Response to Critiques and Suggestions Regarding Dynamic Number System (DNS)

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Reply to Critical Questions:

1. How can you say that dynamic equilibrium runs from gain (+) to loss (−)? In the abstract, you wrote that DNS runs from Quento to Quetta.

The terms "gain (+) to loss (−)" and "-Quento to +Quetta" are not contradictory but layered. The former describes a behavioral or energetic transition model within the Dynamic Number Line (DNL), reflecting states like prosperity (gain) and hardship (loss), similar to thermodynamic or economic gradients. The latter, "minus Quento to plus Quetta," represents the magnitude and scale—from smallest measurable minus quantities (-10^-30) to largest (+10^+30). Dynamic equilibrium in DNS reflects transitions across these ranges, where zero (Al-Asr) is the moment of decision, akin to a balance point.

Example: In leadership modeling, decision-making at pico levels can alter organizational outcomes drastically, making scale (-Quento to +Quetta) vital.

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2. How can you claim that you are the founder of DNS? See the book titled "Dynamics of Number Systems: Computation with Arbitrary Precision" by Petr Kurka.

 

The claim of founding DNS is rooted in the unique conceptual, philosophical, and mathematical integration of:

• The Quranic concept of Al-Asr as Zero.
• Re-defining zero as a dynamic transition point, not a null.
• Introducing DNS as a unified scale-based number system applicable across scales (minus Quento to plus Quetta).

While Petr Kurka's work concerns computation with arbitrary precision and symbolic dynamics, this DNS is a new mathematical philosophy encompassing behavior, physics, leadership, and time. The nomenclature may be overlapping, but the structure, definitions, and philosophical roots differ significantly.

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3. There are unnecessary keywords, e.g., behavioral forecasting.

Behavioral forecasting is essential in DNS, particularly when modeling decision-making, transitions, and leadership responses. DNS’s structure supports forecasting systems where micro-decisions (at pico/nano levels) impact macro outcomes.

Example: Predictive modeling in crisis leadership or AI ethics employs dynamic decision nodes—applicable through DNS principles.

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4. How can you say that Natural Numbers, Whole Numbers, Integers, Rational Numbers are different from Real Numbers?

Natural, Whole, Integers, and Rational Numbers are subsets of Real Numbers. The wording intends to clarify that DNS includes and transcends all traditional subsets by introducing infinitesimals and massive dynamic scales (minus Quento to plus Quetta). Future revisions will specify this hierarchy.

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5. How can you justify that the multiplication and division operations are the same for the dynamic number in DNS: Al-Asr × Al-Asr = Al-Asr and Al-Asr ÷ Al-Asr = Al-Asr?

In DNS, Al-Asr represents a dynamic zero, not a classical zero. It is a transition state that retains properties of change. Therefore:

• AlAsr × AlAsr = AlAsr  : Self-multiplication keeps the state of balance.
• AlAsr ÷ AlAsr = AlAsr : Division preserves the dynamic zero identity.

This aligns with self-reflective systems, where feedback loops do not diverge but maintain identity.

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6. Can you prove that 1 ÷ Al-Asr = Al-Asr?

This formulation reflects a paradigm shift. Classical mathematics would reject this due to zero-division paradoxes. But in DNS:

• Al-Asr is not a static zero.
• 1 ÷AlAsr =AlAsr  implies feedback stability at the zero decision moment, a characteristic of dynamic systems in equilibrium.

This could be proven within the DNS framework using limits and continuous feedback operators.

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7. How can you apply DNS in computer science and financial mathematics?

Computer Science Example: DNS offers dynamic scaling in AI decision trees, enabling logic that adapts between infinitesimal and maximal values (from minus quento to plus quetta) to enhance learning models.

Financial Mathematics Example: DNS enables modeling of crisis events where stock values move from peak to collapse—using transitional zero points (Al-Asr) to forecast turning points.

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8. Is it a book or a manuscript?

It is currently a manuscript under development for submission to a journal. The work will evolve into a full book upon peer review and refinement.

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9. What do you mean by "any number"? Is it a fixed or dynamic number?

In DNS, "any number" refers to a dynamic quantity that may change based on scale (nano to giga) and context (gain or loss zone). It contrasts with static interpretations in classical systems.

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10. What is m in the DNL system?

"m" represents the magnitude coefficient for scale assignment on the Dynamic Number Line. It acts like a scaling operator to shift numbers across exponential stages (m × 10^±n).

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11. How can you use dynamic zero as a navigational tool?

Dynamic zero (Al-Asr) serves as a pivot or transition signal. In AI or control systems, this point flags critical decision moments.

Example: A self-driving car uses dynamic thresholds to switch from cruise to brake mode—mirroring DNS zero behavior.

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12. Justify − × − = − ?

In classical mathematics, − × − = +. However, DNS redefines negative as a zone of correction and loss. Thus, when two losses interact without transformation, the system remains in loss, hence:

• (−) × (−) = − in DNS unless a positive decision (Al-Asr) intervenes.

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13. How can you refer to unpublished data?

In scientific development, new theories begin unpublished. The current references are original and will be published through peer-reviewed platforms. Citation will be adjusted upon publication.

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Suggestions and Acknowledgments

1. Surah is not a reference but the Quran.
• Correction noted. Future versions will cite the Quran directly.
2. Write the document in a manuscript or book style.
• This is being done. A complete manuscript is in progress.
3. There should be some examples to emphasize your findings.
• Examples have been inserted. More will be added in applied chapters.
4. Make a comparison with the traditional number system.
• A new table comparing classical vs DNS is being developed.
5. Write the physical and philosophical realities of DNS clearly.
• A dedicated section will be included in the introduction.
6. Avoid repetition of words in the document.
• Editorial revisions are underway to improve clarity and reduce redundancy.

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Thank you for your rigorous review. Your feedback strengthens the work and its journey to publication.

  

G. Mustafa Shahzad
Email: gmshahzad@yahoo.com & scientificet@gmail.com
Affiliation: Founder & President, Qalim Institute, Pakistan / Independent Researcher
Year: 2025