The Mathematician's Mind

Jacques Hadamard was a well know French mathematician who undertook a monograph length exploration of "the psychology of invention in the mathematical field" (as the subtitle has it).  The essay is particularly interesting because it combines introspection into his own working process with reports from a variety of other mathematicians to concoct a basic theory of how it feels to discover a new mathematical idea.  The upshot is that most mathematician's seem to work with various visual, auditory or even motor (in the case of Einstein) images at a pre-verbal level.  Hadamard takes these images to be conscious representatives of unconscious processes that get linked together as so many stepping stones that later guide linguistic or conventionally symbolic arguments.  In short, there's nothing deductive about mathematical invention, which in Hadamard's view is not a substantially different process than what we might more readily associate with poetic invention.  The conscious mind prepares the field with a long immersion into the subject.  Then the mathematician sleeps on it, so to speak, and their unconscious tries out various combinations until a successful one bubbles to the surface in the form of concrete images.  Finally, these images must be consciously and painstakingly translated back into a form that will stand up to the scrutiny of logical communication.  I would reserve judgement on whether Hadamard's is an adequate description of all possible types of invention; surely the question has been studied in much greater depth in the 70 years since his publication.  But it is a coherent and interesting one that definitely fits with my own experience of writing.

Cutting Through Spiritual Materialism

I picked up Chögyam Trungpa's classic about three years ago and found I couldn't get into the first few chapters.  I'm not sure what I didn't like back then because this time I found the book really insightful and engaging.  These transcriptions of talks he gave to Western students back in the seventies fall into two sections.  In the first half, Trungpa explains what the spiritual path is not, and in the second he begins to progressively explain what it is.  

The title of the book stems from the message of the first part.  The spiritual path is not another attainment that we can "get".  It's not another skill or notch in our belt or collectible display item for the modern home.  The idea that the path leads to a goal is what stops us from walking down it.  Trungpa spends many chapters warning about the various illusions and self-deceptions we will accidentally create for ourselves as we try to use our concept-addicted ego to navigate.  It's only when we give up this ego's desire to possess wisdom, when we surrender and open up to our inability to grasp things that we begin get an idea of where we are going.  The overall message is very similar to The End of Your World -- let go of your expectations about how things should be.  Since giving up is a lot harder than it sounds, it's nice to hear many of these same lessons repeated.

The second half of the book contains Trungpa's own presentation of the path from the perspective of his Kagyu lineage.  Since this is a Vajrayana tradition, the presentation works its way up through the three vehicles.  His discussion of the Hinayana tradition begins with a particularly interesting chapter on dependent arising ("The Development of Ego"), passes through the four noble truths, and gives a great reading of our circulation through the six realms.  Then there are a couple of chapters devoted to the core ideas of the Mahayana tradition: the Bodhisattva and Emptiness.  Finally, his view of the path culminates in the Tantric practice of transmuting energy.  It's probably more of a commentary on my own practice than the book to observe that this chapter seemed somewhat vague and ripe for abuse.  In Tantra, everything is legal, so to speak.  When seen properly, anger, lust, etc ... are all just various flavors of awake energy that need not be avoided.  While this is a satisfyingly non-dual philosophical conclusion, it leads to some obvious practical difficulties.  Trungpa seems to want to instill in us a confidence that everything we do from true awareness is correct and appropriate.  While he himself acknowledges the danger this attitude represents, he points out that this teaching only occurs at the end of the path, when the student should know how to use it properly.  Given that anyone with an internet quickly discovers Trungpa himself arguably fell victim to some of these dangers, it seems relevant to ask if his "crazy wisdom" was something we should learn from rather than emulate.

TechGnosis

I've been meaning to read Eric Davis's classic account of the religious and mystical roots hidden in our modern attitudes towards technology for a long time.  Fortunately, it did not disappoint.  Though the book is plainly over-written in a sense (Davis calls it, "almost ridiculously dense" in his afterword -- a hypertext of a text) and lacks anything like a simple thesis, it's unfailingly engaging throughout.  I got to learn about Gurdjieff, the Extropians, Hermes Trismegistus, and, of course, the Gnostics, among many other cult-like groups.  Davis' main point is that these "fringe" beliefs have always been tied up with and reflective of society's relationship to its technology, and that they remain deeply ingrained in our experience of technology today.  Consider, for example, our constant faith in progress and the techno-capitalist utopia we are always being promised, and see if it is at bottom any different from John's New Jerusalem in the Book of Revelation.  Or, ask yourself if the stark dualism and paranoid society of control we immediately relate to in the Matrix movies is anything but an update of the Gnostic myth that we have been imprisoned in this material world by a conspiracy of archons who have hidden our true spiritual nature from us.  The goal of the book is not really to trace the provenance of these ideas with academic rigor, but just to point out connections and correspondences that can shed some light on the psychology of our relationship to current our technology in general, and to the internet in particular.  Today, almost our whole sense of self and world is mediated through various information technologies, so perhaps it's inevitable that when we go looking for our selves, we find their refracted and reflected images in the nature of those very technologies.  

Moby Dick

The whale wins.

 

#reread  

Pointing Out the Great Way

While the subtitle of Dan Brown's massive tome is: "The stages of meditation in the mahamudra tradition", it doesn't really read as yet another meditation map book.  In part, this is because it focuses less on what results the meditator should expect at each stage, than on what the meditation instructions are for that stage.  Of course, you could use it to check off a list of meditative accomplishments and find a rank for your practice in the same way that The Mind Illuminated lends itself to.  But it seems more useful as a guide for how to order a series of techniques so that they point you gradually towards deeper levels of emptiness.  

This view of it is reinforced if you consider how tremendously repetitive the book is.  Crudely summarized, the whole path is just one long series of alternations between stabilizing and letting go.  To give it slightly more detail, we could notice that the major chapters correspond to the "main sequence" Michael Taft teaches in his Vasy Sky Mind class (and which form the backbone of his guided meditations).  

1. Shamata with an object -- "Formal Meditation: Concentration with Support"
2. Shamata without an object -- "Formal Meditation: Concentration without Support"
3. Vipashyana -- "Special Insight"
4. Dropping the Ball -- "Extraordinary Practice"

Because Brown aims to develop a very traditional account, he gives us way more substages for each of these practices, and includes several (kinda uninteresting) chapters on the preliminaries to formal mediation (like guru yoga), but the basic trajectory is recognizably the same.  While I learned all sorts of things from it, I can't say there's anyone I would really recommend the book to.  The language and presentation are just so specialized that I don't think I would have gotten much out of it if I hadn't already been exposed to these ideas in a more modern and informal way.  Which perhaps means that the book is most useful as a sort of reference manual for people already deeply familiar with the Mahamudra tradition.

Silence

I don't really have anything interesting to say about Erling Kagge's little book Silence.  It's a thoughtful if a bit whimsical and scattershot reflection on the importance of silence, and more generally inner peace, from a guy who has spent some time by himself being quiet in extreme conditions.  Kagge's fame seems to revolve around the fact that he's gone to both the North and South Pole on foot; he describes the solitude of solo-skiing across Antarctica in several places in the book.  Does spending 50 days cold and alone make you an expert on silence?  I suppose more of an expert than most of us.  So what, then does Kagge actually have to say about the subject?  

Basically, the book is a long apology for the value of silence and solitude in a world increasingly obsessed with connecting everything together and making it move as fast as possible.  This speed, this noisy profusion, it sometimes seems, has become an end in itself, so that we no longer even ask why we wanted to clink 'refresh' yet again.  Kagge rightly argues that the key to breaking this cycle is to somehow find a moment in the midst of the color-coded traffic jam of our calendars to actively do nothing.  The silence he has in mind isn't a passive lack in our experience but an active engagement with what's before us here and now in itself, rather than as the mere representative of conversations past or future.  Without trying to experience the intrinsic value of a moment, we are never able to ask what all our ever-so-efficient activity is for.  Unfortunately, while I think this is ultimately a sneakily profound idea, I don't think Kagge's exposition of it really contributed all that much to my understanding of this concept.  So unless you haven't thought very much about the problem, you might want to pass over this one in ...

Dhamma Everywhere

At the Alexis Santos retreat last year, he gave all of us a copy of his teacher Sayadaw U Tejaniya's little Dhamma Everywhere book.  It was interesting though strange to be encouraged to read a few pages of the book while on retreat; meditation and words still don't mix all that well for me.  But in retrospect, the exercise was very revealing.  Trying to bring the dhamma to everyday life in the simplest possible terms is the core of Tejaniya's teaching.  What good are fancy concentration techniques and exalted states if they fall apart the moment we have a conversation or even just pick up a book?  Instead of providing an elaborate theory or set of special practices, Tejaniya encourages us just to keep investigating what's happening in awareness right now.  While at first this might sound like mindfulness 101 or perhaps something similar to noting, it quickly becomes clear that awareness is a broader concept than attention or focus.  Tejaniya's goal is an awareness wide open and unfixated, even temporarily.  So instead of focusing on noting the details individual objects, he's really interested in our being aware of the moment to moment quality of our awareness itself.  Is there craving present in the way we're aware right now?  Is there aversion?  The idea is that if we just keep checking what we are aware of, we gradually build up a picture of the patterns in our mind, the habits of thought that dictate not only which objects we are aware of, but how we are aware of them.  Ultimately then, we become aware of awareness itself, so to speak. Which might just be the end.  Or the beginning.