The Mathematics of the Path

Series: The spiritual path in Dzogchen

Beginning the Dzogchen path

The Mathematics of the Path

When we begin, it is often easier to start than to finish. There’s the drive of a beginner: the thirst for novelty, the desire to conquer, the hope of success. But as we proceed, nothing happens exactly as we had planned…

The reasons for starting may vary (see an example with the article Why we take the path of Great Perfection), and in the end, we may not really have much of a choice. However, our motivation is the key. Why embark on such an adventure? Out of curiosity, to suffer less or think less, for my own happiness, or to help others… or to bring all beings to Enlightenment ? To this fundamental motivation, the bodhicitta that lies at the root of the Dzogchen path, is gradually added a deep trust in this path, as well as trust in the one who guides us. This guide becomes our link to the primordial nature, our true face. Trust will grow over time, because, let’s face it, very few of us are granted direct access to the emptiness of the Vidyadharas (you can read the post (False) start)—bad karma! But let’s not be discouraged. Whatever our apparent initial motivation may be, let us wear our seven-league boots to follow in the footsteps of those who walked before…

“The path – straight or curved, broken, circular or spiral—was nothing more than yet another story we were telling ourselves. For since always and forever, the ultimate oneness sphere of Reality is present.”

ཁྱེད་ཀྱི་རྗེས་སུ་བདག་བསྒྲུབ་ཀྱི (khyed kyi rjes su bdag bsgrub kyi) – “I practice in your footsteps” (or “In your steps, I follow [to accomplish your nature]”), says the famous “Seven Line Prayer” addressed to the most renowned of Tibetan masters, Guru Rinpoche, Padmasambhava, one of the initiators of Buddhism and Dzogchen in the Land of Snow. So off we go, to adventure!

When we first embark on a spiritual path, we often tend to think of it as linear. We go from A to Z. All the maps have taught us this; our GPS confirms it—thanks to mathematics and now algorithms! On the road, there’s a longer, cheaper route, and a faster one, with tolls. It’s up to us to decide what’s more important and what our resources (and not necessarily financial) are . In any case, on the road, as on the spiritual path, we start from one place to arrive at another. So, a line, with a beginning and an end, straight or curved, circular or spiral, but always a line; or lines. 

Let’s dare to compare the spiritual path with mathematics. The Dzogchen path may appear to be a linear journey with stages. But we must remember that these stages, and the whole path itself, are ultimately illusory… (you can read the article The path that leads nowhere). These stages are simply broad markers, milestones along the path to give us some points of reference. After all, each journey will always be unique and filled with exceptions to the rule.

To refine our geometric description of the gradual path of Dzogchen, let’s say that a line may not be the most accurate shape. The line path is actually more like… a circle – a line closed on itself!

Since Dzogchen is a result-oriented vehicle, the result is already present at the Base. The Alpha is therefore the Omega. The beginning is the end. And to move further away from the illusory perspective of the gradual path in Dzogchen, this path might be better described as… a point; a non-circle, an absence of path, a still journey.

We then return to the aforementioned direct path of emptiness, that of radical Dzogchen, once the gradual path has reached its completion. To continue the mathematical metaphor, once the gradual linear path has been walked, it closes into a circle that is recognized as a point: here and now, immediately, everything has always been Great Perfection – vast and sublime bliss, radiant emptiness! 

A point, we said, or even better… a sphere. This is how the tradition sometimes describes ultimate reality – the single sphere of Reality, the sphere of oneness (thig le nyag gcig). According to Dzogchen, this sphere (thig le) is not located in physical space (‘mkha), nor even in “internal”, matrix space (klong), but in the primordial space of the phenomena of Reality (dbyings). As for time, we are beyond its usual three components—past, present, and future. The non-path of Dzogchen transcends time, without chronology, a kind of fourth time, that of equality. This is how the ordinary yet extraordinary Great Perfection will be revealed. Patience!

The path – straight or curved, broken, circular or spiral—was nothing more than yet another story we were telling ourselves. For since always and forever, the ultimate oneness sphere of Reality is present. Line, circle, point, and then sphere—this is our little journey through the mathematics of Dzogchen. Everything is just beginning… It’s time to play!