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Good Morning All, Haiku and Zen are among the most wildly abused words in
any language. My 6200 word piece "Lanterns Floating Downstream: 17 Syllable
Zen" attempts to correct that regrettable condition. Please don't feel
obligated to read it. I will try to flog it to some unsuspecting literary
agency or publisher of arcane material. If that doesn't work, I'll send it
as a freebie to every Sangha in America, Ireland, Scotland, and Japan. I
have the necessary email addresses. This is a crusade.

Lanterns Floating Down Stream: Seventeen Syllable Zen

"But with a little more familiarity you realize that haiku poetry excels in
one of the rarest artistic virtues, the virtue of knowing when to stop."
-Alan Watts
"Brevity is the soul of wit." -Shakespeare
1. Tedious
Master Shogun, the Abbot of Zuigan Temple, loved teaching haiku to his
monks. "Haiku," he lectured, "is the ideal poetry form. It captures the
thing-in-itself and nothing more. There is nothing extraneous. Haiku
measures both the amount of Zen in the writer and in the reader." Shogun, a
lifetime devotee, read one haiku per day and rarely wrote more than five in
a year.
"Why is it you only read one haiku each day, Master?" asked Daitsu, one of
his most promising students.
"Because reading one per day is sublime," replied the old Zen Master,
"reading two is tedious."

2. Seventeen Syllable Zen
Two of the most wildly misused words in any language are Zen and haiku. Zen
is a branch of Mahayana Buddhism focusing on meditation, taming the mind,
and the direct perception of reality. Haiku is its poetic expression.
Haiku forms a natural land bridge over the deep gorge separating the
absolute and relative realms. A haiku conveys those moments when nirvana is
glimpsed directly within everyday samsara. This is not a poetry of the
imagination. This is the poetry of mindfulness taken from direct experience.
There are ten thousand opportunities to write a haiku each day, and every
one of them benefits a Buddhist practice.
A haiku is subtle and slender. It does not employ rhyming, metaphors,
similes, and other conceits common to other forms of poetry. The poet
isolates imagery in an understated way that reflects his understanding,
however deep or shallow, of the Dharma. Originating in Japan, the form
consists of three segments, or lines, and 17 syllables, structured by a
5-7-5 syllable count. This structure is preferable, and makes the purest,
classical presentation. There are natural inconsistencies between the
Japanese and English grammars and vocabularies, and the correct format can
seldom be achieved in translations.
Traditionally, there is a seasonal referent. The reference may ne direct, a
mention of a migratory bird, or some other phenomena associated with a
particular season. Many anthologies, notably the R.H. Blyth series, are
sorted by season, and then subdivided by subject. In the haiku below, the
extreme low tide and the heat identify the season.
Stench of dead plankton,
Reeks from the lagoon's low tide:
The barrier island.

3. Black Widow Spiders
Preface:
Black widow spiders, a highly venomous Arachnid, are ubiquitous across the
temperate zones and the tropics. The female has a red hourglass on its
abdomen. There are 31 recognized species in this genus, and the hourglass
may range from a bright red to a barely distinct orange. A sturdily built
spider, the female devours the male after mating.

Spikey egg cases,
In a dirty, twisted web:
Black widow crawling.

Commentary:
Sean Yeats asked Master Bankei, Abbot of The Clear Bell Monastery, "How can
I most directly experience the Dharma?"
A kindly old man who had, himself, been awakened many years ago, Bankei
reached into the folds of his robes and pulled out three female black widow
spiders on the palm of his extended left palm. "Put one of these in your
mouth," replied the Master.
Note: The historical Master Bankei experienced a Zen experience with three
spiders.

4. Kireji
The kireji is a cutting word, a powerful element of the haiku that divides
the verse into two parts, parts that can either be compared or contrasted.
Frequently, the cutting word separates the poem into two independent halves:
in other poems, it may form a correspondence between two images. The Kireji
may also be a word that provides a dignified ending to the haiku.
Kireji are missing from most modern haiku, or missing and difficult to
detect in haiku's classical period. Most writers of haiku are familiar with
the 5-7-5 syllable format. Few poets are mindful of the kireji. The
intended kireji may be so subtle that it is missed entirely. Even in the
Blyth haiku volumes, there is little attention paid to the cutting word, the
word that is frequently merely a pleasant statement about nature and the
crafting of a poem reflecting the acuity of the poet's Zen eye.

Before the Sun rises,
Peacocks in tree roosts crying:
Faint stars in the east.

Crying is the kireji. It changes the focus from the peacock's cries to the
stars fading in the eastern sky. It separates the poem into two halves
while still allowing the third line to modify the first two lines.

5. Lanterns Floating Downstream

Preface:
Suffering results from pain and dissatisfaction, desires, and attachments
formed in a world characterized by impermanence. Each micro-second brings
changes. We possess mind-streams, not minds. And we are like lanterns
floating downstream. Attempting to live as if there were a reified,
unchanging reality only increases our suffering.

Molecules alter,
As each second passes by:
Lanterns floating downstream.

Commentary:Prince Shakyamuni, despite his father's efforts, discovered this world's
round of birth, sickness, age old and death. His union with his wife
Yashodhara resulted in the birth of a son, Rahula, a word that translates
into "fetters."

When Siddhartha Gautama looked down upon his sleeping wife's seductive
geometry, he saw the endless cycle of birth and death, and the snare of
Mara's daughters. Earlier in the evening, in their love making, he'd
prolonged the pleasure of their joining to the best of his physical
capabilities, and known one last time the breath extinguishing bliss buried
within her lap.

With a bodhisattva's perfect compassion and absolute non-attachment, the
Omniscient One disengaged from his beloved Yashodhara and their infant son,
departed Kapilavstu, and entered the homeless life.

6. Icicles

Preface:
Seasonal references are a mark of the natural world best displayed in the
world's temperate zones such as Japan. Much of the planet, such as the
tropics and the arctic regions, do not easily produce an image identifying
the season. Even in the classical period, the poets used to frequently
satisfy this requirement via a blatant naming of the season in the verse's
three lines.

Bone freezing nights,
Thick icicle dislodges,
Piercing the snow's crust.

Commentary.
Dislodges is the cutting word, setting up the satisfying sound of the icicle
crunching through the crust.

7. Rainbows
Preface:
Photons, massless light particles, are inherently without any specific
color.

The shower subsides,
Light flows through water droplets:
Our brains see rainbows.

Commentary:
The cutting word is droplets.
Abbot Seizi tired of teaching the Dharma. When asked by a monk why he was
leaving the monastery, the Abbot replied, "There is not much really much
involved with teaching Zen. After a while, all the teacher does is repeat
himself. And there is no point to that."

8. Ants and their Mounds
Preface:
Dead raccoons, opossums, and other animals are a common sight along
roadways.

The crushed raccoon's corpse,
Is partially decomposed:
Ants begin to feed.

The Buddha-To-Be sat beneath a banyan (ficus/Bodhi) tree, moments away from
his Awakening. The full moon shone through the tree limbs and leaves. A
colony of ants by his feet tended their mound, following pheromone trails,
turning over the soil, heedless of Shakyamuni"s strivings. Siddhartha,
Prince of the Shakya clan, smiled. Venus rose dimly above the horizon.
Mara the tempter vanished.

The Buddha placed his right hand on the Earth, and rejoiced. "I, along with
the Earth, am enlightened," he said. From that moment forward, samsara (the
physical realm) and nirvana (the absolute realm) were joined.

9. Dark Matter
Preface:
Dark matter, hitherto unobserved by science, comprises approximately 85% of
the matter in the Universe. It does not react with light or other
particles, but it does interact with gravity. Findings in physics and
astrophysics in the last 100 years now define our natural world. Our
understanding of nature and the heavens has changed greatly since the 17th
century in Japan. Life at the sub-atomic level and on the grandest scales
of existence are suitable subjects for haiku, and do not violate the form's
purity. Buddhism adapts.

Unseen dark matter,
Is sculpting the Universe:
Maple's buds open.

Commentary:
The cutting word is Universe. While dividing the verse into two very
distinct segments, it also confirms dark matter is just as valid as the
mundane maple tree as a subject for haiku.

10. Spiders

Two spiders,
In nook of the shower stall,
Safe from water spray.

Golden orb weaver,
Perfectly still in its web,
In the mangrove swamp.

Commentary:
After morning meditation, Master Bankei led all of his monks out onto the
lawn in front of Ryomonji Temple. The early light illumined hundreds of
small spider webs spun into the wet grasses. "Whoever can look at this
field," he said, "and tell me what he sees has entered the Tao."


11. One Drop of Water

The brief squall passes,
One drop of water glistens,
On each pine needle.
Commentary:
In samsara, the conventional world, we are each have the delusion of
existing as discrete beings, like separate H2O molecules, and have a sense
of duality with the world around us. But at the ultimate Big Mind state of
being, we are fungible, indistinguishable entities like the drops of water
in the streams and oceans. This is the truth of non-duality.
"In one drop water, no matter how tiny a drop, the water's great value
doesn't change at all. If you can't understand the value of one single drop
of water, no matter how hard you train, you'll never become someone who can
give life to that training." -The Path of Bodhidharma, Shodo Harada Roshi

12. The snapping Turtle
Preface:
The alligator snapping turtle makes its home in the waters of the south
eastern United States. This is a powerful creature, with a bite that can
easily amputate a man's finger. Fully grown, it has three rows of spikes on
its carapace.

A snapping turtle,
The spike on its carapace,
Punctures the cosmos.

Commentary:
The cutting word is carapace, the animal's shell.

13. Water Striders
At dokusan, the private interview between a roshi and a student, Zenkai
assigned his most advanced student the koan, "Why did Bodhidharma come to
the East (to America). This was a simple variation on the widely known koan
regarding Bodhidharma coming from the West (from India to China).
Responses from monks and students over the years had always provided the
Master with great amusement and sometimes with keen Zen insight.
Zenkai selected this koan because it was the third day of sesshin, and he
believed the student's nature might be ripe for a breakthrough. Also, he
was curious to hear what a Westerner could do with Bodhidharma's journeys.
The long time Buddhist student bowed with his hands in gassho, and without
hesitation replied:

Zig-zagging insects,
Hundreds of water striders,
Leaving V-shaped wakes.

Zenkai said, " That makes as much sense as any response I've heard." He
immediately certified the student's mild enlightenment experience, and gave
him the Dharma name Mumon, meaning "no gate."

14. Sandhill Cranes
Preface:
Sandhill cranes are large birds, native to North America and parts of
Siberia, that have gray feathers, red foreheads, long legs, and a long neck.
Their distinctive trumpeting is a cry that can assist any meditation. They
live in mated pairs, and are frequently seen with a chick in their company.

Drowned out by the rain,
The sandhill cranes' trumpeting,
Now just faintly heard.

Returned to their nest,
Mated sandhill cranes trumpet:
Drought in the wetlands.
Commentary:
Across Asia, cranes are symbols for youth, happiness and long life, a ready
inspiration for Taoists. In Japan, cranes have a legendary lifespan of 1000
years. In the second verse the kireji is trumpet.

15. Dragonflies

Perched on my finger,
Black pennant dragonfly,
Claspers holding tightly.

Commentary:
Several years ago I was paddling the Loxahatchee River in southern Florida
when I passed what appeared to be a dead dragonfly floating motionlessly on
the low tide. About 50 yards upriver, I decided to circle back and have a
closer look at my favorite insect.

When I scooped it up with my paddle, its transparent wings began to move. I
brought him into the boat, and maneuvered it onto my ball cap. I knew there
was a sloped beach access near my put-in, and to there I paddled. The
dragonfly a black pennant, recovered quickly, but showed no inclination to
take flight.

I beached the boat, coaxed it on to my finger, and scrambled up the bank.
The dragonfly wouldn't budge. He dug into my finger with six strong legs.
We remained in a stalemate for a few minutes before I maneuvered it on to a
palmetto frond. It seemed fine. One last look, and then I returned to my
kayak.

16. Bees
Preface:
The bee's hive possesses all the well-ordered behavior of a monastery. Each
bee knows, and is adept, at its job. Science has affirmed all of mammalian
life is dependent on the bees to fertilize crops and flowers.

Bees swarm in the grass.
Tasting the clover's nectar:
Broad swatches of sand.

Commentary:
The cutting word is nectar, a delicious word. The traveler has made many
attempts, but has never been able to locate the bee hive in the pine flat
woods. The Royal Jelly is the sweetest honey in the hive. There is a
period in almost every meditation when you taste the Royal Jelly.

17. The Soft Shell
Preface:
Turtles in fresh or brackish waters have the local name "cooters." Most of
them are red eared sliders.

Hauling the soft shell,
To the St. Lucie's shoreline:
Plop! Of a turtle.

Commentary:
This soft shell was found approximately 200 yards from the river, making it
way to the steep bank. The traveler provided an assist, setting the turtle
down about 10 yards from the water. Moments later: the extremely pleasant
plop! As it dove into the river, and swam northwards.

18. The Slough
Preface:
This verse was written in the Ten Thousand Islands on Florida's southwest
coast. The slough would make a strong support for meditation. Better than
a wall, a statue, or a hermit's cave.

Hundreds of islets,
Strewn across the shallow slough:
Osprey gathers nest.

Commentary:
Slough is the cutting word.
The islets are limestone, stained brown by tannin, that have built by
mangrove trees taking root, and trapping sediment. Each individual islet or
island is "a jewel in the heart of the lotus," Om Mani Padme Hum.

19. Mulch

Disc shaped depression,
In the wet red cedar mulch:
A box turtle's nest.

Commentary:
One good haiku should occupy the reader's mind uncluttered, by itself, not
one of twenty read in three minutes. Reading haiku is an art form, just
like writing the verse. A distracted mind will miss the mulch's essence.

20. Wake of Vultures

Preface:
The collective noun for vultures feeding on carrion is wake. Vultures are
the hardest working birds in the animal kingdom, feeding on animal corpses,
and reducing the possibility of diseases spreading.

A Wake of Vultures,
Mobbing the caracara:
Swales fill with water.

Commentary:
The caracara is a raptor, a fierce opportunist. Known as the Mexican Eagle,
it is equipped with powerful beak and claws.
In Tibet, vultures are accorded the status of dakinis, female bodhisattvas.
In a Tibetan "Sky Burial," a human corpse is chopped up, sent aloft, and fed
to the vultures.

21. The Donkey Brays

Pausing to moon-view,
While a nearby donkey brays:
Venus trails behind.

Commentary:
The sound of a donkey braying is the Buddhist "Call to Prayer." Pause when
you hear this unique, comforting sound. It is the voice of Shakyamuni
experiencing Awakening as Venus rose in the sky.
22. A Blow Hole
Preface:
A blowhole is a gap in a reef through which the surf enters and leaps
skywards.

Sound of breaking waves:
A spray of sea-water shoots
Through the reef's blow hole.

Commentary:
The spray of water acts as a prism.

23. Maggots
Preface:
Haiku's subject matter is wide open and non-judgmental. There are no
appropriate or inappropriate topics. Typically, haiku journals abound with
moonlit pine branches, the cry of the osprey, dragonflies perched on bamboo
shoots, and the reflection of stars in a pond. But a poem could readily
address maggots wriggling in a trash heap as evening rain glistening on
banana leaves. In Zen doctrine, all phenomena are empty, empty of inherent
self-existence. All phenomena are equal.

Fat maggots wriggle,
On the open trash can's lid:
Late afternoon light.

Empty trash barrels:
Catfish swim the riverbed,
Devouring debris.

24. Pelican Skull

The pelican's skull,
Beak and jaw disintegrate,
After forty years.

Commentary:
The coral reef refracted as the ocean swells rose and fell. Sean Yeats had
paddled his eighteen foot fiberglass kayak out the St. Lucie inlet, then
north along Hutchinson Island to a familiar dive site located approximately
two miles offshore. Certified in kayak rolls and self-rescues, Yeats
capsized the boat, detached the spray skirt, and performed a wet exit.
A bungee cord connected his ankle to the boat as he kicked, and dove down 10
through the clear water to the ocean floor. There, among sand dollar shells
and the fire coral, was the pelican skull, fully intact, and the last piece
Yeats needed for his personal meditation altar.

25. The Tao

In the pine flat woods,
The orchids present the Tao,
And so do the rocks.

Commentary:
As do the trees, the lake, and the woodpecker's cry.
26. Mayflies

Always in motion,
The scarcely noticed mayfly,
Alights so briefly.

Commentary:
Many phenomena, such as the mayfly, elude our notice. It is worth noting
that ontological reality consists of what the brain/ mind perceives. This
differs somewhat for each of the seven billion people on this planet,
depending on the acuity of their senses, causes and conditions, and karmic
emotional states. For some, the blind, deaf, and head trauma victims,
reality's texture varies dramatically and greatly. Few ever notice the
mayfly.

27. The New Moon

The winter solstice,
New moon black against the stars:
Rustling sounds are heard.

Commentary:
Stars are an effective cutting w forming a juxtaposition between empty moon
and rustling sounds of a small animal in the brush. This haiku makes a
companion verse to the first verse of The Taoteching.

28. Lungfish

Million years past,
The first lungfish flopped on land:
Suffering ensues.

Commentary:
Haiku originated from "Play Verse," and did not always have a intimate
connection with Zen. Nevertheless, this lighthearted haiku does ask the
question, "When did Buddha Mind manifest in sentient and insentient beings?"

29. Wary

Two bobcat kittens,
Warily follow mother,
Across the driveway.

30. Kindness

Opossum ambles
Back to its nest in the woods:
A donkey braying.

Commentary:
Sean Yeats' meditated each morning after sunrise on his screened- in patio,
in front of a Buddha statue surrounded by orchids in bloom and a pelican
skull. Typically, this entailed 20 or 30 minds of calm, abiding, followed
by either tonglen or reflection on Buddhist aphorisms.
One December day as he was "breathing out, breathing in," one of the nearby
donkeys in the agricultural community began, and continued braying. No Zen
Master could have shown greater kindness. Yeats's mind had gradually been
ripened. The donkey's Great Cry shattered Yeats' drifting thoughts, and,
for a brief time, he experienced Big Mind unfettered. Such kindness he'd
received!

31. The Viewing

Lying in coffin,
No longer animated:
Mourners mumble prayers.

Commentary:
I knelt at the railing in front of the coffin at All Soul's Funeral Home,
and looked in at the corpse of my old friend Judy. "You are in the bardo,
the between state," I said quietly. "Be calm. What you see and hear are
your own peaceful and wrathful deities. Don't be afraid. They cannot harm
you and wish only to lead you to the serenity and wisdom of your innate
Buddha nature.

A Catholic prayer service was scheduled to begin in fifteen minutes. I made
the sign of the cross for Judy, whispered the Hail Mary, and rejoined my
friends at the back of the hall.

32. Senryu

Tangles of pine roots,
I plant my staff carefully,-
But still stumble!

Commentary:
Senryu are an important subset of haiku. These are the seventeen syllable
verses that deal with human affairs and emotions. The original form had not
the least bit of an "I" involved in the composition. But this cannot truly
be done without involving the workings of the self and the senses.

33. The Summit

Mountain range of clouds,
Illumined by the sun,
Summiting each one.

Commentary:
While sun is not really a cutting word, it does set up the third line.
All Buddhists, on a daily basis, are attempting to summit Mount Kailash, the
sacred mountain. The toeholds are difficult to find.

34. Lightning Awakening
Preface:
Lightning flashes may be perceived as either cloud-to-Earth, cloud-to-cloud,
or Earth to cloud.

A thin lightning bolt,
Leaps from Earth to the cloud tops:
Pleasant ozone smell.
Commentary:
The two major Zen schools are the Rinzai and Soto. Rinzai aims for sudden
enlightenment, Soto for gradual, achieved through many hours of zazen
meditation. Our minds are always ripening when we practice. All Awakenings
are lightning flashes.

35. The Red Claw

Mouse runs for wood line,
At first threat of predator:
Safe in its burrow.

Commentary:
All sentient beings are both predator and prey. Large animals feed on small
animals, the small, even microscopically small, feed on the large creatures.
This is the Buddhaverse of the red claw and the red tooth.

36. The Path
Preface:
The path to an Emergency Room is one dreaded by all, and one that is
constantly looming.

Fearful, bored people
In the ER's waiting room:
Suffering and pain.'

Commentary:
The path to the liberation from suffering is The Four Noble Truths. -.
First Truth: An unenlightened life consists of suffering. -Second Truth:
Suffering results from pain, dissatisfaction, unsatisfied desires and
attachments in a world characterized by impermanence. - Third Truth:
Suffering can be ended. - Fourth Truth: Suffering can be ended by
meditation, compassion, mindfulness, and an understanding of the ultimate
nature of reality (Emptiness).

37. The Day's Cycle

Birdsongs replace stars.
And then the birds are silent:
Crescent moon at night.


38. The Moon

The moon is immune
To the Earth's weather patterns:
It waxes and wanes.

Commentary:
Wu-Wei is an essential Taoist concept meaning action created out of
non-action. Sages are in accord with the Tao, therefore they act without
effort. Every action, every spoken word, every thought is in harmony with
nature. The Earth and the moon represent wu-wei.
39. Not Today

Water lily leaves,
Uprooted by the storm's winds,
Float across the pond.

Commentary:
Sean Yeats leaned on his bamboo staff, and thought fondly of the Holy Fools
and Crazy Wisdom Sages for whom the lake is Buddha, the uprooted water lily
leaves are Buddha, the pines and the hog ruts are Buddha. The alligators
and the cooter turtles are Buddha. Mind is Buddha and mind is unbound
emptiness, thought Yeats; pleasant, so pleasant, he reflected, but for me,
not today.

40. Ferocity

Piglets crossing path,
While the tusked boar stands guard:
Hiker leans on his staff.

Commentary:
Master Nansen was asked by Ganto, a young novitiate, how he would
characterize a man whose life was driven by anger, attachment, and delusion.
"Such a man," replied the Zen Master, "is like a contented pig lying at the
feet of its butcher."
Nansen was ferocious in his pursuit of the Dharma, a tusked boar.

41. Survival instincts

Earth's revolution,
Triggers ancient migrations:
Encodes all species.

Many species of animal life follow this encoded map to locate mating grounds
that may be located thousands of miles from their natural habitat. They are
following instinct, which in the animal kingdom is Right Effort, one of the
steps in the Eightfold Path.

In humans, Right Effort is a dangerous path. To become an Awakened One, the
practitioner must be capable of doing things of which less enlightened
beings are capable. This requires the bodhisattva to act against many of
the ego-driven survival instincts wired into our brains in the last 170000
years.

42. The Milky Way

Venus shines aloft,
In the cloudless pre-dawn sky:
An early moon set.
Commentary:
The moon's early setting removed the light pollution, displaying the Galaxy.
At age 23, Bankei returned to his angya, the travel that is part of a Rinzai
Monk's education. Still consumed with a longing to attain Buddha Mind, he
sought solitude, and moved into a hut in the village of Nonaka. No teacher
had been able to point a finger at the moon.
Bankei spent the next two years enduring an ascetic's hardships, starving
and depriving his flesh. He seldom left his hut, devoting upwards of 18
hours per day to deep meditation. He learned to resist both heat and cold.
His only sustenance was a bowl of rice brought to him by a monk from nearby
Zuioji Temple.
In the spring of 1647, Bankei lay on his mat, ill, emaciated, and seemingly
close to death. On the night of his Enlightenment, Bankei, sick from the
Three Poisons (anger, attachment, delusion), dry heaved twice, and then
puked out the Milky Way.

43. Pilgrimage to Bodh Gaya

Journeying to see
The jacaranda tree in bloom,
Ah, purple flowers.

Commentary:
Many people traveled a great distance to view a grove of exotic jacaranda
trees in bloom. Purple bell shaped flowers filled the tree's gray limbs.
Thousands of gray flowers were sown in the field's grasses. Each year,
Master Bankei spoke at the jacaranda Festival, teaching monks and lay people
about the Unborn Buddha Mind.

"I have always dreamt of sitting on the Buddha's Diamond Throne beneath the
Bodhi tree and meditating while the morning star rises," said a samurai who
followed the Dharma. "What merit will I gain by making the pilgrimage to
Bodh Gaya?"

"None, whatsoever," replied Bankei. The Buddha, himself, hasn't been at
Bodh Gaya for over 2,500 years. All latitudes and longitudes are the same.
All trees are the Bodhi tree. Meditate beneath that jacaranda after the
rest of us have departed.

44. A Pine Twig

Long Winter's darkness:
Through pine trees an orange moon,
Is quickly hidden.

Commentary:
Darkness is the cutting word.
Taibi complained to Master Baso during dokusan: "For three months now I've
been meditating on the sound of one hand, but all I've heard is the
scratching of a pine twig against the wall of my hut."

45. Fiery Orchids

Winter in the woods:
Acres of sharp palmettos:
Orchids bloom in fire.

Commentary:
The cutting word is palmettos.
Any day that includes a hike in the woods, along the shore, or in the
mountains in a meditative state of mind is a worthy day. This confers the
seldom mentioned virtue of contentment while you enjoy right-concentration.
Even orchids will bloom in fire. But be careful of those pointy palmetto
fronds!

46. Ghost Crabs

Ghost crab waves eye stalks,
Then disappears down burrow,
In the sandy beach.

Commentary:
Daydreaming is very pleasant and, in doing so, you can disappear down a
ghost crab burrow for hours, time during which you do not fully exist. How
soothing it is to replay events in our mind, shifting around the events to
provide different, more felicitous outcomes.

47. The Four Seals

Waves lap against the pier,
Pipefish nibble at wharf pilings:
The planks well weathered.

Clear to the heavens,
Blue sky teems with energy:
Motionless tree tops.

Commentary:
Haiku correlates well with Buddhism's Four Seals. First Seal: All entities
are impermanent. Second Seal: All phenomena are, by nature, unsatisfactory
to the unenlightened being. Third Seal: All phenomena both sentient and
insentient, are empty. Fourth Seal: Nirvana is true peace, and suffering
can be ended. A true understanding of the everyday world is the liberation
from suffering. Haiku can assist that understanding. Well weathered.
Space teeming with energy.

48. No preferences

Fed from underground,
Mushroom caps swollen from rain,
Appear suddenly.

Commentary:
Prior to his testing for his Geshe degree at Samye monastery, Thubten Norbu
undertook Tibetan Buddhism's rigorous three year, three month, three day
solitary retreat. Norbu selected a high altitude cave as his hermitage.
This was a barebones retreat. He slept in his meditation box, gathered food
from the vegetation growing at lower altitudes, and collected water using
buckets and siphons.
When the period of solitary meditation was completed, Thubten Norbu returned
to his monastery. The head lama greeted him warmly, asking, "During the
three years, three months, and three days, what did you learn?"
I learned," responded the monk, that mushrooms appear suddenly, and that I
no longer have any preferences."

Note: Hsin Hsin Ming, attributed to Seng-t'san, the third Chinese Zen
Patriarch, develops "No Preferences" as a practice. The text also contains
many Taoist influences.

49. Validating Science

Energized protons,
In the Hadron Collider:
The Higgs-Boson forms.

Commentary:
After 2500 years, Buddhism is still validating scientific findings. Recent
advances in Quantum mechanics and astrophysics have accelerated this
process.
If I had presented my 12th grade physics teacher with The Heart Sutra (Form
is emptiness, Emptiness is form), he would have said "Absurd," and maybe
made disparaging comments. Now if I were to present him with the Sutra,
he'd exclaim, "This is it! This is the essence of our Universe."

50. The Mundane

The longhorn steer rests,
Oblivious of the rain,
Calm in pasture.

It is the third month:
The food market's parking lot,
Is scavenged by crows.

Commentary:
Haiku has a definite affinity for the mundane. Everyday life with its
common images and familiar sights are the basis of mindfulness. Be aware of
the local, not so spectacular, flora, fauna, and human activities. For the
most part, we live in the familiar.

51. How Hard Could it be?

The manta ray glides,
Tracelessly through sea grass:
Lagoon's nursery.

Commentary:
One day Master Bankei addressed the multitudes who had come to his Temple at
Ryomanji: "just yesterday a monk from Kyoto came to me asking how many
lifetimes he could expect to spend in samsara, providing he was on the
Dharma Path. He was ready to toil through hundreds of rebirths, purifying
his karma in order to solve the great mystery of existence."
"I told him to leave the monastery if he didn't believe he could achieve
enlightenment before nightfall. Live the life if a drunk, I told him. He'd
be better off."
Enlightenment resides within our minds. Don't accept your own delusions, or
those of others. The manta ray glides tracelessly across the ocean floor.
How hard could it be?

52. Invisible Forces

The magnetic pull,
Pulls iron chunks through space:
Invisible force.

Commentary:
"But why is it real? Because mind conceives it."- John Blofeld, Bodhisattva
of Compassion.
Reality is as our five senses conceives it .This differs, at least somewhat,
for each of the seven billion human beings on this planet, depending on the
acuity of their senses. For some, the blind, head trauma impact patients,
etc., ontology may vary greatly.
And there are many forces we can't perceive with our senses. The
electromagnetism that moved the iron in the haiku above, gravity, the Higgs
field, certain broad bends of light, dark matter, and dark energy comprise a
few of these invisible forces. There might well be spirits whose realm lies
beyond our senses. "True, true," thought Sean Yeats, whose life had
interacted with a dakini, sometimes wrathful, since his Junior High School
years.

53. Disparate Elements

Particles decay,
To much lighter neutrinos:
Three pink flamingoes.

The cawing of crows,
On a sweltering hot day:
Kudzu vines shroud pines.

Commentary:
The cutting words are, respectively, "neutrinos" and "day." They juxtapose
two seemingly disparate elements of the Earth into two elements. By doing
so, they have the paradoxical effect of eliminating the illusion of duality.
All entities are One, though do not appear so to the cognitive brain. In
this regard, haiku may act in a way similar to koans.

54. The Ocean Changes Hands

Plastic container,
Washes up on the shoreline:
Seaweed floats in surf.
Commentary:
Bankei incensed Eshun with his boasts that "the waves, the fishes, sea.all
of this belongs to me." Enshun knew ownership to be illusion. Cultivation
of personal property, he insisted, strengthens your tie to the origin of
suffering. "You're a likeable fellow," Bankei stated, "but you still
haven't developed a sense of non-attachment."
One night the monks departed the monastery for a walk along the nearby
beach. Can any man rival my wealth?" he said as they watched the breakers
slam into a reef. Outraged, Enshun challenged his audacious friend, "If the
ocean really is yours, take it back with you to your room when we leave.
Fishermen along the coast frequently use Clorox jugs as buoys to mark their
lobster traps. One of these bottles had snapped loose during a recent
storm, and washed up on shore. Bankei retrieved the opaque container,
unfastened the cap, and submerged it in the surf. After a minute, he
withdrew the bottle, and held it aloft. He was unsatisfied as the bottle
was only 2/3 full. "You see," he explained. "all of the air has not been
displaced."
He dunked the vessel once more, this time until it would not absorb a single
additional drop. "Let's return to the monastery." He said, tucking the
bottle under his arm. I've got what I need," he said, "you may have the
rest."

55. Opossums

Pits dug in the soil,
Where the opossums forage,
Near the ficus tree.

Commentary:
Ficus trees are commonly referred to as banyan trees. It was beneath a tree
of this species that Shakyamuni was enlightened.
Sean Yeats delighted in watching these marsupials. One had several babies
clinging to her fur. Generally, they are solitary and nocturnal. But this
grouping had become comfortable on Yeats' 5 wooded acres. They practice
wholeheartedly, thought Yeats.

56. An Atom

In the nucleus,
Three quarks are bound together:
Electrons revolve.

Commentary:
In the past 50 years particle physics have made many discoveries about the
components of the natural world.

57. Early Life Forms

From the ocean floor,
Single cell archaea,
Pour from thermal vents.

Commentary:
Current studies indicate life may have begun on this planet with the archaea
that formed colonies around thermal vents, breaks in the ocean floor through
which volcanoes delivered extreme heat and chemicals. Did the archaea have
Buddha nature? If not, at what point in evolution did Buddha nature
manifest.
58. Perfect Balance

Mottled snake skin shed,
On the ficus bonsai's limbs:
No Yin and No Yang.

Commentary:
Perfect balance: no Yin and no Yang.

59. Paganism and Seagrass

Autumnal equinox:
Balance between light and dark:
Seagrass flows with tide.

Commentary:
Seagrass is the cradle of the life cycle in an estuary. It is the where the
small fish and the rest of the food chain's bottom hide. Similarly,
Paganism, still widely practiced today, was the cradle of many benevolent
religions. Like the seagrass in many lagoons, Pagan covens have been under
stress. Many of us, if not all of us, had ancestors who practiced Paganism.
We still practice it today. It is embedded in our culture and our
religions.

60. The Waterfall

Wood rat roams mud flats:
The tide drains the mangroves,
A waterfall sound.

Commentary:
The cutting word is flats.
I have kayaked the Loxahatchee River many times, on many different tides.
On this day I was startled to hear a thunderous waterfall sound as the tide
drained. I paddled over and saw a section of the bank, elevated above the
rest of the shore, that produced the roaring. I also saw the wood rat
scurrying.

61. Reading Haiku
Reading haiku is an art form, just like writing the verse. A distracted
mind will miss the essence of the poet's insight. The haiku reader has only
seventeen syllables with which to work. He must be able to make
associations, have the ability to see, hear, and smell images vividly. In
some cases, the reader may even have to "fill in the blanks," know how to
comprehend, using only a fragment of an image. One is expected to complete
what, in many cases, the poet has just begun.
Haiku do not really require commentary or explanations. Just read them
mindfully. Here are a series of "stand-alone" verse.

The snow is falling,
Trespassing on hilly ground,
Skidding down the slope.

Meteor shower
As the Earth passes through,
A comet's debris.

In mid- November,
Black pennant flag dragonflies,
Replace green darners.

From drought to monsoon,
The unseen steering currents,
Bring the wind and rain.

Brownian movement,
Makes an atom's path random:
Tree frogs bark at dawn.

Behind the worm reef,
Glint of a barracuda,
Small, bright fish scatter.

As the rain tapers,
Flying insects leave shelters,
And the sky whitens.

Barrier Island,
Reshaped by tides and weather,
Protects the coastline.

A sudden cloud break,
The bamboo leaves glistening
In the sun shower.

The cottonmouth swims,
Then ascends the river's bank:
Moss grows on oak limbs.

62. The Dharmakaya

Neutron stars collide:
Gold and heavy metals sown,
Throughout the Universe.
Commentary:
At what point did Buddha Nature enter the Universe? The answer is from the
moment of the Big Bang. Matter, energy, time, and gravity originated from
the Dharmakaya.

20 Aug 2017 »
Entrusting vs. Reasoning

“Sentient beings” are so called because they have sensations, feelings and emotions, which are invariably arbitrary, defiled and self-indulgent. Hence the terms “defiled emotions” and “obsessive emotions.” Passions are the roots of various afflictions. We see that emotional and sentimental people tend to suffer more from the vexations of life. In order to curb vexations, one turns to reasoning. To reason means to think, act and make decisions and choices in a calm and rational way, so as to avoid impulsive behavior.

“Don’t get emotional, be rational” is a universal guiding principle, including for Amitabha-reciters of the Pure Land school. However, this approach to life is at a lower plane than “entrusting”: to dedicate our lives totally to Amitabha Buddha and have complete faith in his deliverance. It is a quest for true life and an awakening. It transcends reason and emotions, yet includes and does not reject rational and passionate expressions. Sentient beings come in different capabilities and aptitudes -- some are more emotional while others more rational.

Schools of the Sacred Path place greater emphasis on being rational. We learn from the Surangama Sutra that if a person “is endowed purely with rational thought, he will soar in the air and be reborn in heaven.” However, “he will descend into the hell domain if his mind is dominated by extremely volatile passions.” The Pure Land path, however, transforms emotions skillfully. In the Contemplation Sutra, we see that Queen Vaidehi was a highly emotional and foolish ordinary being. When tormented by extreme suffering and feeling despondent, she cried out for mercy and yearned for a new life from the core of her being: “I beseech you, World-Honored One, to reveal to me a land without sorrow and affliction. I should seek rebirth there. I do not wish to live in this defiled and evil world of Jambudvipa anymore.”

Entrusting our lives to Amitabha Buddha is largely viewed as a manifestation of emotion. This is because sentient beings are inherently oriented to sentiments. They perceive Amitabha’s deliverance as benevolence and loving-kindness. Even our weariness of the Saha world, our delight in the Pure Land and aspiration for rebirth there can be said to be a form of emotion.

Compared with reason, sentiments are more susceptible to being defiled and clinging. Normally, the anguish experienced by those who are fettered and hurt by love is heart-breaking, much more so than that felt by those who are pained by a conundrum of rational thinking. For most people, the vitality and sensation they feel from passions are much more intense than those experienced from an obsession with reason. As a result, they are much more eager and motivated to be rid of afflictions brought by passions, compared to those who are preoccupied with rationality.

The Pure Land teachings skilfully steer passion-ridden ordinary beings towards purity and serenity. For example, in the Commentary on the Treatise on Rebirth in the Pure Land, Master Tanluan uses the metaphor of “making a fire on ice” to explain that even the most degraded beings who do not know that the intrinsic nature of existence is non-birth would, if they recite the name of Amitabha Buddha and aspire to be reborn in his Pure Land, have the fire of their wrong views spontaneously extinguished, since the Land of Bliss is a realm of non-birth. The deluded views are like a fierce fire which melts the ice; when the ice melts, the fire is extinguished. This is why Pure Land practice is also called the Easy Path.

That said, we Amitabha-reciters should strive to be more rational than emotional, while not losing sight of the paramount importance of entrusting our lives entirely to Amitabha Buddha and his deliverance. In any event, if we recite his name, our minds will naturally become more peaceful and rational as we are being embraced by Amitabha’s light. The result is that our afflictions and troubles will be minimized.

-- Master Jingzong
(English translation by Foying, edited by Fojin)
归命与理性
众生又称“有情”,即有情识、情感、情绪。众生之情总是主观的、染污的、执著的,故说情染、情执。由情生出种种苦恼>。现实所见情绪比较重的人,总比别人多一重烦恼。为对治情绪,故说理性。理性,乃是按事物本来之理,冷静合理思维>、行动、判断抉择等,以减少情绪冲动。

“理性不情绪”是所有人的通则,净土念佛人当然也不例外。但这是次一级层面的,更深层面的是“归命”,即全副生命归投>弥陀救度,这是生命的渴求与觉醒,超越理性、情绪的层面,也包含、不拒绝理性、情绪的表现。因众生根机不等,或重>情绪,或较理性。
圣道法门更重理性,《首楞严经》言:“纯想即飞,纯情即堕。”净土法门巧化情绪,《观经》韦提希夫人即是情绪很重、>不理性之凡夫,为苦恼所逼,无路可走,才从生命之底发出呐喊、渴盼,“唯愿世尊,为我广说无忧恼处,我当往生,不乐
阎浮提浊恶世也。”

归命阿弥陀佛往往表现为情感的成分多,这是因为有情众生本来偏重于情,弥陀慈悲救度在众生边也多体会为慈爱温情,>乃至厌秽欣净、愿生净土也是一种情。
情、理相比,情较染著,粘腻,为情所困、所累、所苦者往往锥心刺骨,其觉受更甚于迷于事理者,于多数人,情之生命>力表现、觉受,以及欲脱情苦之盼望、动力或更甚于迷理者。
净土门善用凡情入于清净,如《论注》冰上燃火喻所明,故是易行道。

话虽如此,在全副生命归投弥陀救度前提下,念佛人亦当注重理性不情绪,这也是佛光照摄心念趣于平静理性之表现,由>此会减少很多不必要之烦恼。


Machine-translation:

Fate and reason.
" empathy that is, empathy, emotion, emotion. All beings are always subjective, stained, obstinate, and. All sorts of afflictions. The reality is that people who are more emotional than others are more upset than others. To be rational, to be rational. Rationally, it is a matter of logic, calm and rational thinking, action, decision-making, and so on, so as to reduce emotional impulses.

"irrational emotion" is the general rule of all, of course, of course. But this is a sub-level, and a deeper dimension is "Life-saving that is to say," life is life that is the thirst and the awakening of life, beyond rational and emotional dimensions, and not to be irrational and emotional. Performance. Because of the creation, or the emotion, or the rationality.
The Holy Spirit is more rational and rational, " first :" " Pure, pure, pure, pure, pure, pure, pure, pure and simple. Not,, no, no,, keen, keen, keen, keen, and. Yan floating is a bad man."

The fate of the Buddha is often shown as an element of emotion. It is because of the emotions and compassion, Amitabha, compassion, compassion and compassion, as well as the warmth and warmth of the people.
In Comparison, it is more painful, sticky, tired, tired, tired and tired of all those who suffer and suffer more than their minds, in the majority, in the life of the people. And the desire, the power, or more than the riddler.
It is an easy way to make good use of the land of pure land, for example, when it comes to light.

Having said that, under the premise of the heavily of life, the Buddhist people also focus on rational and irrational behaviour, and this is also a manifestation of calm and rational behaviour in the light of the Buddha, which will reduce many unnecessary worries.
31 Jul 2017 »
Happy B-day to Dr. Laird ! Yeh... CVS order due to be picked up after Aug. 2nd Bronx NYC 235 Ave(?)
10 Jul 2017 »
《弟子規》原名《訓蒙文》,為清朝康熙年間秀才李毓秀所作,後來清朝賈存仁修訂改編《訓蒙文》,並改名《弟子規》。

李毓秀(公元1662年至1722年),字子潛,號采三,清代康熙時山西絳州人,生於清代康熙年間,卒於乾隆年間。清初著名學者、教育家。從師黨冰 壑游歷近二十年。精研大學中庸,創辦敦復齋講學。 李毓秀學問好,修養好,來聽課的人很多,門外滿是腳印。太平縣御史王奐曾多次向他請教,十分佩服他的才學,被人尊稱為李夫子。他的著作有《弟子規》、《四 書正偽》、《四書字類釋義》、《學庸發明》、《讀大學偶記》、《宋孺夫文約》、《水仙百詠》等,分別藏於山西省圖書館和北京大學圖書館。 因撰寫《弟子規》,去世後他的牌位被供奉在絳州先賢祠。

特別是《弟子規》(初版時稱《訓蒙文》,浮山賈木齋修訂為《弟子規》),輾轉翻印,流傳甚廣,成為清代至民國年間通用的兒童啟蒙讀物。此書以淺近通 俗的文字、三字韻的形式闡述了學習的重要、做人的道理以及待人接物的禮貌常識等等。
總敘

弟子規 聖人訓 首孝弟 次謹信
汎愛眾 而親仁 有餘力 則學文
入則孝

父母呼 應勿緩 父母命 行勿懶
父母教 須敬聽 父母責 須順承
冬則溫 夏則凊 晨則省 昏則定
出必告 反必面 居有常 業無變
事雖小 勿擅為 苟擅為 子道虧
物雖小 勿私藏 苟私藏 親心傷
親所好 力為具 親所惡 謹為去
身有傷 貽親憂 德有傷 貽親羞
親愛我 孝何難 親憎我 孝方賢
親有過 諫使更 怡吾色 柔吾聲
諫不入 悅復諫 號泣隨 撻無怨
親有疾 藥先嘗 晝夜侍 不離床
喪三年 常悲咽 居處變 酒肉絕
喪盡禮 祭盡誠 事死者 如事生
出則弟

兄道友 弟道恭 兄弟睦 孝在中
財物輕 怨何生 言語忍 忿自泯
或飲食 或坐走 長者先 幼者後
長呼人 即代叫 人不在 己即到
稱尊長 勿呼名 對尊長 勿見能
路遇長 疾趨揖 長無言 退恭立
騎下馬 乘下車 過猶待 百步餘
長者立 幼勿坐 長者坐 命乃坐
尊長前 聲要低 低不聞 卻非宜
進必趨 退必遲 問起對 視勿移
事諸父 如事父 事諸兄 如事兄


朝起早 夜眠遲 老易至 惜此時
晨必盥 兼漱口 便溺回 輒淨手
冠必正 紐必結 襪與履 俱緊切
置冠服 有定位 勿亂頓 致污穢
衣貴潔 不貴華 上循分 下稱家
對飲食 勿揀擇 食適可 勿過則
年方少 勿飲酒 飲酒醉 最為醜
步從容 立端正 揖深圓 拜恭敬
勿踐閾 勿跛倚 勿箕踞 勿搖髀
緩揭簾 勿有聲 寬轉彎 勿觸棱
執虛器 如執盈 入虛室 如有人
事勿忙 忙多錯 勿畏難 勿輕略
鬥鬧場 絕勿近 邪僻事 絕勿問
將入門 問孰存 將上堂 聲必揚
人問誰 對以名 吾與我 不分明
用人物 須明求 倘不問 即為偷
借人物 及時還 後有急 借不難


凡出言 信為先 詐與妄 奚可焉
話說多 不如少 惟其是 勿佞巧
奸巧語 穢污詞 市井氣 切戒之
見未真 勿輕言 知未的 勿輕傳
事非宜 勿輕諾 苟輕諾 進退錯
凡道字 重且舒 勿急疾 勿模糊
彼說長 此說短 不關己 莫閒管
見人善 即思齊 縱去遠 以漸躋
見人惡 即內省 有則改 無加警
唯德學 唯才藝 不如人 當自礪
若衣服 若飲食 不如人 勿生慼
聞過怒 聞譽樂 損友來 益友卻
聞譽恐 聞過欣 直諒士 漸相親
無心非 名為錯 有心非 名為惡
過能改 歸於無 倘揜飾 增一辜
汎愛眾

凡是人 皆須愛 天同覆 地同載
行高者 名自高 人所重 非貌高
才大者 望自大 人所服 非言大
己有能 勿自私 人所能 勿輕訾
勿諂富 勿驕貧 勿厭故 勿喜新
人不閒 勿事攪 人不安 勿話擾
人有短 切莫揭 人有私 切莫說
道人善 即是善 人知之 愈思勉
揚人惡 即是惡 疾之甚 禍且作
善相勸 德皆建 過不規 道兩虧
凡取與 貴分曉 與宜多 取宜少
將加人 先問己 己不欲 即速已
恩欲報 怨欲忘 報怨短 報恩長
待婢僕 身貴端 雖貴端 慈而寬
勢服人 心不然 理服人 方無言
親仁

同是人 類不齊 流俗眾 仁者希
果仁者 人多畏 言不諱 色不媚
能親仁 無限好 德日進 過日少
不親仁 無限害 小人進 百事壞
餘力學文

不力行 但學文 長浮華 成何人
但力行 不學文 任己見 昧理真
讀書法 有三到 心眼口 信皆要
方讀此 勿慕彼 此未終 彼勿起
寬為限 緊用功 工夫到 滯塞通
心有疑 隨札記 就人問 求確義
房室清 牆壁淨 几案潔 筆硯正
墨磨偏 心不端 字不敬 心先病
列典籍 有定處 讀看畢 還原處
雖有急 卷束齊 有缺壞 就補之
非聖書 屏勿視 蔽聰明 壞心志
勿自暴 勿自棄 聖與賢 可馴致
弟子規終
7 Aug 2016 »
hey, finally took the trouble to syndicate one of my Chinese blog content with my diary config... it looks like working great!

which is the more disappointing that this instance isn't working at the moment...
7 Aug 2016 »
why is diary editing not working ?
6 Oct 2015 »
source:
http://moneyandtech.com/july-11-news-update/

Japan’s new Bitcoin business advocacy group, The Japan Authority of Digital Asset, has launched with the government’s explicit support, aiming to help establish standards and codes of conduct for its member organizations. The group was formed by Japanese parliament member Mineyuki Fukuda and his IT Committee, after consulting with Japan’s Financial Services Authority and speaking with the country’s resident Bitcoin ATM companies and exchanges, which include digital currency exchange Kraken and its parent company Payward Inc.

Major music streaming service Grooveshark has started accepting Bitcoin for both their monthly and annual subscriptions, after receiving several requests from users to add the digital currency as a payment option. No official statement has yet been heard from the company, but several forum reports of the new payment option have begun surfacing from Grooveshark users in response to their requests.

Prominent porn video site xHamster, the 56th most popular website on the internet, has also reportedly started accepting Bitcoin as a payment option, which has sparked a slightly Not Safe For Work thread on the Bitcoin subreddit.

Bitcoin entrepreneur and nextcoin investor Androklis Polymenis is offering a 500 bitcoin bounty for the return of his lost 1170 bitcoin and 6 million nextcoin, which were stolen when a hacker posed as Polymenis on bitcoin exchange Bter.com and requested the removal of the funds.
27 Sep 2015 »
EQUILIBRIUM POINTS IN N-PERSON GAMES
By John F. Nash, Jr. , Princeton Univ.
Communicated by S. Lefschetz, Nov. 16, 1949

One may define a concept of an n-person game in which each player
has a finite set of pure strategies and in which a definite set of payments
to n players corresponds to each n-tuple of pure strategies, one strategy
being taken for each player. For mixed strategies, which are probability
distributions over the pure strategies, the pay-off functions are the
expectations of the players, thus becoming polylinear forms in the
probabilities with which the various players play their various pure
strategies.

Any n-tuple of strategies, one for each player, may be regarded as a
point in the product space obtained by multiplying the- n strategy spaces
of the players. One:-such n-tuple counters another if the strategy of each
player in the countering n-tuple yields the highest obtainable expectation
for its player against, the n - 1 strategies of the other players in the
countered n-tuple. A self-countering n-tuple is called an equilibrium point.

The correspondence of each n-tuple with its set of countering n-tuples
gives a one-to-many mapping of the product space into itself. From the
definition of countering we-see that the set of countering points of a point
is convex. By using the continuity of the pay-off functions we see that the
graph of the mapping is closed. The closedness is equivalent to saying:
if Pi, P2, ... and Qi, Q2, .... Qn, ... are sequences of points in the product
space where Q. -n Q, P n P and Q,, counters P,, then Q counters P.

Since the graph is closed and since the-image of each point under the
mapping is convex, we infer from Kakutani's theorem' that the mapping
has a fixed point (i.e., point contained in its image). Hence there is an
equilibrium point.

In the two-person zero-sum case the "main theorem"2 and the existence
of, an equilibrium point are equivalent. In this case any two equilibrium
points lead to the-same expectations for the players, but this need not occur
in general.

* The author is indebted to Dr. David Gale for suggesting
the use of Kakutani's theorem to simplify the proof and to the A. E. C.
for financial support.
1. 'Kakutani, S., Duke Math. J., 8, 457-459 (1941).
2 Von Neumann, J., and Morgenstern, O., The Theory of Games and Economic Behaviour,
Chap. 3, Princeton University Press, Princeton, 1947.

source:
http://www.pnas.org/content/36/1/48.full.pdf+html
21 Sep 2015 »
howdy!