Letter Numbering — Conversion and Representation for LLM
Abstract:
This paper presents a novel methodology to represent words in a two-dimensional coordinate system by numerically categorizing consonants and vowels. This representation can be further simplified to be visualized as a vector in terms of its magnitude and direction. Using this approach, we can graphically represent words in an abstract manner, potentially enabling new applications in linguistic studies and word pattern recognition.
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1. Introduction
Traditionally, the alphabets are treated as standalone entities without numerical representation, barring encoding schemes like ASCII. By providing each letter with a unique numerical identity, we explore how words can be mapped onto a coordinate plane, offering a unique trajectory and vector representation.
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2. Methodology
2.1. Letter Numbering
- Consonants: The 21 consonants of the English alphabet are assigned values from 1 to 21. They represent movement on the Y-axis of our coordinate system.
- Vowels: The 5 vowels are assigned values ranging from 1 to 5, dictating movement on the X-axis.
2.2. Converting a Word into Coordinates
Starting from an initial point (0,0), we can represent a word by sequentially moving along the X and Y axes based on the assigned values of its letters.
*Example*:
Considering the word “casa”:
1. The consonant ‘c’ gives a Y displacement of 3 units, resulting in the point (0,3).
2. The vowel ‘a’ gives an X displacement of 1 unit, shifting to (1,3).
3. The consonant ‘s’ causes a Y displacement of 19 units, resulting in (1,22).
4. Another ‘a’ gives an X displacement of 1 unit, leading to the final point (2,22).
Thus, the trajectory for “casa” is visualized as the movement from (0,0) to (2,22) through the intermediate points.
2.3. Representing a Word as Tangent/Angle + Resultant Vector
Using basic trigonometric principles, we can calculate the angle between the origin (0,0) and the final point of the word’s trajectory.
For the example word “casa”, the angle θ is given by:
\[ \theta = \arctan(\frac{22}{2}) \]
To compute the total displacement or the resultant vector, the Pythagorean theorem is employed:
\[ magnitude = \sqrt{²² + 2²²} \]
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3. Conclusion
The method of mapping words onto a coordinate plane by numbering letters provides a refreshing geometrical interpretation of linguistic elements. By representing words as vectors, we can study relationships, patterns, and perhaps even gain insights into the intrinsic nature of language. This representation paves the way for potential applications in the realms of linguistics, cryptography, and data visualization.
