Notes: Platonic Lambda at High Peaks

Notes to Poem: "Platonic Lambda at High Peaks"

Peter Y. Chou
WisdomPortal.com

Preface: Pinnacles National Monument is a protected mountainous area located east of central California's Salinas Valley. The Monument's namesakes are the eroded leftovers of half of an extinct volcano that erupted 23 million years ago. On Sunday, June 14, 2009, Hendrik, Connie, and I went to the Pinnacles National Monument, Paicines, CA for a whole day hike. We went up the Condor Gulch Trail and High Peaks Trail, and came down on the Bench Trail and Bear Gulch Trail. The hike took five hours with many scenic sights and breathtaking views. The most memorable scene was a mountain ridge resembling the Platonic Lambda and a Cubic Rock nearby. Plato's Platonic Lambda even & odd series that add up to 55 has fascinated me for many years because Plato called it "the soul of the universe". It has inspired the poem "Speculations on the Soul" (1993); an essay "Dante's 55 & Platonic Lambda" (2001); and the poem "Meditations on 55" (2006). Seeing the Platonic Lambda mountain ridge at High Peaks, I felt transported back to the Platonic Academy in Greece to learn about the mystery of the soul that inspired this poem. Here are Notes to the poem with photos from the Pinnacles hike.

Commentary on "Platonic Lambda at High Peaks"

On the High Peaks Trail at the Pinnacles
in a gap of trees, I spot a mountain ridge
that resembles the Platonic Lambda.

Starting out at Condor Gulch Trail at the Pinnacles at 2 pm on June 14, 2009, it took about two hours to reach the High Peaks Trail. After 40 minutes on this trail, I spotted the mountain ridge in a gap of trees that resembled the Platonic Lambda (see photo at left). The rocky climb made this view quite exhilarating. Here's a close-up photo.

Eleventh letter of the Greek alphabet
which looks like an upside down "V" that
Plato called the Soul of the Universe—

Lambda is the 11th letter of the Greek alpahbet, corresponding to the 12th letter "L" in English. Λ & λ are the uppercase and lowercase letters in Greek. Λ resembles the English letter "V" upside down. Plato describes the creation of the cosmos in Timaeus 37a: "The body of heaven is visible, but the soul is invisible and partakes of reason and harmony."

The even series— 1, 2, 4, 8, and
the odd series— 1, 3, 9, 27
woven from the sacred source of Oneness.

The Platonic Lambda, the Soul of the Universe,
is the sum of the two series (Timaeus 35b):
Sum of the double interval series (powers of 2) =
2⁰ + 2¹ + 2² + 2³ = 1 + 2 + 4 + 8 = 15
Sum of the triple interval series (powers of 3) =
3⁰ + 3¹ + 3² + 3³ = 1 + 3 + 9 + 27 = 40
Sum of the double & triple interval series (Timaeus) = 15 + 40 = 55 (Notes: Speculations on the Soul; Meditations on 55; Dante's 55 & Platonic Lambda)

Around the bend, I get a closer glimpse
of this moving image of eternity—
how time and heaven were born together,

Plato, Timaeus, 37b & 38b: "Wherefore he resolved to have a moving image of eternity, and when he set in order the heaven, he made this image eternal but moving according to number, while eternity itself rests in unity, and this image we call time... Time, then, and the heaven came into being at the same instant in order that, having been created together, they might be also dissolved together."

God fashioning the four elements by
form and number— fire, water, air, earth—
perfected and harmonized in proportion.

Plato, Timaeus, 53b & 56c: "God fashioned by form and number four elements shaken by the receiving vessel to form the universe— fire and water, earth and air, made them as far as possible the fairest and best... And the ratios of their numbers, motions, and other properties, everywhere God, as far as necessary allowed or gave consent, has exactly perfected and harmonized in due proportion."

Pyramid assigned to fire, cube to earth.
While my friends hike ahead, I stay behind
at trail's bend to learn from Cubic Rock.

The five Platonic solids were assigned to elements by Plato in the Timaeus 56b, 55d— fire (tetrahedron), earth (cube), air (octahedron), water (icosahedron), ether (dodecahedron). "To earth, let us assign the cubic form, for earth is the most immovable of the four and the most stable of all bodies... the pyramid is the solid which is the original element and seed of fire, and let us assign the element which was next in the order of generation to air, and the third to water."

"O teach me what you've learned all these years
on the Soul's mysteries?" And after a long
silence he says: "Absolutely Nothing!"

In Sanskrit, Upanishads means "to sit under"— inferring that disciples are sitting at the feet of a sage learning about spiritual wisdom. So I imagined Cubic Rock sitting below the Platonic Lambda, as one of Plato's disciple learning about the mysteries. His answer "Absolutely Nothing" conjured up "Absolute Zero" or 0^o Kelvin, where all matter becomes motionless and is at absolute rest (NOVA).

"That's why they call me a blockhead" he laughs.
And leaving him, I wonder if he's a fool
or me wasting time learning from a rock.

Talking to a rock may not be so foolish, as Annie Dillard has a book Teaching a Stone to Talk (1982). In his novel Going Deeper (2004), Jean-Claude Koven tells about speaking to stones and learning from them in his spiritual journey. Hence "stone" may be rendered as "St-One" or Saint One. That's why I stayed with Cubic Rock, hoping that he would be my mentor. Since "rock" in Greek (petras) means "Peter" (Petros), I would be communing with myself.

Later I come to Blue Sage who tells me:
"Cubic Rock is Tarot's Fool whose wisdom
of No-Mind is knowledge of the Absolute."

Blue Sage (Salvia farinacea) is a wildflower that grows up to 3-4 feet. It is a perennial with vivid blue color. Since a sage is an enlightened being, I asked this "Flower Sage" about Cubic Rock whom I left behind. Blue sage's answer gave a new insight on "Absolutely Nothing"— The Zero does not mean "Nothing" in The Fool's Tarot card, but the wisdom of a sage's No-Mind of Zen (Fool's symbolism).

This was my surprise at the Pinnacles—
Meeting Platonic Lambda at High Peaks
and Uncarved Block's lesson on Emptiness.

"Pinnacle" means "a lofty peak" as well as "the highest point of development or achievement". That a mountain ridge resembling the Platonic Lambda was seen on the High Peaks Trail of the Pinnacles during the hike was surely symbolic and delightful. Cubic Rock is Lao Tzu's "uncarved block", cited in Tao Te Ching, XV: "The wise ones of old— / Simple as the uncarved block, / open-minded as the valley."

********************************************************************************

Meditation on the Uncarved Block:

"The Uncarved Block— remain at the Center,
which is yours and that of all humanity.
For those goals which it gives to your life,
do the utmost which, at each moment,
is possible for you. Also, act without
thinking of the consequences, or
seeking anything for yourself."
— Dag Hammarskjöld (1905-1961),
Markings (1957), p. 159

UN Meditation Room

Taoist Meditation on Emptiness:

Tao Te Ching, IV:
The Tao is an empty vessel,
yet use will not exhaust it.
Like a deep fathomless abyss
it is the source of all things...
Its fountain is deep and everlasting.
I know not who gave it birth,
it came even before the gods.
Tao Te Ching, XI:
Thirty spokes converge in the hub of a wheel;
It is the center hole which makes it useful.
Mold clay to form the walls of a pot;
It is the emptiness within which gives its use.
Cut out doors and windows to make a room;
It is the space therein which makes it useful.
Therefore, we profit from the existence of things,
but are served by things which are non-existent.

Zen Meditation on Emptiness:
When a mind, thoroughly understanding the emptiness of all things, faces forms, it at once realizes their emptiness. With it emptiness is there all the time, whether it faces forms or not, whether it discourses or not. This applies to everything which belongs to our sight, hearing, memory, and consciousness. Why is it so? Because all things in their self-nature are empty; and wherever we go we find this emptiness. as all is empty, no attachment takes place; and on account of this non-attachment there is a simultaneous Use of Dhyana (meditation) and Prajna (wisdom). The Bodhisattva always knows how to make Use of emptiness, and thereby he attains the Ultimate.
— Ta-chu Hui hai (8th century A.D. Zen master)
from D. T. Suzuki, The Zen Doctrine of No-Mind (1949)
also in Zen Buddhism: Selected Writings of D.T. Suzuki
Edited by William Barrett, Anchor Books, NY, 1956, p. 181

Meditation on the Don't Know Mind:
At the conclusion of Theaetetus, Socrates said "you know what you do not know". The Korean Zen Master Seung Sahn (1927-2004) taught that enlightenment is keeping a "Don't Know Mind". He told the students that everyone's "Know Mind" is different but everyone's "Don't Know Mind" is the same. The Buddhists teach that Enlightenment is experienced by an "Empty Mind", "No-Mind", or "Don't Know Mind".

Commentary on "Platonic Lambda at High Peaks"
	On the High Peaks Trail at the Pinnacles in a gap of trees, I spot a mountain ridge that resembles the Platonic Lambda. Starting out at Condor Gulch Trail at the Pinnacles at 2 pm on June 14, 2009, it took about two hours to reach the High Peaks Trail. After 40 minutes on this trail, I spotted the mountain ridge in a gap of trees that resembled the Platonic Lambda (see photo at left). The rocky climb made this view quite exhilarating. Here's a close-up photo.
Eleventh letter of the Greek alphabet which looks like an upside down "V" that Plato called the Soul of the Universe— Lambda is the 11th letter of the Greek alpahbet, corresponding to the 12th letter "L" in English. Λ & λ are the uppercase and lowercase letters in Greek. Λ resembles the English letter "V" upside down. Plato describes the creation of the cosmos in Timaeus 37a: "The body of heaven is visible, but the soul is invisible and partakes of reason and harmony."
The even series— 1, 2, 4, 8, and the odd series— 1, 3, 9, 27 woven from the sacred source of Oneness.	The Platonic Lambda, the Soul of the Universe, is the sum of the two series (Timaeus 35b): Sum of the double interval series (powers of 2) = 2⁰ + 2¹ + 2² + 2³ = 1 + 2 + 4 + 8 = 15 Sum of the triple interval series (powers of 3) = 3⁰ + 3¹ + 3² + 3³ = 1 + 3 + 9 + 27 = 40 Sum of the double & triple interval series (Timaeus) = 15 + 40 = 55 (Notes: Speculations on the Soul; Meditations on 55; Dante's 55 & Platonic Lambda)
Around the bend, I get a closer glimpse of this moving image of eternity— how time and heaven were born together, Plato, Timaeus, 37b & 38b: "Wherefore he resolved to have a moving image of eternity, and when he set in order the heaven, he made this image eternal but moving according to number, while eternity itself rests in unity, and this image we call time... Time, then, and the heaven came into being at the same instant in order that, having been created together, they might be also dissolved together."
	God fashioning the four elements by form and number— fire, water, air, earth— perfected and harmonized in proportion. Plato, Timaeus, 53b & 56c: "God fashioned by form and number four elements shaken by the receiving vessel to form the universe— fire and water, earth and air, made them as far as possible the fairest and best... And the ratios of their numbers, motions, and other properties, everywhere God, as far as necessary allowed or gave consent, has exactly perfected and harmonized in due proportion."
Pyramid assigned to fire, cube to earth. While my friends hike ahead, I stay behind at trail's bend to learn from Cubic Rock. The five Platonic solids were assigned to elements by Plato in the Timaeus 56b, 55d— fire (tetrahedron), earth (cube), air (octahedron), water (icosahedron), ether (dodecahedron). "To earth, let us assign the cubic form, for earth is the most immovable of the four and the most stable of all bodies... the pyramid is the solid which is the original element and seed of fire, and let us assign the element which was next in the order of generation to air, and the third to water."
	"O teach me what you've learned all these years on the Soul's mysteries?" And after a long silence he says: "Absolutely Nothing!" In Sanskrit, Upanishads means "to sit under"— inferring that disciples are sitting at the feet of a sage learning about spiritual wisdom. So I imagined Cubic Rock sitting below the Platonic Lambda, as one of Plato's disciple learning about the mysteries. His answer "Absolutely Nothing" conjured up "Absolute Zero" or 0^o Kelvin, where all matter becomes motionless and is at absolute rest (NOVA).
"That's why they call me a blockhead" he laughs. And leaving him, I wonder if he's a fool or me wasting time learning from a rock. Talking to a rock may not be so foolish, as Annie Dillard has a book Teaching a Stone to Talk (1982). In his novel Going Deeper (2004), Jean-Claude Koven tells about speaking to stones and learning from them in his spiritual journey. Hence "stone" may be rendered as "St-One" or Saint One. That's why I stayed with Cubic Rock, hoping that he would be my mentor. Since "rock" in Greek (petras) means "Peter" (Petros), I would be communing with myself.
	Later I come to Blue Sage who tells me: "Cubic Rock is Tarot's Fool whose wisdom of No-Mind is knowledge of the Absolute." Blue Sage (Salvia farinacea) is a wildflower that grows up to 3-4 feet. It is a perennial with vivid blue color. Since a sage is an enlightened being, I asked this "Flower Sage" about Cubic Rock whom I left behind. Blue sage's answer gave a new insight on "Absolutely Nothing"— The Zero does not mean "Nothing" in The Fool's Tarot card, but the wisdom of a sage's No-Mind of Zen (Fool's symbolism).
This was my surprise at the Pinnacles— Meeting Platonic Lambda at High Peaks and Uncarved Block's lesson on Emptiness. "Pinnacle" means "a lofty peak" as well as "the highest point of development or achievement". That a mountain ridge resembling the Platonic Lambda was seen on the High Peaks Trail of the Pinnacles during the hike was surely symbolic and delightful. Cubic Rock is Lao Tzu's "uncarved block", cited in Tao Te Ching, XV: "The wise ones of old— / Simple as the uncarved block, / open-minded as the valley."

Meditation on the Uncarved Block:
"The Uncarved Block— remain at the Center, which is yours and that of all humanity. For those goals which it gives to your life, do the utmost which, at each moment, is possible for you. Also, act without thinking of the consequences, or seeking anything for yourself." — Dag Hammarskjöld (1905-1961), Markings (1957), p. 159	UN Meditation Room

Taoist Meditation on Emptiness:
Tao Te Ching, IV: The Tao is an empty vessel, yet use will not exhaust it. Like a deep fathomless abyss it is the source of all things... Its fountain is deep and everlasting. I know not who gave it birth, it came even before the gods.	Tao Te Ching, XI: Thirty spokes converge in the hub of a wheel; It is the center hole which makes it useful. Mold clay to form the walls of a pot; It is the emptiness within which gives its use. Cut out doors and windows to make a room; It is the space therein which makes it useful. Therefore, we profit from the existence of things, but are served by things which are non-existent.
Zen Meditation on Emptiness: When a mind, thoroughly understanding the emptiness of all things, faces forms, it at once realizes their emptiness. With it emptiness is there all the time, whether it faces forms or not, whether it discourses or not. This applies to everything which belongs to our sight, hearing, memory, and consciousness. Why is it so? Because all things in their self-nature are empty; and wherever we go we find this emptiness. as all is empty, no attachment takes place; and on account of this non-attachment there is a simultaneous Use of Dhyana (meditation) and Prajna (wisdom). The Bodhisattva always knows how to make Use of emptiness, and thereby he attains the Ultimate. — Ta-chu Hui hai (8th century A.D. Zen master) from D. T. Suzuki, The Zen Doctrine of No-Mind (1949) also in Zen Buddhism: Selected Writings of D.T. Suzuki Edited by William Barrett, Anchor Books, NY, 1956, p. 181
Meditation on the Don't Know Mind: At the conclusion of Theaetetus, Socrates said "you know what you do not know". The Korean Zen Master Seung Sahn (1927-2004) taught that enlightenment is keeping a "Don't Know Mind". He told the students that everyone's "Know Mind" is different but everyone's "Don't Know Mind" is the same. The Buddhists teach that Enlightenment is experienced by an "Empty Mind", "No-Mind", or "Don't Know Mind".