Comments on "The mechanics of embodiment: A dialogue on embodiment and computational modeling."
By Pezzulo, G., Barsalou, L.W., Cangelosi, A., Fischer, M.A., McRae, K., Spivey, M. Frontiers in Cognition, 2(5), 1-21 (2011). Full text.

I read this extraordinary paper in May 2012. It contains a review of state of the art and current trends in Computational Psychology, particularly the fundamental aspects of grounding, embodiment, and situation. I found it very close to my own thinking, being as it is that I am a Physicist/Mathematician and no expert in Psychology. I am sure this paper will be very influential and goal-setting for years to come. It inspired me with much thinking, and I created many comments, which I share in this short article.

While working with the Mathematics of causal sets in the last few years, I came to realize how important they are for understanding high brain function. Causal sets are used in Physics to capture cause-effect relationships in causal systems. The brain is a causal system, and causal theory applies to its function just as well as it applies to the function of any other causal system.

In the context of causal theory, I will address grounding and embodiment first. Consider any sensor, for example a TV camera where light coming from the world illuminates a "retina" made of pixels, and is converted into electric signals. Those signals are a causal set. Each pixel receives a beam of light and generates an electrical signal. That is a cause-effect relationship. That simple. There is no need to understand how the pixel works. The output cable from the camera carries a giant, constantly changing causal set, consisting of millions of unrelated, completely independent signals. This causal set is said to be in an *unbound* or *unstructured* state, because there is no binding among the various signals.

Consider now the retina of the human eye. It is just the same thing. The optical nerve carries a giant, constantly changing causal set of action potentials, in an unbound state, and delivers it to the brain.

Consider now any of the other senses. Stereocilia in the inner ear converts sound pressure patterns into electrical signals, and the auditory nerve carries them to the brain. A finger touching Braille dots sends an unbound causal set to the brain via afferent sensory nerves. Even chemical signals are describable by unbound causal sets.

The brain receives only unbound causal sets. Those causal sets carry no information whatsoever regarding meaning. If you are a teacher and teach a class, your voice is converted into and unbound causal set representation before it even reaches any of your pupil's brains. The brain makes its own meaning on-the-go, from the causets it receives. Someone has compared an unbound causal set to a snowfall. The flakes are beautiful, and they fall, but they don't know each other. And they don't know how to make patterns. This is a central concept in this article, and the reader is advised to take it very seriously, because it is not so easy to grasp. A surprise is coming before the end of this article.

Next, consider the output from the brain. The brain sends its output out via efferent nerves. The output also consists of causal sets. But this time the causal sets are in a *bound* state. They are organized and structured, and they carry meaning. Causal sets are isomorphic to algorithms, or "behaviors." They directly control the behavior of the muscles that that make us write, or speak, or move, and the centers that control the chemistry of the body, such as the levels of hormones and other chemicals. If you are the teacher, they control your tongue and your gestures, if you write, they control your hand.

But then, what happens in-between? How do unbound causal sets become bound? What process converts unbound causal sets into bound causal sets? I said above that the brain is a causal system, and causal theory should apply to it just as it applies to any other causal system, independently of how complex is the implementation. A causal system is mathematically described by a causal set. If the brain receives unbound causal sets as input, sends out bound causal sets as output, and is itself mathematically described as a causal set, then it is natural to assume that the conversion process is based on a causal set as well, and that the brain itself works as a causal set. This is the central hypothesis of this effort. It is a *working hypothesis*, meaning that we are going to use it for all our future work, unless it is disproved by experimental evidence. It is also known as the *principle of feature binding*.

Having made that hypothesis, we can now forget about the brain and start considering the entire process, input, binding, and output, in terms of causal sets alone. We have created a mathematical model of the brain, and are going to build a theory on top of that model. Now, consider the most fascinating part, the process of binding.

The process of binding is a form of inference. Inference is a part of logic that allows one to derive new facts from known facts. Clearly, binding does allow us to derive new facts such as structure, organization and meaning, none of which exists in the unbound sets. So binding is a form of inference. Physiologist and Physicist Hermann von Helmholtz was the first to predict this inference ca. 1850, in his studies of vision. He called it "unconscious inference," because we are not aware we are doing it. The fact that this inference is unconscious has important consequences: it means we can not describe it or simulate it in a computer program. But that's another story. But von Helmholtz did not formalize his prediction.

Many of the greatest minds of the 20th. century tried to formalize binding, among them Bool, Bertrand Russell, Church, Goedel, Hilbert, Turing. Wittgenstein proved the problem unsolvable in the context of first order Mathematical Logic. The famous and closely related Entscheidungsproblem posed by Hilbert in 1928 was also proved to be unsolvable by Church and Turing.

I believe I solved the binding problem a few years ago. We see binding at work all the time in ourselves so we know there must exist a solution. If a solution exists, someone would some day find it, one way or another. Well, that was me, I think. I named the inference "Emergent Inference" (EI), because it pertains to causal sets alone, irrespective of whether the brain uses it or not, or how it uses it if it does, and because it explains the phenomena of emergence in complex systems. EI bounds a causal set, there is no argument about that. The theory, as well as hundreds of computational experiments on causal sets summarized in [1] confirm that. The interested reader can also see [2] and [3]. But what does this binding have to do with binding in the brain?  Everything, as confirmed by several computational experiments where results from high brain function were compared with results from EI.

If the brain can be described as a causal set, then it can not be described in any other way, for example, as an artificial neural network, because artificial neural networks do not have the properties of causal sets. Describing the brain as an artificial neural network would be like describing a jet engine as a coal-burning steam engine.

Grounding and embodiment are now examined in the context of this causal theory of the brain. Information that the brain needs to embody and to ground itself comes from stereoscopic vision and hearing, touching and grabbing, the perception via afferent nerves of the relative positions of body parts, and the fact that sensory organs are mounted in fixed positions on those body parts. But the brain does not "know" all that, in the sense that we use the word "know." The brain does not know the exact geometric position where each finger or each eye are located at every instant, or how each arm and each eye are moving.

The brain only receives unbound causal set signals from the muscles that move the eye, or the fingers, or the head, or the limbs and hands, and also unbound causal set signals from both eyes and both ears. If the hand touches something that the eye is seeing, the brain receives causal information about that. That's how infants learn to touch and gtrab. If the brain directs a hand to grab something that the eye can see, the brain receives causal information about that.

All that enormous volume of causal information arriving at the brain must be considered as a whole. It all consists of exactly similar electrochemical signals, the action potentials of the neurons, all of the signals completely unrelated to each other. There is nothing in it telling the brain where each pulse comes from, or what kind or category of information it pertains to, or how the pulses could or could not be related to each other. There is just a pulse. And another pulse. And another. It is just one single huge unbound causal set, just one huge body of dispersed information, and the brain's task is to make sense of it as a whole.

Isn't this the same problem that robots confront? Or the same problem that AI confronts? Or the same problem that Software Engineering confronts, where human analysts are unavoidably required to create the objects in object-oriented designs? Each one of those is a different story, but they all converge on EI.

The brain does not run any algorithms or do any calculations. All it does is binding, by way of EI. The inadvertent reader may have been expecting me to provide an explanation, that is, an algorithm, that would reconcile grounding and embodiment information coming from various different sources, such as vision, hearing, or touch, and would ultimately allow one to "calculate", mathematically, the exact geometric positions of the sensory organs or the body parts relative to each other or relative to some external fixed system of coordinates. Then, for example in Robotics, one would be able to use other algorithms to control physical interactions among robots or between robots and humans. I already have answered that. But it's not an algorithm. It is a process that generates the algorithms you need. Each robot, or human, receives information via sensors or senses, and bounds it by way of EI to directly obtain the algorithms needed for controlling the body or acting upon the environment. The brain *interprets* all the information without the need for any coordinate transformations. That's why, if the tongue of a blind person is connected to electrodes activated from a camera, the brain will learn to see through that camera. All this can now be done on a computer that is running EI. At least one such machine has been built by the author (my PC). It works, in small problems for now, and it has been operational for some time. That's it. This is the surprise I promised.

In the process of binding, the brain generates behaviors, which we also call *algorithms*. This statement explains the origin of algorithms. The behaviors, or algorithms, are used to control muscles in the body. Or, they can be copied to a computer and become computer programs. But that's another story.

In my view, binding in the brain is unconscious. It is the process where inter-neural connections grow shorter (by what process, I don't know). By doing that they cause the binding to occurr. The memory itself is conscious. When synaptic contraction imposes structure on memory, and neural cliques appear, then inter-clique connections start contracting themselves, causing a new level in the structural hierarchy to appear. And so on, all the way to high brain function. It's a start.

Two very different issues were discussed in these article. One is the mathematical theory of causality, based on causal sets, and on emergent inference, a new form of logical inference that is a mathematical property of causal sets. The theory is currently solid. The foundation of the theory has been proposed in Section 3 of [1], and hundreds of examples of its application have been summarized in Section 4 of [1]. The theory is also self-consistent, meaning that it does not depend on any hypothesis about the brain or another physical system.

The second issue, is the hypothesis that the brain uses emergent inference to create meaning and bind incoming unbound causal sets into bound outgoing behaviors. To test the hypothesis, a small number of computational experiments have been performed, where the output from a machine running emergent inference was compared with the output generated by a human analyst when both received the same input. They are summarized in Section 4.5 of [1]. No disagreements with the hypothesis were found. Of course, more experiments and a larger scale are needed. But the hypothesis will always remain a hypothesis. No amount of experimental work can ever prove a hypothesis.

I know by myself and independently that our knowledge is grounded in in sensory and motor experiences. I need no convincing about that. But "The mechanics of embodiment" is enormously important because it represents the exact convergence of two very different lines of thought to the same target. It provides me with an extensive observational verification of my hypothesis, and at the same time it provides you with a theoretical infrastructure from which detailed experiments can be planned.

This is not, however, my first "convergence of very different lines of thought." I'll tell you about this some other time.

The approach presented here satisfies all three requirements proposed in "The mechanics of embodiment." Cognition is not studied as a module independent from sensory and motor modules. The representation (a causal set) is grounded from the start, and all its processing (EI) is fully grounded as well. It could be said that the representation is multi-modal and remains as such during processing. But the notion of modal/amodal is a little different here, because the architecture of the system is a consequence of the process, not a pre-requisite. Modalities have a hierarchical structure, EI is strictly hierarchical (see [1], Section 4). EI is the "principle of feature binding." Abstraction and abstract thought is build atop of sensorymotor experience, as a higher level in the EI hierarchy, by reusing sensorymotor patterns (naturally, as a property of EI).

Brain dynamics is an area where more evidence is needed. The main question here would be whether the brain can support EI, and how. In [1], I have proposed a simple model where neurons first connect to support memory, and then shrink or tighten their connection as much as they can. If these features alone can be demonstrated, then it would be sufficient to argue in favor and plan more experiments. There is some encouraging evidence: the existence of neural cliques, and the recent (2012) proposal of underlying simplicity in the brain. More is needed. Perhaps brain-on-a-dish experiments can help.

The requirements are satisfied naturally, as a property intrinsic to causal sets. It is not that I have somehow "invented" EI, or "engineered" or "adjusted" the functional in such a way that it works. I only found EI, I discovered it in the course of research, it was there all the time. All we humans need to do, is to use it.

The thinking in this article shows how utterly inadequate are the efforts of those who try to model grounding problems by way of geometric constructs and centers of gravity. It also argues that grounding and embodiment are integrated with the rest of the brain's process in an inextricable way. These concepts acquire meaning and become "grounding" or "embodiment" only after the binding process is complete, and as a result of the binding process. It is only our heuristic thinking that came up with the names once the meaning was there. Trying to model them by a traditional computational approach would make no sense, and would never succeed. EI is uncomputable.

Cross-fertilization between disciplines such as Computational Psychology and Robotics will not help. Neither one has applied EI yet. The correct course of action is to introduce EI in both disciplines, and then let them mutually cross-fertilize.

[1] Emergence and self-organization in partially ordered sets. Sergio Pissanetzky. Complexity (Wiley InterScience), Vol.17, Issue 2, pp. 19-38 (2011). Article first published online: 22 OCT 2011 | DOI: 10.1002/cplx.20389. Note: The type of partially ordered sets discussed in this publication are known as causal sets, or causets.

[2] Structural Emergence in Partially Ordered Sets is the Key to Intelligence. Sergio Pissanetzky. Lecture Notes in Artificial Intelligence, a subseries of Lecture Notes in Computer Science, LNAI 6830, pp. 92-101. Springer-Verlag.

[3] A New Universal Model of Computation and its Contribution to Learning, Intelligence, Parallelism, Ontologies, Refactoring, and the Sharing of Resources. Sergio Pissanetzky. International Journal of Information and Mathematical Sciences, Vol. 5, no. 2, pp. 143-173 (2009). Published on-line: August 22, 2009. Please note that "International Journal of Information and Mathematical Sciences" (IJIMS) is the new name of "International Journal of Computational Intelligence" (IJCI).