Reviewer-Response Justification for the Al-Asr Dynamic Number System (ADNS)
Author: G. Mustafa Shahzad, Quranic Arabic Research Scholar & Theorist of the Al-Asr Dynamic Number System (ADNS)
Date: December 2025 qaliminstitute@gmail.com +1 908 553 3347
Purpose
of This Section
This document anticipates and
addresses likely reviewer concerns regarding the Al-Asr Dynamic Number
System (ADNS), its axioms, treatment of zero, sign interpretation, and
divergence from classical mathematical conventions. Each response is grounded
in logical consistency, physical realism, and mathematical necessity.
Reviewer
Concern 1:
“Zero is universally defined as a
dimensionless point. Introducing duration into zero violates standard
mathematics.”
Response:
The reviewer’s concern assumes that
mathematical definitions must remain independent of physical reality. ADNS
deliberately challenges this assumption.
Classical zero is an abstraction
that fails at event boundaries, especially in:
- Division by zero
- Indeterminate forms
- Physical transitions
- Temporal asymmetry
ADNS does not redefine zero
arbitrarily; it extends zero to include event duration,
consistent with physics, where no transition is instantaneous.
Justification:
- At pico and sub-pico scales, all measurable changes
occur over finite time.
- A dimensionless zero contradicts empirical observation.
- ADNS zero (0ₐₗ-ₐₛᵣ) resolves known singularities
without contradiction.
Thus, ADNS is an extension,
not a rejection, of classical zero.
Reviewer
Concern 2:
“The distinction between +0 and −0
is artificial and unnecessary.”
Response:
In classical arithmetic, +0 and −0
are numerically equal because time and direction are ignored. ADNS
explicitly encodes temporal polarity.
In ADNS:
- −0
= terminal boundary of a past event
- +0
= initial boundary of a future event
These are not numerically distant,
but they are temporally distinct.
Justification:
- Physical systems (e.g., switching, quantum transitions,
biological signals) exhibit asymmetric entry and exit states.
- Event termination and event initiation are not
interchangeable.
- Treating ±0 as identical erases causal direction.
Therefore, ±0 distinction is necessary
for event-based mathematics.
Reviewer
Concern 3:
“The statement 0/0 = Al-Asr
contradicts established mathematical doctrine.”
Response:
The classical declaration that 0/0
is “undefined” is a consequence of modeling zero as emptiness.
ADNS models zero as event
duration, not emptiness.
-2p
-1p -0.5p 0AlAsr +0.5p
+1p +2p
<----|----|----|----|----|----|---
0AlAsr
0
/ 0 =Al-Asr / Al-Asr = Al-Asr
= 
= Al-Asr
Justification:
- Dividing an event by itself preserves identity.
- Indeterminacy arises only when time and structure are
removed.
- ADNS eliminates paradoxes by restoring physical
meaning.
This resolution is internally
consistent, non-contradictory, and singularity-free.
Reviewer
Concern 4:
“Interpreting signs (+, −) as future
and past is philosophical, not mathematical.”
Response:
In ADNS, signs are not philosophical
metaphors; they are formal polarity operators.
Classical mathematics already
assigns directional meaning to signs (left/right on number line), but does
not explain why.
ADNS formalizes this implicit
meaning:
- +
→ forward temporal progression
- −
→ backward temporal reference
Justification:
- This interpretation aligns arithmetic with causality.
- It explains sign multiplication rules naturally.
- It unifies number systems with physics and systems
theory.
Thus, sign polarity in ADNS is mathematically
operational, not philosophical.
Reviewer
Concern 5:
“ADNS departs too far from classical
mathematics to be considered rigorous.”
Response:
All major mathematical advances
initially departed from classical norms:
- Negative numbers
- Zero
- Imaginary numbers
- Non-Euclidean geometry
- Calculus itself
ADNS follows the same historical
pattern:
- Identifies unresolved contradictions
- Introduces minimal axioms
- Restores coherence
Justification:
- ADNS preserves arithmetic consistency.
- Classical results remain valid as limiting cases.
- No established theorem is contradicted; only extended.
Hence, ADNS is complementary,
not destructive.
Reviewer
Concern 6:
“The system lacks experimental or
physical relevance.”
Response:
ADNS is explicitly designed to model
real events, including:
- Pico-scale transitions
- Quantum boundary behavior
- Biological rhythms (ECG-like signals)
- System start-stop processes
Justification:
- Physical events always have duration.
- Mathematical models without duration fail at
boundaries.
- ADNS provides a direct bridge between mathematics and
observation.
The system is therefore empirically
motivated, not abstractly speculative.
Reviewer
Concern 7:
“Why is Al-Asr central to the number
line?”
Response:
Al-Asr represents the minimal
meaningful duration of any event.
Without Al-Asr:
- Numbers are detached from reality
- Zero collapses into paradox
- Signs lose meaning
With Al-Asr:
- Numbers gain temporal anchoring
- Arithmetic becomes event-consistent
- Start and end are formally defined
Thus, Al-Asr is not symbolic—it is structural.
Concluding
Justification Statement
ADNS restores time, direction, and
duration to mathematics without violating internal consistency. It resolves
classical paradoxes by extending—not denying—established theory. The Al-Asr
framework is therefore mathematically legitimate, physically motivated, and
logically necessary.
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