Dr. Jillian T. Weiss

Weekend Reading: Godel, Escher, Bach...and Butler

Filed By Dr. Jillian T. Weiss | May 30, 2010 2:30 PM | comments

Filed in: Entertainment
Tags: Douglas Hofstadter, Godel Escher Bach, Judith Butler

I went to the bookstore last night, which is one of my favorite things to do in the whole world. godel escher bach.jpg

I came across a book that fascinated me when I was a kid. It's Douglas Hofstadter's "Godel, Escher, Bach: an Eternal Golden Braid," which came out when I was 18.

I remember reading it, and being completely and utterly fascinated, though I didn't understand much of it.

Godel was a mathematician who proved that any mathematical system must necessarily be built on unprovable elements. Escher was a painter who drew optical illusions that seemed to put elements both on top of, and underneath, the rest of the picture. Bach was the famous musician, whose works often made harmony from elements that were overlaid on top of themselves backwards, upside down and inside out.

It's not a book about mathematics, art and music. Hofstadter was an early computer scientist (and still one, over at Indiana University). It's about how how meaningless elements get arranged into sequences full of meaning that we call thinking and creativity. Its fascination lies in its tying together of a wide range of seemingly unrelated subjects, all of which show how thought and creativity get expressed through elements that, in and of themselves, have no inherent meaning.

It reminds me a lot of the work of Judith Butler on gender.

The book is 742 pages of goodness, filled with mind-blowing stuff about how thinking and creativity relies upon the concept of infinity. Like this:

Mathematicians were among the first admirers of Escher's drawings, and this is escher-waterfall-small.jpg understandable because they often are based on mathematical principles of symmetry of pattern...But there is much more to a typical Escher drawing than just symmetry or pattern; there is often an underlying idea, realized in artistic form. And in particular, the Strange Loop is one of the most recurrent themes in Escher's work. Look, for example, at the lithograph Waterfall, and compare its six step endlessly falling loop with the six step endlessly rising loop of the Canon per Tonos. The similarity of vision is remarkable. Bach and Escher are playing one single theme in two different keys: music and art.

..Implicit in the concept of Strange Loops is the concept of infinity, since what else is a loop but a way of representing an endless process in a finite way?

If you look at Escher's picture "Waterfall" above, and you follow the water with your eye, you see that it is very odd, indeed. It seems to flow upward and sideways at the same time.

Below is Bach's Canon per Tonos. It's the same rising and falling melody on top of itself, but each ending stops on a higher note, until it reaches the same ending note as the first iteration, and continues.

Of course, Lamb Chop's "This Is The Song That Never Ends" does the same thing.

I remember Judith Butler's "Gender Trouble" saying something similar about sex and gender.

"Sex" is an ideal construct which is forcibly materialized through time. It is not a simple fact or static condition of a body, but a process whereby regulatory norms materialize "sex" and achieve this materialization through a forcible reiteration of those norms. That this reiteration is necessary is a sign that materialization is never quite complete, that bodies never quite comply with the norms by which their materialization is impelled. Indeed, it is the instability, the possibility for rematerialization opened up by this process, that mark one domain in which the force of the regulatory law can be turned against itself to spawn rearticulations that call into question the hegemonic force of that very regulatory law.

In English, this means that both "sex" and "gender" are a function of physical differences, but these physical differences are invested with meaning by culture.

This is not to say that culture causes sexual differences. Rather, the culture promulgates an ideal -- standards of "normality" for our bodies and how we think about them.

At the same time that we create this unreal ideal from our bodies, this ideal forces our bodies into the standards of the ideal.

Thus, "sex" is a continuing process, like Hofstadter's Strange Loops.

We could make it into a verb: "sexing," as Riki Wilchins suggested. Constant "sexing" is necessary because how we think of our bodies never quite conforms to the standards. The process of creating the standards automatically calls into question the authority of the standards. The standards can be (and are) re-created slightly differently in every generation.

That's why Gloria Brame's pictures are so interesting -- I see these antiques and most immediately notice how different the standards of physical beauty and sexuality are.

Therefore, while "sex" is in one sense a physical fact, it is also an ideal in the sense that we create artificial standards of normality to which we must continually strive to conform.

This is, I would argue, similar to Hofstadter's Strange Loop, wherein meaningless elements become a pattern, and the pattern is looped infinitely but in a different key each time, to become a recurring but constantly shifting theme. The theme appears to be real and solid because it is supported by all of these elements and patterns, but the theme itself is what gives meaning to all of the elements and patterns.

She goes on to say

When the sex/gender distinction is joined with a notion of radical linguistic constructivism, the problem becomes even worse, for the "sex" which is referred to as prior to gender will itself be a postulation, a construction, often within language, as that which is prior to language, prior to construction. This "sex" posited as prior to construction will, by virtue of being posited, become the effect of that very positing, the construction of construction. If gender is the social construction of sex and if there is no access to this "sex" except by means of its construction, then it appears not only that sex is absorbed by gender, but that "sex" becomes something like a fiction, perhaps a fantasy, retroactively installed at a prelinguistic site to which there is no direct access.

In other words, "sex" may itself be an artificial concept.

The idea that different people with the same organs are ipso facto the same in certain predefined ways may be as pseudo-scientific as phrenology.

We don't argue that people with green eyes are inherently different from people with blue eyes, even though these are immediately noticeable physical differences.

As Riki Wilchins more colloquially said:

Maybe the formula is reversed. Gender is not what culture creates out of my body's sex.

Rather, sex is what culture makes when it genders my body.

The cultural system of gender looks at my body, creates a narrative of binary difference, and says, "Honest, it was here when I arrived. It's all Mother Nature's doing."

We make all sorts of patterns of meaning out of anatomy, social conditioning and behavioral difference, but the theme we call "sex" is as meaningless as any Strange Loop.

But no less powerful.

Thank you, Douglas Hofstadter. I feel positively high when I read this kind of stuff. I can't wait to sit by the pool and read more.

Leave a comment

We want to know your opinion on this issue! While arguing about an opinion or idea is encouraged, personal attacks will not be tolerated. Please be respectful of others.

The editorial team will delete a comment that is off-topic, abusive, exceptionally incoherent, includes a slur or is soliciting and/or advertising. Repeated violations of the policy will result in revocation of your user account. Please keep in mind that this is our online home; ill-mannered house guests will be shown the door.

Try to get "The Mind's I" by the same author.
It has some interesting musings in personal identity - something that is particularly relevant when going through transition, though not so much afterwards.

Glad you have this book - should keep you out of mischief for a while. Let the world turn without you for a little, I think that not only do you deserve a break, you need it.

Hugs, Zoe

Thanks, Zoe. Yes, I went to the lake today for about 4 hours. I rowed and read, rowed and read. It was wonderful. Now I'm exhausted but happy.

Thanks for the book suggestion.

This is more a sidenote: but how you describe Godel is wrong. He proved that any language that contains basic mathematical functions will produce sentences that contain the proof predicate but not the truth predicate or will contain the truth predicate but not the proof predicate. Its a much smaller claim then what you are proposing.

Another formulation is that any consistent system contains axioms - unprovable truths, and is thus incomplete.

If all truths are provable, ie it is complete, then some falsities are provable too, and is thus inconsistent.

A system can be either complete or consistent, not both. Of course it can be both incomplete and inconsistent instead.

Now the definition of "system" - explaining that is non-trivial, and indeed may be more limited than the normal, non-mathematical meaning of the term.

The study linked to below may be of interest. Research has demonstrated there to be only a 0.21 standard deviation difference between genders in a wide variety of typically gendered characteristics.

To relate this to something more familiar consider IQ. The average (mean) score for Westernized Caucasians is 100 with a standard deviation of 15. Multiplying 15 by 0.21 results in 3.15. Half of this is 1.575. I'll round this up to 2.

Imagine if we were to split people into two groups with one group having an IQ of 99 and one group having an IQ of 101. The difference in measured by IQ intelligence between these groups would be greater than the difference between genders in various behavioral characteristics. I.E. there is essentially no difference between genders in most areas per the study linked to below.

My experience transitioning MTF supports this contention. Most so-called gender differences, other than the obvious anatomical ones, are encultured fabrications of each gender. Since women have far more rights in the USA than men to express nearly anything they wish in an open and fair society men would be much more obviously like women than they are presenting to the world as being today.

The Gender Similarities Hypothesis
Janet Shibley Hyde
University of Wisconsin—Madison

Michael RF | May 31, 2010 9:20 AM

I tried to read this book some 18 years ago when it came out, but I don't think that my mind was quiet enough at the time to focus on the book. This article has encouraged me to try it again. Thank you!