that the ability to clearly understand the system in the present state is paramount to be able to give better predictions in the future.

    I work as an NLP Coach and I'm always looking for effective ways to help my clients achieve the change they need in their lives. Thanks a lot for this great article, I have been looking for a while for a good explanation about this topic and only found it with you article :)

  32. I mention your blog post in my thesis AI will eat the earth, i hope you don't mind, i also would love to hear your thoughts on my post.

  33. hey there i'm currently working on a school project and i am trying to code the pseudocode behind Alex wissner gross's entropica software as shown in the supplemental materials paper:

    I'm currently stuck and your help would be appreciated.

  34. I'm the Mysterious who posted answers above on the present date, and I needed to make some broad remarks as well. In the first place, the condition appears to demonstrate a course to development, which I have assumed was inconceivable - yet on later idea, advancement as of now appears to be coordinated toward lessening asset request. Second, there likewise is by all accounts a general law, not expressed yet AFAIK, that systems tend to focus after some time - yet somehow this propensity must contradict entropy. So third, there appears to me to be a requirement for a compromise between these thoughts - advancement, knowledge, focus and entropy.
    Artificial intelligence

  35. It really does seem profound despite my earlier complaints. Someone has to estimated the cosmological constant from it. Someone else has written a program that can play all the old Atari video games better than people unless they already have a great deal of experience and it doesn't require any training by playing the game or any memory, but just the rules so that it can measure future options. One interesting thing he has said is that keeping options open actually looks like intelligence more than intelligence generates keeping options open. So the force that results from options being open is intelligence but it's not a force that is coming from intelligence. He has written other articles that roughly speaking indicate intelligence equals potential energy equals Freedom equals wealth.

  36. Thanks for providing the information

  37. This is very logical thing. Anyone can learn from this.
    signs of genius

  38. Great blog. Your blog is so convincing that I never stop myself to say something about it. this is very informative and interesting for those who are interested to know What is Artificial Intelligence there is inspiration for us because we need it. You’re doing a great job, Keep it up. Artificial Intelligence is all about creating and developing machines it is very important to know what is it.
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  39. This is mind blowing... How can we skip the equation part
    ..!!! Awesome...