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Updated: Sep 19, 2023

Neurological Intelligence Model of Needs:

A Mathematical Approach

For the summer of math exhibition I am submitting this math problem: What are the fundamental human needs? This might not seem like a math problem, but I learned how to derive a mathematical solution from a class I took about a type of math called control systems.

Psychologists have sought to define fundamental human needs since 1942 (A.H. Moslow, A Theory of Human Motivation, Psychological Review, 50, 370-396, 1943). because it helps us understand human behavior and personality. It may even help you understand your behavior and personality. Solutions to our problem have been found using surveys. The first, and most famous, answer to this question was provided by Moslow's Hierarchy of Needs (Moslow, A Theory of Human Motivation). Another well known solution is the Max-Neef model (M. Max-Neef, Human Scale Developement, 1981) . I will examine the details of their answers to our question after I explain my approach.

To begin my model, we need to generalize the question to include the needs of all intelligences. My new model of neurological intelligence, shared in my first blog post, The Basics, provides a foundation for defining the needs of intelligences. It is summarized below.

The Basics of Neurological Intelligence

Neurons are things that work together to form intelligences. Neurons are not just the cells in your brain, but can include many other things. In this post I will focus on the neurons that are people and cars, for example. There are three aspects of neurons that are necessary for them to work: an identity, an epistemological method, and a type of relationship. In addition, there are four types or levels of neurons. The first type has a collective identity. It uses propositional logic as its epistemological method, and it has surface level relationships. The second level of neuron also has an individual identity. It uses abductive logic as its epistemological method, and it has personal relationships, or relationships that affect its inner workings. In addition to the characteristics of the lower levels, the third level neuron has a representative identity, it uses induction as its epistemological method, and it has a leadership identity. Lastly, the fourth level neuron has all of the properties of the previous neurons, and also has a moral identity, deductive epistemological reasoning, and a safety leadership relationship.


Epistemological Method




Role Play









Safety Leadership

Utilizing Control Systems Theory to Define Needs

The identity, method, and relationships of each type of neuron are associated with a need. Therefore, each neuron, and by extension everything that has some form of intelligence, has up to twelve needs. Control systems theory can help define these needs. Control systems are systems that are able to take an input and give back a stable output. The system below takes an input function u and gives an output function y.

In order to model a control system, it needs to be complete, consistent and stable. Each of these traits has two different levels: inner and outer. The most basic traits are the external or outer level.

Outer completeness means that for every scenario that a system could be in, there is some way that it should behave—a rule it must follow. An example of an incomplete system would be if you were at an intersection and it had a green light, but not a red light. You would know when to go, but you wouldn’t know when to stop. All of the road signs, and the roads themselves, are necessary so that drivers can safely interact with their environment. This is a need that all neurons (in this case, drivers) share due to their collective identity. There are rules, or necessities, that must be provided to neurons so they can interact with other neurons within their collective identity.

Outer consistency means that the rules provided by the system agree with each other. If there is a contradiction in the rules in the system, then there is a lack of consistency. If you were at an intersection and you had a green light, but the traffic that intersects with you also has a green light, then you have an inconsistency, and a car crash will probably occur. Consistency is a need of all neurons because it enables propositional logic. If two of your propositions contradict each other, then you can infer any conclusion. This renders your logic useless.

Outer stability means that if a system is given a bounded input it will get a bounded output. For example, if you are driving in a car and you let go of the steering wheel, but keep your foot on the gas, you have created an unstable situation. A bounded input to the car would be anything applying a finite amount of force to the system, such as a bump in the road. In this scenario even that bump will be enough to permanently change whether the car is on course. This is an unbounded output because the car will continue to get further off course unless a corrective action is taken. This is why you shouldn't drive with cruise control on while you are half asleep. All neurons need outer stability because of their superficial relationships—their interactions with other things. Otherwise, the system will fall apart.

The State Space Model

The inner traits of a system define the way a system interacts with itself. When I learned about control systems in school, I learned about modelling control systems using the state space model. As shown below, this is a system of two differential equations where u is the input function to the system, y is the output function of the system, x is an internal variable, and A,B,C,and D are constant matrices that represent the system:

When writing out a system the only thing that changes is the matrices, the following example is a state space model with two internal variables x1 and x2:

State space models make use of matrices to compact the many different differential equations in the model down to two differential equations. The expanded version of the matrix equation above has three different differential equations, they are:

A state space model may have one, two, or more internal variables, which changes the size of the matrices being used in the equation. The matrices are formed so that each of the derivative equations have one derivative equal to a combination of the inputs and the internal variables. The output equations show one output equaling a combination of the internal variables, and some constant which forms the D matrix. (In the above case the constant is zero.) The reason that the matrix form is used is so that similar parameters in the equations can be grouped together. The A matrix states how the internal variables affect themselves. This matrix will always be a square matrix. The B matrix states how the inputs affect the internal variables. The C matrix shows how the internal variables affect the output, and the D matrix is an input that affects the output directly, and is not affected by the internal variables.

Internal Operations

When you perform operations on a system that only concern the input and output, u and y, those are called outer operations. An operation that changes the variable x, or the system constants (A,B,C,D) it is called an inner operation.

Inner completeness means that a system has all the necessary components to work independently from its surroundings. If you were missing the A matrix, for example, there would not be the necessary components for the system to work. In real life, you could equate this to having a car without an engine. This system is internally incomplete; it cannot move or perform the way it needs to. When a neuron is internally complete it is capable of having an individual identity, because it can exist on its own.

Inner consistency means that when a system is directed to perform an action, it always does that thing. In our car and driver example, a driver that sometimes stops the car for a red light, but other times ignores the red light, represents a system with inner inconsistency. For this system to have inner consistency, the driver must always obey the rules of the road. Inner consistency is necessary in order for a neuron to act with abductive reasoning. If its decisions do not have consistent reasoning, then none of its conclusions will be meaningful.

Stability and Eigen Values

A system with inner stability will return to an equilibrium position no matter the starting internal conditions. For the state space model, inner stability can be found by finding the eigen values of the 'A' matrix. If multiplying a vector by the A matrix produces that same vector as you started with, but scaled by a number, that number is an eigenvalue of the matrix. There is one eigenvalue for every vector this works for. Essentially these represent the matrix's multiplicative properties with a single number. When the eigenvalues in the states space model have negative real parts then the system is stable. In the state space model shown above, the eigen values are '-1' and '-3'. Since both of the eigen values are negative, the model is stable.

Each eigen value corresponds to a mode of the system. If even one of the eigen values is positive, the model is internally unstable. In our driving example, there are two main things that keep a car stable: the steering wheel and the gas. These could be thought of as different modes. If your car’s steering wheel gets locked when it is placed in the wrong position, then it is internally unstable. The driver will not be able to reposition the car to the center of the road, and a collision is almost certain. If the driver manages to hit the breaks, averting a crash, then the system is demonstrating external stability, because the car did not crash, even though it was not internally stable. A neuron that has interactions that change it internally must be internally stable, thus allowing it to get back to being itself in its equilibrium.

Beyond Basic Needs

The needs mentioned so far are called deficiency needs. If they are not fulfilled, a proper model cannot be created. With those deficiencies filled, the system can exist and become useful as higher level needs are addressed. The first of these higher needs is the need to be internally realizable.

To be realizable, in mathematical terms, means that it is possible to make physical representation of a mathematical model. A system that has a state space model representation is always realizable. This makes it a very type of modelling.

For a neuron to have a representative identity, it needs to be capable of realizing the thing it represents. For a real life example, lets say you have to haul a trailer down the highway. If you have a pick-up truck, this task is realizable—it is possible to do with the truck. If you have a formula one race car, then this task is impossible. The race car is incompatible with the trailer, and the system has no physical representation.

The next higher level need is called observability. If a system is observable then you can determine the initial conditions of the system just from observing the output. Inner observability is necessary for inductive logic. In inductive logic you make a broad claim using a few examples of the claim holding true. For this to work you must be able to observe those few examples holding true. Cars include indicator lights so that you can easily observe whether or not there is a problem. This includes whether the doors are open, if you are almost out of gas, if you need an oil change. These are different internal indicators that allow the car's internal state, including it's initial state, to be observable. Without those indicators, it would be a lot harder to take care of your vehicle, or make it to your destination.

Last of the higher level needs is controllability. A neuron needs to be controllable. This means that, given the correct input, a system will give the desired output. A leader needs inner controllability, so that they can set an example for others. A car without a steering wheel is not controllable; don’t use it.

When a model is realizable, observable, and controllable it has obtained what is called the minimal realization of the system. For state space models, there is a theorem that we use to check if a system is observable or controllable using the system matrices as follows:

Using this theorem, we can create the controllability and observability matrices to see if the system is observable or controllable. The example we used when explaining state space models has the following controllability and observability matrices, with their rank written beside them.

Rank is a measure of how much non repeated information there is. The controllability matrix is of rank one because the second row is a repeat of the first row, times three. This lower rank means the system is not controllable. The observability matrix has rank two because the second row is not a repeat of the first row. Because of the lack of repeated information we know that the system is observable.

Additional Needs Based on Symmetry

That was the last of the needs that I learned in my control systems class, but they are not the last needs that intelligences have. The last set of needs can be found using symmetry. For a neuron to have a moral identity it must have outer realization. That is, to have any moral meaning, its actions must have an impact. For example, if you are in your work truck, then putting it to work is an outer realization of its purpose. If there is bad weather that prevents using the vehicle, then you are not able to have this realization, even if your vehicle is suited to the task at hand.

The next need is outer observability. For a neuron to deduce understanding from a situation, it needs to be able to understand the situation it is in. For instance, if you are using your truck to go through some questionable roads, then you might want to send a person out in front of the vehicle to check how muddy it is. With that information, you will be able to deduce the chances of getting stuck as you attempt to get through. You should also check the weather, and plan your trip so that you can prepare for it properly.

The last need is outer controllability. For a neuron to be a safety leader, it must be able to take control of a situation. Using our driving example, a driver needs to use correct signaling to indicate his intentions to others. In addition, other people need to know the meaning of the signals, so that they can react properly.

Neurological Intelligence Model of Needs

The model of needs of intelligences can be summarized in the following chart:

Identity Needs

Epistemological Needs

Relationship Needs

Collective Needs

Outer Completeness

Outer Consistency

Outer Stability

Individual Needs

Inner Completeness

Inner Consistency

Inner Stability

Representative Needs

Inner Realizability

Inner Observability

Inner Controllability

Moral Needs

Outer Realizability

Outer Observability

Outer Controllability

Applying the Model to Humans

Do human needs fit into this model of needs for intelligences? Yes, they do. Let me explain:

  • Outer completeness means that you have all the things you need to survive, including food, clothing and shelter, as well as having a social group you belong to. These are sometimes called subsistence needs.

  • Outer consistency means that the values that you hold (and society holds) are consistent. It also includes having consistent access to your completeness, or stability needs.

  • Outer stability means that you are safe and protected. People are getting along, and there is no threat to your survival. You could call this the need for protection.

  • Inner completeness means that you have all the skills you need to function fully in society. Things like being literate and being physically whole and well would fall under this need.

  • Inner consistency means that your beliefs and your actions must line-up. In other words, this is the need for cognitive consistency.

  • Inner stability means that you are able to focus on positive things and stay optimistic, even if you are going through hard times. This includes the need for mental stability.

  • Inner realizability means that you have found your purpose in life and you are living in such a way that you can achieve that purpose and live up to your full potential. It also includes having a purpose at all.

  • Inner observability means that you understand the motivations behind your actions and you are willing to let those motivations be seen by others.

  • Inner control means that you are able to control your actions, or in other words, you have self mastery.

  • Outer realizability means that you are in a position that you can achieve your purpose in life, and that you can live up to your fullest potential. If you always dreamed of being a doctor, then becoming a doctor would be the outer realization of your dream.

  • Outer observability means that you understand the people and the things around you. This includes a need for education and the need for meaningful, loving, or intimate personal relationships.

  • Outer controllability means that you are able to control your surroundings and accomplish your desires. Practical education might be included in this need, since you must learn the skills required to properly manipulate the environment. Having the trust of peers and society could also be included, as those trusting relationships will lead others to help you accomplish your goals.

How does this model of needs measure up to other models that try to define human needs? Well, it outperforms them, of course. Apart from the fact that it applies to all intelligences, it also more accurately depicts the human experience. Let's compare it to the two most famous models of human needs.

Comparison to Maslow’s Hierarchy of Needs

Moslow’s model of needs depicts a hierarchy, where each of the higher level needs, we are told, can only be met after the lower level needs are satisfied. Due to its popularity, this hierarchy has been examined very thoroughly and its flaws are well known. First, reproduction is a physiological need, but not in the same way that food is. Your life will go on just fine if you are not procreating or giving birth. In fact, in some cases, reproduction could put your own life in danger. In my model, reproduction would fall under the realization needs. If having children is a goal in your life, then you need to be capable of reproduction, an internal realization, and you must have a partner, and a place to raise your children. The latter two are external realization needs, that put reproduction on a completely different level than the other physiological needs, which are subsistence needs.

The second problem with Maslow’s model is dealing with the issue of suicide. Many people who commit suicide do so because they are lacking in one of the higher needs in Moslow’s pyramid. This goes against the hierarchy model, because a person should always put their physiological need to live ahead of all other needs. I should note that this might not have been the way Moslow interpreted his model. He may have thought of it more like a ladder, where you could focus on only a few rungs at a time. The hierarchy he proposed was later interpreted into his model. Nevertheless, the issue of suicide is still a problem with the current understanding of his model, and researchers have found that his hierarchy is more of a rough guide to how a person may obtain their needs, and not a strict rule.

The neurological intelligence model removes this flaw by understanding needs differently. The needs are not built one on top of each other, like a pyramid. Instead, each fulfilled need enables you to have one basic property of an intelligence. The model allows for the fact that a person may have some higher level needs fulfilled while some more basic needs are yet unsatisfied. It also means that one individual might care about a certain need more than another just because of his/her personality. Since we are all fourth level intelligences, we could have suicidal thoughts when any of the needs that we value are missing.

In the model I propose, different levels of needs cater to different levels of intelligences. Each successive level of intelligence is a smaller subset of the last, so you might expect the same with the roles people play in society, and the needs that they have. Fewer people will care greatly about the moral needs than the number of people that value the collective needs.

Maslow's hierarchy mostly isolates human interactions into needs for love and belonging. This does not represent real life, because most human needs are related to interactions with others. The intelligence model removes this obstacle; each need category is related to one of the ways that people interact.

Comparison to Max-Neef Model

Under the Max-Neef model there are many needs that are all equal, but a person may put a greater emphasis on one depending on their personality. The needs are subsistence, protection, affection, understanding, participation, leisure, creation, identity and freedom. The benefit of this model is that it puts a greater emphasis on how needs can be satisfied and the behaviors of people who are trying to meet their needs. In this way, the model has a completely different purpose than Maslow's and it does not have the glaring inconsistencies I noted above, yet there are a few problems that stick out to me.

First, the Max-Neef model gets rid of all hierarchies. However, there are intuitively some needs that are more important and more universal than others. For example, ants, so far as I can tell, do not care about their freedom or leisure. Perhaps these needs should not be on the same level as subsistence and protection, which all living things care about. The neurological intelligence model of needs overcomes this by following the hierarchy of greater intellectual function.

Another problem that the Max-Neef model has is that there are needs that overlap. For instance, subsistence needs could be seen as the same as outer completeness needs in the neurological model. Yet, subsistence needs is also just a subset of identity needs, which is listed as a separate need in the Max-Neef model. The neurological intelligence model attempts to overcome this by linking each need in the model to a distinct mathematical concept.

One of the big focuses of the Max-Neef model is on how our drive to meet our needs affects our personality. The neurological intelligence model of needs links needs and personalities together, as well. However, the symmetries present in the model can also be used to explain the major different personality types such as neuroticism, extraversion, etc. This will be covered in a later post.

Now that I’ve explained my neurological model of needs, it’s time for you to do some homework. Think of all the things you need, and see where they fit in the model. Are there some needs, or groups of needs, that are more important to you? What do you think that means about your personality?

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