May 29, 2017 | By George Gantz

## Philosophical Speculations on the Meaning of Spirals

According to Emmanuel Swedenborg, the form of a spiral lies at the heart of the created world. While this idea faded into obscurity as the mechanistic worldview of Newtonian physics came to dominate our sensibilities, it is finding resurgence in the science and mathematics of complexity.

Swedenborg’s cosmology was laid out in detail in his defining treatise in natural philosophy, __The Principia, First Principals of Natural Things__ (1734, tr. Clissold, 1846). The __Principia__ is one of Swedenborg’s most important scientific works and predates his spiritual experiences and theological writings. It is not an easy book. For one thing, the language and context is dated to the early 18^{th} century, well before much of modern mathematics and experimental science had been developed. In addition, the work is unique and conceptually dense. A complete understanding would require a deep immersion in the minutiae of his arguments and examples, something few have attempted. The best modern attempt is found in __The Listening Threads__, by Rev. Norman Newton (2000).

Everything starts for Swedenborg with the First Finite, a dimensionless point that embodies both “passive” and “active” attributes. It is active in the sense of a propensity for perfect movement (circular), and passive in the sense of restriction or confinement. Borrowing from ideas in fluid dynamics, the movement observed is thus circular, but with a boundary subject to constraint or friction — and the pathway is that of a spiral. From these “gyres” or “vortices” all phenomena in the created natural world arise.

*“the essence of the point consists in motion… it’s motion is most perfect in its nature… it must necessarily resemble a circular figure… the motion above described must be the perpetually circular… must proceed from the centre to the periphery, and from the periphery to the center… it must necessarily be of a spiral figure…” *Principia Part I, Ch. 2, Sec. 20 and 21)

Rev. Newton represented the concept as spiral figures – as these indicate the motion can be seen as perpetually spiraling inward, and simultaneously perpetually spiraling outward. But he adds the cautionary note, “these are proto-spirals, existing only in conceptual forms. WE cannot speak of geometrical or mechanical spiral form in non-time and non-space.” (Newton p 88.)

The mathematics and observational science of spirals are now far better known than they were in Swedenborg’s time. Some of the modern concepts are highlighted in How Can There Be Order in Randomness? Remarkably, spirals are prevalent throughout the created universe in forms as diverse as wave propagation, galaxy formation, meteorology and fluid mechanics, and the growth of living things.

Spirals also have remarkable mathematical properties, linking together the seemingly diverse concepts of the Fibonacci Sequence, the Golden Ratio, and the number phi (φ). These were highlighted in an earlier post as well.

These fascinating mathematical features and the ubiquitous appearance of spirals in nature raise another interesting question. According to Emanuel Swedenborg’s later spiritual writings, numbers correspond to spiritual concepts in profound ways. So, what is the spiritual significance of spirals? For some speculations on that question, I refer readers to the article I write in The New Philosophy, the journal of the Swedenborg Scientific Association in 2000, “The Spiritual Significance of the Number Phi (φ)”

## 7 Responses to “Philosophical Speculations on the Meaning of Spirals”

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I am still looking forward to a picture of what many have intended, namely a non-terminating spiral. One without a beginning or end, and thus persists without stopping. Swedenborg clearly intended that.

I have some images on http://www.spiralinquiry.org you can check out! But of course no image can possibly capture something with no beginning and no end. I am amused when people (especially well educated experts) throw around the word infinity without really grasping how ineffable the concept is. No mathematician has ever counted infinity. No physicist has ever seen infinity. Yet they talk about it all the time. Cheers!

The orbit of the earth around the sun has no end (yet), yet that does not stop us drawing at least one orbit that goes on repetitively.

Can we see all of the curves on your spiral website (not cut off out of frame), and see if any look like Swedenborg’s description?

On both websites, what you see is what you get. Here is another computer generated image that I like, which repeats inward – we can’t see outward. In the sense Swedenborg is talking about, we are dealing with a perfect spiral where every arc is identical to every other arc— essentially a fractal.

I’ve always been puzzled by spirals in Swedenborg, and struggle to get specific ideas of how they work.

Is there anything about the spiral which tells us the inner limit or the outer limit? Are there such limits? If so, does the motion simply reverse at those points on the spiral? If not, are the mean size and mean density unbounded?

The entry for “golden spiral” in Wikipedia has a nice animated picture of a perfect spiral. https://en.wikipedia.org/wiki/Golden_spiral. There is no inner limit. There is no outer limit. It is as perfectly reversible and symmetrical (and infinite) in three dimensions as a circle is in two – add the fourth dimension (spiraling in space) and you have a true perfect gyre / vortice. I think that is what Swedenborg was describing…..

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