The Way Forward

In this section we discuss and illustrate the development path that we anticipate for Matheta. Our goal is to show what we’ve done beyond what we’ve already demonstrated, our vision of the capabilities we know we are able to but have not yet developed, and the future development path.

Everything we’ve shown so far, both in the demos and in descriptions of capabilities on the web site is based on a very simple model of a nervous system. The diagram below shows a schematic of the control system we’ve modeled. (By control system, we mean that part of the nervous system that makes decisions and learns, it does not include incoming sensory input.)


You can see from this diagram that there is a hunger system that generates appetitive behaviors and that the “Positive” and “Negative” fixer are release in direct response to external input and operate independently.

The diagram below shows the five known learning paradigms of operant conditioning. The nervous system Robby had replicates two: Positive Reinforcement and Positive Punishment.


In order to demonstrate the potential and power of the Matheta nervous system simulator, we modified our original nervous system so as to enable it to additionally replicate the Escape Negative Reinforcement paradigm. We used the same program that controlled Robby, only adding a couple of additional neurons and modifying some connections. Below is the schematic diagram of this model nervous system:

In the figure above “Goal!” should be seen as a neuron (or set of neurons) that fire when the organism obtains food.

“Goal Press” neurons fire in response to deficits in food, i.e., it creates the experience of “hunger.”

When “C/J” (Contentment/Joy) fires it releases the positive fixer.

Arrows represent excitatory synapses while dashes are inhibitory.

“Acquisitive Behavior” are a set of command neurons that, when stimulated by Goal Press, result in varied (species-specific) food seeking behaviors (operants).

“F/T” (Fear/Terror) is fired by “aversive” stimuli, e.g., loud noise, electric shock. It releases the negative fixer.

“F/T” Behaviors” are a set of command neurons generating species-specific responses to threats, for example, freezing or fleeing.

“I/E” is Interest/Excitement, another basic affect, generated by slowly raising stimulus input. It is not modelled here.

The circuit worked as expected but, unexpectedly, some very interesting results “fell out” of this effort.

The primary modification was that now it is the OFFSET of aversive stimuli (hunger and danger) that generates the Positive fixer. As a result, this new nervous system can model/replicate all five of the known operant conditioning paradigms shown in the diagram above. Since virtually everything known to science that any animal (except primates) can learn is learned through these five paradigms, it is clear this represents a considerable advance in capability.

It also turns out that this nervous system allows replication of another vital behavioral/motivation capability: the approach-avoidance conflict of getting food vs. avoiding becoming food. Those two tasks are the most fundamental realities of most animals’ daily lives and at the same time, they are the most fundamental threats to life. Quite unexpectedly, our new circuit suggests that the neural basis for deciding this conflict is deep in the heart of the architecture of the basic animal nervous system. This again suggests that the Matheta approach to modeling animal nervous systems has utility.


Finally, an even more important capability was “discovered:” affect, that is, the biology of emotion. In brief, the new circuitry replicates some basic affects described in Sylvan Tomkins’ affect theory. Further, the design of the nervous system makes it obvious how to extend the model so as to include almost all the basic affects he described. His powerful theory places affect (emotion) at the center of human behavior and convincingly describes its function. That affect is inherently built into Matheta means that systems built using it can be motivated by, responsive too, and displaying of fundamental emotions. Even more significantly, however, since the nervous system will be rationally designed, errors produced by natural selection can be eliminated. For a more thorough understanding of the theory of emotion that Matheta is based on, please go here:

Intriguingly, what I discovered when “playing” with the model is that it appears that a “solution” to the fundamental approach-avoidance conflict of animal life falls out of the model. That is, by designing a neural network that modeled active avoidance learning, I inadvertently stumbled on a nervous system architecture that appears to represent a neural solution to controlling the behavior of an organism so that it will search for food when hungry, will do little or nothing when not hungry, will stop searching for food and take evasive action when threatened, and will resume searching when the threat is alleviated. That is, I believe, a fairly accurate general description of the daily behavior of most animals. In addition, this circuit straightforwardly suggests how to include additional Tomkins’ affects such as Fear/Rage, and, when relevant, Distress/Anguish.

A non-obvious and counter-intuitive aspect of Tomkins’affect theory is his contention that the biological affects are triggered by changes in the level and rate of nervous system activity (most easily understood as that produced by a particular sensory input, but more accurately, as the sum of all afferent neuronal activity).  The abstractness of this runs so counter to our lived experience that particular stimuli elicit affect-fear from seeing spiders, for example.  I’ve developed the chart below to try and schematically represent this idea, hopefully making it more understandable and illustrating it’s power.

This graph illustrates that varying rates and levels of nervous system activity will produce different affects.  Thus a low or vary slowly rising level of activity will produce no affect (perhaps experienced as boredom). However a somewhat higher rate of increase in activity will produce interest-excitement, while a still higher rate of increase will produce fear-terror.  Similarly, when nervous systems activity increases to a certain level, irrespective of how rapidly it gets to that level in will produce distress-anguish, and, at still higher levels, anger-rage. Note also that any rapid decrease in activity will produce relief-joy. (Thokins call this affect enjoyment-joy but I think that fails to capture the lower range of the affect which might be more accurately characterized as a feeling of relief.)

A comprehensive understanding of this schematic will explain a lot about emotions and their relationships.  It also clearly points to how to directly add affects to models of organismic actions and learning (and affective communication)>

Future Development

There are at least two development paths to pursue that will result in synergistic benefits if pursued in tandem. There are also three methods of modeling available.

First we can continue to develop models of existing (animal) nervous systems. By examining existing comparative anatomical and functional data, we can model the demonstrated capabilities of primitive organisms first and then move “up” the evolutionary ladder to species with additional capabilities.

Second, we can attempt to model particular known learning capabilities by improving the present basic system. For example we could adapt the present system to focus on pattern recognition, running a maze, or learning a complex behavioral chain (like pigeons playing Ping-Pong.) We can also further develop the affect-based motivational/decisional control system.

The three available methods are:

  1. Modeling using high level languages and matrices to represent nervous systems and inputs, i.e., the way we’ve done it so far.
  2. Modeling based on low-level machine language where individual bytes of memory represent individual synapses while banks of memory are neurons.
  3. When our knowledge is sufficiently advanced, it is possible to make dedicated monolithic chips replicating complete nervous systems.

Each of these methods can be scaled over vast ranges, presenting the possibility of similarly scaled capabilities.


Because any source of input can be used as the “stimuli” that control behavior (output) we could use what’s already known about machine vision, natural spoken language processing, even human EEG, as inputs that could provide Matheta with extensive “off the shelf” sensory capabilities with far less costs than if we had to develop it ourselves.

Similarly, virtually any machine output can be easily controlled by Matheta. This includes computer interfaces, automation systems, and robotics.

Thus, as Matheta’s capabilities mature, it will be possible to integrate them with existing systems. For example, because of its inherent capability to learn through reward and punishment, it could be integrated into a Siri-like system that can be corrected when it makes a mistake: “No Siri, not bucket, bouquet.” “That’s right.” Similarly, it can be adapted to special purpose robots to add to their capability. And, with more extensive development, eventually to general-purpose industrial robots.

The possibilities and potential rewards are exciting. We are looking for those that feel similarly to join this effort.