
Fractal Mathematics and Jungian Archetypes with Harry Shirley Dr. Harry Shirley is a chemist with a deep interest in Jungian psychology. His paper The Buddhabrot and the Unus Mundus: A Qualitative Exploration of Fractal Patterns and Archetypal Symbols ...
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Once you learn what a fractal looks like and how it behaves, I think actually we see fractals everywhere. Self similar repeating patterns seem to be the way that the universe and nature creates order. So the spiraling of galaxies, the shapes of plants, the shapes of coastlines all seem to mirror fractal dynamics.
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Thinking allowed.
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Conversations on.
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The Leading Edge of Knowledge and Discovery with psychologist Jeffrey Mishlove.
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Hello and welcome. I'm Jeffrey Mishlove.
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Today we'll be exploring mathematical fractals and Jungian archetypes.
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My guest is Dr. Harry Shirley, a chemist with an interest in Jungian psychology.
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His paper the Buddha Brot and the.
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Unus A Qualitative Exploration of Fractal Patterns and Archetypal Symbols was published this year in the International Journal of Jungian Studies. Harry is based in the United Kingdom. And now I'll switch over to the Internet video. Welcome Harry. It is a pleasure to be with you today.
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Thank you so much for inviting me here, Jeff. It's a real pleasure to get the opportunity to talk to you today about my work.
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Well, you have a very unusual background. I'm not aware of anyone else with a doctoral degree in chemistry who has bright into Jungian psychology. Can you describe what pulled you in that direction or in those two directions?
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Well, I guess it can look unusual on the surface, but I wonder if the first half of everybody's life is focused on kind of egoic pursuits using the rational mind. And that was very much what I was doing. I was scientist focused on organic chemistry and then I think, you know, perhaps the second half of life, or maybe I'm not quite there yet. I've become much more interested in the subjective aspects of reality. And somehow for some reason I was really drawn to Jungian psychology. As soon as I learned about Jung's core concepts, I was immediately gripped and it changed my view of everything. I think for me Yong was right about lots of things and for me he's kind of been forgotten. We talk about Jung at kind of the outskirts of society. We don't. He's not integrated properly into modern academic thought, especially in psychology. But for me, Jung was something I had to explore. How it came about, I don't know. But as I say, I think it's to do with the different sides of the brain becoming important at different stages of life.
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Well, that makes perfect sense. And I do know Jung is almost never taught in any depth in colleges and universities. Of course, his mentor, Sigmund Freud, who once had a stronger role within academia, is also largely ignored these days. I think it's fair to say probably depth psychology in general is out of favor, at least in academia.
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Well, it's ironic in a sense, because I think Freud and Jung's work both point to the idea that the ego wants full control, control and how the ego can actually reject the unconscious, can reject the irrational. So I wonder if modern academia is simply a reflection of egoic rationalism. And in fact, maybe Freud and Jung perhaps could have anticipated that their work wouldn't have been as easily accepted as they had hoped because of the very findings that they came across.
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Freud, for one, certainly was very clear in his concept of defense mechanisms that we don't want to know what's in our own mind.
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Yeah, I think lots of people are scared of the unconscious for good reason. There's a hell of a lot of danger there. We have the dangers of psychosis, schizophrenia. It's much greater and more powerful than we are. So one should be scared of the unconscious. But it's like a snake bite. It's the poison, but it's also the great transformative power to heal us.
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You began your career in chemistry, so I'm assuming that means you have a very strong mathematical background.
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I wouldn't say really strong, but yeah, parts of my degree and PhD were mathematical, but lots of my chemistry was quite hands on. I was mixing potions together in the lab and. And it wasn't all as. As purely mathematical as it might seem. Some parts probably slightly more alchemical or mystic than perhaps I'd like to admit. But yeah, yeah, definitely. Lots of my training was. Was mathematical.
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It is true, as you point out, that chemistry had its origins in the ancient art of alchemy, which was deeply imbued with symbolism. And Carl Jung himself took a very deep interest in alchemy.
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Yeah, absolutely. There's a huge amount of mystery still surrounding the alchemists and what exactly they were doing or trying to achieve. But from a Jungian Point of view. Yeah, the alchemists were projecting their unconscious content onto matter and, and it became alchemy, in, in a way is a metaphor or a symbol for inner transformation. So the kind of the, the acquisition of the philosopher's stone or the creation of gold from lead, really what that is a symbol for is, is, is finding the self. So the higher self, the true self. That's really what alchemy was, was all about. And Jung saw that because Jung saw lots of his patients produce dream imagery that was strikingly like alchemical emblems. And some of your audience may have gone through this themselves as I have lots of my own dream is images and symbols I've been able to track to alchemical imagery as well. So there's definitely something going on there. And Jung being a genius, was able to see this straight away.
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Now that you've described your background in chemistry as having some aspects of it that are akin to alchemy, it makes much more sense to me that you might be drawn to Jungian psychology.
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Yeah, absolutely. In fact, my PhD was a part of organic chemistry called total synthesis, where you take inexpensive starting materials, so things that are derived from petroleum, often and over many, many steps you transform them into a valuable end product. It'll often be a chemical that's perhaps got anti cancer properties or something like that, which is strikingly alchemical. It's taking something of no value like lead and turning it into something that is healing. So I really do wonder, of course we'll never know for sure, but I wonder whether really my PhD was a warm up to the latter stages of the second half of my life where it won't be focused on matter, it will be about an inner psychic transformation which is very much akin to my PhD. Very interesting parallel.
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If we talk about fractal mathematics, of course that's a little different than alchemy. It's much more Platonic, one might even say abstract in that sense. But the realm of mathematics and the realm of Jungian archetypes seem to me to be related.
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But it's interesting that you think of fractals as abstract because we really perhaps shouldn't think of fractals like that because once you learn what a fractal looks like and how it behaves, I think actually we see fractals everywhere. Self similar repeating patterns seem to be the way that the universe and nature creates order. So the spiraling of galaxies, the shapes of plants, the shapes of coastlines all seem to mirror fractal dynamics. So for me in fact, and the same Goes for Benoit Mandelbrot, who discovered fractals. Fractals are the way that nature creates geometry. So yes, we can call them abstract, but they also seem to be intimately related to matter.
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As I recall, the great Nobel laureate physicist Eugene Wigner published a paper on the unreasonable application of mathematics in general to the physical world. He was amazed that the mathematical abstractions used by physicists seem to predict so precisely the results in the physics laboratory.
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Science has used mathematics very well. It's been able to use mathematics to predict, let's say, predict and model the behavior of matter. So we're used to thinking of numbers as these cold logical tools that scientists use. But if we zoom out a bit and look at the bigger picture, we've had a relationship to numbers, to mathematics for millennia. And our relationship with them hasn't always been cold and calculated. It's been psycho spiritual. And like I've said, we see fractals around us lots. We see it in, see them in plants and coastlines, but also walk into churches and temples and cathedrals. You will see self similar recursive patterns. And for me, that's striking evidence that fractals themselves could potentially be a Jungian archetype. Think of that as fractals, as a Jungian archetype, an actual component of the unconscious mind. Why hasn't this been said lots before? As you've seen, there are a few articles out there, there's been a number of people kind of proposing that fractals do psycho spiritual relevance. But we quote Jung lots and Jung died in 1961 and fractal mathematics weren't formalized until the 80s. So had Jung seen the Mandelbrot set? Had he seen the Buddha Brot? I wonder whether Jungian psychology would be in a different place right now.
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Well, Harry, I think for the benefit of some of our viewers who have not heard these terms before, Mandelbrot and the Buddha broat and fractals. Let's begin by defining each of these.
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Sure. So a fractal in a broad sense is a type of mathematical image and it's self similar and repeating at different scales. It's like a fern leaf. So if you look at a fern leaf, you have obviously the main shape of the leaf, but if you look at a branch coming off the main part, it's actually also just like a fern leaf. But actually if you keep zooming in further, you'll see one of the parts coming off the branch is also shaped like a fern. We can keep zooming in like this for some Time. So a fern is a fractal like shape, fractal like image itself, similar at different scales. Really, that's all that a fractal is in a mathematical sense. But the Mandelbrot set is a special type of fractal. It's a complex, complex iterative formula. What we mean by complex is very simply it's composed of real numbers. The numbers that we're all very familiar with, you know, 1, 2, the natural numbers if you like. But it's also got an imaginary component, let's not go into this in too much detail, but essentially an imaginary number is composed of or related to the square root of minus one. So it's like a different realm, if you like, of numbers with different behavior and non natural mathematical behavior, if you like. Basically the Mandelbrot set is a very simple iterative formula that was discovered in the 80s and it's a fractal, so it's self similar at different scales. Now we'll probably share an image of the Mandelbrot set and many people have seen it already. It's very well known. In fact, it's one of the most astonishing mathematical discoveries. The reason why it's so astonishing is, as I say, it's a very, very simple formula. Really simple. But we can zoom in for infinity, we can zoom in an infinite amount of times, and at the border we have these amazing fractal mandala type shapes that keep repeating again and again and again. The Mandelbrot set is quite intriguing because it also contains lots of physical constants, contains PI, it contains the exponential E, and it also contains the Fibonacci sequences. So when we look at the Mandelbrot set, it echoes something familiar to all of us. And another intriguing aspect of the Mandelbrot set is how it's already been intimately tied to psychedelic experiences. Many psychedelic users report seeing fractal like imagery that is strongly reminiscent of the Mandelbrot set itself. So there's already this link between the Mandelbrot set, the patterns we see in nature, which is what Mandelbrot himself was discussed. He published a book called the Fractal Geometry of Nature. He was discussing how fractals appear in matter and life around us. But the connection that Mandelbrot didn't make was the connection between the Mandelbrot set and perhaps the fractal organization of the mind. So he saw the outer. And I guess my work is about seeing the inner relevance of the Mandelbrot set.
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And you also mentioned the Buddha Brot set, which I guess is a subset of the Mandelbrot. In fact, the name is obvious, a takeoff on Mandelbrot's actual name.
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Yeah, well, actually, it's really important to know that the Buddhabrot is actually just the Mandelbrot set. We shouldn't really even call it a subset. It's the same mathematical equation, but it's just about how we visualize it. There's lots of different ways that we can visualize the Mandelbrot set. We've got the traditional way. The traditional way to visualize the Mandelbrot set is with this black center region and the black head. What we're doing in the traditional visualization is we're just viewing the pathways within the equation that remain bound. So they Perhaps go to 202 million, 3 million, 4 billion, but actually they return to zero. Some of the pathways within the Mandelbrot set are not bound. What we mean by that is actually they escape to infinity. The Buddha Brot simply tracks those paths within the Mandelbrot set that fly off to infinity. So it might go to 2, 2 million, 4 billion, 5 trillion, and eventually it's flying off to infinity. We're simply tracing those pathways to infinity. So is actually just the Mandelbrot set, but it's a. It's a. It's an. It's an alternative way to visualize it that Mandelbrot himself didn't actually do. It wasn't until 1994 Melinda Green was the first person to sit down, and she just was intrigued to know. These paths that go to infinity, I wonder what they look like. And by pure chance, she found that 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.
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Now, your article that was recently published in the Jungian International Journal of Jungian Studies refers to the unus mundus, which is important concept in metaphysics in general and in particular in Jungian psychology. So I'd like you to define that term as well for our viewers.
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So unus mundus is an alchemical term that Jung refers to in his collective works numerous times. It's the alchemical idea of a complete, united realm where matter and mind are no longer divided. You can think of it as an underlying, united, unified reality, but it's not. It's not as an archetype. It's not restricted to alchemy. The archetype of the Unas Mundus can be seen in lots of spiritual systems. In Hinduism, I compare the unus mundus to the idea of Brahman kind of this formless realm before creation. In Chinese philosophy, we might call it the Tao. In Christianity, we might call it the Godhead. So it's not. It's not the Father, it's not the Holy Spirit, it's not the Son, it's all three. It's everything unified together. In Hollywood. In Hollywood, we might see the archetype of the unus mundus in the Matrix, the idea that there is an illusion, there's an egoic illusion, and behind that there is a formless realm where mind and matter are one and the same. The interesting thing that the Matrix does is it brings in the idea of numbers. And that was also what Jung thought about. He felt that the idea of the unus mundus, or sometimes what he refers to it, is the psychoid. So the psychoid within Jungian thought is the psychoid realm is in between the unconscious and matter. And this relates to lots of his work with Pauli, where they both felt that archetypes aren't just related to the inner world, but the psychoid is where the inner archetypes, so perhaps the ordering principles of the mind actually begin to relate to the outer world as well. So the psychoid is this intriguing layer between mind and matter. So what did Young think the psychoid was composed of? Well, he didn't know for sure, but he had a strong intuition, as did Pauli, that the psychoid was intimately related to numbers, because Jung saw numbers as the primordial archetypes. He thought that if you strip everything away from an archetype, eventually you're simply left with number. He also felt that numbers were the primordial ordering principles of the mind, and therefore intimately related to the idea of the self. For Jung, the self was really just the ordering principle of the mind. There's an intriguing link here to fractals before they were discovered, because Jung was very interested in mandalas. He felt that mandalas actually were symbols that emerged spontaneously as a way for the unconscious to compensate for chaos, for perhaps psychosis, or just complete disarray in patience. And he felt that mandalas were actually representative of the ordering principles of the mind. He felt that they were perhaps related to the ordering of the self. And mandalas are fractal, like they have geometric portions. They're related to quaternity, self similar patterns. So Jung actually himself had already made the connection between the self, mandalas, the psychoid, numbers. But of course, Fractal mathematics wasn't discovered until, you know, wasn't formalized until 20 years after he died. And for me, fractal mathematics, the Buddha brought is the missing link. And I'm very biased, of course, but I would love to see Jung's reaction to the Buddha Brot. I wonder whether it would sweep him off his feet and he would think, this is it. This is the ordering principle of the self. So, yeah, that's the unus mundus and its connection to my work and Jung's ideas.
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You have a graphic that shows many different iterations of the Buddha brought superimposed on other. Because, as you point out, it's self similar, it keeps expanding infinitely, but yet if you superimpose the different patterns, it begins to take a shape. It does look like a Buddha or a deity of some sort, perhaps in a meditative pose.
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Yeah. Many cultures and spiritual traditions seem to have intuited the Buddha brought. We see the Buddha brought as an archetype. I see the Buddha brought as an archetype, an aspect of the mind that spontaneously emerges in cultures in the same way that a mandala does. So that's why I see the Buddha brah echo many different types of art form across the globe, across time. But we shouldn't just really compare the Buddha brought to random pieces of art. Like, eventually you're gonna find a match. Right. What we should be doing is looking at art that seems to art or aspects of culture that seem to be an exploration of the unus mundus or a related concept. You know, what were when ancient mystics were kind of grappling with this idea of this unified reality? What were they drawing, what shapes and patterns? And that's where we come to the tree of life motif. This is really an archetype, if you will. It's something that Jung identified. And it's related to the idea of the axis mundi, essentially. The axis mundi is very similar to the idea of the unus mundus. It's related to the interplay of mind and matter and how perhaps they both evolve over time. And we have the idea of this ascent up the tree of life towards God or unity, etc. There's really the evolution of consciousness over time. Something striking for me was how tree of life motifs are from across the globe. So Mayan, Indian, European, Egyptian, Persian, many of them, time and time again, appear to echo the patterns of the Buddha bro, in particular, up the vertical axes of the Buddha brot. It's as though ancient mystics were able to Intuit the fractal forms of the Buddha brah. And perhaps then the Buddha brought is the organizing component of the psyche. It could potentially be intimately related to the idea of the psychoid, of the unus mundus. So there's the possibility here that the Buddha brought is very important, not just psychologically, but also to the organization of matter.
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Carl Jung had a deep relationship with the physicist Wolfgang Pauli in which Pauli had a series of dreams. In those dreams, a wise figure came to him and began explaining the relationship between the physical world and the mental world and used an image similar to what you described earlier of the conjunction of the normal number plane with the imaginary number plane and suggest that that's where they come together.
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Well, this is where I get goosebumps, because I had been going through my work, exploring my ideas with the Buddha brought. I didn't realize that Pauli had had these dreams. And as soon as I've realized that Pauli had these dreams related to imaginary numbers, complex numbers, but also lots of dreams related to rotation, self similarity, it's as though Pauli's dreams were a reflection of fractal mathematics. Yeah, for me that's, you know, it's not empirical evidence, but for me it's striking symbolic evidence that I might be on the right path here. Yeah, absolutely crazy. But when I found that, I was very surprised.
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And the idea that mathematics itself is what underlies both the mental and the physical worlds is something that goes back to Plato and Pythagoras.
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Yeah, absolutely. But the only thing they didn't have was fractal mathematics. We have the idea of Platonic forms, these perfect spheres and these perfect cuboid shapes that, although they're pleasing to the eye, are not an appropriate description of reality. They simply didn't have the computational power to see. To see things like the Mandelbrot set, which is why we had to wait until the 80s to really understand. But, you know, we're now in 2025, and I think there's still been a significant delay in the scientific and the psychological fields in really grappling the importance of fractal mathematics. But, yeah, I think Plato on the right path, but didn't have the computational power. It's no criticism, it's just. Yeah, it's a technological limitation.
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Now, I'd like to go back to what you were describing earlier. You referred to the Tree of Life as image that appears in many cultures. I'm aware of some of those. I have Islamic ceramics, for example, that depict the Tree of Life as an actual tree. On the other hand, in the Jewish Kabbalah you have an image called the Tree of Life. It doesn't really exactly look like a tree at all. It supposedly represents the 10 emanations of the deity, different from the Greek or Hindu pantheons, actually. And it's a geometric image. But I assume that when you refer to the Buddha Broat as resembling the Tree of Life, it actually resembles both of these.
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Yeah, absolutely. I think the Tree of Life is just a broad description of an ascending fractal like concept for the emergence of duality, the resolution of duality towards complete unity with, with God or, or the Tau or, or Brahman, the union of, of Shiva and Shakti. And, and for me, really, the shack, the chakra system is, is really a Tree of Life archetype as well. It's simply projected onto the body. And in fact, this was one of my first insights into the Buddha bro. I, I saw, I saw the Buddha brah and I saw the third eye of the Buddha brah and I decided to zoom in and I noticed that the third eye of the Buddha brat was geometrically very similar to how the third eye is described in the ancient Tantric text texts. And I thought to myself, what kind of a coincidence is this? It looks like a Buddha, but it's also echoing the chakras. So, yes, any, lots of spiritual systems, anything that seems to be related to the interplay of mind and matter, or heaven and earth, or body and spirit, or masculine and feminine, as we see in alchemy. Lots of these again and again resemble the Buddha Brot. So there's alchemical emblems that kind of ways of symbolically depicting the philosopher's stone. They have this ascent in a similar way to the chakra system. These as well appear to echo the Buddha Brot. There's always this idea of masculine and feminine intertwining, like Shiva and Shakti, as they ascend towards unity. All of these types of ideas time and time again echo the Buddha form.
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In your article that appeared in the International Journal of Jungian Studies, you compare the Buddh image to many other classical images that resemble Jungian archetypal patterns.
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Yeah, absolutely. So we don't just stop at things like the Tree of Life. We can go further. So we need to think about other art forms that might be related to the interplay of mind and matter, or more symbolically, heaven and earth. And then we can look at perhaps larger structures, for example, St. Peter's Basilica, the Vatican, which is a symbol for the unity of earth with heaven. It's supposed to be a place where, you know, God is united with earth. Of course, that's intimately related to the idea of the unas mundus. And then I see that we can trace the Buddha brought onto the geometric shape and proportions St. Peter's Basilica. We can even perhaps see traces in Stonehenge and other ancient sites as well. For example, ancient Hindu temples, the gates of Petra can all be seen to embody the proportions and shapes of the Buddha brah. But another art form as well, but of course is related to the interplay of mind and matter, is psychedelic art. The psychedelic experience has always been intimately tied to fractal shapes. I'd say as well, the psychedelic experience is also intimately tied to the psychoid, to the idea of the unus mundus. We often talk about the idea of entering this different realm or being able to see consciousness. In matter, things come alive, right? We look at a clock and it starts talking to us. This is simply the merging of mind and matter. And therefore. Well, I'm not surprised that psychedelic art, therefore time and time again seems to echo the fractal forms of the Buddha brah. In fact, for me, psychedelic art is characterized by the Buddha Brahmin. We often have these spiritual images are often about this ascent from kind of a circle type form to duality to at the top, often something related to complete unity. And for me, a big turning point in my work was some psychedelic art doesn't just trace the the Buddha brought. Actually, when you overlay them with the Buddha brot, the accuracy of the alignment appears to be statistically significant. Though I haven't done statistical tests just from viewing it. The alignments are mind blowing. So, yes, we see the Buddha bro, echoed in lots of different art forms, not just ancient.
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A lot of this goes back to Pythagoras and his mathematics, where he talks about how you start out with the one, and then the one divides and becomes the two, and then the two divides and becomes the many.
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Yeah, absolutely. And what we're talking about there is the interrelation of numbers to one another. So we should never really teach that numbers can ever be single entities. So in school we teach 1, 2, 3. And this idea that a number can be isolated and trapped, and that's not a reflection of reality. Numbers are these interconnected frameworks within reality. They probably almost exclusively fractal, like in reality. And anything that's not that is probably just a gross approximation. So what you've touched on there though, for me is the symbolic component of number. How we like to think of numbers as kind of logical, cold, logical tools, but number is also, it's about, there's an aspect of it that's a qualitative relationship. How one goes to two, goes to three, goes to four, that, that is symbolic of, of, of individuation, if you like. It's about one complete unity. What Eric Newman might call like the ouroboric stage of psychological development to 2. So the development of the ego duality, right and wrong, good and bad, black and white. But then three is, is, becomes the resolution, the symbolic solution to two opposites. Four is universally, universally thought of as a symbol for stability and groundedness. So numbers are much more than these logical tools. They've always been these symbolic components of our, of our lives. And for me, that's what the Buddha brought is all about. Yes, it's a mathematical image, but it's strikingly symbolic, it's strikingly synchronistic. What are the chances, what's the probability that the Mandelbrot set can churn out something that reflects psycho, spiritually relevant art across millennia in the way that it does? So, yeah, for me, something interesting to explore is this symbolic component of numbers.
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Well, another aspect of numbers and mathematics in general, which has always fascinated me, is their ontological status. In a sense, one has to acknowledge numbers are very real and the sequence of numbers is very real. The sequence of patterns in the Mandelbrot set is very real. And yet, of course, we can create a video of the unfolding geometrically in time, but for the most part, these pure mathematics exist outside of time and space. And yet they're real.
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Yeah, absolutely. And I think that's why they're so important in a Jungian sense, because they are related to timelessness, to the eternal, to something greater than us. And I think that's why numbers, for me, why numbers are intimately related to the self, I think in a strict Jungian sense. I do think, I do believe that the self is something we can never fully grasp. But for me, the closest we can glimpse at the self is through numbers. And then we start to think, what are numbers? As you've kind of touched upon, they're definitely not things that we invented. They seem to be things that we discovered and they were there before us. They seem to be, perhaps they are, in a symbolic sense, the tools that God uses to create.
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I gather that the Jungian definition of the self would be the part of us, the part of our psyche that is the closest to the divine.
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Yeah, well, I think it is the Divine. For me, the self is. The self encompasses everything. It encompasses the idea of the eternal, infinite, organizing and directing principle of reality. Jung didn't really talk about the self and how it manifests as matter and in matter. That's all related to his work with Pauli and the psychoid. Yeah, the self is a sense. We could really think of self in a Christian sense. We might call it the Godhead. It's impossible to know the self fully. We can only glimpse it perhaps in dream or visions or perhaps numbers.
B
Well, earlier we were discussing the unus mundus as the organizing principle. I tend to think of it as the ground of being. And I suppose one could say that the self is just about the same as that.
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Yeah, the self and the unus mundus appear to be really related. I think really we can just think of the self as the psychological heart of the unas mundus. Unas mundus is psyche and matter. But perhaps in actual fact, the self and the unas mundus are actually the same thing. Perhaps there is just one organizing principle that is related to both matter and mind. I think Jung uses the self when he's talking purely about psychology and the inner world, and then he's using words like the unus mundus when he's talking about more metaphysical concepts. So I think at one point it just becomes nomenclature. It just becomes we've got different names, and perhaps we need a new system, new names. Perhaps we. Perhaps I need to create a new. New terminology for all of this. But, yeah, the self is the organizing principle of the mind. The unus mundus appears to be kind of related to perhaps the formless or the formless realm before creation.
B
It sounds very similar to the Hindu concepts of Brahman and Atman.
A
Yeah, absolutely. I think Brahman, Brahman, we can equate to the unas mundas and Atman to the self. Yeah, I think that's probably accurate. And then what do we do with Shiva and Shakti? Well, Shiva is. Seems to be related to form and pure consciousness. So for me, Shiva is. Is. Is related to. Really related to the idea of the Buddha brought. It's the first form from. From Brahman, from formlessness, from the void. And then Shakti. Shakti is a tricky one. I think she's kind of the irrational component of reality, the thing that can't be expressed in number, perhaps, but she's related to the ascent. So whether that's in Hinduism, in Tantric, in Kabbalah, there's always an ascent. And that's for feminine. That's the rising serpent. And I don't think we've really grasped what exactly that could symbolize fully, but it's related to transformation.
B
And I gather you can find all of these things in the Buddha broad image.
A
Well, one really interesting thing is how in the Tantric texts they describe, in some versions they describe a small ethereal force form of Shiva being within the third eye. And I was really surprised when I zoomed into the third eye a lot. I did eventually see this little form, this ethereal form. And I thought to myself, is it possible that the ancient mystics were intuiting this little figure I can see in the Buddha brah, who knows? Who knows? But yeah, the Buddha brought does seem to echo, echo the Tantric descriptions of the chakra systems and where kind of Shiva may be symbolized and where Shakti unites with Shiva, these important parts of the system, all of that.
B
Well, Harry, surely this has been a very exciting and adventurous discussion. I gather that you've received a lot of positive feedback from the Jungian community regarding your paper that in a way you're taking Jungian and thought to a new level.
A
Yeah, lots of really nice comments made. A couple of Jungians kind of, yeah, really, really blew their mind a few times. But I'm still in the stage of trying to get my work out there. There's a lot of competition for, for attention online these days. So I'm just waiting for more and more people to come across my work and hopefully I can make a change to the field and we'll see where we go.
B
Well, I'm very happy to be able to share your work with the New Thinking Allowed audience. Harry, thank you so much for being with me.
A
Thank you so much, Jeffrey. It's been really great. Maybe come back one day. Thank you so much.
B
I hope so. And for those of you watching or listening, thank you for being with us because you are the reason that we are here.
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Book four in the New Thinking Allow dialogue series. Charles T. Tart, 70 years of exploring Consciousness and Parapsychology. Now available on Amazon.
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New Thinking Allowed is presented by the California Institute for Human Science, a fully accredited university offering distant learning graduate degrees that focus on mind, body and spirit. The topics that we cover here. We are particularly excited to announce new degrees emphasizing parapsychology and the paranormal. Visit their website@cihs.edu. you can now download all eight copies of the New Thinking Allowed magazine for free or order beautiful printed copies go to newthinkingallowed.org it.
Podcast: New Thinking Allowed Audio Podcast
Host: Jeffrey Mishlove
Guest: Dr. Harry Shirley, chemist & Jungian psychology researcher
Date: October 13, 2025
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.
Fractal Ubiquity ([10:44])
Mathematics as Archetype ([12:12])
Symbolic Role of Numbers ([39:51])
Mathematics Outside Time and Space ([42:36])
Self and Organizing Principles ([44:29])
Parallel with Eastern Philosophy ([46:58])
Buddha Brot and Chakras ([48:25])
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]
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.
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].