Math and Alchemy

Is it possible there might be a connection between math and alchemy, the ancient art of transformation? As alchemy seeks to transform lead into gold, so does math seek to transform lesser truths into proofs through a series of arguments. This mathematical gold is the transformation of these bit-parts of mathematical life.

Handwriting, math, and the psyche

An intimate way that math is connected to psyche is through handwriting. Handwriting analsysis has developed to show definite personality traits. If one looks at the curves and lines of handwriting as mathematical graphs, one can see that handwriting is also connected with math. Therefore, math --> graph --> handwriting <-- personality and psyche.

Concepts and Ideas

Concepts are groupings of phenomena and relationships in a given category and is similar to a general idea - which is an abstraction from several specific ideas. A concept has structure in that things are either contained by extensions to the concept or not.

Concepts can be blending by structural mapping. A class of conceptual blends are metaphors.

Metaphor and Structure

How does metaphor add to structure? Metaphor can replace certain ideas with other ideas for which there is a well-understood symbolization (WDMCF p. 375) Structure can be stable, real, and precise. Next, what is the relationship of metaphor to concept and concept to idea?

Structure and the Psyche

What is the notion of structure in psychic process? Part of structure consists of adequate explanations of why things are the way they are and how they came to be. In religious thought, this is termed cosmology and cosmogony. Of particular interest in this blog is the question of how math might be of aid in structuring the psyche in ways that psychological symbols might not be able to.
Since explanation often comes from reflection, aspects of math that promote reflection seem specially important. Some of this comes from breaking apart an issue and asking what are the limits and implications of it. The graphs of circulant matrices (see post on the Tao) are like broken mandalas whose pieces are able to catch the reflections of many different issues.

Math versus psychological symbols

How is math different from psychological symbols? Both are elements of the psyche. One hint comes from the book "Where Mathematics Comes From" (WMCF), where we find that math is stable, precise, generalizable and consistent within each of its subject matters. It is also creative and open-ended by its ability to use conceptual metaphors and blends to create new forms.
Psychological symbols, on the other hand, can change or even lose their value and meaning. Play and active imagination are then required to find those references again. Psychological symbols may also be fuzzier, less generalizable, and more difficult to blend into new forms as they are often specific to a culture. Symbols' main advantage lies in being able to convey a much larger feeling component, however, than math. It is hard to imaging a national flag with an equation on it, for example!

The Middle Way and Math

Mathematical ideas are sometimes thought to be transcendental - existing independently in a world of pure thought. How is it that equations and concepts enter into the world of dreams, then? Are certain mathematical ideas favored by the psyche, especially when it is at play and not searching for the solution to a particular problem?
Assuming the psyche is attempting to find its' way to wholeness, how does math relate to this?
An article of mine A Mathematical Journey from the “Middle Way” to the Circle describes some ideas of how the Tao, math, and wholeness (and therefore Psyche) can be related.

Where Math comes from

An interesting book on Math and the mind is "Where Math Comes From: How the Embodied Mind Brings Math into Being" by Lakoff and Nunez. The approach of the book is to illustrate the different types of metaphors which generate and capture mathematical concepts. The book is cognitive in emphasis and it might well be interesting to ponder the similarities and differences between cognition, embodied mind, and psyche!
Metaphor seems to fit more with cognition as there is a bit more focus and intention with metaphor. Psyche, on the other hand, has its symbols and not so much metaphors. Is there a reason for this? I still think the book is useful to those who may want to know more about the connection with psyche as psyche is pretty close to the embodied mind (and what about subtle body?).
The title can also be reversed and one can ask, "Given Math, how does it influence the Embodied Mind?". Such an approach would be useful in working with math in an active imagination session in analysis.

Shape, Form, and Pattern

From the Wikipedia, shape is the two dimensional outline of a thing whereas form is the three dimensional outline as opposed to the matter contained within it. How do shape and form relate to order and structure? Order seems to be a repetition of shapes and structure is more often a repetition of forms. I think of order and pattern together, but pattern can be a repetition of shapes or forms.

Psyche, Order, and Structure

Before I begin, I would like to comment that the blog format really helps get ideas moving, as it seems to be less constricting than trying to write for a journal or book, but a little more demanding than just note-taking.

I reviewed some Jungian models of the psyche and found that the common view of the psyche involves the collective and personal unconsciousness as areas of chaos and consciousness as an area of order. The issue of structure initially is taken to be the boundaries between these areas and the ego. Going a little farther into Jungian analysis, we find symbols are the structures which connect the subconscious to the conscious and provide a sense of living order in the psyche, hence Jung's emphasis on symbolic interpretation of dreams. This order is not a static order as it is not a collection of facts but living references to important life issues.

Structure and order are very close to each other in meaning but structure seems imply support and being able to grasp where order is more of a reference to the rate of chang - a sense that things are static and not flying about in a state of chaos. A set of blocks stacked together can be ordered by any number of characteristics (size, color, shape, etc.) , but may not provide much support. And a framework can support weight but not be very ordered - for example, a tree can support a treehouse but is less ordered than the beams in a building. How would one select symbols to support versus order the psyche? Is support better than order? Does structure also shelter or provide containment? In many cases, yes.