2001. Introduction to the Relation Between Transcendental Numbers (Created Numbers) and Their Projection - Algebraic Numbers (Invented or Constructed Numbers)

24 February 2026
The feast of St. Matthias (1st Century AD)

Necessity of Transcendental Constants for Universal Units of Measurement

Before proceeding with Universal Units of Measurements of physical quantities, it is necessary to introduce a couple of Transcendental Numbers that are crucial in those calculations.

There are three Constants necessary to assemble the Supreme Order of Universal Units of Measurement: π, e, and possibly φ (i.e., the Golden Ratio). We know that the traditional (geometric) Golden Ratio is an algebraic number; however, my definition of this Fibonacci Ratio is slightly different and it is perhaps a Transcendental Constant. (Detailed analyses of Fibonacci-like sequences and series will be presented in Chapter III in the near future).

Definition of the Transcendental Fibonacci Ratio (the Golden Ratio)

The Transcendental Fibonacci Sequence is the result of operation on two Parent Sequences – Pater and Filius (this is a Catholic website, so I hope you do not mind a bit of ‘Mathematical Theology’).

The Pater Sequence

The definition of a Pater Sequence is:
PAT(er) = (7 / 5)^1/2 * π = 3.71718255693…

The Filius Sequence

The definition of a Filius Sequence is:
FIL(ius) = (5 / 7)^1/2 * e = 2.29736745287…

The Spiritus Sanctus Sequence (SSS)

The division of PAT(er) / FIL(ius) formulates Spiritus Sanctus Sequence (SSS) and is equal to:
SSS = [ (7 / 5)^1/2 * π ] / [ (5 / 7)^1/2 * e ] = (7 / 5) * (π / e) = 1.61801828971…

Notice that the Transcendental Fibonacci Ratio (SSS) is a product of a quotient of two transcendental numbers π and e and of a fraction 7/5, which I think is also transcendental.

So, we have a connection between irrational number and transcendental numbers in the case of PAT(er) and FIL(ius), and in the case of SSS (Spiritus Sanctus) we have the relation between a fraction and a transcendental quotient.

Comparison of the Traditional Golden Ratio and the Transcendental Golden Ratio

Geometric Fibonacci ratio: Φ ≈ 1.6180339887…
Transcendental Fibonacci: SSS = φ ≈ 1.61801828971…

If Transcendental Fibonacci Ratio is true, then the ‘relative error’ of Geometric Golden ratio equals:
ε ≈ 0.000970261 %

The difference is very tiny indeed. I claim that the Transcendental Fibonacci Ratio is far superior to Traditional Golden Ratio in quantum calculations, allowing for example many simplifications, reductions and first of all relation between Higher dimensional Transcendentals and their projection on our three-dimensional world and as a result making algebraic numbers as a shadow of Transcendental Numbers.

PAT(er), FIL(ius), and Spiritus Sanctus (SSS) Ratios and definitions connect high-level transcendentals with low-level algebraic numbers.

Practical Application in Universal Units

In practice, not all Transcendental Numbers will appear in calculations of the Universal Units. We will mostly use two or one transcendental, i.e., 'π', ‘e’ and/or ‘φ’.

Before I discuss Universal Units of Measurements (Chapter II), I will post a couple of links to Transcendental Fibonacci Sequences and Series. I will elaborate on this topic in depth later in Chapter III.

The following articles are from the year 2024.

Sources

LuxdeLuce.com and ExtraUniversum.com

LuxdeLuce.com and ExtraUniversum.com