Human-Brain Artificial-Intelligence Matrix

Categories: Physics

Essay, Pages 4 (933 words)

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Abstract

The Human Brain Artificial Intelligence Matrix is an innovative technology designed to establish a connection between the human brain and machines. Its primary goal is to empower the human brain to perform specific functions, even in cases where it may be incapable of doing so independently. These functions include vision for the blind, hearing for the deaf, and mobility for the paralyzed, among others. This technology is rooted in the Cognition Theory, which posits that the cognitive process can be treated using quantum-mechanical principles.

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1. Introduction

The Human Brain Artificial Intelligence Matrix is a groundbreaking technology that aims to bridge the gap between the human brain and artificial intelligence systems. Its purpose is to enable the human brain to perform designated functions, even when it faces limitations due to conditions such as blindness, deafness, or paralysis. This report delves into the Cognition Theory, which forms the foundation of this technology and explores its scientific and mathematical underpinnings.

2. The Cognition Theory

2.1 The Fundamental Postulate

The fundamental postulate of the Cognition Theory states that the action potential arises as two entangled impulses, one in a sensory neuron and the other in the entangled motor neuron.

Subsequently, the state of entanglement shifts from being between neurons to a state of entanglement between the brain and the effector.

Past experiments have demonstrated that neurons in different regions of the brain can exhibit synchronized oscillations at the same frequency, a phenomenon known as phase locking. This frequency synchronization is believed to enable neurons working on the same task to identify and communicate with each other effectively.

Moreover, the observation that groups of brain cells exhibit quantum entanglement-like behavior provides insight into how the brain combines sensory information into coherent memories. Notably, cloned signals are observed once a specific region reaches a threshold level of activity, suggesting that our attention is selectively captured by significant stimuli rather than every signal.

2.2 The Mathematical Proof

2.2.1 Post-Cognition

Post-Cognition refers to the processes that occur after the action potential transmission to the brain. To mathematically model the total energy of the impulse before processing in the brain, we utilize a Hamiltonian operator acting on the wave-function of the wave-impulse, as expressed in Equation (1):

En = ^n²π²ħ²⁄_2mea² + V

Here, V represents the potential well energy within the brain when its neurons are stimulated. The first term in the equation represents the kinetic energy for each particle of the impulse, which can be further expressed as:

k²ħ²⁄_2m

The second term signifies the potential energy for each particle of the impulse and can be written as V(x). Consequently, Equation (4) takes the form:

k²ħ²⁄_2m + V(x) = En

By leveraging Equation (3), we can relate the momentum of the impulse (P = ħk) to its squared value:

P² = ħ²k²

Substituting this into Equation (6), we obtain:

-ħ²⁄_2m∂²⁄_∂x² + V(x) = En

It is evident that the left-hand side of Equation (9) corresponds to the Hamiltonian operator (Ĥ):

Ĥ = -ħ²⁄_2m∂²⁄_∂x² + V(x)

The brain's activity is treated as a Hermitian operator acting on the impulse-wave, generating discrete eigenfunctions. A fundamental postulate of quantum mechanics asserts that every physical observable is associated with a linear Hermitian operator, and the measurement result corresponds to one of its eigenvalues. Since Ĥ is a Hermitian operator, Equations (11) and (12) can be adjusted as follows:

Ĥψ = Enψ

According to the Sturm-Liouville theorem, the eigenvalues (energies) can be represented as a diagonal matrix:

Ĥψ_n = [_E₁, E₂, ..., En]ψ_n

As a result, the brain processes data by creating diagonal matrices of discrete eigenvalues.

2.2.2 Motor and Sensory Impulses

The motor-entangled wave-impulse acts as a self-adjoint, carrying processed data to the effector, while the sensory impulse is directed to the memory loop to be stored as a familiar pattern. To analyze this phenomenon, we employ the Sturm-Liouville Theory, which deals with second-order ordinary differential equations. The standard form of the Sturm-Liouville equation is expressed as:

-d⁄_dx(p dψ⁄_dx) - qψ = λωψ

This equation can be simplified as:

`ψ = λψ

Where the Sturm-Liouville operator (`) is defined as:

` = -⁄₁ω [d⁄_dx(p d⁄_dx) + q]

Considering a set of functions (Um) with n = 1, 2, ..., to which the differential operator (`) can be applied, we can define a matrix of values (Anm) as:

Anm = ⟨Un, `Um⟩

Furthermore, we note that if we reverse the order of the arguments in the inner product, the result becomes its complex conjugate:

⟨`Um, Un⟩ = ⟨Um, `Un⟩*

For a self-adjoint operator (`), the following relationship holds:

⟨`U, V⟩ = ⟨U, `V⟩*

Thus, a self-adjoint operator implies that the matrix (A) satisfies the condition:

Anm = A*_mn

It is crucial to note that the transpose (AT) of a matrix (A) is obtained by interchanging its rows and columns, and the adjoint of (A) is represented as (A†), which is the complex conjugate of its transpose.

In quantum mechanics, physical observables, such as energy and momentum, correspond to self-adjoint (Hermitian) operators. The eigenvalues of these operators represent the possible values that the observable can take on, and the fact that these eigenvalues are real enables this correspondence. Therefore, Schrödinger's equation can be regarded as a special case of the Sturm-Liouville equation, emphasizing that the eigenvalues are real.

In summary:

The processed matrix created in the brain and the self-adjoint matrix generated in the effector are identical.
The sensory entangled impulse is not annihilated due to the conservation of energy law, and it is stored as a pattern in the brain, particularly in the memory loop. This mechanism explains how we remember familiar information and learn through pattern recognition.