Mathematics, Logic, and Number Theory
Group Theory: Order of an Element
An introduction to a fundamental idea in group theory: the order of an element.
Using modular groups and worked examples, this article shows how successive
exponentiation leads back to the identity element and provides a practical
method for calculating element orders.
Palindromes on the 12-Hour Clock
A mathematical exploration of the palindromic patterns hidden in an ordinary 12-hour clock. Beginning with naturally occurring symmetric times, the
investigation develops sets of palindromes and asks what new patterns emerge when those sets are repeatedly combined through arithmetic operations.
Gödel Numbering
An introduction to Gödel’s remarkable method of translating the language of formal mathematics into numbers. By assigning numerical representations to
symbols, axioms, and statements, Gödel made it possible for a formal system to reason mathematically about its own structure.
The System of R-Exp: Expanding the Algebraic Number System
An exploration of an alternative extension of algebra in which addition is
introduced as an exponential operation. The article develops the proposed
R-Exp system and considers how changing the structure of exponentiation may
produce new mathematical operations and relationships.
Cantor Set Theory & Transfinite Mathematics — Foundations of Set Theory
An examination of Cantor’s foundational ideas in set theory and the mathematics
of the infinite. The article explores cardinality, infinite sets, and transfinite
numbers, showing how Cantor’s work created a rigorous mathematical framework
for comparing different orders of infinity.
Palindromic Mappings
An investigation of mathematical structures generated from palindromes and
mappings between palindromic sequences and natural numbers. Beginning with
letter patterns, the article develops numerical transformations and palindromic
N-tuples, revealing unexpected relationships between cardinal and ordinal
palindrome constructions.
Personal Essays & Philosophy
The Existential Concept: Existentialism 1
An exploration of existentialism through the question of whether perfection has any intrinsic meaning. Using mathematical “perfect numbers” as a revealing example, the essay examines how human beings assign concepts and standards to reality—and asks whether those labels describe something inherent in the world or something we ourselves create.
The Meaning Of Freedom and Death: Existentialism 2
An existential examination of freedom, choice, and mortality. Confronting death and a reality without predetermined purpose, the essay argues that human freedom lies in choosing how to live within those conditions—and in the conscious acts of thought and creation through which we give form and meaning to existence.
Meaning and Interpretation: Existentialism 3
An exploration of how human beings create meaning from an external world that does not inherently provide it. Drawing on everyday experiences of sound, sight, and smell, the essay distinguishes sensory perception from the interpretations we impose upon it—transforming what we perceive into judgments such as desirable or unpleasant, beautiful or offensive, and ultimately meaningful.
Iconoclasm: Existentialism 4
An examination of iconoclasm as existentialism expressed through a rejection of culturally assigned meaning. The essay questions rituals,
celebrations, institutions, traditions, and social conventions, while exploring how satire and cultural criticism challenge beliefs that society
often treats as inherently significant.
What Is Naturalism?: Existentialism 5
An exploration of what it means to call something natural. Rejecting the idea that nature represents an ideal condition, the essay argues that everything occurring within reality—including human action—is natural,
while moral judgments such as good, bad, desirable, or undesirable remain interpretations we impose upon events.
Numeration and Uniqueness: Existentialism 6
A philosophical examination of humanity’s fascination with counting, ranking, records, and uniqueness. Using mathematical and everyday examples, the essay argues that distinctions such as first, tallest, shortest, or one-of-a-kind acquire significance only because human beings
define attributes and then assign meaning to the differences they discover.
English Words That Are Becoming Archaic and Words That Are Not
An examination of changing English usage through words and contractions
that are disappearing, surviving, or changing their function. The essay
considers why familiar forms become uncommon while closely related
expressions remain part of everyday speech and writing.
A Look At Compound English Words
An exploration of the remarkable ability of English to combine words
into new expressions. Beginning with its Germanic linguistic inheritance,
the essay investigates compound and reversed compound words and asks how
extensively new meaningful constructions can be generated from the
existing English lexicon.
Linguistic Combinatorics: Infinity and Human Language
A mathematical and linguistic investigation of whether human language
can truly generate an infinite number of meaningful sentences. Using
combinatorial reasoning, the essay questions linguistic infinity and
distinguishes an enormous potential number of expressions from an
actually infinite human language.
An Adulterous Affair: What Happened Between Him and Her
A fictionalized narrative of a real life experience I had with a Filipina woman 30 years ago. It examines an adulterous relationship through
anticipation, memory, secrecy, and desire. Written in a diaristic style it catalogs the perspectives of the two lovers, and involves the emotional complications
surrounding an illicit affair.
Are Our Devices Becoming Sentient?
An examination of increasingly autonomous communication among computers,
phones, and neural-network systems. The essay considers whether
sophisticated machine-to-machine interaction represents genuine sentience
or merely creates the appearance of independent intelligence.
Are We Really Finite?
An exploration of the boundary between finitude and infinity, asking
whether finite individuals and objects can participate in processes that
are effectively continuous or unbounded. The discussion moves through
production, networks, reproduction, mathematics, and theoretical physics.
