RGB Plait: A General Purpose Theory of the Human Brain

Published by Reblogs - Credits in Posts, January 14th, 2023

Published on January 12, 2023 4:01 AM GMT

Key Words—Intrinsic brain networks; large-scale brain networks; AIXI; Kolmogorov; algorithmic information theory; Conway's game of life; Godel, Escher, Bach; Hofstadter; Metaphysics; Triangles

Abstract—We propose a theoretic and empirically backed structure of the human brain, using a short novel general purpose framework for categorizing symmetries in a given system. We show an approximation of the large-scale intrinsic brain networks as the (partial sums of elements in the (cartesian product of (the three concepts of identity metaphysics that yield different bit strings for a given system, mapped to the cube roots of unity)). In other words, the brain physically forms a triangle with {information, time, space} for its vertices, with six main types of symmetries found by interpolating those vertices. We argue that this framework approximates the human brain and is a novel general-purpose problem-solving tool. This framework can be interpreted geometrically, in relation to agents, and in relation to culture in general. Thus it is relevant to biology, business, psychology, philosophy, computer science, ethics, culture, and personal productivity. The argument rests on the idea of equivalent substrings between spatial data, time series, the information-theoretic concept of the hypothesis, and the relation between those equivalences. It rests on the notion that the information for a given system has rearrangeable hierarchically nested functions not necessarily found in space or time. It also rests on the concept of identity across space, time and simulation levels, which is discussed in decision theory and identity metaphysics. These ideas have been investigated and developed elsewhere, but this framework provides a shorter synthesis.

Introduction

Let identity_axes := {space, time, information} := {x | x^3 = 1}
{sum(s) | s ∈ identity_axes^2} ~ large scale brain networks



Fig. 1. Left side: color-coded large-scale intrinsic brain networks. Upper right: multiscale modeling. Lower right: a new framework called the "RGB Plait" roughly approximates the intrinsic brain network structure. Note: The color scheme on the left and right are unrelated.

Introduction
Contents
1 Setup
    Space, Time, Information bit strings
        The Information bit string
        Three Bitstrings in AIXI
        Some symmetries within the information bitstring correspond to simulation
        Three Identity Axes
        Illustrative Toy Example
    Six Symmetry Types
        R_Type
        B_Type
        M_Type
        Y_Type
        C_Type
        G_Type
    The Cube Roots of Unity Model
2 The RGB Plait
3 Interpretations of the RGB Plait
    Organic
        Human Brain
            Network Correspondence
                Default Mode Network
                Language
                Visual
                Salience
                Dorsal Attention
                Auditory
                Somatomotor
                Frontoparietal
                MTN
            Other Observations
    Geometric
        Graph Traversal
        3 Sub-triangles
        3D
        Polar Opposites
        Real Modular Addition
    Agentic
        General link to Agents and Decision Cycles
        Nesting Subagents
        Meta Circular Self Interpreter
        Observer's Location within the bitstring
    Cultural
        Godel, Escher, Bach
        Ethics
        Popular Culture 
        Sacred Geometry
    Personal
4 Conclusion
5 References

1 Setup

Space, Time, Information bit strings

The Information bit string

In algorithmic information theory, information, is often defined as weighted Kolmogorov Complexity. This means that an observed object's information is roughly the length of the extremely dense computer code needed to generate it. This is also called the hypothesis. The hypothesis is computer code and can be represented as a bit string.

Three Bitstrings in AIXI

AIXI[1] is a notable theoretical model of superintelligence that performs optimally in many different environments. There are discrete terms for space, time, and information. The formula is as follows:

Fig. 2. The AIXI equation[2].

The a and o terms are the individual observation and actions, which we will call events. Events occur in a sequence, which represents time. An event can have any amount of data associated with it. For example, an animal seeing a spatial 2D image could be an observation. The rightmost summation is essentially the expected amount of bits necessary to encode the observed universe and represents information[3]. From this equation, we can identify three types of bitstrings: space, such as a bitmap image at one event; time, as a bitstring slicing through the bitmap images across events; and information, which is roughly equal to maximally compressed computer code that sequentially generates the bitmap images, whose code can be seen as a bitstring.

The exact decision processes and rewards in decision theory are an open problem and are often open to debate, and thus are not colored here. Although AIXI has been criticized for various reasons[4][5], such as being too powerful to implement, not being embedded in the universe, and using a questionable decision model, it serves as a useful starting point. We note the core idea of sequential events and information, which can be modeled as bitstrings.

Some symmetries within the information bitstring correspond to simulation

To simulate something is to transfer it to another type of computer. There are many different types of computers and many different ways to run the same program. One example is the addition of decimal numbers, which can be done on a mechanical calculator, in one's mind, or on an electronic calculator. Another example could be the system of a teapot, along with sunlight shining on it. This teapot system could exist in multiple places, such as in one's mind, implemented as physical atoms and waves in real life, or simulated on various types of computers[6].

The hypothesis of the world for an observer seeing these various runs of the "teapot" would most likely have some data for a teapot, which is then compiled separately to different substrates. So the hypothesis would contain code such as:

teapot = teapot.raw
add_to_world(compile_to_atoms(teapot))
add_to_world(compile_to_atoms(compile_to_human_neurons(teapot)))
add_to_world(compile_to_atoms(compile_to_transistors(teapot)))

It can also be nested in different ways:

add_to_world(compile_to_atoms(compile_to_human_neurons(compile_to_transistors(teapot))))
add_to_world(compile_to_atoms(compile_to_transistors(compile_to_human_neurons(teapot))))
add_to_world(compile_to_atoms(compile_to_transistors(compile_to_transistors(teapot))))

The first is a human thinking of an entire computer running a teapot simulation, the second is a computer running an entire human imagining a teapot, and the third is a computer emulating another computer running the teapot simulation. An abstract syntax tree representing a system or a variable representing it can compile into different substrates. Therefore the hypothesis/information captures the idea that there can be identical pieces of information running in different places and simulation levels but not explicitly written down anywhere.

Three Identity Axes

An observer in the universe would feel the same internally if changes along any of these axes happened:

Time translation: They skipped 1 second forward in time.
Space translation: They moved 1 meter across space.
Information translation: They were simulated on 1 more computer.

The concepts of space, time, and information are three axes where an observer may find identical copies of themself, which they could causally interact with. Problems in identity metaphysics and theoretical decision theory deal with agents located in different places, at different times, and at different levels of simulation.

Let identity_axes  := {space, time, information}

Illustrative Toy Example



Fig. 3. Upper left: Justification for Conway's Game of Life. Upper right: Conway's Game of Life runs in itself multiple times via an emulator. Lower left: Observations of a zoomed-out Conway's Game of Life level. Lower right: Identifying what each bitstring corresponds to.

Assume that the simulation hypothesis is true and that a universal Turing machine can simulate the universe. Then, the universe can run in Conway's Game of Life because Conway's Game of Life is a Turing complete computer[8][10]. If it keeps nesting with different "unit cell" emulators, the information bit string will contain a series of different compilers for Conway's Game of Life unit cells. A few of these cells are known[7][9], but they can be nested to generate different variations. To move from a cell into any other cell, we can move spatially in the grid, forward or backward in time, or raise/lower the emulation level. This can be visualized in Figure 3[11][12].

Six Symmetry Types

For a given system, we can take time series data, spatial data or compress the system to get information. Each one of these can be roughly represented as a bitstring. We can then draw connections between potential identical or nearly isomorphic substrings among the bit strings, similar to array slicing. A symmetry type is a 2-element multiset of elements of identity_axes that links analogous bitstrings. For each symmetry type, real-world devices create or break symmetry for future observers. We briefly discuss the meaning of each symmetry type. We will call the symmetry type homogenous or heterogeneous if its elements are equal or unequal, respectively. Devices for heterogeneous symmetry types can be split into two types based on which domain serves as input or output. We give two different examples of those symmetry types. The polarity of the symmetry can be tracked depending on if the string is reversed or not. Instances of symmetries also have a magnitude, meaning the length of the bitstring.

Fig. 4. Diagram showing the symmetries between multiple data types for a given system.

Let symmetry_types := {R_type, Y_Type, G_Type, C_Type, B_Type, M_Type}

R_Type

Let R_Type :=               [space, space]

Meaning: Two things that look alike.

Examples: An object and its photocopy. Reproduction.

B_Type

Let B_Type :=                [time, time]

Meaning: The same thing happens at different times.

Examples: A sound repeating, like an echo. Tradition, routine, habits, parroting, homeostasis, reiteration.

M_Type

Let M_Type :=              [space, time]

Meaning: A schedule and the related events which happen.

Example 1: A computer system executes and writes logs during runtime.

Example 2: A phonograph playing a record.

Y_Type

Let Y_Type := [information, space]

Meaning: The scientific hypotheses of the world written out, and the world. In general, an object and its description. Written descriptions and what they describe. Scientific literature and what it refers to.

Example 1: An atomic physicist observes some atoms and writes an atomic physics textbook.

Example 2: An engineer reads design documents and builds a system using the waterfall model.

C_Type

Let C_Type := [information, time]

Meaning: The scientific hypotheses of the world spoken aloud. In general, an object and someone verbally describing it. Spoken language and the thing being described.

Example 1: An atomic physicist observes some atoms and gives an atomic physics lecture.

Example 2: An engineer listens to user feature requests and builds a system using the agile model.

G_Type

Let G_Type :=[information, information]

Meaning: Symmetry within the hypothesis of the world.

Example: Nested emulators. See "Illustrative toy example"

Note: There are other symmetries as well, but this requires further investigation. The information bitstring is essentially extremely dense computer code, but we know that there are nested functions and functions with varying levels of abstraction. If too many symmetries existed in the information bitstring, it would be compressed further, so it likely only contains a few symmetries at the highest levels.

A good example is software development; engineers do not put boilerplate everywhere but make functions, macros, and compilers that abstract over boilerplate code unless the boilerplate only occurs a few times, in which case it is not worth creating a separate function or macro.

The Cube Roots of Unity Model

We will now assign numbers to the identity axes and symmetry types.

Let identity_axes  := {x | x^3 = 1}
Let plot := {sum(s) | s ∈ identity_axes^2} = {sum(s) | s ∈ symmetry_types} 
(optional: Let information := 1, because it is conceptually very different from time or space).

Fig. 5.

After adding labels and complex domain coloring

Fig. 6.

2 The RGB Plait

Showing vectors and partial sums for symmetry devices, and rotating:

Fig. 7.

Thesis: RGB_Plait ~ intrinsic brain networks

3 Interpretations of the RGB Plait

Organic

Human Brain

The large scale intrinsic brain networks are collections of widespread brain regions showing functional connectivity from analysis of the fMRI BOLD signal, EEG, PET, and MEG[13]. Meaning researchers have recorded the brain states of different people, run mathematical models showing which areas of the brain are correlated, and deduced that there were six main networks and a few other networks, giving maximum total estimates of around 17.

The intrinsic brain networks have been shown to lie along two gradients: the visual-sensorimotor and the unimodal-transmodal[26][27], forming a triangle[14][15][16][17] (Fig. 8). This has been reproduced at both high fidelity and low[18][19][20][21][22][23][24] fidelity. Sometimes, another gradient is added, which raises the center of the triangle into a tetrahedron (Fig. 9). Brain waves have been shown to travel in a cycle along the unimodal-transmodal axis and loop around, forming a cycle[25].




Fig. 8. Images showing the triangle with the visual network, sensorimotor, and default mode as the vertices. Upper left [32] Upper middle[33] Upper right[36] Middle left[38] Middle middle[39] Middle right [40] Lower left[34] Lower middle[35] Lower right[37]



Fig. 9. Images showing the tetrahedron with the visual network, sensorimotor, default mode, and frontoparietal networks as the vertices. Upper left[28] Upper right[29] Lower left[30] Lower right[31]

Network Correspondence

Intrinsic Brain Networks

RGB Plait Model:

Default Mode

The Default Mode Network[56]'s function is conjectured to be thinking about people, including oneself, when not doing anything else [37]. It is in the same place as "Simulate," therefore, it seems its purpose is to simulate people.

Language

The Language Network is in the same place as the "Lecture" edge, which corresponds to writing out the code of the hypothesis into time, also known as speaking.

Visual

The Visual Network is in the same place as "Photocopy," and the brain stores a copy of images the human eyes capture in memory with little modification[57].

Salience

The Salience Network[58] is in the same place as "Engineer, Agile," The similarity is that they both listen and try to detect important information relayed through time.

Dorsal Attention

The Dorsal Attention Network[59] is also called the task-positive network. Its purpose is thought to be the top-down control focusing one's eyes on things. This seems very closely related to the "Scheduled Events" node and "Playback" edge, as the task can be seen as a sort of schedule that one has to stick to.

Auditory

The Auditory Network[60] processes time and frequency data and is close to the "Record" edge because they both record sounds.

Somatomotor

The Somatomotor Network[61] is activated during motor tasks. It is near the "Reiterate" edge and seems related to repeating what is heard if combined with the Auditory Network or repeating known motions, but this connection is debatable.

Frontoparietal

The Frontoparietal Network is thought to be the brain's control center. It thus does not correspond to any particular symmetry or symmetry device but rather the orchestrator of such devices residing on a third axis.

MTN

This network is not a main network but is thought to be involved in the spatial processing of locations [36][38]. Therefore, it is similar to the "Scientific Journal" node in that it may contain images and pages that need to be comprehended and navigated through.

Other Observations

Notably, there seems to be a void where "Engineer, Waterfall" should be. We speculate that this is because "Engineer, Waterfall" is just "Engineer, Agile," with the document being read out loud, so it is, in some sense, redundant.

Assuming information :=1, the real axis becomes the sensory-transmodal gradient and the imaginary axis becomes the visuospatial-sensorimotor gradient. Brain waves cycle from 1 to -½ and wrap around again [25], and the harmonics from [32] look like rotations.

Geometric

Graph Traversal

Traversing the graph from the center to the edges shows how symmetry can be achieved. For example, Y-Type symmetry "Scientific Journal" can be achieved by moving from the center along the information axis, meaning bits are showing up in the hypothesis, and some object is forming. Once "kB" is reached, we move along the space axis, whose particular edge is called "illustrate," corresponding to writing a document. Thus we arrive at "Scientific Journal" symmetry, where there is a document describing reality. The inverse is to create the document first, then travel along the "Engineer Waterfall" edge to create the object. For B-Type symmetry "Reiteration," we move along the time axis first to reach "hr," upon which we reiterate what just happened to reach "Reiteration" symmetry.

3 Sub-triangles

In the RGB Plait, three sub-triangles are centered around one of space, time, or information. Each sub-triangle contains three symmetry types. This means:

Documents can be copied, contain a schedule, or describe things.
Sounds can be echoed, recorded, or describe things.
Things can be simulated, documented, or discussed.

3D

We can instead Let identity_axes := {i, j, k} in a 3D grid of voxels. This is essentially reverse isomorphically projecting the complex plane defined from before or visualizing the hexagon in the RGB Plait as a cube. Then, objects can be plotted according to their position, time, and information content. This also fits with the three gradients model of the brain more than a flat triangle, making the center of the RGB plait the vertex of a tetrahedron.

Sans the symmetry types, this diagram appears to have been used in business intelligence[41], multiscale modeling[42][43][44], systems theory[45], big history[46], and esoteric philosophy[47].

Polar Opposites

This predicts that devices on opposite sides of the triangle will have little in common. That is, the similarity between them can be described by the cosine of the angle between them and, thus, their compatibility.

compatibility(Type1,Type2) := Type1*conjugate(Type2)/|Type1 * Type2|

This also appears to model the harmonics from [32].

Real Modular Addition

The cycle from 1->-½, which loops back around, models a human's awareness cycle [25].

Agentic

General link to Agents and Decision Cycles

The symmetry types are defined in a general way that happens to approximate the human brain's intrinsic anatomy. If evolution has found this solution after billions of years, it is likely a good solution[48]. Agent-like systems like organisms, social groups, businesses, civilizations, and computer systems exhibit these six symmetries to various degrees. In particular, it seems related to the "social pyramid" where you have different people specializing doing different tasks, and the different symmetries get prioritized differently at different points in history, such as thinking, computing, researching, building, speaking, listening, recording, following directions, manufacturing, reproducing, and providing stability. It has the elements of a decision cycle disregarding choice. This theory could be useful to identify, create, monitor, control and modify different agents in a standard way.

Nesting Subagents

Symmetries with large magnitude can be partitioned into multiple symmetries with smaller magnitude. An agent which creates large symmetries can be made of smaller agents which create smaller symmetries. This can be depicted by scaling and connecting axes of multiple RGB Plaits.

Meta Circular Self Interpreter

This triangular pattern is a spatial diagram, components of a decision cycle, and possibly a string in the hypothesis. So the complete collection of symmetry devices and this pattern, applied to itself, would cause it to spread across the three identity axes with increasing levels of magnitude. This mirrors what humans have been able to do, which is spread across the earth, and build complex cultures over time.

Observer's Location within the bitstring

We can attempt to specify where the observer is located in the respective bitstrings, similar to an origin point with positive and negative directions. We can mark a location in the time bitstring that separates the past, now, and future for the observer. We can distinguish between near and far locations in the space bit string relative to the observer. We can pick a valid hypothesis that contains an identifiable copy of the observer and distinguish between parts of the hypothesis which are more complex and less complex than it, although the exact details of this may be ambiguous. This specifies the particular symmetry type instance in relation to the observer, and many combinations exist.

Relative values for <, =, > also called - 0, +

Space bitstring: back, here, front
Time bitstring: past, present, future
Information bitstring: low-level functions, observer's data, high-level functions

Cultural

Godel, Escher, Bach

The RGB Plait appears to be the central structure of the book "Godel, Escher, Bach" by Douglas Hofstadter. It even appears on the book's cover as an impossible triangle or cube, although not explicitly mentioned in the book itself. Godel is the idea of information symmetry, or information nesting information. Escher is spatial symmetry, and Bach is time symmetry. The book presents identical arguments such as self-similarity, isomorphisms, the phonograph, record, the idea of information bearers and revealers, relation to ancient traditions such as Zen Buddhism mirroring modern discussions of information, levels of complexity in biological systems, and the human visual system making a copy of image the eyes see[57]. Thus, the RGB Plait can be seen as a summary of "Godel, Escher, Bach."

Ethics

If symmetry is considered good[49] and asymmetry bad, then in general, the symmetry devices are ethically good, and the asymmetry devices which interfere with them are unethical[50]. Alternatively, agents need the symmetries of the RGB Plait to function, so if what is good or bad is what enhances or interferes with one's life, then in general, symmetry devices are good, and asymmetry devices are bad.

Popular Culture

In real and fictional stories, there are often characters with different relationships to space, time, and information, forming teams. A common team is strong, fast, and smart. What causes this to happen? We propose that the team try to form the elements of the RGB plait[51]. In other stories, the characters will seek out special artifacts which symbolize RGB Plait elements.

Sacred Geometry

Sacred geometry is an ancient practice that attempts to assign geometric figures to different aspects of reality. It usually contains circles, positive/negative, vectors, agents, and the number 3. We suggest that this pattern underlying the human brain is the template on which the popular symbols of sacred geometry are based. Naturally, multiple geometric approximations to the RGB Plait would develop across cultures, given that the human brain is structured this way, and millions of humans have had thousands of years to iterate on culture.

Personal

Using the RGB Plait, one can identify the different symmetry types in their environment that may have previously been unnamed. One can iterate through all the symmetry types, noting their magnitude and what devices may increase or decrease those symmetries. Then, one could act to obtain or remove those devices in numerous ways. One can identify complete collections of symmetries gathered in one place and whether those are small or large or mixed in some way.

4 Conclusion

In this paper, we developed a novel general-purpose framework for categorizing the symmetries of the universe. We did this by considering what variables constitute identity and deduced that they involve spatial translations, time translations, and simulation/compiler/substrate translations. These correspond to space, time, and information. Taken together, we called these the "identity axes." We showed three bitstrings corresponding to each type of unit translation, then listed the simplest symmetries between these bitstrings. Then we plotted these symmetries on the complex plane and showed the resulting set approximated the large-scale intrinsic brain networks. The set also had geometric properties related to graph traversal, sub-triangles, three dimensions, and polar coordinates. The elements of the set could be applied to various types of agents and the systems they form. There was also evidence of this set in cultural artifacts. Finally, we noted how a person might use this to make decisions. We could conduct further investigations to see how different parts of the universe exemplify the symmetries.

There is no modern well-accepted name for the set of concepts {space, time, information}, the set of symmetry types and devices built on combinations of those, or the real-world functional objects based on those. The closest name for this set we could find was the "stoic asomata"[52][53][55]: time, place, sayable (and void). Most disciplines consider these things so fundamental that there is no name for them, and "metaphysics"[54] does not capture the idea of the set because it includes other concepts.

Please let us know if there are any errors in this paper, and thanks for reading.

5 References

Discuss

https://www.lesswrong.com/posts/crmt8NuPxFsGLxyRX/rgb-plait-a-general-purpose-theory-of-the-human-brain