Fibonacci Strings: Integrating the Something–Nothing Spectrum

Abstract

This paper introduces Fibonacci Strings, a novel framework that uses the mathematical elegance of the Fibonacci sequence to encode semantic meaning directly into binary data. The approach is simple yet powerful: we convert Fibonacci numbers (like 1, 2, 3, 5, 8) into their binary code and then translate this code into language. Each '1' is mapped to a word representing “something” (e.g., 'presence,' 'entity'), while each '0' becomes a word for “nothing” (e.g., 'void,' 'absence'). This process is guided by the Something-Nothing Spectrum (SNS), a system where modern AI helps classify word. The result is a method for transforming pure numbers into meaningful phrases, allowing binary data to carry semantic weight.

1. Introduction

1.1 Motivation

While in most digital architectures binary digits (0 and 1) serve as foundational placeholders without inherent semantic meaning, the Something–Nothing Spectrum (SNS) propose that each word in a language can be assigned a numerical value (0–1) reflecting its proximity to “nothingness” (0) or “somethingness” (1).

Fibonacci Strings bring these two ideas together by: (1) Generating binary sequences from Fibonacci numbers, and (2) Mapping each digit (0 or 1) to an SNS-based word (e.g., “void” vs. “being”).

2. Background

2.1 The Fibonacci Sequence

The Fibonacci sequence (F_n) is defined as:

F₀ = 0, F₁ = 1, F_n = F_n-1 + F_n-2, for n ≥ 2

yielding 0, 1, 1, 2, 3, 5, 8, 13, … . Converting F_n to binary provides a sequence of 0s and 1s for each term. For instance, F₂ = 1 → “1”, F₃ = 2 → “10”, F₄ = 3 → “11”.

2.2 The Something–Nothing Spectrum (SNS)

According to the SNS, words can be assigned values in the interval [0,1], where 0 represents “non-existence” and 1 represents "existence.” This foundational concept allows for the quantification of a word's ontological weight. Examples:

• Words near 0: “void,” “absence,” “nothingness.”
• Words near 1: “being,” “presence,” “entity.”

2.3 The Rationale for Choosing the Fibonacci Sequence

While other mathematical series (e.g., prime numbers, geometric progressions) could generate binary sequences, the Fibonacci sequence is uniquely suited for this framework for several profound reasons:

• Inherent Connection to Growth:The Fibonacci sequence often emerges in plant growth patterns and other natural spirals, paralleling concept emergence—the way complexity arises from simple, foundational rules. Each Fibonacci String can be seen as a snapshot of this self-organising growth process.
• Recursive Simplicity: The rule F_n = F_n-1 + F_n-2 models how new states of being are built upon the sum of what came immediately before. This recursive structure perfectly mirrors how complex semantic ideas can be constructed from a sequence of simple "something" (1) and "nothing" (0) concepts.
• The Golden Ratio (φ) as Aesthetic Composition: The golden ratio, often called the “divine proportion,” has been a cornerstone of artistic and architectural composition for centuries, believed to produce aesthetically pleasing and natural harmony. In this framework, choosing the Fibonacci sequence is a deliberate artistic act. It implies that the resulting strings are not just data, but semantic compositions intended to achieve a form of linguistic balance and beauty.

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3. Constructing Fibonacci Strings

We outline how to generate Fibonacci Strings by blending Fibonacci binary sequences with SNS-based word mapping.

3.1 Binary Sequence Generation

1. Fibonacci Series: Select the first n Fibonacci numbers (F₀, F₁, ..., F_n).
2. Convert each number to its binary representation.
3. Concatenate if needed to form longer binary strings.

Example: F₃ = 2 → 10, F₄ = 3 → 11. Concatenated → 1011.

3.2 SNS Mapping

Each binary digit b (0 or 1) is mapped to a word chosen from an SNS-scored vocabulary:

• 1 → “something” words (e.g., “being,” “presence”).
• 0 → “nothing” words (e.g., “void,” “absence”).

Multi-LLM Classification:

1. A curated vocabulary is assigned SNS values (v ∈ [0,1]) via multiple LLMs.
2. Values ≥ 0.5 map to “something,” while values < 0.5 map to “nothing”.
3. Contextual or grammatical filtering can refine which specific “being” or “absence” words to use, ensuring better linguistic coherence.

3.3 Example of Mapping

Using the concatenated binary 1011:

• 1 → “presence” (or another “something” word),
• 0 → “void,”
• 1 → “entity,”
• 1 → “being.”

Hence, the sequence 1011 might become “presence void entity being.”

3.4 Grammatical Filtering

Grammatical filtering ensures that any phrase formed from a 0/1 sequence respects basic language rules:

• Part-of-Speech Tagging: Certain “nothing” words may function differently (e.g., noun vs. adjective), guiding their placement in a phrase.
• Local Context: If the Fibonacci String grows into multiple sentences, the system can choose synonyms of “nothing” or “something” that align with the preceding text’s structure.

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4. Conclusion

Fibonacci Strings offer a captivating fusion of mathematical recursion and an ontological scale via the SNS. By mapping binary digits to “nothing” or “something” words, bits evolve from inert tokens into meaning-bearing elements. The choice of the Fibonacci sequence is not arbitrary; its inherent properties of natural growth, recursion, and its convergence toward the golden ratio provide a mathematical backbone that mirrors the very process of ontological creation from simple foundations.

This framework is made tangible through modern tools. Drawing on large language models for classification ensures scalable and relatively unbiased word assignments, while grammatical filters help maintain the linguistic coherence of the resulting strings. Ultimately, Fibonacci Strings propose a paradigm shift in how we conceive of information—turning pure data into poetry.