Human Behavior, Set Theory and How the Brain is Always Self-Optimizing

“The Human Brain is an incredible pattern-matching machine.” — Jeff Bezos

I have had the amazing opportunity of working with a genius for the past few weeks, a literal walking wikipedia of knowledge and information. One of the early pioneers, helping create what we know today as the world wide web. He contributed to many of the existing protocols (NAT, IPV6, TCP/IP) in the networking world that helped you reach this very article. Over a few drinks on a rooftop hotel, overlooking Time Square in New York City, he began explaining his views on how the human brain works, his definitions of what spirituality, consciousness and reality are from a ‘mathematical’ perspective.

tl;dr — We can categorize our memory into 3 tier types, the unconscious, consisting of basic biological functions of the human body, the conscious where we experience the memories and the subconscious where groups of memories influence our behavior and responses to everyday experiences. Following this we can begin to categorize or group memories into sets that are bulked with other similar types of memories. We translate a memory into what we call mathematical “patterns.” We then apply the idea of Set Theory to the function of pattern storage in the brain. For an even deeper understanding beyond just cognition, we can apply a theorem, Fuzzy Set Theory (FST), where we then suggest that human behavior and character are derived from specific ‘dominating’ subsets in the brain. FST also suggests that our brains are always self-optimizing on how it stores and manages patterns/memories in the brain as we grow and develop over time.

Let’s quickly define some language used in this paper.

1. Memories: own cognitive actions, cognitive analysis of others actions or instances of reality.
2. Patterns/Memory Patterns: Mathematical way of expressing “memory”, how a computer stores memories… “Memories”, “Patterns”, “Data” are interchangeable by definition.
3. Data: Patterns in regards to computer storage, strings and clusters of characters, numerical and other character values.
4. Binary: Numerical values of base 2 instead of base 10… all values consist of strings of 0’s and 1’s. (ex. 101 = 5)

Patterns and Tiers of Cognitive Storage

By his explanation of the brain structure, for simplicity of this article, we are focused on the four primary lobes (occipital, frontal, parietal, temporal) where different forms of memory are stored, temporal lobe (acting as an intermediary) where specifically short term memory is stored and the hippocampus where memory patterns form.

Tier 1

This is the most complex, yet simplest type of memory. This goes beyond the human subconscious to the form of activities that are in a sense beyond our cognitive thinking. These include human organ functions, sleepiness, feeling of pain, healing of wounds, and so forth. These are developed and programmed in the brain during birth through the human genome and activities of the many cells that are part of the human biological ecosystem. These patterns are never lost or forgotten by the brain but can become lost or destroyed through some diseases like Alzheimer’s, dementia, paralysis, and severe head trauma damaging the brains physical form.

Tier 2

Begin by taking any lobe of the brain and unfolding it until it is a giant sheet of tissue, like a massive canvas where we can we print and store patterns of our functional neural network. The brain processes numerical patterns of memory for every experience and/or action that take place in our lives. Think of binary strings (0110100…), large strings of random 0’s and 1's. The brain triggers neural signals that travel from the temporal lobe down into the hippocampus,, each jump triggering a value within the pattern. Each jump recording either a value 1 or 0 to the string of values. After the nth jump, the pattern is recorded and stored in the temporal lobe of the brain, our “short term” memory.

For the sake of simplicity, let’s say the brain handles strings up to 32-bits in binary numerals, simplest of pattern strings being just a few bits long. If we only consider length of 32 characters, this would give us

2³² = 4,294,967,296

or around 4.3 billion possible unique singular patterns to store. Dependent on how often a pattern is created, shows how quickly and easily our brain retrieves the pattern and loops it back to us. The simple capture and storing of a single pattern we classify as a Tier 1 level of memory, a single entity of an action in reality. These patterns frequently get overwritten or simply ‘lost’… which can be re-used once it’s recycled by the hippocampus.

Tier 3

Say we create and store a specific pattern x times per day for a year straight. The probability of retrieving this pattern and re-looping it is extremely high, in fact, it will be so well programmed, you may not even need to ‘think’ about it. These are our subconscious patterns or ‘programs’. These typically consist of everyday activities and strong long term memory storage such as, remembering someones name, opening a door, signaling to turn when driving, opening a jar, swimming… you get the idea. By increasing how often we repeat a pattern, the higher probability it is of retrieving easily accessing said pattern. These patterns are moved from our temporal lobe and stored in the brains cerebral cortex or lob of relevance.

In mathematical context, these patterns are categorized into a subset of relative patterns. Each lobe is essentially the largest of possible subsets of the brain. With there being 4 lobes, this allows us to break down our entire set of patterns into 4 distinct subsets.

Let’s label each lobe (A),(B),(C) and (D)

where B𝑛 = {(A),(B),(C ),(D)} , B𝑛 is set of all possible patterns in the brain.

We first define a binary string

Definition: Let B𝑛 be the set of binary strings of length n. Define r : B𝑛 → B𝑛 to be the operation that cyclicly shifts each string s in B𝑛 to the right once. Now let 1+r : B𝑛 → B𝑛 be defined by the equation (1+r)(s) = s+r(s) for all s in B𝑛.

It is useful to observe the property that r(s + t) = r(s) + r(t) for all s and t in B𝑛. Then by definition we have (1 + r)(s + t) = (s + t) + r(s + t) = (s + r(s)) + (t + r(t)) = (1 + r)(s) + (1 + r)(t) for all s and t in B𝑛.

Starting with some element s𝟶 in B𝑛 we apply the operation 1 + r over and over, forming a set {s₀, s₁, s₂, . . . , s𝘮}, where s𝘪+1 = (1 + r)(s𝘪). We call this set the orbit of s0 under the operation 1 + r. Since B𝑛 is finite, the orbit of any binary string is also finite. Thus for any s0 in B𝑛, there is a positive integer m such that s𝘮+1 = s𝘬 for some positive integer k, with 0 ≤ k ≤ m

Let x = {{0},{1}} and y = {{0},{1}}

giving us substrings (xy) where set of binary strings B𝑛 = (xy | Bn-₂).

For simplicity we are setting n=32, where we get

A = B₃₂ = (00 | B₃₀)
B = B₃₂ = (10 | B₃₀)
C = B₃₂ = (01 | B₃₀)
D = B₃₂ = (11 | B₃₀)

Each lobe would hold B₃₀ = 2³⁰ = 1,073,741,824, a quarter of all possible patterns. This is the highest level of a subset we would categorize. Let lobe A be the storage of patterns that pertain to logical thoughts… A is identified by strings that start with (01), thus all patterns that begin with (01…) are then stored in lobe A.
Our brain groups patterns into groups that more closely resemble each other, memories of your puppy will all have similar binary strings where maybe the first 8 digits are the same, then they are distinct beyond 8th digit. These patterns are stored within the same region of the brain, sort of like storing files on your laptop with drives > folders > files… it’s a filing system for the brain but with a digital footprint for reference.

Human Behavior is Simply Sets of Patterns

Research has shown that from an infant up to 4 years of age, our brain consumes around 46% of our bodies total energy. Take the average adult, say early to mid 30s, their brain is consuming around only 20% of the calories that the body uses. Our brain at a young age is working A LOT. This, we believe, is due to the fact that the brain is still learning to create the simplest sets of patterns, the wiring of our mainframe for how our brain begins to organize and store memories. When we try to look back at an extremely young age, most memories are extremely fuzzy or non-existent because our brain wasn’t efficient enough at bulking sets of patterns together and storing for long term cognitive use. The mind was too busy storing subconscious patterns that eventually define our behavior and personality.

We have many forms of problems, characteristics, anxieties, and other behaviors that we ourselves can’t even begin to comprehend or explain. Spiritual beliefs, fears, how we handle relationships, communication, how we react to certain situations… all tier 3 type patterns are programmed at a young age. Maybe you grew up in a very strict and closed religious environment where day to day was being told to speak when spoken too, doing your chores, eating and sleeping, with minimal outside interaction. The repetition of this day to day life, for many years, you would notice “abnormalities” in your behavior and communicating with other people. Some of us learn to break these abnormal patterns and rewrite the code in our programs… others not so much. If you lived such an enclosed lifestyle for so long, the subset patterns that pertain to closure, silence, and obedience would overwhelmingly outweigh any other subset of behavioral patterns. Our subconscious is always looking to validate what it already believes to be the truth of any thoughts or ideas. So given any situation where you need to acquire some pattern of respond to the situation, pretty high probability you’ll have to reach into the subset that pertains to your closed in experiences, what we would call, dominant subset of patterns.

Optimizing

In Set Theory elements strictly intersect and can be found within a set or subset of other values, or not existent in the set altogether. With Fuzzy Set Theory, derived from Cantor, ‘a degree of membership’ exists with the patterns relationship to subsets. For instance, say I have a pattern of how to solve a Rubik’s Cube. Let’s say this pattern is 30% part of the subset that deals with puzzle solving (Set A), but also partially part of the subset that deals with color matching (Set B)… but only a 20% member. If we drew something to express this, it may look something like this.

Just try and visualize how complex and massive this mesh of sets and patterns must be that formulates our entire neural net… a vast network of interoperable patterns that all play a role within each and every experience. This network becomes more optimal the more data we store within it, the larger the network becomes, the more connections we can apply to an experience... we call this wisdom. As we grow and expand this network of sets, our brain acts like a brute force, machine learning algorithm, that is always improving and rewriting itself to make the effort of pattern matching more efficient with every new version. All patterns must then play a vital role in the networks neural communication with any or all patterns that are created or already exist.

Conclusion

The idea that our brain operates similar to a computer processing bits of data and information. A brute force approach to storing and utilizing patterns for humans to function and communicate every day. Although counter-intuitive to the idea of the human experience being more than just experiences but also the existence of higher levels of spirituality beyond just the human mind and body… are you one with the force? Do you think there’s more to the human mind and experience than just brute force operations that allow us to function in this world we live in? Let me know what you think.