Zero as the Living Center of Mathematical Transformation

The Al-Asr Dynamic Number System (ADNS)

Author:
G. Mustafa Shahzad, Research Scholar, Director Qalim Institute
Quranic Arabic Research Scholar | Discoverer of Islamic Meditation for Healing | Theorist of ADNS

scientificet@gmail.com '  +19297398633

---

Abstract

For centuries, mathematics has treated zero as a static placeholder or symbol of nothingness. This traditional interpretation works in basic arithmetic but fails when describing real-world transitional phenomena such as quantum jumps, pulse ignition, and cosmological origins. Division by zero is treated as undefined, and multiplication by zero is viewed as annihilation, both of which contradict physical reality.

The Al-Asr Dynamic Number System (ADNS) redefines zero as the Al-Asr Moment — the living transitional instant between past and future, loss and gain. By introducing a pico-scale temporal model, ADNS integrates mathematics with time, directionality, and event ignition. This paper outlines the problem of static zero, presents the ADNS methodology, formulates directional arithmetic rules, and discusses applications in physics, cosmology, electronics, and energy systems.

---

1. Introduction: The Problem of Static Zero

The number zero is typically understood as a neutral element in arithmetic operations. It adds nothing, subtracts nothing, annihilates values in multiplication, and causes undefined behavior in division. This view stems from classical number systems and has remained mostly unchanged for centuries (Kline 45–49).

However, the physical world does not support such a static notion of zero.

• In electronics, a pulse trigger happens exactly at the zero-crossing point.
• In quantum mechanics, wavefunctions collapse at an instantaneous zero moment (Zeilinger 743).
• In cosmology, the Big Bang represents a zero-state ignition (Misner et al. 3).

This reveals a fundamental mismatch between mathematics and reality:

Mathematics stops at zero. Reality begins at zero.    

The Al-Asr Dynamic Number System offers a new framework. Inspired by the temporal language of Qur'an, Surah Al-Asr (103), it defines zero as a temporal, directional, and transitional moment rather than an absence.

---

2. Methodology: Pico Scale Model

2.1 Temporal Resolution at the Pico Scale

Natural phenomena such as electronic switching, quantum tunneling, and nuclear transitions occur on the pico scale (10⁻¹² seconds) or below (Feynman 12–18). This ultra-short timescale captures the “moment of becoming” — the birth of an event.

2.2 Al-Asr Moment on the Number Line

The ADNS number line repositions zero as:

Past (−)⟶[ 0:Al-Asr Moment ]⟶Future (+)      

• Negative values = past, loss, decay
• Zero = Al-Asr transitional ignition
• Positive values = future, gain, expansion

2.3 Event-Based Representation

Each number is interpreted not just as magnitude but as an event in time.
Zero is the event origin, not an inert symbol. Operations involving zero are interpreted as temporal state transformations.

---

3. Mathematical Framework: Sign Rules and Operations

3.1 Directional Sign Interpretation

Sign	Direction	Polarity	Meaning
+	Future	Gain	Growth, expansion
−	Past	Loss	Decay, regression
0	Present	Transition	Al-Asr ignition moment

3.2 Addition

a + 0 = a  

In ADNS, this equation is not simply identity; it indicates stability or pause in the event flow.

• +a + 0: gain remains stable
• −a + 0 : decay continues
• 0 + 0 : system remains in transition.

3.3 Subtraction

a – 0 = a and 0 − a =−a  

Zero acts as a pivot: subtracting a value from zero reverses the temporal direction across the Al-Asr moment.

3.4 Multiplication

a × 0 = 0  

Classical arithmetic says the product vanishes.
ADNS interprets this as energy or state being absorbed into the Al-Asr transformation point.

• +a × 0 = 0  : future gain paused
• −a × 0 = 0  : past decay neutralized
• 0 × a = 0  : no new event initiated

Also:

(−) × (−) = (−)  

Repeating decay in the past does not produce gain — it compounds loss. This diverges from classical arithmetic but reflects temporal reality.

3.5 Division

0/a = 0  

The event has not propagated — still at rest in Al-Asr.

a/0 = Al-Asr Transformation Event   

This is not undefined, but the moment of ignition or state transition.

---

4. Results: Directional Interpretation of Multiplication and Division

4.1 Multiplication

(+3) × (+2) = +6      

Forward gain repeated forward: expansion.

(−3) × (+2) = −6  

Decay repeated forward: sustained loss.

(−3) × (−2) = −6    

Past decay repeated past: deepening decay.

(a) × 0 = 0    

Transition absorbed at Al-Asr.

4.2 Division

+6 / +2 = +3    

Forward gain unfolding forward.

−6 / −2 = −3    

Past decay unfolding past.

a/0    \frac{a}{0}​

Transformation event — ignition point of system evolution.

This framework resolves the classical division-by-zero paradox by replacing “undefined” with physical meaning.

---

5. Applications: Physics, Time, Energy, and Systems

5.1 Quantum Physics

• Wavefunction collapse occurs at zero moment (Zeilinger 743).
• ADNS models transition timing precisely.

5.2 Electronics

• Signal edges occur at zero volts.
• Zero represents trigger points, not absence of signal.

5.3 Cosmology

• The Big Bang is modeled as zero ignition (Misner et al. 3).
• Zero is the temporal origin of cosmic expansion.

5.4 Biological Systems

• Neural and cardiac electrical signals fire at threshold crossing (zero).

5.5 Energy Systems

• Control systems begin cycles at zero crossings.

---

6. Discussion and Conclusion

The Al-Asr Dynamic Number System challenges the classical view of zero as a void. By defining zero as an event, ADNS:

• Introduces temporal directionality into arithmetic.
• Provides physical meaning to division by zero.
• Reflects real pico-scale dynamics found in nature.
• Bridges mathematics, physics, and cosmology.

“Zero is not nothing. Zero is the beginning of everything.”

ADNS offers a unified framework where mathematical operations and physical events are synchronized. This conceptual shift is not merely symbolic — it can impact modeling in physics, control theory, signal processing, and cosmological research.

---

7. Works Cited

• Qur'an. Surah Al-Asr (103).
• Boyer, Carl B., and Uta C. Merzbach. A History of Mathematics. Wiley, 2011.
• Dirac, P. A. M. The Principles of Quantum Mechanics. Oxford UP, 1930.
• Feynman, Richard P. QED: The Strange Theory of Light and Matter. Princeton UP, 1985.
• Kline, Morris. Mathematical Thought from Ancient to Modern Times. Oxford UP, 1972.
• Misner, Charles W., Kip S. Thorne, and John Archibald Wheeler. Gravitation. Freeman, 1973.
• Stewart, Ian. In Pursuit of the Unknown: 17 Equations That Changed the World. Basic Books, 2012.
• Zeilinger, Anton. “The Message of the Quantum.” Nature 438 (2005): 743.

---