



Historically long perspective

Suggests it as possible

That many of the intriguing

Yet ineffable experiences

Which humanity thus far

Has been unable to explain,

And, therefore, treats with only superstitiously,

May embrace phenomena

Which in due course

Could turn out to be complexes

Of physically demonstrable realities

Which might even manifest

Generalized principles of Universe.



For this and similar reasons

I have paid a lot of attention

To ancient numerology,

Thinking that it might contain

Important bases for further understanding

Of the properties of mathematics

And of the intertransformative

Structurings and destructurings

Of the cosmic scenario yclept

"Eternally self-regenerative Universe."



My intuition does not find it illogical

That humanity has developed and retained

The demisciences of

Astrology and numerology__

Demi because they are

Only partially fortified by experimental proofs__

Which nonetheless challenge us tantalizingly

To further explorations

Within which it may be discovered

That generalized scientific laws

Are, indeed, eternally operative.



Our observational awareness

And Newton's proof

Of the mass-attraction law

Governing the Moon's powerful tidal pull

On the Earth's oceans,

In coincidence with our awareness

Of the Moon phase periodicities

Of female humans' menstrual tides,

Gave the Moon's (men's month's) name

To that human blood flow.

Conceivably there could be

Many other effects of celestial bodies

Upon terrestrially dwelling human lives.



In the late 1930s,

When I was science and technology consultant

On its editorial staff, with Russell Davenport

Then managing editor, of Fortune magazine,

I found him to be deeply involved with astrology.

Russell couldn't understand why I was not actively excited

By the demiscience__astrology,

Since the prime celestial data derived

From scientific observations.

I was not excited

Because I had no experience data

That taught me incisively

Of any unfailingly predictable influence

Upon myself or other Earthians

Which unerringly corresponded

With the varying positions of the solar planets

At the time of the respective human births.

While the planetary interpositionings

At any given time had been scientifically established,

I had no scientifically cogent means for exploring

Their effect upon terrestrial inhabitants.



On the other hand, I found many cogent clues

For exploring the ancient demiscience of numerology.

Ancient numerologists developed

Many tantalizingly logical theories,

Some of which were

Partially acceptable to formal mathematics,

Such as enumeration by "congruence in modulo eight,"

Or, "congruence in modulo ten,"

Or in increments of twelve.



"Congruence in modulo ten" seemed

Obviously induced by

The convenience of the human's ten fingers

As memory-augmenting,

Sequentially bendable,

Counting devices of serial experiences.

Their common appendages of ten fingers each

Provided humans with "natural" and familiar sets

Of experience aggregates

To match with other newly experienced aggregates

As congruent sets.



There was also the popular enumeration system

Based on modulo twelve.

Human counting systems of twelve were adopted

Because the decimal system

Does not rationally embrace

The prime number three.

Since humanity had so many threefold experiences,

Such as that of the triangle's stability,

Or that of the father-mother-child relationships,

Humanity needed an accounting system

That could be evenly and alternatively subdivided

In increments either

Of one, or two, or three.

Ergo, "congruence in modulo twelve"

Was spontaneously invented.



"Invention" means

To bring into novel special-case use

An eternal and universal principle

Which scientific experiment and comprehension

May attest to be generalized principles.



"Etymology" means

The scientific study of words and their origin.

Through etymology man gave names

To their abstract number set concepts.



English is a crossbred

Worldian language.

It is interwoven with Anglo-Saxon,

Old German, Sanskrit, Latin and Greek roots

Interspersed with Polynesian, Magyar, Tatar, et al.

The largest proportion of English words

Are derived from India's Sanskrit,

Which itself embraces hundreds

Of lesser known root languages.



There are a few words whose origins

Have thus far defied scientific identification.

There are not many unidentified root words.

Those of unknown origins

Are classified etymologically as "Old Words."

All but one of the world-around

Words or "names" for numbers

Are classified etymologically as "Old Words."

The one exception is the name for "five,"

Whose conceptual derivation comes directly or indirectly

From word roots identifying the human "hand."

None of the other names for numbers

In any of the human languages

Have pragmatic identifiability

With names for any other known

Physical-experience concepts.



To accommodate the cerebrations

Of those who are reflexively conditioned

To recount their experiences

In twelvefold aggregates__

That is, "congruence in modulo twelve"__

Unique names were etymologically evolved

For the numbers eleven and twelve

As well as for the numbers one through ten.

In the new world-around-accepted computational system

Of "congruence in modulo ten"__

That is, the decimal system__

The numbers zero through ten

Are called "cardinal" numbers.



But the English names "eleven" and "twelve,"

Or French names "onze" and "douze,"

Or the Germans' "elf" and "zwoelf,"

Likewise are cardinal numbers

In the duodecimal system,

And their cardinal names are used

Even when employed in the decimal system.



Following twelve in the duodecimal system

The number names are no longer cardinal.

They are called ordinal numbers, which are produced

By combining one, two, or three with ten:

Thir-teen, four-teen, fif-teen, etcetera,

Which are three-ten and four-ten, alliterated

In English, French, and German.

It is not until thirteen is reached

That the process of counting ordinally (three plus ten)

Is employed in the ordinal naming of numbers

Where numbers are communicable by sound.



There are, however, number systems

Based on other pragmatic considerations.

Roman numerals constituted

An exclusively visual method

Of tactilely scoring or scratching

Of a one-by-one exclusively "visual" experience.

When nonliterates were assigned

To counting items such as sheep,

They made one tactile scratch

For one visually experienced sheep,

And a second tactile scratch

As another sheep passed visually,

And another scratch

As the next sheep passed.

The scratch was not a number,

It was only a tactile reaction

To visual experience.

It was a one-by-one,

Tooth-by-tooth intergearing

Of two prime

Sensorially apprehending systems__

Those of touch and sight.



While literate you, in retrospect, could say

That you see three scratches,

That is reflexively occasioned

Because you have learned to see groups

And because you have

A sound word for a set of three;

But nonliterate Roman servants who were scoring

Did not have to have number words

To match with tactile one-by-one scratching

Their one-by-one visually experienced,

One-by-one passing-by sheep.

The man doing the scratching

Did not have to have

Any verbal number words or set concepts.

Those landlords, priests, bankers,

Or unsolicited "protection" furnishers

Who were interested

In trading, taxing, or extracting

Life-sustaining wealth__

As sheep or wheat productivity__

Alone were concerned

With the specific total numbers of scratches

And of the total sheep or bags of grain

The ignorant servants had scratchingly matched.

From these total numbers

They calculated how many sheep or bags

They could extract for their taxes

Or landlord's tithe,

Or protectionist's fee,

Or banker's "interest"

Without totally discouraging

The sheepherders' or farmers' efforts.



"Pays" means land.

The shepherds and farmers

Were known as pagans

Or paysants, peasants,

I.e., land-working illiterates.



Because the first millennium A.D.

Roman Empire dominating Mediterranean world

Was so pragmatically mastered

By landlords and their calculating priests,

It is in evidence

That the Roman numerals constituted only

A one-by-one scoring system

In which the V for five and X for ten

Were tactilely "sophisticated" supervisor's

Tallying or totaling check marks

Which graphically illustrated

Their thumb's angular jutting out

From the four parallel packed fingers

Or digits of the totaler's free hand.

On the other hand, the intellectually conceived Arabic

numerals

Were graphic symbols

For the named sets

Of spontaneously perceived number aggregates.

The Arabic numerals

Did not come into use in the Mediterranean world

Until 700 A.D.

This was a thousand years after the Greeks had developed

Their intellectually conceived geometry.



The 700 A.D. introduction of Arabic numerals

Into the knowledge-monopolized economic transactions

Of the ignorance-enweakening Roman Empire

And Mediterranean European world in general

Occurred under the so-called "practical" assumption

That the Arabic numerals were only

Economical "shorthand" symbols

For the Roman scratches.

To the nonliterate ninety-nine percent of society,

It was obviously much easier to make a "3" squiggle

Than to make three separate vertical scratch strokes.

But to the illiterate the symbols

Did not conjure forth a number name.



The earliest calculating machine

Is the Chinese-invented abacus.

It is an oblong wooden frame

Which is subdivided

Into a large rectilinear bottom

And small top rectilinear areas

By a horizontal wooden bar

Running parallel to the top of the frame.

The frame's interior space is further subdivided

By a dozen or more

Perpendicularly strung parallel wires

Or thin bamboo rods.

There are four beads

Strung loosely into each of the wires

Below the horizontal crossbar,

And one bead strung loosely

Above the bar on each wire.

Start use of the abacus

With all the beads at bottom

Of their compartments.

In this all-lowered condition,

The columns are all "empty."

To put the number one

Into the first column on the right,

The topmost of the bottom four beads

Is elevated to the horizontal mid-bar.

To put the number two,

Two bottom beads are elevated to this bar.

To put five into the first column,

Lower all four bottom beads

And elevate the top bead.

To enter nine, leave the top bead elevated

And push up four beads

In the bottom section

On the first right-hand wire.

To enter ten,

Lower all beads in the right-hand column

Both above and below the crossbar;

Now elevate one bead In the bottom section

Of the second column from the right.

The first two right-hand columns read

One and zero, respectively,

Which spells out "ten."

The totaling bead

With a value of five In the separate compartment

At the head of each column

Permitted the release to inactive positioning

At the bottom of their wires

Of the one-by-one elevated bead aggregates.

Lowering of all beads

Permitted "empty columns" to occur.

Moving of the tenness leftward

Permitted progressive positioning,

Which integrated or differentiated out

As multiplication or division.



To those familiar with its use,

The tactile-visual patterns

Of the bead positions of the abacus

Could be mentally re-envisioned, or recalled

And held as afterimage sets

In the image-ination,

Which could be mentally manipulated

As columns of so many beads

Which read out progressively

As successively adjacent columns

Of so many beads,

Which, when reaching fiveness,

Called for moving "up" the one bead

Of the totaling head-compartment set,

While releasing the previously aggregated

Lower four beads

To drop into their empty-column condition.

When an additional four beads

Were pushed upwardly in the column,

An additional fiveness accrued.

All the beads in the column were lowered,

And one was entered

On the bottom compartment

Of the next leftward column,

As the two columns now read as "ten."

It was easier to enter

Many columned numbers in the abacus

And to add to them

Multicolumned numbers.

This process then permitted

Multiplication and division as well.



When an abacus was lost overboard or in the sands,

The overseas or over-desert navigator

Could sketch a picture

Of the abacus in the sand

Or on a piece of wood

With its easily remembered columns.

These abacus picturers invented

The "arabic" or abacus numerals

To represent the content

Of the successive columnar content of beads.

Obviously this abacus column imagining

Called also for a symbol

To represent an empty column,

And that symbol became the cyphra__

Or in England, cypher,

Or in American, cipher,

Or what we symbolize as 0,

And much later renamed "zero"

To eliminate the ambiguity

Between the identity of the word cypher

With the word for secret codes

And the word for the empty number,

All of which mathematical abacus elaboration

Became known scoffingly as "abracadabra"

To the 99 percent nonliterate world society,

And to the temporal power leaders

Who feared its portent

As an insidious disrupter

Of their ignorance-fortified authority.



Because of its utterly pragmatic bias,

The Roman culture had no numerical concept

Of "nothing"

That corresponds to the abacus's empty column__

That is, the idea of "no sheep"

Was ridiculous. Humans cannot eat "no sheep."

When the Europeans first adopted the Arabic numerals

in 700 A.D.

As "shorthand" for Roman numeral aggregates,

They of course encountered the Arabic cypher,

But they had no thinkably identifiable experiences to

associate with it.

"Nothing" obviously lacked "value."

For this reason, the Mediterranean Europeans

Thought of the cypher only as a decoration

Signifying the end of a communication

In the way that we use the word "over"

In contemporary radio communication.

The cypher was just an end period,

Just a decorative terminal symbol.



It was not until 1200 A.D.

Or five hundred years later,

That the works of a Persian named Algorismi

Were translated into

Latin and introduced into Europe.

Algorismi lived in Carthage, North Africa.

He wrote the first treatise explaining

How the Arabic cypher functioned calculatively

By progressively moving leftward

The newly attained tenness

By elevating one bead at the bottom

Of the bottom section

Of the next leftwardly adjacent column in multiplication

And next rightwardly in division.

Thus complex computation could be effected

Which had been impossible with Roman numerals.

The Arabic cypher had been used

For several millenniums

In the computational manner,

First in the Orient,

Then in Babylon and Egypt.

But such calculations had never before been made

In the Roman Empire's Mediterranean world.

No matter how intuitively

A man might have felt

About the probable significance

Of the principle of leverage

Or about the science of falling bodies,

Previous to the knowledge

Of the cypher's capabilities to position numbers,

He could not compute

Their relative effectiveness values

Without "long" multiplication and division.



The introduction into Europe

Of the computational significance of the cypher

Was an epoch-initiating event

For it made it possible for anybody to calculate.

And this was the moment in which

For the first time

The Copernicuses and Tycho Brahes,

The Galileos and Newtons,

The Keplers and Leonardos

Had computational ability.

This broke asunder the Dark Ages

With intellectual enlightenment

Regarding the scientific foundations

And technological responsibilities

Of cosmic miracles,

Now all the more miraculous

As the everyday realizer

Of all humanity's innate capabilities.



When I first went to school in 1899,

The shopkeepers in my Massachusetts town asked me

If I had "learned to do my cyphers"

By which key word__"cypher"__

They as yet identified all mathematics.

Even in 1970

Accountants in India

Are known officially as "cypherists."



Tobias Dantzig, author of Number: The Language of Science,

Has traced the etymological history

Of the names for the numbers

In all the known languages of the Earth.

He finds the names for numbers all classifiable

As amongst the "oldest" known words.

Sir James Jeans said "Science is the attempt

To set in order the facts of experience."

Dantzig, being a good scientist,

Undertook to set in order

The experienced facts of the history

Of the language of number names.

He arranged them experimentally

In their respective ethnic language columns.

Juxtaposed in this way

We are provided with new historical insights.

For instance, we learn

That if we are confronted

With two numbers of different languages,

Words that we have never seen before,

And an authority assures us

That one of these words means "one"

And the other means "two,"

And we are then asked to guess

Which of them means "one"

And which means "two,"

We will be surprised to find

That we can tell easily which is which.

"One" in every language

Starts with a vowel__

Eins, un, odyn, unus, yet, ahed__

And has vowel sound emphasis,

While "two" always has a consonant sound in the front__

Duo, zwei, dva, nee, tnayn, and so forth,

And has a consonant sound emphasis.

For instance, the Irish-Gaelic

Whose ancestors were sea rovers

Say "an" for one and "do" for two.

These vowel-consonant relations

Hold through into the teens__

Eleven, twelve__in English

Onze, douze__in French

Elf, zwoelf__in German,

With vowels for "oneness"

And consonants for "twoness."



Despite the dissimilarity in different languages

For the names for the same experiences,

And despite the unknown origins of the concepts

From which all numbers but five were derived,

The whole array of names for the numbers

In different languages

Makes it perfectly clear

That the names given the numbers around the world

Grew from the same fundamental

Conceptioning and sound roots.



In view of the foregoing discovery,

We either have to say that some angels

Invented the names for numbers

And the phonetically soundable

Alphabetical letter symbols

With which to spell them

And wrote them on parchments

And air-dropped those number-name leaflets

All around the spherical world,

Thus teaching world-around people the same number names:

Or we have to say that the numbers were invented

By one-world-around-traveling people.



However, if we adopt the latter possibility,

It becomes obvious that no single generation of people

Could, within its lifetime,

Or, in fact, within many lifetimes

Travel all around the world on foot,

For the world's lands are islanded.

But one way humans could get around,

And in a relative hurry,

Was by "high-seas-keeping" sailboats.

It thus becomes intuitively logical

To assume that sailors discovered

And invented the numbers

And inculcated their use

All around the world.



The Polynesians, we know,

Sailed all over the Pacific.

They probably sailed

From there into the Atlantic and Indian oceans

By riding ever-west-toward-east "Roaring Forties"__

The Forty-South latitudes'

Ever-eastward-revolving

Waters and atmospheric winds

Which circle around the vast Antarctic continent.

The "Roaring Forties"

Constitute a gigantic hydraulic-pneumatic merry-go-round,

Which as demonstrated by

World-around single-handing sailors of the 1960s

Enables those who master its ferocious waters

To encircle the world

Within only a year's time.

The Magellans, Cooks, and Slocums

With slower vessels circumnavigated in two years,

In contradistinction to the absolute inability

To go all around the world on foot.

The circumnavigation of the one-ocean world

Which covers three-quarters of our planet

Makes it obvious that the names for numbers

Were conceived by the sailors.

As Magellan, Cook, and later Slocum

Came to the Tierra del Fuego islanders,

They were surrounded by the islanders,

Who lived by pillaging passing ships

And must have been doing so

Profitably for millenniums.

To explain their sustained generations

In an environment approximately devoid

Of favorable human survival,

Except by piracy and salvage

Of the world-around sailing vessels

Funneled through the narrow

And incredibly tumultuous

Waters of the Horn Running between Antarctica and South America,

With often daily occurring

One-hundred-feet high waves

Cresting at the height

Of ten-story buildings,

Their thousand-ton tops

Tumblingly sheared off to leeward

By hundred-miles-an-hour superhurricanes

Avoidance of whose worst ferocities

Could be accomplished by winding

Through the Strait of Magellan,

Whose fishtrap-like strategic enticement

Often lured Pacific-Atlantic sea traffic

Into those pirates' forlorn domain.



With eighty-five percent of Earth's dry land

And ninety percent of its people

Occupying and dwelling north of the Equator

In the northern, or land-dominant, hemisphere;

And with less than one-tenth of one percent of humanity

Dwelling in the southernmost half

Of the southern, or wave-dominated, Earth hemisphere,

There is more and more scientific evidence accruing

That sailors have been encircling the Earth

South of Good Hope,

North or south of Australia,

And through the Horn

Consciously and competently

For many thousands of millenniums

All unknown to the ninety-nine percent of humanity

That has been "rooted" locally To their dry-land livelihoods.

The European scholars of the last millennium

Have considered the Polynesians to be illiterate

And therefore intellectually inferior to Europeans

Because the Polynesians didn't have a written history

And used only a binary mathematics,

Or "congruence in modulo two."

The European scholars scoffed,

"The Polynesians can only count to two."



Since the Polynesians lived on the sea

And were naked,

Anything upon which they wrote

Could be washed overboard.

The Polynesians themselves

Often fell overboard.

They had no pockets

Nor any other means

Of retaining reminder devices

Or calculating and scribing instruments

Other than by rings

That could not slip off

From their fingers, ankles, wrists, and necks,

Or by comblike items

That were precariously

Tied into the hair on their heads

Or by rings piercing their ears and noses.

These sea people had to invent ways of calculating and

communicating

Principally by brain-rememberable pattern images.

They accomplished their rememberable patterns in sound,

They remembered them in chants.

With day after day of time to spend at sea

They learned to sing and repeat these chants.

Using the successive bow-to-stern,

Canoe and dugout, stiffing ribs and thwarts

Or rafters of their great rafts

As re-minders of successive generations of ancestors,

They methodically and recitationally recalled

The experiences en-chantingly taught to them

As a successive-generation,

Oral relay system

Specifically identified with the paired ancestral parents,

Represented by each pair of ship's ribs or rafters.

When they landed for long periods

They upside-downed their longboats

To provide dry-from-rain habitats.

(The word for "roof" in Japan

Also means "bottom of boat.")

Staying longer than the wood-life of their hulls,

They built long halls patterned after the hulls.

Each successive column and roof rafter

Corresponded with a rib of their long boat.

Gradually they came to carve

Each stout tree column's wood

To represent an ancestor's image.

Each opposing pair of parallel columns

Represented a pair of ancestors:

The male on the one hand

And the female on the other hand.

While most Europeans or Americans can recall

Only ten or less generations of ancestors,

In their chants

The Polynesians can recall

As much as one hundred generations

Of paired ancestors,

And their chants include

The history of their important discoveries

Such as of specific-star-to-specific-star directions

to be followed at sea

In order to navigate from here to there.

While many of the words

That their ancestors evolved

To describe their discoveries

Have lost present-day identification,

They continue to sing these words

In faithful confidence

That their significant meaning

Will some day emerge.

Therefore, they teach their children

As they themselves were taught__

To chant successively the special stories

Which include words of lost meaning__

Describing each one of every pair of ancestors.

That is why the Vikings

Had their chants and sagas

And why sailors all around the world

Chant their chanties__"shanties"

As they heave-hoed rhythmically together.



Thus too did the Viking sing their sagas;

And the Japanese and Indian sailors their ragas;

And the Balinese sailors their gagas,

Meaning "tales of the old people,"

Amongst all those high-seas-living world dwellers

Whose single language structure

Served the thirty-million-square-mile living Maoris;

Whereas hundreds of fundamentally different languages

Were of static-existence necessity developed,

For instance, by isolatedly living tribes

Of exclusively inland-dwelling New Guineans.



A nineteenth-century sailor's shanty goes

"One, two, three, four

Sometimes I wish there were more.

Eins, zwei, drei, vier

I love the one that's near.

Yet, nee, same, see

So says the heathen Chinese.

Fair girls bereft

Then will get left

One, two, and three."



As complex twentieth-century,

Electronically actuated computers

Have come into use,

Ever improving methodology

For gaining greater use advantage

Of the computers' capabilities,

As information storing,

Retrieving, and interprocessing devices,

Has induced reassessment

Of relative mathematical systems' efficiencies.

This in turn has induced

Scientific discovery

That binary computation

Or operation by "congruence in modulo two"

Is by far the most efficient and swift system

For dealing universally with complex computation.

In this connection we recall that the Phoenicians

Also as sailor people

Were forced to keep their mercantile records

And recollections in sound patterns,

In contradistinction to tactile and visual scratching__

And that the Phoenicians to implement

Their world-around trading

Invented the Phoenician,

Or Phonetic, or word-sound alphabet,

With which to correlate and record graphically

The various sound patterns and pronunciations

Of the dialects they encountered In their world-around

trading.

And we suddenly realize

How brilliant and conceptually advanced

Were the Phoenicians' high-seas predecessors,

The Polynesians,

For the latter had long centuries earlier

Discovered the binary system of mathematics

Whose "congruence in modulo two"

Provided unambiguous,

Yes-no; go-no go,

Cybernetic controls

Of the electronic circuitry

For the modern computer,

As it had for millenniums earlier

Functioned most efficiently

In storing and retrieving

All the special-case data

In the brains of the Polynesians

By their chanted programming

And their persistent retention

Of the specific but no-longer-comprehended

Sound pattern words and sequences

Taught by their successive

Go-no go, male-female pairs of ancestors.

This realization forces rejection of the European scholars'

Former depreciation of the Polynesian competence,

Which reversal is typical

In both conceptioning and logic

Of the myriad of concept reversals

That are now taking place

And are about to occur

In vastly greater degree

In the late twentieth-century academic world.

The general education system

Has not yet formally acknowledged

The wholesale devaluation

Of their formally held

"Scholarly opinions and hypotheses,"

But that devaluation

Is indeed taking place

And is powerfully manifest

In the students' loss of esteem

For their intellectual wares.



All of the foregoing

Newly dawning realizations

Point up the significance

Of the world-around physically cross-bred kinship

Of the world's "one-ocean" sailors

Whose Atlantic, Pacific, and Indian waters

Were powerfully interconnected

By the Antarctic-encircling

"Roaring Forties."

Polynesians, Phoenicians, Venetians, Frisians, Vikings

(Pronounced "Veekings" by the Vikings)

All alliterations of the same words.

All evolved from the same ancestors.



The sea was their normal life,

And since three-quarters of the Earth's surface

Is covered with water,

"Normal" life would mean living on the sea.

The Polynesians spontaneously conceive of an island

As a "hole" in the ocean.

Such conceptioning of a negative hole in experience

Brought about their natural invention

Of a symbol for nothing__the zero.

This is negative space conceptioning

And is evident in the Maori paintings.

What is a peninsula to land people

Is a "bay" to them.

The Maori also look at males and females

In the reverse primacy of the land-stranded Western

culture.

Seventy-five percent of the planet is covered by the sea.

The sea is normal.

The male is the sailor.

The male is normal.

The penis of the normal sea

Intrudes into the female land.

The bay is a penis of the sea.

The females dwell upon the land.

To the landsman the peninsula or penis

Juts out into the ocean.



On the Indian Ocean side of southeast Africa,

The Zulus are linked with this round-the-world water

sailing.

They are probably evolved from the Polynesians of long

ago

Swept westward by the monsoons.

I found some of the Zulu chiefs

Wearing discs in their ears

Upon which the cardinal points of the compass

Were clearly marked.

The "Long Ears" of Easter Island

Had their ears pierced and stretched

To accommodate their navigational devices.

Many of the items which European society

Has misidentified in the Fijis as superstitious decoration

Were and as yet are

Navigational information-storing devices,

Being stored, for instance,

As star-pattern combs in their hair,

As rings around their necks,

Or as multiple bracelets

Mounted on their two arms and two legs,

And multiple rings

Upon the four fingers of their hands.

They had thirteen columns of slidable counters,

One neck, eight fingers, two arms, two legs.

Most of the earliest known abacuses

Also have thirteen columns of ring (bead) counters

Which became more convenient to manipulate and retain

When rib-bellied ships

Supplanted the open raft and catamaran.

Once the mathematical conceptioning

Of sliding rings on thirteen columns

Had been evolved by the navigators, traders, magicians,

It was no trick at all

To reproduce the thirteen-column system

In a wooden frame with bamboo slide columns.



By virtue of their ability to go

From the known here to the popularly unknown there,

The navigators were able to psychologically control

Their local island chieftains.

If a chieftain needed a miracle

To offset diminishing credit by his people,

He could confront them with his divine power

By exhibiting some object they had never seen before,

Because it was nonexistent

On their particular island.

All the chieftain had to do

Was to ask the navigators

To exercise their mysterious ability

To disappear at sea

And return days later with an unfamiliar object.

But the navigators kept secret

Their mathematical knowledge

Of offshore celestial navigation

And the lands they thus were able to reach.



To the landed chieftains

The seagoing navigators were mysterious priests.

The South Seas navigators lived and as yet live

Absolutely apart from the chieftains and the tribe

The "priests" taught only their sons about navigation

And they did so only at sea.

A new era dawned

For humanity on our planet

When the Polynesians learned

How to sail zigzaggingly to windward

Into the prevailing west-to-east winds.

Able to sail westward__

Able to follow the Sun__

At far greater sustainable

(All day and all night, day after day)

Sailing speeds than those attainable

By paddling or rowing into head seas;

Having for all time theretofore drifted

In predominantly eastward windblown directions,

Or gone aimlessly where ocean currents bore them,

Yielding to the inevitable

From-west-to-east elements

Bearing them to the American west coasts

And to all the Pacific islands

Throughout the previous x millions of years.



Whereas the Southern Hemisphere ocean

Was dominated by the west-east "Roaring Forties,"

The Polynesians when entering the Northern Hemisphere

Were advantaged not only by their ability

To sail into the wind,

But also by the east-west counter-currents

Of the tropical westward trade winds,

Which they discovered and

Called so because they made it possible

To go back where man had previously been

And thus to integrate world resources.

Thus the secretly held navigational capability

And knowledge of the elemental counting and astronomy

Went westward from Polynesia

Throughout Malaysia and to southern India,

Across the Indian Ocean to Mesopotamia and Egypt

And thence into the Mediterranean.

The powerful priests of Babylon, Egypt, and Crete

Were the progeny of mathematician navigators of the Pacific

Come up upon the land

To guide and miracle-ize the new kings

Of the Western Worlds.

Knowing all about boats,

These navigator priests were the only people

Who knew that the Earth is spherical,

That the Earth is a closed system

With its myriad resources chartable.

But being water people,

They kept their charts in their heads

And relayed the information

To their navigator progeny

Exclusively in esoterical,

Legendary, symbolical codings

Embroidered into their chants.



But some of their numbers

Also sailed deliberately eastward

Carrying their mathematical skills

To west-coast America.



The Mayans used base twenty in their numerical system

By counting with both their fingers and toes.

The number twenty often occurs

In a "magically" strategic way.

For an example

We can look at symmetrical aggregates

Of progressively assembled spheres

Closest packed on a plane__a pool table.

First take two balls and make them tangent.

Tangent is the "closest"

That spheres may come to one another.

We may next nest a third ball

In the valley between the first tangent two.

Now each of the three spheres is tangent to two others

And none can get closer to each other.

These three make a triangle.

There is no ball in the center

Of the triangular group.

We can now add three more balls to the first three

By arranging them tangentially in a row

Along one edge of the first three's triangle.

As yet, all six balls are arranged

As outside edges of the triangle.

Not until we add a fourth row of balls

Nested along one edge of the triangular aggregate

Does a single ball become placed as the nuclear ball

In the center of the triangular "patterned" ball pool-table array.

Ten is the total number of balls

In this first nuclear-ball-containing triangle:

Nine surround the nuclear tenth ball.

And since a triangle is a fundamental structural pattern,

And since the triangular aggregate

Of nine balls around a nuclear one

Is a symmetrical array,

Man's intuitive choice of "congruence in modulo ten"

May have been more subtly conceived

Than simply by coincidence

With the ten digits of his hands.



We will now see what happens experimentally

When sailors stack coconut or orange cargoes

Or when we stack planar groups of triangular aggregates of spheres

On top of one another in such a manner that they will be

Structurally stable without binding agents.



First we will nest six balls

In a closest-packed triangular planar array

On top of the first triangularly arranged ten-ball aggregate.

And on top of those six balls

We can nest three more.

We now have a total of nineteen balls.

We may now nest one more topmost ball

In the one "nest" of the three-ball triangle.

We now have a symmetrical

Tetrahedral aggregate

Consisting of twenty balls

Without any nuclear ball

Occurring in the center

Of the symmetrical tetrahedral pyramid of balls.

We began our vertical stacking

With a symmetrical base triangle of ten balls,

And now we have a tetrahedron composed of twenty balls.

Just as fingers alone may not have been the only reason

For the choice of base ten,

Fingers and toes together may not have been the only reason

That the Mayan priests chose

Congruence in modulo twenty

Or that twenty was considered a magical number.

It might have been the result of an intuitive understanding

Of closest packing of spheres,

Which is something much more fundamental.

For unlike our fingers which lie in a row,

The packing of twenty spheres

That can be grouped symmetrically together without a nucleus

Is a fundamentally significant phenomenon.

In a tetrahedron composed of twenty balls

There is no nucleus.

This may be why twenty appears so abundantly

In the different chemical element isotopes.

And "twenty" is one of the "Magic Numbers"

In the inventory of chemical-element isotopal abundancy in Universe.



In order to position a nuclear ball in the center

Of a symmetrical tetrahedral pyramid of balls,

We need to add another or fifth nested layer of fifteen

balls

To one face of the tetrahedron of twenty.

The total number of balls is then thirty-five,

Of which one is the nuclear ball.

If, however, we add four

Progressively larger

Triangular layers of balls

To each of the four triangular faces

Of the twenty-ball, no-nucleus tetrahedron,

It will take exactly one hundred more balls

To enclose the twenty-ball, no-nucleus tetrahedron__

This makes a symmetrical tetrahedron

Of one hundred and twenty balls.

This symmetrical tetrahedron

Is the largest symmetrical assembly

Of closest-packed spheres nowhere containing

Any two-layer-covered nuclear spheres

That is experimentally demonstrable.

In the external affairs of spheres

Such omnidimensional spherical groupings

Of one hundred and twenty same-size balls

Without a nucleus ball

Can be logically identified

With the internal affairs

Of individual spheres,

Wherein we rediscovered

The one hundred and twenty,

Least-common-denominator,

Right spherical triangles of the sphere,

Which are archeologically documented

As having been well known to the Babylonians'

Come-out-upon-the-land-ocean,

Navigator-high-priest mathematicians.



The number 120 also appears as a "Magic Number"

In the relative-abundance hierarchy

Of chemical-element isotopes of Universe.

One hundred and twenty accommodates

Both the decimal and the duodecimal system

(Ten multiplied by twelve).



The Mayans too may have understood

About the tetrahedral closest packing of spheres.

They probably made such tetrahedra

With symmetrically closest-packed stacks of oranges.



The twentieth-century fruit-store man

Spontaneously stacks his spherical fruits

In such closest-packed

Stacking and nesting arrays.

But the physicists didn't pay any attention

To the fruit-store man until 1922.

Then for the first time physicists

Called the tetrahedral stacks of fruit

"Closest packing of spheres."

For centuries past

The numerologists had paid attention

To the closest packing of spheres In tetrahedral pyramids,

But were given the academic heave-ho

When in the mid-nineteenth century

Physicists abandoned the concept of models.

We have seen

That there are unique or cardinal names

For the concepts one through twelve

In England and Germany,

And for the concepts one through sixteen in France,

But that after that they simply repeat

In whatever congruence modulos

They happen to be working.

The Arabic numerals as well as their names

Are unique and stand alone

Only from zero through nine.

However, eleven is the result of two ones__11,

And twelve is similarly fashioned from two

Previously given symbols,

Namely, one and two__12.



But certain numbers

Such as prime numbers

Have their own cosmic integrity

And therefore ought to be integrally expressed.

What the numerologist does

Is to add numerals horizontally (120=1+2+0=3)

Until they are all consolidated into one integer.

Numerologists have also assigned

To the letters of the alphabet

Corresponding numbers: A is one, B is two, C is three, etc.

Numerologists wishfully assume

That they can identify

Characteristics of people

By the residual integer

Derived from integrating

All of the integers,

(Which integers

They speak of as digits,

Identifying with the fingers of their hands,

That is, their fingers.)

Corresponding to all the letters

In the individual's complete set of names.

Numerologists do not pretend to be scientific.

They are just fascinated

With correspondence of their key digits

With various happenstances of existence.

They have great fun

Identifying events and things

And assuming significant insights

Which from time to time

Seem well justified,

But what games numerologists

Chose to play with these tools

May or may not have been significant.

Possibly by coincidence, however,

And possibly because of number integrity itself

Some of the integer intergrating results

Are found to correspond elegantly

With experimentally proven, physical laws

And have subsequently proven to be

Infinitely reliable.

Half a century ago I became interested in seeing

How numerologists played their games.

I found myself increasingly intrigued

And continually integrating digits.