Podcast Summary: Fractal Mathematics and Jungian Archetypes with Harry Shirley

Podcast: New Thinking Allowed Audio Podcast
Host: Jeffrey Mishlove
Guest: Dr. Harry Shirley, chemist & Jungian psychology researcher
Date: October 13, 2025

Overview

In this intellectually adventurous episode, host Jeffrey Mishlove interviews Dr. Harry Shirley, a chemist with a unique passion for Jungian psychology. The conversation dives deep into the surprising interplay between fractal mathematics, especially the Mandelbrot and Buddha Brot sets, and Jungian concepts of archetypes, the self, the unus mundus, and the symbolic foundations of consciousness and reality. Dr. Shirley elucidates how fractal patterns are not only pervasive in nature, but also serve as profound Jungian symbols, possibly representing fundamental organizing principles of mind and matter.

Key Discussion Points & Insights

The Journey from Chemistry to Jungian Psychology

• Career Beginnings ([03:07])
  • Dr. Shirley explains his path: the rational, outwardly-focused work of chemistry (particularly organic synthesis) led him to a personal and professional curiosity about the subjective, unconscious dimensions explored by Jung.
  • "I wonder if the first half of everybody's life is focused on kind of egoic pursuits using the rational mind... the second half becomes much more interested in the subjective aspects of reality." — Dr. Shirley [03:21]

Jung, Freud, and Academia’s Bias Toward Rationalism

• Academic Neglect ([04:42])
  • Mishlove and Shirley note the scarcity of Jungian ideas in modern psychology programs and suggest this may reflect a cultural overvaluation of rational, ego-driven thought at the expense of exploring the unconscious.
  • "I wonder if modern academia is simply a reflection of egoic rationalism." — Dr. Shirley [05:18]

Alchemy as a Bridge

• Alchemy, Chemistry, and Transformation ([07:21])
  • The discussion highlights alchemy as both a material and metaphorical journey: the transformation of base matter into gold parallels the psyche’s journey toward the true self.
  • "Alchemy... in a way is a metaphor or a symbol for inner transformation... the acquisition of the philosopher's stone... is finding the self." — Dr. Shirley [07:45]
  • Shirley describes his PhD research as an "alchemical" process—transforming humble substances into valuable medicines mirrors inner psychic transformation [09:18].

Fractals: At the Intersection of Nature, Mathematics, and Mind

• Fractal Ubiquity ([10:44])

  • Fractals are not just abstractions: "Self similar repeating patterns seem to be the way that the universe and nature creates order." — Dr. Shirley [10:47]
  • Examples abound: spiraling galaxies, ferns, coastlines, and even sacred architecture.

• Mathematics as Archetype ([12:12])

  • Fractals and recursive geometries have long played a “psychospiritual” role in human experience, echoed in religious spaces and sacred art.
  • "Fractals themselves could potentially be a Jungian archetype, an actual component of the unconscious mind." — Dr. Shirley [12:45]
  • Shirley speculates that had Jung lived to see fractal mathematics, he might have integrated these images directly into depth psychology.

Defining Key Terms: Fractals, Mandelbrot Set, Buddha Brot

• What is a Fractal? ([14:19])
  • “A fractal in a broad sense is a type of mathematical image... self similar and repeating at different scales. It's like a fern leaf... you keep zooming in, you'll see it repeats.”
• The Mandelbrot Set ([14:40])
  • A simple formula with infinitely complex boundary behavior, producing mandala-like imagery; intimately tied to both natural phenomena and internal states, as evinced by similarities to psychedelic visions.
• The Buddha Brot ([18:41])
  • An alternative visualization of the Mandelbrot, focusing on points whose trajectories escape to infinity. Its resulting image evokes spiritual figures (e.g., Buddha) across cultures.
  • "The Buddha Brot... suddenly has an image which is immediately evocative of Eastern spiritual drawings of Buddha or Ganesh or other deities." — Dr. Shirley [19:32]

The Concept of Unus Mundus and the Psychoid

• Unus Mundus in Depth Psychology and Culture ([21:14])
  • Unus mundus is an alchemical idea describing a unified reality where mind and matter are undivided; mirrored in concepts like Brahman (Hinduism), the Tao (Chinese philosophy), and the Godhead (Christianity).
  • The “psychoid” refers to the ontological layer where psyche and matter intersect—a realm that Jung and physicist Pauli saw as mediated by the archetype of number.
  • Numbers are not just quantitative but primordial archetypes, “the ordering principles of the mind.” ([22:10–25:30])

Art, Archetypes, and the Buddha Brot

• Fractal Archetypes in Art and Culture ([26:58])
  • The Buddha Brot form recurs across art and religious motifs, particularly in the Tree of Life, axis mundi, and sacred architecture (e.g., St. Peter’s Basilica, Stonehenge, Hindu temples).
  • "Tree of life motifs... appear to echo the patterns of the Buddha Brot, in particular up the vertical axes." — Dr. Shirley [28:43]
  • Psychedelic art shows statistically impressive alignment with Buddha Brot forms, reflecting the archetypal union of mind and matter [36:00].

Archetypal Number, Psychological Development, and Ontology

• Symbolic Role of Numbers ([39:51])

  • Numbers not as isolated entities but as interconnected, fractal-like frameworks; their relationships—one to two to the many—reflect spiritual and psychological processes ("individuation").
  • "Numbers are these interconnected frameworks within reality... almost exclusively fractal-like." — Dr. Shirley [40:10]

• Mathematics Outside Time and Space ([42:36])

  • Numbers and mathematical patterns are real but exist "outside of time and space." This timelessness makes them especially significant as Jungian archetypes.

The Self, Unus Mundus, and Non-Duality

• Self and Organizing Principles ([44:29])

  • For Shirley, the Jungian Self is identical with the divine, the “infinite, organizing and directing principle of reality.”
  • Unus mundus and the Self may be two names for the same archetypal unity.

• Parallel with Eastern Philosophy ([46:58])

  • Brahman (unus mundus) and Atman (self) in Hindu thought; the union of Shiva and Shakti; the rising serpent as an image of psychic ascent.
  • "Shiva is related to form and pure consciousness... Shakti is the irrational component of reality... related to the ascent." — Dr. Shirley [47:24]

• Buddha Brot and Chakras ([48:25])

  • Intriguing correspondences between the Buddha Brot's structure and the chakra system—e.g., an “ethereal form” in the fractal’s “third eye.”

Notable Quotes & Memorable Moments

• On the Recurrence of Fractal Patterns:
  "Once you learn what a fractal looks like and how it behaves... we see fractals everywhere. Self similar repeating patterns seem to be the way that the universe and nature creates order."
  — Dr. Harry Shirley [00:00, repeated at 10:47]

• Alchemy as Psychological Metaphor:
  "Alchemy, in a way, is a metaphor for inner transformation... finding the self."
  — Dr. Harry Shirley [07:48]

• On Fractals as Archetypes:
  "Fractals themselves could potentially be a Jungian archetype, an actual component of the unconscious mind."
  — Dr. Harry Shirley [12:45]

• Discovering the Buddha Brot:
  "When she visualized these paths to infinity, she suddenly has an image which is immediately evocative of Eastern spiritual drawings of Buddha or Ganesh or other deities."
  — Dr. Harry Shirley [19:32]

• Self/Unus Mundus as Organizing Principle:
  "The self encompasses everything... the infinite, organizing and directing principle of reality."
  — Dr. Harry Shirley [44:29]

Highlighted Timestamps

• Dr. Shirley’s background and motivation — [03:07]
• Egoic rationalism and academia’s blind spot — [05:15]
• Alchemy as a metaphor for personal transformation — [07:37]
• Fractals visible in nature and culture — [10:44, 12:12]
• Defining fractals, Mandelbrot set, and Buddha Brot — [14:19, 18:41]
• The archetype of unus mundus and psychoid — [21:14]
• Buddha Brot and archetypal art forms — [26:58, 28:43]
• Fractal archetypes in sacred architecture & art — [36:00]
• Numbers as qualitative, symbolic relationships — [39:51]
• Numbers’ ontological mystery — [42:36]
• Self, unus mundus, and their unity — [44:29, 45:43, 46:58]
• Buddha Brot and the chakras — [48:19]
• Final reflections, community feedback — [49:37]

Tone and Style

Throughout, the tone is thoughtful, intellectually adventurous, and gently speculative—combining rigor from science and mathematics with the openness and depth of Jungian psychology and comparative mysticism.

Conclusion

This episode offers a profound exploration of how mathematical fractals may serve as modern archetypes, bridging the outer world of matter and the inner world of psyche. Shirley’s integrative vision suggests that timeless symbols and organizing principles—once sought by alchemists and mystics—may now be glimpsed through mathematics, art, and the patterns of the unconscious. As Shirley aptly summarizes, “Perhaps there is just one organizing principle that is related to both matter and mind” [45:43].