OUR COMMON HOURS

The Golden Ratio

Back in middle school art class, we learned about something called the “golden ratio.” It is basically a mathematical concept where two given numbers follow this basic rule: the ratio of the sum of the numbers to the larger of the two numbers is the same as the ratio of the larger number to the smaller number. The ratio is typically represented by the Greek letter phi (φ) and is equal to approximately 1.618.

It gets really interesting when Fibonacci is involved. In the Fibonacci sequence, the first two numbers are 0 and 1, with each subsequent number being the sum of the previous two. For example, the first ten numbers in the sequence are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34. Using this series of numbers, and creating arcs in each rectangle, one can create an approximate logarithmic spiral (though not a true logarithmic spiral, which involves a lot of mathematics that I don’t understand, though I really wish I did!).

So this:

Gives you this:

Which in turn can be found throughout the universe…

…even in your ear! Amazing!

Seven times around the sun.

On October 26, 2003, Lillia Nora was born.  And, in that moment, all the hopes and dreams of a lifetime began.  My love for her is infinite and true.  May she have many more trips around the sun.

Layers of Being

Last night I was reading an article in the July/August 2010 issue of Scientific American Mind, titled “Me, Myself and I.”  In this article, the author, Dr. Uwe Herwig states that human beings experience “Layers of Self-Awareness” (Herwig, 2010).  Dr. Herwig writes,

“To begin with, there is the ability to recognize one’s own face and body and to know what those body parts are doing at any given moment.  There is also the sense of ownership–you perceive your body as belonging to you–and the sense of agency: you feel responsible for your own movements and actions.  And at the highest level, there is the awareness of one’s own emotions and the ability to link disparate life experiences to a stable self-image.” (Herwig, 2010)

I was instantly reminded of Rudolf Steiner’s fourfold human being; the four bodies being the physical, etheric, astral, and the ego or “I”.  (I don’t have a source for the following material, other than my own knowledge based on various conversations with others.  My daughter attended a Waldorf school for kindergarten, and I took a year-long professional development course for early childhood educators that dealt, in part, with Rudolf Steiner’s philosophy, otherwise known as anthroposophy. )  According to Steiner, the physical body is simply that–a physical body.  For me, it was helpful to compare these bodies to something, so I will do that here, for illustrative purposes.  So, the physical body is what we share with all the inorganic material in the universe.  For example, we share the characteristic of the physical body with a rock.  The etheric body is the life force.  We share the etheric body with plants.  So, plants have both a physical body an an etheric body.  They have form, and they are alive, whereas the rock is not.  The astral body is the body of impulses and desires.  We share the astral body with animals.  The astral body is somewhat linked to instinct.  The last body, the ego or “I”, is something that, Steiner asserts, is something that human beings alone can possess.  Human beings, unlike animals, can regulate their impulses and desires, and this is done by the ego.  This table, which I stole from http://www.kheper.net, is particularly helpful:

I see a strong connection between what Rudolf Steiner says about the four bodies, and what Dr. Herwig is saying about the Layers of Self-Awareness (and, for that matter, what Freud says about the Id, Ego, and Super-ego, which I will discuss in a minute).  Herwig’s, “ability to recognize one’s own face and body” is very similar to Steiner’s “etheric body”, his “sense of agency” can be compared to Steiner’s “astral body”, and his ” awareness of one’s own emotions” could be connected to Steiner’s “I”.  I find it so fascinating that all of these people (and many more) are saying exactly the same thing, just in different ways.

For example, Freud talked about the “Id” or “pleasure principle”, nothing more than a mass of instincts and impulses (sounds a lot like the astral body to me).  Of the next level, the ego, Freud writes, “The ego represents what may be called reason and common sense, in contrast to the id, which contains the passions” (Freud, 1927).  This is very similar to Steiner’s “I” and Herwig’s “awareness”.  Freud also discusses the “Super-ego”, which is a sort of overlord that punishes the “self” for its misdeeds.  I don’t see any connection to either of the other works in this regard; I believe this aspect of the theory is one of Freud’s more strange personal demons.  To me, it seems like the force at work in the Super-ego is actually just a human emotion–guilt–which has come to the forefront of consciousness through the Judeo-Christian moral tradition.

All of this strikes me as profoundly fascinating.  Of course, I could be more scientific, but I am not a scientist.  I am trying to find a connection that rises above reductionism.  So, the fact that three men, from very different backgrounds, developed theories of “self” that are very similar leads me to believe that there is some kernel of truth hidden in all three theories. I can see how Steiner is undoubtedly saying very much what Dr. Herwig and Freud were saying, just using a different vocabulary and different imagery in order to create the same basic picture of the multi-faceted “I”.  I’m looking forward to exploring this further, and perhaps creating some kind of chart that will illustrate not only these three theories, but the many others that exist, and try to find how they compare to one another.

Herwig, U. (2010, July/August). Me, myself and i. Scientific American Mind, 21(3), 59-63.

Freud, S. (1927) The ego and the id (J. Riviere, Trans.). London: Hogarth Press. (Original work published 1923).

Who shoves whom around?

Last night, I started reading Doug Hofstadter’s book, I Am A Strange Loop.  I am now on the 4th chapter, and all I can say is that this is the book I NEED to be reading right now.  In his book, Hofstadter discusses a topic dear to my heart, at least as of late: do our thoughts/feelings/desires control the processes in the brain, or is it the other way around?  Are we nothing more than a series of neuron impulses, or is there something greater, more profound, at work?  According to Hofstadter, at least as far as I’ve read, the answer is actually “yes” to both.  He provides several analogies to support this theory, and I will do my best to relate, with as much accuracy as possible, what he wrote.

First of all, he says, imagine a frictionless pool table covered with thousands, maybe millions, of tiny, magnetic marbles (which he calls “simms”).  The simms “bash into each other and also bounce of the walls, careening about rather wildly in their perfectly flat world” (Hofstadter, 45).  If the simms collide at a low velocity, they stick together (due to their magnetic quality) and form “simmballs” (clever pun, no?).  The simmballs are not only influenced by the movement of the simms, but more particularly by movement that happens outside the surface of the table (breezes, knocks, etc).  The movements are then internalized by the simmballs.  This is all related to brain function, as Hofstadter writes, “Such internalization of the outer world in symbolic patterns in a brain is a pretty far-fetched idea…yet we know it somehow came to exist, thanks to the pressure of evolution.” (Hofstadter, 46).

Now, if one were to look very closely at this table (reductionism), all that REALLY matters are the simms.  After all, the simmballs are simply balls of simms.  So, this would be something akin to particle physics (which I know pretty much nothing about, nor do I need to, in order to understand Hofstadter’s analogy).  A physicist might say that the simmballs are epiphenomena*, meaning “they are undeniably there [but] they are not essential to an understanding of the system…” (Hofstadter, 46).  The physicists are certainly right.  But, the problem with this “enormous escalation in complexity…[is that] we are condemned to seeing only untold myriads of particles…there are no natural sharp borders in the world.” (Hofstadter, 47).  Another way to describe this problem would be to say that, when reduced to the level of particles, or neurons in the brain, nothing has any definition or meaning, which is something that I have struggled with since letting go of the one great explanation for everything that ever was and ever will be, otherwise known as God.  It is so easy to reduce the human being to a collection of molecules, thus negating all meaning and purpose in life.

On the one hand, the fact that I am nothing but a bunch of molecules, and that my thoughts and feelings are somehow derived from neuron activity in my brain, the finale of Hofstadter’s analogy provides some glimmer of hope.  He suggests that we, instead, use time-lapse photography to zoom out from the simm level, and speed up the action, the picture we see is of simballs “richly interacting with each other…triggering other simballs in a kind of ‘logic’ that has nothing to do with the [simms] churning around them…” (Hofstadter, 47).  He continues, writing,

“The simms are still there, to be sure, but they are simply serving the simmballs’ dance, allowing it to happen, with the microdetails of their bashings being no more relevant to the ongoing process of cognition than the microdetails of the bashings of air molecules are relevant to the turning of the blades of a windmill…the windmill will turn no matter what…the ‘thoughtmill’ will churn no matter what, thanks to the symbolic nature of its simmballs.” (Hofstadter, 50).

So, what I have taken from this reading of Hofstadter’s theory so far, is that, on a larger scale, human beings can be reduced to almost nothing.  In fact, on the molecular or atomic level, there is no difference between me, and everything else in the universe.  However, there is more than one way to look at something, and human beings are particularly good at simplifying things.  It has something to do with causality; both the simms and the simmballs are causal forces.  But, in Hofstadter’s words, who shoves who around? That is the bigger question, and the answer will make all the difference.  If we are nothing more than a bunch of molecules interacting, there’s certainly just cause for nihilism.  However, it is possible, and I think Hofstadter is suggesting, that we are something greater the sum of our parts, so to speak.  Updates to follow, as I read more of the book.

* Epiphenomenon, as defined by Merriam Webster, is : a secondary phenomenon accompanying another and caused by it; specifically : a secondary mental phenomenon that is caused by and accompanies a physical phenomenon but has no causal influence itself.

Hofstadter, D. (2007). I am a strange loop. New York: Basic Books.

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