The Al-Asr Number Line: Pico-Scale Origin of Dynamic Zero
Author: G. Mustafa Shahzad, Quranic Arabic Research Scholar & Theorist of the Al-Asr Dynamic Number System (ADNS)
Date: December 2025 qaliminstitute@gmail.com +1 929 739 8633
Abstract
Classical mathematics treats the number line as static, continuous, and centered on an absolute zero. The Al-Asr Dynamic Number System (ADNS) introduces a fundamentally different interpretation: numbers exist only as part of events, and every event is bounded by a finite duration called Al-Asr. This paper elaborates the Al-Asr Number Line, beginning at the pico scale, where zero itself is not singular but dynamically split into +0 and −0, representing future-directed and past-directed infinitesimal transitions. This framework resolves long-standing ambiguities surrounding zero, sign, and infinitesimal change.
1. Classical Number Line vs. Al-Asr Number Line
1.1 Classical View
In conventional mathematics:
· The number line is static
· Zero is a dimensionless point
· Positive and negative numbers are abstract directions
· Time is external to the number system
This abstraction works for many calculations but fails to explain:
· Division by zero
· Indeterminate forms
· Physical event boundaries
· Temporal asymmetry (past vs. future)
1.2 ADNS View
In ADNS:
· The number line is event-based
· Zero is dynamic, not empty
· Signs represent temporal polarity
· Time is intrinsic, not external
Thus, the ADNS number line is centered not on static zero, but on 0ₐₗ-ₐₛᵣ (Al-Asr Zero).
2. Definition of the Al-Asr Number Line
ADNS Statement
Numbers lie on a bidirectional number line centered at 0ₐₗ-ₐₛᵣ, evolving dynamically at the pico scale.
Formally, the ADNS number line is:
⋯−n
⟶ −ε ⟶ −0
∥ 0Al-Asr ∥ +0⟶ +ε
⟶ +n⋯
Where:
· −0 is the terminal boundary of the past
· +0 is the initial boundary of the future
· 0ₐₗ-ₐₛᵣ is the duration-bearing transition state
3. Pico-Scale Origin of the Number Line
3.1 Why Pico Scale?
At macroscopic scales, zero appears singular. However, at the pico scale (10⁻¹²) and below:
· All physical changes occur as discrete transitions
· No event is instantaneous
· Every change has a minimum duration
Thus, zero must possess internal structure.
3.2 Emergence of −0 and +0
At pico resolution:
· −0 represents the final measurable state before transition
· +0 represents the first measurable state after transition
They are distinct, though arbitrarily close.
−0 ≠
+0 in ADNS
This distinction is meaningless in classical math but essential in event-based systems.
4. Meaning of Signs at Pico Scale
In ADNS, signs are not merely algebraic.
|
Symbol |
ADNS
Meaning |
|
− |
Past-directed progression |
|
+ |
Future-directed progression |
|
−0 |
Event termination boundary |
|
+0 |
Event initiation boundary |
Thus:
· Negative numbers represent recorded or completed events
· Positive numbers represent projected or unfolding events
5. Dynamic Zero (0ₐₗ-ₐₛᵣ)
5.1 Definition
Al-Asr Zero is not a point but a finite-duration interval:
0Al-Asr = [−0,+0]
It is the minimum event duration separating past from future.
5.2 Properties
· Carries time information
· Cannot be collapsed to nothing
· Exists even when numerical magnitude is zero
· Resolves indeterminate expressions
6. Illustrative Examples
Example 1: Physical Event (Light Switch)
· −0: Finger just before contact
· 0ₐₗ-ₐₛᵣ: Electrical transition interval
· +0: Current begins flowing
No true instant exists; the event has Al-Asr duration.
Example 2: Mathematical Transition
Consider function sign change:
f(x) = x
Classical view:
ADNS view:
· Approach to −0 ≠ emergence from +0
· Transition passes through 0ₐₗ-ₐₛᵣ
Example 3: Division Identity
0
/ 0 =Al-Asr / Al-Asr = Al-Asr
= 
= Al-Asr
Because:
· The event is divided by itself
· Duration remains preserved
· No infinity or collapse occurs
7. Implications of the Al-Asr Number Line
1. Zero becomes meaningful
2. Time is embedded in arithmetic
3. Signs gain physical interpretation
4. Indeterminate forms are resolved
5. Pico-scale physics aligns with mathematics
8. Conclusion
The Al-Asr Number Line redefines the foundation of numerical representation by recognizing that:
· No event is instantaneous
· Zero has duration
· Signs encode temporal direction
· All numbers emerge from pico-scale transitions
By starting at the pico scale, ADNS restores coherence between mathematics, physics, and lived reality, positioning Al-Asr as the true center of numerical meaning.
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