35. The Principle of Three in Physics and Theology

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Lecture Notes

Main Topics #

Three Universal Constants in Physics #

• Heisenberg’s argument: Physics requires at least three independent fundamental constants of nature
• The three constants identified:
  1. Planck’s quantum of action (h)
  2. The velocity of light (c)
  3. A universal length of atomic order of magnitude (approximately 10⁻¹³ centimeters)
• Measurement systems: All conventional physical systems contain three units (CGS system: centimeter for length, second for time, gram for mass)
• Theoretical implication: Success in combining quantum theory and relativity theory requires accounting for this universal length as a third basic structure

Three in Theology and the Divine Structure #

• The Trinity: The most famous theological example of three
• The three offices of Christ: King, Priest, and Prophet/Teacher
• Three theological virtues: Faith, Hope, and Charity (following Augustine and Thomas Aquinas)
• Three hierarchies of angels: Each hierarchy contains three orders
  • Highest: Seraphim, Cherubim, Thrones
  • Middle: Lords (or Dominions), Virtues, Powers
  • Lowest: Princes (or Principalities), Archangels, Angels
• Within each order: Beginning, middle, and end create a nested structure of three

The Vestige of the Trinity in Creatures #

• Definition: A vestige (vestīgium) is the footprint or trace of divine perfection found in creatures
• Structure of the vestige: Three things appear in every creature
  1. Beginning (principle)
  2. Middle
  3. End (perfection achieved)
• Theological significance: This three-fold structure in creatures represents the distinction of the three divine persons
  • The Son is the “middle person” in the Trinity
  • The Holy Spirit is where the procession of persons is terminated
• Application to attributes: Although God has many attributes, they all have the order of beginning, middle, and end, under which notions they lead us to the three persons

Three in Scripture and Liturgical Tradition #

• Division of the Psalms: Augustine and Thomas divide the Psalms into three groups of fifty
  • First fifty: Psalms asking for forgiveness (penance, fighting against vices and sins)
  • Second fifty: Psalms dealing with good action (advancement in virtue)
  • Third fifty: Psalms of praise (resting in God)
• Three stages of charity: Beginners, middle, and perfect (contemplative) stages correspond to the structure of the Psalms

Three in Natural Philosophy and Ancient Thought #

• Pythagoras: Called three “the perfect number” and saw perfection in every creature as beginning, middle, and end
• Classical mythology: Three fates, three furies, three graces; Jove with three-forked lightning; Neptune with trident; Pluto with three-headed dog
• Aristotle on the Trinity: Thomas addresses an objection from Aristotle’s De Caelo et Mundo, where Aristotle praises God “by this number, namely three”
  • Thomas’s response: Aristotle did not intend to place a trinity of persons in God, but recognized that in all creatures, perfection appears as beginning, middle, and end
  • Therefore, ancients honored God with threefold sacrifices and prayers

Three in Common Usage and Tavern Signs #

• Heisenberg’s observation: Three is the most frequently used numeral in tavern signs
• Examples of three signs: Three Angels, Three Crowns, Three Cups, Three Horseshoes, Three Tons, Three Nuns
• Explanations offered:
  1. Primitive man divided the universe into three regions: heaven, earth, and water
  2. Pythagorean influence on the perfect number
  3. Classical mythological associations

Key Arguments #

The Necessity of Three in Physical Systems #

• Any complete system of measurement requires exactly three independent fundamental units
• While many constants of nature exist, all others can be traced back to three through mathematical relations
• This is “most simply made clear” by observing that conventional measurement systems universally employ three units

The Manifestation of Divine Perfection in Creatures #

• Structure argument: Creatures imitate divine perfection through the structure of beginning, middle, and end
• Why three and not two? A creature’s perfection is not found in its isolated principles (matter and form, each imperfect alone) but only in their joining to the creature’s end
• Nature’s principle: Nature does not join distant things without something in the middle
• Therefore: Creatures necessarily exhibit beginning, middle, and end, representing the three divine persons

The Role of Three in Understanding Completeness #

• Two is insufficient: binary structures are incomplete
• Three provides what is necessary without excess
• This appears across domains because it reflects the fundamental structure of reality itself

Important Definitions #

Vestige (vestīgium) #

• A footprint or trace of divine perfection in creatures
• Distinguished from the “image” of the Trinity (which appears in rational creatures with memory, intellect, and will)
• Found in creatures insofar as they imitate the divine perfection

The Three Offices of Christ #

• Prophet/Teacher: The teaching or prophetic role
• Priest: The sacrificial and mediatorial role
• King/Ruler: The governing and lordly role
• These are shared analogically by bishops, priests, and laity in different ways (following Vatican II)

Perfection (perfectio) #

• One meaning: Whole or complete, lacking nothing of its kind
• Another meaning: Having reached its end or purpose
• In creatures: Perfection consists in the proper ordering of beginning, middle, and end

Examples & Illustrations #

From Physics #

• Planck’s constant and relativity: The two fundamental constants of the early 20th century (h and c) proved insufficient; a third universal length was theoretically required to combine quantum and relativistic theories successfully
• Measurement in centimeters, seconds, and grams: Even students of practical measurement recognize that three independent units are necessary

From Scripture and Liturgy #

• The Psalms structure: The liturgical arrangement of Psalms into three fifties creates a spiritual journey from repentance through virtuous action to rest in God
• The three-fold nature of stages in the spiritual life: This reflects cosmic order rather than arbitrary division

From Mythology and Popular Culture #

• Olympian imagery: Jove’s three-forked lightning, Neptune’s trident, Pluto’s three-headed Cerberus all demonstrate how ancient peoples instinctively recognized three as divine
• Tavern names: The Three Cups (highly popular in London’s City proper), the Three Tons, the Three Nuns in Elder Gate High Street (noted for excellent punch)

From Theological Texts #

• Vatican II documents: On bishops, priests, and laity—each section articulates how the respective state shares in the three offices of Christ in different ways
• Dionysius: Hierarchical structure of angels and the principle that each order contains beginning, middle, and end

Notable Quotes #

“Following recognition of the basic significance of the two universal constants of nature, Planck’s quantum of action, right, and the velocity of light, right, it was natural to ask how many such independent constants of nature there can actually be. Three… the answer is, there must be at least three such universal constants.” — Heisenberg, Across the Frontiers

“The perfection, however, of the creature is not had at once in its principles, in its beginnings, right? Which are perfect, as is clear in matter and form, of which neither has by itself for perfect being. But in the joining of the creature to its end.” — Thomas Aquinas, on why creatures manifest three-fold structure

“Nature does not join things that are a distance without something in the middle.” — Thomas Aquinas, fundamental principle explaining the necessity of a middle term

“No one can glance even casually over a list of tavern signs without observing how frequently the numeral three is used.” — Henry Shelley, The Inns and Taverns of Old London

Questions Addressed #

Why does three appear so universally across domains? #

• Physics: Three independent fundamental constants are mathematically necessary for any complete measurement system
• Theology: Three reflects the divine structure itself—the Trinity—which creatures imitate through their own three-fold perfection
• Popular culture and tradition: Recognition of three as the perfect number appears in mythology, tavern signs, and common usage

How does the vestige of the Trinity differ from merely multiple divine attributes? #

• Although God possesses many attributes, all can be ordered according to beginning, middle, and end
• This ordering itself leads us to the three persons, not the multiplicity of attributes
• The structure (not the content) is what represents the divine persons

Why is Thomas concerned to address Aristotle on this point? #

• The objection: If Aristotle praised God “by the number three,” does this suggest he knew of the Trinity?
• Thomas’s resolution: Aristotle recognized three as perfect because he observed it in creatures’ natural structure, not because he understood the Trinity as three divine persons
• The deeper point: Even pagan philosophers could recognize divine perfection reflected in creation’s three-fold structure, though they did not understand its trinitarian source

How does understanding the role of three aid theological education? #

• Students recognizing this pattern see how different areas of theology (Trinity, Christology, angelology, Scripture) exhibit unified principles
• The principle of three becomes an interpretive key for understanding Vatican II’s teachings on bishops, priests, and laity
• Appreciation for the harmony between natural philosophy (Heisenberg’s physics) and theology demonstrates the unity of truth