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Title: The Dynamic Number System (DNS): A Multiscale Framework for Mathematical
and Real-World Applications
Author: G. Mustafa Shahzad
Affiliation: Scientific Engineering & Trading | Quranic Arabic Research
Scholar
Email: scientificet@gmail.com
Date: 2025
Abstract
The Dynamic Number System (DNS) introduces a novel mathematical model
integrating both infinitesimally small (quecto, 10^-30) and enormously large
(quetta, 10^+30) values within a unified framework. DNS recognizes a special
dynamic zero, termed Al-Asr, which represents a transition or decision
point between gain and loss. This system extends classical number operations
and applies to various fields including mathematics, physics, engineering,
behavioral forecasting, and leadership sciences.
1. Introduction
The DNS presents a number line beyond traditional real number systems, with a
center marked by Al-Asr—denoting a moment of dynamic equilibrium rather than
nullity. The system runs bidirectionally from minus quento (10^-30) to plus
quetta (10^+30), encompassing both physical and metaphysical interpretations.
2. Mathematical Framework of DNS
2.1 Addition and Subtraction
· Positive (+) implies potential, future, or gain.
· Negative (-) implies loss, memory, or past.
· Al-Asr acts as a balance point, physically existence, or action point..
2.2 Multiplication
·
o + * + = +
·
o - * - = -
·
o + * - = -
· Commutative and associative laws hold.
2.3 Division
·
o + / + = +
·
o - / - = -
·
o - / - = -
· Special case: Al-Asr / Al-Asr = Al-Asr
2.4 Infinitesimals and Continuity
· Between any two dynamic numbers, a third dynamic number exists.
· Infinitesimal transitions are recognized at pico, nano, and even quecto scales.
3. Al-Asr: Dynamic Zero
Al-Asr is not an empty value but a state of potential decision, equilibrium, or
moment of change. The concept is rooted in Quranic verse Surah Al-Asr and
interpreted beyond religious boundaries to denote physical and metaphysical
moments of decision.
4. Applications
4.1 Mathematics & Physics
· Calculus with infinitesimals
· Quantum behavior and pico-level transitions
4.2 Computer Science
· Binary logic with a third state (Al-Asr) for decision-making systems
4.3 Financial Mathematics
· Risk prediction using dynamic zeros and behavioral forecasts
4.4 Behavioral and Leadership Sciences
· Decision-making modeled as transition through Al-Asr
5. Response to Critiques
1. From Gain to Loss? – DNS is dynamic, with transitions bidirectionally. Gain (+) and loss (-) represent movement through time or change, not linear gain-to-loss.
2. Founder Claim? – DNS as presented is distinct in its zero definition (Al-Asr) and multiscale dynamic continuum; Kurka’s work is acknowledged but unrelated.
3. Keywords? – Behavioral forecasting aligns with decision science applications.
4. Numbers? – Real numbers encompass others, but DNS emphasizes structure and dynamism.
5. Al-Asr × Al-Asr = Al-Asr? – Represents equilibrium moments—logically justified under DNS.
6. 1 ÷ Al-Asr = Al-Asr? – Reflects DNS rules, not classical math.
7. Applications? – DNS logic gates in AI (Computer Science); Market phase detection (Finance).
8. Book or Manuscript? – Academic manuscript.
9. Any number? – DNS numbers are dynamically contextual.
10. What is m? – Scale multiplier on the Dynamic Number Line.
11. Navigational Tool? – Al-Asr helps orient decisions under uncertainty.
12. Justify − × − = −? – In DNS, the multiplication of two losses amplifies negative history.
13. Unpublished Data? – Clearly marked and attributed to author's research.
6. Comparison with Traditional Number Systems
|
System |
DNS Extension |
|
Natural |
Included with dynamics |
|
Integers |
Enhanced with scale & sign |
|
Real |
Subset of DNS |
|
Complex |
DNS includes imaginary axis |
7. Philosophical and Physical Significance
DNS bridges philosophical time perception (past–present–future) and physical
transitions in microstates. The use of pico-scale change reflects real-world
scenarios in nanoengineering, neurology, and quantum computation.
8. References
· Al-Quran: Surah Al-Asr (103:1–3)
· Petr Kurka, Dynamics of Number Systems: Computation with Arbitrary Precision, Birkhauser
· Shahzad, G. M. (2025). Research notes on DNS [Unpublished]
· NIST. SI Prefixes from quecto (10^-30) to quetta (10^30)
· IEEE Papers on numerical models in computer science and quantum logic
Appendix
Glossary, scale chart from quento to quetta, DNS equation table
End of Manuscript
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