The Mathis Number System: An Exploration
An alternative mathematical framework
Introduction
The Mathis Number System is an alternative mathematical framework developed by Dr. Theo Mathis to incorporate the principles of duality. This system redefines traditional mathematical concepts by viewing numbers and operations through the lens of duality, offering innovative approaches to solving complex problems. Here's an exploration of its key features, principles, and applications.
Core Principles
Dual Numbers:
Definition: In the Mathis Number System, each number is represented as a pair (a, b), where 'a' and 'b' are complementary aspects of a single entity. These pairs reflect the inherent duality in all quantities and operations.
Notation: A dual number is denoted as D=(a,b)
\(D=(a,b).\)
Dual Operations:
Addition: The addition of dual numbers is defined as (a,b)+(c,d)=(a+c,b+d)
\((a,b)+(c,d)=(a+c,b+d)\)Subtraction: The subtraction of dual numbers is (a,b)−(c,d)=(a−c,b−d)
\((a,b)−(c,d)=(a−c,b−d)\)Multiplication: Multiplication is defined to reflect the interaction of dual aspects: (a,b)×(c,d)=(ac,bd)
\((a,b)×(c,d)=(ac,bd)\)This operation emphasizes the product of individual aspects.
Division: Division is more complex and involves the inverse of dual aspects: (a,b)/(c,d)=(a/c,b/d), assuming c and d are non-zero.
\((a,b)/(c,d)=(a/c,b/d)\)
Duality Equations:
Basic Equations: Equations in the Mathis Number System are structured to solve for dual pairs. For instance, solving (a,b)+(x,y)=(c,d) involves finding (x,y) such that both aspects of the equation are satisfied simultaneously.
\((a,b)+(x,y)=(c,d)\)
Applications and Advantages
Solving Intractable Problems:
Complex Systems: The dual nature of the Mathis Number System is particularly useful in modeling and solving complex systems where interactions between dual aspects are critical. This includes fields like quantum mechanics, where particles exhibit wave-particle duality.
Nonlinear Dynamics: The system is adept at handling nonlinear dynamics by allowing a more nuanced representation of variables and their interactions.
Mathematical Modelling:
Physics: In theoretical physics, the Mathis Number System provides new tools for modeling fundamental interactions, potentially offering insights into unifying general relativity and quantum mechanics.
Economics: In economic modeling, dual numbers can represent complementary factors such as supply and demand, enabling more sophisticated analyses of market behaviors.
Enhanced Calculus:
Dual Calculus: The Mathis Number System extends calculus to dual numbers, allowing differentiation and integration of functions that depend on dual variables. This approach can simplify the treatment of functions with intertwined variables.
Partial Dual Derivatives: New concepts such as partial dual derivatives help in analyzing systems where changes in one aspect affect another in a complementary manner.
Practical Example
Let's consider a practical example to illustrate the use of dual numbers in solving a problem:
Problem: Solve the dual equation (x,y)×(2,3)=(6,12)
Solution:
Represent the dual equation: (x×2,y×3)=(6,12).
\((x×2,y×3)=(6,12)\)Solve for each aspect:
For x:
\(𝑥 × 2 = 6 x×2=6 ⟹ 𝑥 = 6 / 2 x=6/2 ⟹ 𝑥 = 3 x=3.\)For y:
\(𝑦 × 3 = 12 y×3=12 ⟹ 𝑦 = 12 / 3 y=12/3 ⟹ 𝑦 = 4 y=4.\)
Thus, the solution is (x,y)=(3,4).
Philosophical Implications
The Mathis Number System reflects a philosophical shift towards recognizing and integrating dual aspects in all areas of thought:
Epistemology: Knowledge is not seen as linear or singular but as a synthesis of dual perspectives.
Ontology: Existence is understood as an interplay of complementary forces, each defining and enriching the other.
Summary
The Mathis Number System redefines mathematical operations by incorporating duality, offering innovative solutions to complex problems. Its application spans various fields, from theoretical physics to economics, providing a nuanced approach to modeling interactions and solving equations. By embracing the dual nature of reality, this system not only enhances mathematical understanding but also aligns with a broader philosophical perspective on the interconnectedness of existence..
OK, perhaps I commented on the wrong version, but those comments are applicable here, as the Sanskrit arithmetic and sum product rules perhaps obviate calculus where this Mathis archetype is proposing an update to the dy/dx differential.
This response is NOT for the numberphobes but is for the numberphile.
The dy/dx differential in TRUTH has the nature of 369 integral in the parabolic differential of y=x^2 where x^2 is c^2=E/M i n Einstein's E=Mc^2 equilibrium of mass and energy. The c^2 is an NXN magic square, even if nobody knows it, or beLIEves it, magic is real in real-ITY and the source of the the miracles Jesus Christ performed on the Sonnet stage.
In Sir Ockham terms of first principle however as Christ is a cross or crux of crucifixion on the hill of Calvary from Latin calvaria "skull") Unam Sanctam "Head of Christ" and the Magdalene is ONE dove, a rose (Venus), in Rose-cross Rosicrucian NOT an avatar, and the cross is four corners in four causal forces of Prime Time TENET (555X555) the Lord's Prayer (PATERNOSTER) and Alpha Omega Yin Yang inversions of the Poincare Disk.
The expression y=x^2 is "equilateral space" in "square space" or area 51 (360/7) terms of perspective of outer space vs inner space.
The parabolic is a dish is a reciever with a focus located at the coordinates (0, 1/4p) which can be determined using p=1/4a, with y=ax^2. In this case, since a=1, so Y=1x^2, the focus is at (0, 1/4)=(0, 0.25) for the math literate, but this has MUCH deeper correlations with the conjugation of 4 and 7 as 2+5=7... that's a longer story in her-story that his-story does not tell.
So, we have: dy/dx=2x, and at x=3, y=9 and dy/dx is 2x3=6 (369) and the inverse square y=1/x^2=x^(-2)=1/9=0.111111... and the differential of the inverse square is dy/dx=-2/x^(3)=-2/27=0.074074... so the 1/4=0.25 reference above is integral.
So y=-2 over a Rubik's CUBE at x=3 as a factor of the Saturn/Lo Shu Magic square and six is sex in the hexagram at the top of Saturn and in the 38 bit rotations of the Strader Machine and the mirror of these dual forms where the 27 is the center cube of the Rubik's cube in the center of the 8X8X8 in MMM in GOC. Clear as mud...
Further the dy/dx differential to a > 2nd degree polynomial represents the instantaneous rate of change AKA "pitch" in musical terms) and the hypotenuse of the Pythagorean triplets eh? The "normal" in para para para normal "junk" in the DNA through the palindromic repeats in the sequence of DNA cryptographic CODE and Code-X that is MMM relative to the radius of curvature and the reason Terrence Howard's statement there are no lines in reality holds true just like math of Mathis and HeartMath as it applies to the biogeometry of the biophonon in the biophoton in the Code-X to the Auric Field (bioinformatics) but NOT this side of Planck scale. Your application of Plato's Ministerial 2520=5040/2 is integral in the calculus of the OI, NOT the infinitesimal zero and approximations and probability though, that is AI and not immaculate like NEYEN in 369.
OK let's see what your archetype Mathis can do with this word salad brother, straight from the heart of the matter of mind over matter and the inner child who is spent...