MULTIPLE PATHS TO TRUTH.

In her painting “The Fellowship of the Timeless”, Sveva Caetani (poet as well as artist) depicts 12 pilgrims – Holy Men (Lohans) who approach from different directions the centre of a luminous circular Mandala, on their way to the White Hole (Whole?) of Divine Reality. In this journey from Transience to Timelessness, the Perennial Philosophers “converge from all directions of the compass toward the central plunge”, drawn by a spiritual gravitation. They move with slow but not hesitant deliberateness to their goal, like “travellers from rooms they have left behind”. (Some of this language is borrowed from Caetani.)

Besides being a good image for the global interfaith movement, it also correlates with images from other situations and contexts. The four yogas of Hinduism are one such example. It is possible to attain the knowledge that “Atman is Brahman” by several routes, climbing to the summit of the mountain either by Jnana Yoga (the route of logical reasoning), or by Karma Yoga (the route of practical good deeds), or by Bhakti Yoga (the path of spiritual devotion), or by Raja Yoga (mysticism and spiritual exercises). (These are well outlined in “The Religions of Man” by Huston Smith.)

Another image is the Arthurian search for the Holy Grail, a supreme Christian vision. There are several versions of this story, but they all involve the notion that only a totally pure person can attain the vision. The morally impure Sir Lancelot could not get it, but his pure son by an innocent maiden, Sir Galahad, finally did. But he did so only by “reaching through the Worlds” from Glastonbury to Avalon, and the touch of it killed him. Just as the person who touched the Ark of the Covenant in the Old Testament.

The final image I can think of comes from an unlikely source: mathematics. In his recent book, “Where Mathematics Comes From”, George Lakoff closes the book with a “case study” of why e πi + 1 = 0. This magical-sounding equation seems mysterious (what does it even mean?), but he shows in several chapters that it represents a pinnacle at which several branches of mathematics come together: algebra, calculus, geometry, analytical geometry, trigonometry, and complex numbers. Moreover, the result can be obtained by at least two kinds of approaches.

One approach starts with differential calculus and the Taylor or McLaurin infinite series. By writing out the series for e x , cos x and sin x, we see immediately that

e πi + 1 = 0

from which e πi + 1 = 0 follows. But this still looks mysterious. It is the way the text books do it, but it does not give us insight, i.e. true understanding.

The second approach, which Lakoff uses, goes into detail of the cognitive “metaphors” used in four kinds of planes: the Euclidean plane which gives us the unit circle, and hence π; the Cartesian plane, in which we can plot two ordered numbers as a point in the plane; the trigonometric plane, which links recursiveness (waves) to periodicity (circle); and the complex plane, which explains i and uses Cartesian plane notations to express complex numbers.

These four planes, plus the idea that exponentials map sums into products and e x is the only function that is its own derivative (first, second, third, etc.), converge to the result ,

e πi + 1 = 0

This makes us realize that insight is different from, and superior to, a formal proof. But it requires considerable “jnana” to follow the argument.

Hanna Newcombe

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