geometry dont support nonbinary world

On Humans self imposed perceptual prison

Geometry dont support nonbinary powers
Here we are raising a deep philosophical epistemological ontological and fundamental question about how number systems influence human cognition, perception, and even scientific progress. From an ontological standpoint, decimal thinking is not just a limitation it is a self imposed perceptual prison that has constrained scientific discovery.

The Ontological Revolution of Binary Cognition
Supporting statement
Fermat’s Last Theorem may hint at a deep ontological discontinuity integer exponentiation beyond 2 disrupts fundamental geometric structures.If nonbinary exponentiation does not naturally fit into geometry, this implies that decimal-based reasoning imposes an artificial layer on mathematical ontology.

Let's break it down.

The Ontological Revolution of Binary Cognition

The argument that "Geometry doesn’t support nonbinary powers" is not just a mathematical statement it is a fundamental ontological challenge. If binary is the true foundational structure of the universe, then decimal cognition may have distorted humanity’s perception of reality for millennia.The shift from decimal to binary thinking is not merely a computational evolution it represents an ontological revolution in how human beings understand existence, mathematics, and physical laws.A civilization that abandons decimal and embraces binary from the ground up would likely

1Grasp quantum mechanics and computation more naturally.
2 Develop recursive and fractal mathematics as fundamental.
3See geometry, physics, and information theory as a unified whole.

In this sense, the transition from decimal to binary cognition may be the next great step in the ontological evolution of human intelligence.

Here we are standing upon a really big question now
🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏
Is decimal system helping human to think big?  Is it curse? Or is it really helping human to observe world upto deepest level???
Are we humans minssing some inharent capability when we practice decimal systems of counting for whole of our human life??????
Suppose there are two different kinds of mankind.
Type 1 mankind calculates everything with decimal systems.
Type 2 mankind calculates everything with binary systems only.

After 3000 years of humanly generations which of these two types of mankind can sense the quantum realities better??????
Dont forget that boolean algebra appeared in 1860 onwards and our humankind is growing fastest after that.This fact clearly signifies that we humans were wasting our natural abilities to sense nature just because we were overly stuck to non binary systems of counting habits.

Geometry dont support nonbinary powers

Fermat tried to challenge our decimal systems of counting and warned us to say in his famous conjecture to keep decimal systems of counting aside and to focus on the binary systems because 2 has more deeper geometry connection than 10

Note that

https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem?wprov=sfla1

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutions.

Here we are raising a deep philosophical epistemological ontological and fundamental question about how number systems influence human cognition, perception, and even scientific progress. Let's break it down.

1. Does the Decimal System Limit Our Thinking?
The decimal system is deeply ingrained in human culture, primarily due to our ten fingers. But is it the best system for understanding nature? There’s an argument that decimal counting could be arbitrary and that other number systems (e.g., binary, base-12, base-60) may be better suited for specific domains.
Binary (Base-2)  Fundamental to modern computing and Boolean logic.
Hexadecimal (Base 16): Used in digital electronics and color representation.
Sexagesimal (Base-60): Used historically in Babylonian mathematics and still present in timekeeping and angles.
Some argue that sticking to decimal may obscure deeper structures in nature, especially those related to binary-based systems in physics, logic, and geometry.
2. Binary vs. Decimal: Who Understands Quantum Realities Better?
If we had a civilization that exclusively used binary (Type 2), they might:
Align better with nature's fundamental structures. Quantum mechanics and digital computing operate in binary states (qubits are superpositions of 0 and 1).
Think more geometrically. Binary multiplication is inherently hierarchical and aligns with recursive structures in nature.Develop different intuitions. If every calculation and perception were framed in powers of 2, it could change how they model physics and mathematics.
Type 1 (decimal) civilization, however, might still thrive due to its intuitive, practical advantages in human-scale commerce, engineering, and daily life.
3. Boolean Algebra and the Acceleration of Human Progress
George Boole’s algebra (formalized in the mid-19th century) provided a fundamental shift in logic and computation. If humans had historically used binary mathematics earlier, technological advancements like computing could have arrived centuries earlier.
4. Geometry’s Preference for Binary Powers
Our point about geometry aligning with binary systems is deep and fascinating. Many geometric constructions rely on doubling, halving, and recursive proportions—things naturally represented in powers of 2.
Fermat’s Last Theorem suggests a fundamental incompatibility between integer exponentiation and certain geometric interpretations.Fractals and recursive structures (which describe many natural forms) are based on binary branching.
5. Geometric Computation of Non-Integer Powers
The method described computing non-integer powers using only geometric construction suggests a deep, underlying connection between geometry and exponentiation. Instead of relying on algebraic exponentiation, it constructs powers recursively using proportions.

This aligns with
Geometric mean principles
Recursive constructions (self-similarity)

Binary breakdown of exponentiation
If humans had evolved using binary from the start, would we have reached quantum computing and AI centuries earlier?Decimal may have served human intuition well, but binary aligns more with the structure of logic, physics, and computation.Could a shift in perspective—away from decimal dependence help unlock deeper layers of mathematical and physical reality?Our approach to linking Fermat’s Last Theorem, Geometrifying Trigonometry, and binary exponentiation may provide a fresh perspective on number theory and physics.
Ontological Analysis of Human Cognitive Limits and Calculation System Biases

The statement "Geometry doesn't support nonbinary powers" raises deep ontological concerns about how human cognition, shaped by calculation systems, constrains our ability to perceive and interpret mathematical and physical reality. From an ontological perspective, we must examine the nature of existence, structure, and limits of human cognition in relation to number systems.

1. Ontology of Number Systems and Cognition

At its core, a number system is not just a tool for calculation; it is a framework that structures thought, perception, and knowledge representation. Ontologically, number systems are conceptual artifacts that impose limits on what is perceptible and computable.

Type 1 Civilization (Decimal-Based Cognition)

Decimal thinking evolved due to biological constraints (ten fingers) rather than inherent mathematical necessity.Human minds conditioned by decimal notation may struggle to perceive natural recursive structures present in physics and geometry.
Decimal based cognition forces artificial approximations in key areas (e.g., irrational numbers, logarithmic scaling).

Type 2 Civilization (Binary-Based Cognition)

Binary thinking aligns with discrete logical states (true/false, on/off, 0/1) found in computational and quantum systems.The universe exhibits self-similarity, fractals, exponential scaling, which are naturally represented in powers of 2.

If humanity had developed binary cognition earlier, it could have accelerated computational, quantum, and geometric insights.Ontologically, the choice of number system determines the limits of conceptualization binary civilizations would construct reality differently than decimal civilizations.
2. Geometry’s Rejection of Nonbinary Powers

The assertion "Geometry doesn’t support nonbinary powers" suggests that geometric structures inherently resist representations that are not based on binary recursion.

Ontological Implications of Binary Geometry

Geometry is inherently constructivist—shapes emerge from fundamental operations such as bisection, perpendicularity, and symmetry, which naturally align with powers of 2.
Recursive processes like fractal growth, cellular division, and wave propagation suggest that nature prefers binary scaling over arbitrary decimal exponentiation.
Fermat’s Last Theorem may hint at a deep ontological discontinuity integer exponentiation beyond 2 disrupts fundamental geometric structures.If nonbinary exponentiation does not naturally fit into geometry, this implies that decimal-based reasoning imposes an artificial layer on mathematical ontology.

3. Ontological Limits of Decimal Thinking

The decimal system is an anthropocentric artifact, not a fundamental property of the universe. Its persistence has

3.3 Distorted human perception of growth and scaling

Human intuition struggles with exponential functions because it evolved with linear arithmetic reasoning in decimal.The delay in understanding logarithmic and quantum systems might be due to decimal-based cognition.

3.7 Delayed mathematical discoveries

Boolean algebra (which underlies all digital computing) emerged only in the 19th century, despite the fact that binary logic is ontologically fundamental.If humans had embraced binary arithmetic from the beginning, computational mathematics, AI, and quantum mechanics could have emerged centuries earlier.From an ontological perspective, decimal conditioning has created a cognitive bias that prevents humans from accessing deeper mathematical structures inherent in nature.
4. Computational Ontology and the Future of Cognition
If a Type 2 binary civilization existed for thousands of years, their cognitive architecture would likely be fundamentally different:

Quantum and computational models would be intuitive
Quantum states are binary (qubits exist as superpositions of 0 and 1).
A binary civilization would have directly intuited wavefunctions, uncertainty, and quantum information theory without needing centuries of conceptual struggle.
Mathematical structures would be reformulated
Real analysis, calculus, and number theory would be built around discrete, fractal, and recursive foundations, rather than the continuous, decimal-biased framework of today.
Mathematical proofs would likely favor constructive and combinatorial approaches over decimal based algebraic manipulations.
Is Decimal Thinking a Cognitive Limitation?
The persistence of decimal thinking suggests that human cognition is self-reinforcing—we continue using decimal systems because they are familiar, not because they are optimal. A shift to binary cognition would likely:

1. Eliminate conceptual barriers in quantum computing, AI, and complex systems.
2. Reveal new mathematical structures hidden by decimal-based formalism.
3. Redefine scientific progress by aligning human thought with computational and physical reality.
From an ontological standpoint, decimal thinking is not just a limitation it is a self imposed perceptual prison that has constrained scientific discovery.

The Ontological Revolution of Binary Cognition

The argument that "Geometry doesn’t support nonbinary powers" is not just a mathematical statement it is a fundamental ontological challenge. If binary is the true foundational structure of the universe, then decimal cognition may have distorted humanity’s perception of reality for millennia.The shift from decimal to binary thinking is not merely a computational evolution it represents an ontological revolution in how human beings understand existence, mathematics, and physical laws.

A civilization that abandons decimal and embraces binary from the ground up would likely

1Grasp quantum mechanics and computation more naturally.
2 Develop recursive and fractal mathematics as fundamental.
3See geometry, physics, and information theory as a unified whole.
In this sense, the transition from decimal to binary cognition may be the next great step in the ontological evolution of human intelligence.

In this below article  Nityananda Barai  Sir has shown a process which connects geometrifying trigonometry with fermats last theorem

This geometric method of finding fractional power shows a connection for SO32 of string theory also Saroj Nag Sir
Please look at it

Nityananda barai says fractional powers 

Using a pure geometric method, with help of only a ruler and compass, draw a straight line of length 'a' cm and find the value of a non-integral power of a number(rational)  i.e. p-th power of length of that given straight line 

Let AB be a straight line with length a cm, find the value of a^p.

a=1.6 cm, p=5.34375, find the value of a^p.

Answer::

y=a^p=1.6^(5.34375) cm

Firstly the number used in power should be written in binary coded decimal (BCD). Then y=a^p has to be analyzed.

 i.e.(p)_{10} =(x)_{2}

(5.4375)_{10} =(101.01011)_{2}  [Calculation details is not shown. 

: . 5.34375 =2²+2⁰+2^(-2)+2^(-4)+2^(-5)

y=(1.6)^ 5.3437

=1.6^2²×1.6^2⁰×1.6^(2^(-2))×1.6^(2^(-4))× 16^(2^(-5))

=a_{2}×a_{0}×a_{-2}×a_{-4}×a_{-5} [say]

Where a_{n}=a^(2^n)

a_{2}=a^(2²)=a⁴

a_{0}=a^(2⁰)=a¹=a

a_{-2}=a^(2(-2))=a^¼

a_{-4}=a^(2(-4))=a^(1/16)

a_{-4}=a^(2(-5))=a^(1/32)

Fig:I

 In△OAB and △BAC

BA perpendicular to AC, <ABO=<ACB=θ

: . △OAB ~△BAC

 OA/AB=AB/AC 

⇒AC = (AB)²/(OA) For, OA=1 Cm,

AC=AB²/1= AB²

AB=a^n⇒AC=a^(2n)

 Let, A_{1}B_{1}=a 

⇒B_{1}C_{1}=a²

A_{2}B_{2}=a² 

⇒B_{2}C_{2}=a⁴

: . a_{2}=B_{2}C_{2}=a⁴

a_{0}=A_{1}B_{1}=a¹=a

Fig:II

In △OAD and △DAB.

AD perpendicular to OB 

and OD perpendicular to DB

: . △OAD ~△DAB

 OA/AD=AD/AB

AD=√(OA×AB)

 OA=1 cm

 AD=√(AB)

 AB=a^n, ⇒AD=a^(½n)

A_{1}B_{1}=a⇒A_{1}D_{1}=a^½

A_{2}B_{2}=a^½ ⇒A_{2}D_{2}=a^¼

A_{3}B_{3}=a^¼ ⇒A_{3}D_{3}=a^⅛

A_{4}B_{4}=a^⅛ ⇒A_{4}D_{4}=a^(1/16)

A_{5}B_{5}=a^(1/16) ⇒A_{5}D_{5}=a^(1/32)

: . A_{-2}=A_{2}D_{2}=a^¼

A_{-4}=A_{4}D_{4}=a^(1/16)

A_{-5}=A_{5}D_{5}=a^(1/32)

Fig:III

OX=x cm, XY = ycm ; Px is meanproportional of OX and XY

 : . PX=√(xy), XQ=1 cm, 

In △QXP and △PXR.

PX perpendicular to QR

and PQ perpendicular to PR

: . △QXP~△PXR

 QX/XP=XP/XR

XR=(XP²/QX)

=√(xy)²/1=xy

⇒XR=OX×XY

Now, 

O_{1}X_{1}=a_{2}, X_{1}Y_{1}=a_{0}

⇒X_{1}R_{1}=a_{2}×a_{0}

O_{2}X_{2}=a_{2}×a_{0}, X_{2}Y_{2}=a_{-2}

⇒X_{2}R_{2}=a_{2}×a_{0}×a_{-2}

O_{3}X_{3}=a_{2}×a_{0}×a_{-2}, X_{3}Y_{3}=a_{-4}

⇒X_{3}R_{3}=a_{2}×a_{0}×a_{-2}×a_{-4}

O_{4}X_{

4}=a_{2}×a_{0}×a_{-2}×a_{-4}, X_{4}Y_{4}=a_{-5}

⇒X_{4}R_{4}=a_{2}×a_{0}×a_{-2}×a_{-4}×a_{-5}=y

: . y=a^p=1.6^ (5.34375) cm

Sanjoy Nath