Frame of Reference - Index

22) Sun is a rather nervous, irascible star, erratically throwing out heat and radiation at intervals, showering Earth with results of its nuclear-reactor storms. Presumably this intimidation factor makes it a fitting subject for worship by many primitive cultures. Even from its distance, which varies from 91,300,000 miles in January to 94,500,000 miles in July, it makes the Northern hemisphere summer barely tolerable to humans, and the New Zealand winter more mild than in the USA at equal latitudes. We receive lethal doses of x-rays along with magnetic radiation, thankfully absorbed by the two polar zones, creating the magnificent, colorful display of the Aurora Borealis (and Aurora Australis).

One important peculiarity of the solar system: although Sun has more than 99 percent of the mass, it has less than 1 percent of the angular momentum. Sun should be spinning much more rapidly if its angular momentum was proportionate to its mass. The explanation goes like this: as magnetic lines of force became entwined in the spinning nebular disc surrounding the forming protosun, this and gravity would actually impart a rigidity to it. The effect of this would be to accelerate the outer parts of the disc, thus increase their angular momentum at the expense of Sun and lead to the formation of the planets along the same orbital plane.

The nuclear fusion reactions in the heart of Sun convert 5 million tons of matter into energy each second. It takes more than a million years for energy from Sun's core to reach the surface and about 8 minutes for it to get to Earth; remember we receive only a fraction of the energy released by Sun--good thing.

23)

The cottonwoods stick
up their life
to touch Sunrise. (IJ - 1998)
24) So Sun, which is often considered a benevolent friend, the source of vitamin D and photosynthesis, is dangerous if taken in too strong a dose. It's nice to have the seasons. These are a favorite source of poetic refrain, as well as a practical life cycle stimulant for many plants. The whole community of agriculture dotes on day length changes (short days between Fall and Spring), diurnal flux (the difference in temperature between hot days and cold nights) and vernal periods (winter freezing, and short day growth) caused by the unique rotation of Earth around Sun and the swaggering tilt of our axis vis--vis Sun. But, alas and unfortunately Sun has no particular expertise in moral education nor does it create any ethical authority...or maybe it does?

25) In the year 1838 Joseph Smith claimed to have received a visitation from a bright light in the Spring of 1820. His account of the events, not published until 1842, goes as follows from The Pearl of Great Price:

Joseph Smith, 2. Vs 16-20

"16 ...just at this moment of great alarm, I saw a pillar of light exactly over my head, above the brightness of the sun, which descended gradually until it fell upon me.

17 It no sooner appeared than I found myself delivered from the enemy which held me bound. [darkness] When the light rested upon me I saw two Personages, whose brightness and glory defy all description, standing above me in the air. One of them spake unto me, calling me by name, and said, pointing to the other--This is my Beloved Son. Hear Him!

18 ...No sooner, therefore, did I get possession of myself, so as to be able to speak, than I asked the Personages who stood above me in the light, which of all the sects was right--and which I should join.


Infinity is beyond our comprehension and talk of beginnings or creation runs into the limits of language and is trapped in paradox. (Septimus Stele: Mathematics, verse 4)


19 I was answered that I must join none of them, for they were all wrong; and the Personage who addressed me said that all their creeds were an abomination in his sight; that those professors were all corrupt; that; 'they draw near to me with their lips, but their hearts are far from me; they teach for doctrines the commandments of men, having a form of godliness, but they deny the power thereof.'

20 ...When I came to myself again, I found myself lying on my back, looking up into heaven. When the light had departed, I had no strength; but soon recovering in some degree, I went home..."

Was this a dream or reality? Or an exercise in creative writing some 18 years after the presumptive facts. For Smith to have seen an overpowering light is not unusual in accounts of such epiphany. (see Nonus Stele: Myths - Telos, verse 47) Moses, Buddha and Paul of Tarsus made similar claims to have been enlightened or overpowered by light. Most of the information about Universe comes from light, and light has been used as a symbol of knowledge, wisdom and truth in many different languages. The message that Smith gives us about religions has some relevance to the present state of society, notwithstanding its use in the establishment of what has become the Mormon religion.

26) Somewhat before Smith had his vision, in 1802, the English physicist Wollaston had identified some characteristic patterns, dark lines, in the solar spectrum. These were rediscovered by the German physicist Joseph Von Fraunhofer in 1814, using very primitive spectroscopes. These Fraunhofer lines are used today to read and identify light sources much like fingerprints can be used to identify people. It was forty-five years later, in 1859, that the German chemist Gustav Kirchhoff discovered that these lines were produced from absorption of wavelengths of light by chemical elements, and subsequently we have learned that gases surrounding Sun do the same thing. Light emanating from the 'photosphere' of Sun passes through the 'atmosphere' of cooler gases surrounding Sun and are absorbed by the constituent gases. In brief, the same effects can be created in the laboratory by passing full light through specific transparent gases to identify specific wavelengths absorbed by the gases thus becoming the known spectrum of these gases.

27) It is both possible to identify the gases surrounding Sun and identify the composition of other stars and sources of light by measuring which wavelengths are emitted and which are not. Now we can learn from the stars and receive direct information about Universe from both bright and dim lights. Because of the proximity of Sun its light is 10 billion times brighter than the next brightest star in the sky.

Using the most recent, massive telescopes, 8.2 meters in diameter, VLT in Chile, astronomers from Sweden, Italy, Denmark and Germany have been measuring and studying light to verify the age of Universe. Measuring minute traces of radioactive uranium and thorium in the oldest stars -- like carbon dating in archeology -- suggests a date of more than 12 billion years old. Leaving, for now, the estimated date of Universe, 14 to 15 billion years, more or less intact.


The search for knowledge and technology brings with it inherent responsibilities to use each new invention wisely. (Quartus Stele: Chemistry, verse 26)

28) Sun is one of many, as we know. Most of what we see as stars are suns of various sizes, Sun being rather less than average in size and brightness. The realization that this is the case is fairly recent. Even Copernicus (1473-1543) and Kepler (1571-1630) held the view that Sun was different than the stars. The attention given to Astronomy before Nicolas Copernicus was piecemeal and completely under the influence of dogma, usually religious dogma. His seminal work, De Revolutionibus Orbium Coelestium Libri IV, was published in 1543 the same year as the author's death, and placed Sun near the center of Universe, 'heliocentric.' He explained how Earth's orbit makes some planets appear to move backward in relation to fixed stars. All planets had the same motion around Sun rather than having a 'punctum aequans' or computational center for their orbit.

There are many cultures that used computations of the motion of the stars and planets, and these are incorporated into the layout of their edifices, i.e. Stonehenge. But none of these computations were in any way an explanation of what was actually going on and in this respect Copernicus' theory was also seriously wanting. Copernicus' main contribution was developing a comprehensive attempt to make the science of that day work better, he being a thorough student of nature. He constructed a systematic scientific theory more complex than anything proposed before which then became the basis for further discoveries and refinements.

29) Copernicus apparently gave credit for his inspiration to a much earlier philosopher, Aristarchus of Samos (310 BC - 230 BC). He was a master of geometry who combined this skill with a propensity to watch the stars. He observed the size of Earth's shadow on Moon during a lunar eclipse, then used his superior reasoning to deduce that Sun was much larger than Earth and much farther away than Moon. He concluded that Sun, not Earth, was the center of the planetary system, that all the planets rotated around Sun and that Earth rotated on its axis. Aristarchus was also given credit for this theory by Archimedes, but alas his views were neglected and not influential in changing the development of intellectual pursuits such as Astrology. Another Greek in about 150 BC, Hipparchus, is known to have charted the positions and relative brightness of 850 stars, calculated accurately the distance between Earth and Moon, and was able to predict the position of Sun and Moon for any day of the year.


Our scant understanding of Universe should make us humble and receptive to learn and find ways to improve our lives. (Septimus Decimus Stele: Morals, verse 13)

30) Humans are a stubborn lot, and it was not until Johannes Kepler that the scientific community began to accept the true nature of Universe. He is often regarded as the father of modern Astronomy because his work was more mathematical, more comprehensive and more accurate. He showed that the trajectory of the planets was elliptic around Sun and convincingly severed the ties between Astronomy and theology, replacing the myths of medieval cosmology with an explanation of physical causation. He developed three laws of planetary motion and is given credit for thus developing the first laws of nature in his work:

A New Astronomy Based on Causation
or A Physics of the Sky
derived from Investigations of the
Motions of the Star Mars
Founded on Observations of The Noble Tycho Brahe
The collaboration between the rigorously accurate observations of the eccentric Tycho Brahe and Kepler set the wheels of natural Astronomy in motion, where it leads is largely determined at the beginning of this 21st century. Because of this early, passionate work and subsequent developments we have learned to more fully trust the sometimes halting process of science as the appropriate source of knowledge about Universe. The wisdom of religious sages has been confined to more mundane activity.

31) Asteroids, meteors and comets are less discussed by religions and myths than other celestial bodies; even so, superstitions have arisen each time a major event occurs. Haley's comet is a famous and frequent visitor (every 76 years, the last time in 1986) to our view from Earth and each time it is accompanied by some bizarre human response. Its orbit was identified and predicted by the British astronomer, Edmund Haley in 1682.

As of 1988 there were eighty-eight large craters identified on Earth attributable to the explosive impact of extra-terrestrial bodies. Some of these events purportedly caused the extinction of dinosaurs and before that other species. A 110-mile wide undersea crater off the coast of Yucatan, Mexico, may explain the extinction of the dinosaurs 65 million years ago. Some scientists think that this crater was caused by a 10 mile wide asteroid. Dust and smoke from the explosion would have hidden Earth from Sun for years, killing most vegetation, causing extremely cold weather and interrupting the food chain upon which the dinosaurs depended. The impact at high speed of even a relatively small object would create a huge explosion and generate a high altitude dust cloud (or splash) that would seriously upset the fragile environment supporting many species. The Arizona Meteor crater, which is about 1 mile in diameter, is believed to have been caused by a meteorite 35 feet in diameter weighing about 5,000 tons, with a velocity of impact of about 12 miles per second. (see Quartus Decimus Stele: Human Sacrifice, verse 20)


The laws of nature have become the substitute for the canons of religion as we gain freedom from the primitive nature of man. (Quintus Stele: Homo sapiens, verse 11)

32) When we gaze at shooting stars and perceive an innocent beauty, and even make a wish, we must think, if only briefly, how fortunate we are that these spectacles occur rather than having these small meteorites crash to Earth. There is cause for concern that a much larger and faster object could be headed our way, asteroid or comet, and we wouldn't know about it because of our speed and its speed and relative invisible, cold nature. We might get less than one year warning after a large object was identified and its trajectory determined.

There is an asteroid belt between Mars and Jupiter composed of many large and small objects. This belt, under the influence of the large planet Jupiter, separates the rocky inner planets from the gaseous outer planets. If all that material were gathered together it would form a globe about 1/2 the size of Moon. Apparently the gravitational force of Jupiter prevented the formation of a planetoid from this matter. Small pieces from the Asteroid Belt, meteors, break away and often fall to Earth, usually being burned by the friction of the atmosphere. This has been a source of wonder and mystery, now largely explained.

33)

SHOOTING STARS

Searching for inspiration to answer your kindness
I return in solitude where we shared intimacy.

Remember stargazing? The most severe darkness
Gave light to our senses most keen in silence.
Listening carefully in the wind we heard a serenade;
Hymns from the lyre of Orpheus illuminated by brilliant Vega.
Denying our inevitable separation we search heaven to identify
That spark within our souls which inexplicably unites us.
A child of Perseus appears bearing a message of hope
Stirring our emotions rekindling youthful infatuation.

This revelation of nature exposed the distance between us
Insubstantial, insignificant in this grand realm.
That solitary shooting star flaming across our hearts
Whispered eloquent tribute to you making mine faint praise.
As Cygnus arched low with outstretched kiss
The heroic swan blessed our union, first tentative then urgent we touched.

Galaxies beyond shared our fondness in mute repose, these reflected
Our loneliness, isolation, which you dispelled with equal grace.
Are we destined to be apart? Your tenderness wills otherwise.
Smooth, gracious, redeeming as gift from heaven sent.

Your divine smile sparkled converting my coarseness
Mysteriously, by your alchemy this common man became aficionado.
That communal spark we shared gave me superior capacity.
Thus enriched, my talent became appreciation of you.

**

Returning there for blessing, supine, submissive, humble
Craving this subtle connection again I awaited memory of you as epiphany.
Majestic Aquila graced my search, strong and healthy in flight
From you chasing the night it soared on errand of love.
I reach to touch Altair so bright in truth so close
Yet so far in temper its rhythm like you puzzles.
Unpracticed in meditation, communing with invisible nature
Is not made as easy for one so spiritually challenged.
The stars offer companionship, a clear visible alternative
No doubts, no chance, no mistake, security on a universal scale.
Yet is there excitement watching a satellite tumble bye
Intersecting the path of Sagitta? Sad arrow never finds it's mark.
Patience shortens as cold rises - from the Earth and my cigar
I draw sustenance, reward from the stars transforming my lazy thoughts.
Not one, clearly two shooting stars appear
Teaming to chase my dreams, enticing my continued tranquility.
The first caresses Delphinus catching my moist eye
Its death scatters stardust to spice my recollection of you.
The second left Ophiuchus born of strife and emotion
Its brighter light passed vivid showing the path love takes.
These marvelous events gave comfort and explanation.
They symbolize our love beyond discretion and denial.
Please accept this love Susan. Like virtue made spectacular
Not by transient flight but by infinite repetition.
Gentle as Sagittarius I labor to serve wisely
But my naive vulnerability creates an unruly caution.
Inspired momentaily - flash - your brilliance is perceived
Then fades as quickly for want of sensitivity.
Let the stable Polaris guide my action instead.
So you may find comfort as we pass the seasons together.
If such love merely flickers it would suffice for now
Because mysterious or sublime it awakens endless possibility.
Now, I accept apologetically the affection you proffered
So sincere and exposed all the more precious.
Life should be simple, but, like the body of Draco
It deceives and eludes sensible patterns and clear definition.
But all these constellations pale compared to your bright charms.
These words not easily spoken, seek your forgiveness and acceptance.
There is no claim here against your logical restraint
Only hope of repeating what shall be my glory.

Another revelation came, calming my intervening sadness.
How insignificant this pain in this grand realm.
You have extended love touching my coarseness
With talent and openess beyond my grandest expectation.
Laugh with me again Susan. Sing for me when you will.
Touch my body as you choose. Take my love, improve it.
Why speak of love so soon? This queer sense of longing
Fulfilled by your presence. What else could it be?
Love begins in embryo, divides and conquers shyness,
Stays and flashes brilliant, but can fade in forgetfulness.
Like riding mighty Pegasus, graceful, power in flight.
Yet to stay this mount requires skill and practice.
Each encounter accumulates riches otherwise how can love grow
If not by cycles resplendent, fulfilling endless potentiality?
Don't casually deny love from discretion or fear.
Accept that spark of unity first felt as fondness.
As the moon blinds so the cares of life
Dim love's comstancy. Yet patience returns its investment.
Appreciate the simple symbol, the shooting star creates.
Exercise this reasonable love, growing beyond passion's exclamation.
Our strange companionship, meeting in the community of stars,
both tragic and comical, but such is the drama of life. (IJ, 1995)

34) There is a vast cloud of comets, the Oort Cloud (first identified by the Dutch astronomer, Jan H. Oort) outside the solar system, beyond Pluto's orbit about one light year from Sun (5.87 trillion miles) that gives birth to the comets. These icy masses begin a vast elliptical orbit around Sun, possibly when they are nudged by the occasional near approach of another sun. These are not messengers from heavenly intelligence or harbingers of evil, just comets probably responsible for having given some water to Earth during the formative years.

35) The meteorite of the Kaaba, the Black Stone, in Mecca, attracts hundreds of thousands of pilgrims of the Islamic faith each year. This may be the most famous and most revered meteorite.

The iron meteorite called the Willamette Meteorite found near Oregon City, Oregon has made its way into the Smithsonian Institution Museum. Local descendants of native Americans of Oregon have successfully disputed the ownership of what is for them a sacred object. In 2000 their court case was settled and they were granted special visiting rights to worship the porous stone each year. Even in modern times religion, government and the heavens come together to affect the behavior of man.

36) Milky Way galaxy is a friendly place to live, from our innocent perspective circling, elliptically, inconspicuously within our solar system. This galaxy has more than 100 billion suns in a spiral pinwheel shaped disc orbit around its mysterious center. Most of Milky Way, in excess of 100,000 light years wide, is empty space, albeit full of fast moving light and a few scattered sub-atomic particles, loose hydrogen, neutrinos, radio waves and electro-magnetic forces whizzing about. That huge space is a busy thoroughfare at many levels of consideration.

The crowded band of stars of Milky Way was considered the road to heaven in some ancient myths. Even when we know the truth, it is hard to visualize the massive pinwheel-shaped galaxy in which we live.

Sirius is the nearest (double) star, about 50 trillion miles away, and its motion has been carefully measured. Sirius is in joint orbit with a smaller, 'dark companion' named Sirius B. Sirius B is a small star about 30,000 miles across, 1/20th of Sun but much hotter. Its vital statistics are interesting: it gives off 1/400th less light than Sun, and curiously has the same mass, a mass compressed 6,000 times as dense as Earth weighing 1,250 lbs. per cubic inch while Earth weighs 0.2 lbs per cubic inch. The gravitational pull on the surface of Serius B is 840 times the pull of Sun's surface, and 23,500 times the force of gravity on Earth. This is the description of a white dwarf which are quite common in Universe, about one in 40 of known stars.

37) The center of Milky Way seems to consist of a powerful electromagnetic field, like a dynamo. This conclusion suggests the presence of a black hole at the center of our galaxy with a mass of a thousand to a million suns. The Sombrero galaxy appears to have a central black hole with a mass of almost a billion suns. M87 galaxy has a central black hole with a mass of three billion suns. Velocity studies of the core of the galaxy NGC 4258 indicate that it contains a central black hole with a mass of 40 million suns. Others are postulated leading to the question: are all galaxies formed with eventual black holes as their centers? Possibly the god of the Old Testament, who some think has died, was devoured after going too close to a black hole?

Covered by thick clouds of dust, Milky Way's center is invisible to normal telescopes, but the Keck observatory, Hawaii, has an infrared light sensitive camera that can effectively see through this cloud. Using this, Andrea Ghez has measured the motions of stars that lie closest to the core. They are orbiting around the galactic center at 1,600 miles per second, nearly 100 times faster than Earth orbits Sun. Using simple math, it is possible to calculate that a mass of 3 million suns is packed into an area no bigger than the orbit of Mars at the center of Milky Way. The only explanation for this is a massive black hole. (We are spiraling down into this drain, as it were.)

38) Sun and our solar system are near the inner edge of one of the spiral arms of Milky Way, about 28-30,000 light-years from the center. Sun travels at a speed of over 600,000 miles per hour, taking 225 million years to make one rotation. Milky Way is one of twenty six or so nearby galaxies called the Local Group. Andromeda galaxy is our nearest large neighbor (2.2 million light years away) and together these two large galaxies provide the center for the Local Group. In addition to spiral galaxies there are elliptical shaped galaxies, barred spirals, irregular-shaped galaxies and dwarf galaxies. Megellanic Clouds (two, Large and Small) are the nearest to Milky Way, both much smaller and of irregular shape.

In the 1980s it was discovered that there are clusters of galaxies organized into giant bubbles measuring some 300 million light-years in diameter. It is widely believed that there are more than 100 billion galaxies in our expanding Universe (probably an under-estimate). Universe being inflationary and otherwise mysterious is without a boundary. With each new technology for seeing the past, 'visible' Universe expands.

39) Man's position, according to Buddhism, is supreme. Man is his own master, and there is no higher being or power that sits in judgment over his destiny.

One is one's own refuge,
who else could be the refuge? (Buddha)
40) More than three fourths of all the suns in Milky Way appear to belong to partner systems or in a family of suns. When two suns are situated close together in the sky and circle each other they are called a 'double-star.' The spectacular light show from Beta Lyrae comes from two stars, one a large blue star and a smaller yellow one, circling each other rapidly they shoot out long colorful streamers of gas. The first family of stars ever to be seen is Mizar, which is located in the handle of Big Dipper (Ursa Major). Another double-star system is the blue giant Sirius, know as the Dog Star, and a white dwarf companion called the Pup. (see verse 36)

The granddaddy of all double-stars is Epsilon Aurigae, with one star a yellow supergiant 250 times bigger than Sun. But that's not all, its companion is even bigger - 3,000 times the size of Sun. Many of the stars we see each night are actually double or triple suns, yet the naked eye sees them as only one star. The North Star, for example, is actually made up of three single suns. Castor is made up of six suns. The instinct many species share to form families and tribes finds its complement in galactic space.

41) The news of August 5, 2000 contained the account of a new discovery. A new planet orbiting Epsilon Eridani, a star very similar to Sun, has been identified. The satellite is about the size of Jupiter (by far the largest planet) according to William Cochran of the University of Texas' McDonald Observatory. This is the closest star for which a planet has ever been discovered, only ten light years away. "Scientists discovered the planet by observing Epsilon Eridani as it wobbled on its axis. That wobble is caused by the planet's gravitational influence as it orbits the star...the similarities to our solar system mean it could harbor a terrestrial planet like Earth that could sustain life."

In 1995, astronomers Michel Mayor and Didier Queloz at Geneva Observatory in Switzerland made headlines with the news that they had found evidence of a planet orbiting 51 Pegasi, about the size of Sun. They suggest the planet is as massive as Jupiter yet very close to its sun, only one-tenth the distance from Earth to Sun. In 1996 a similar discovery for Sun-sized stars occurred in 70 Virginis, in Virgo near Arcturus, and 47 Ursae Majoris, near Big Dipper (about 35 light years from Earth). The planet at 70 Virginis is 8.1 times the mass of Jupiter and lies about as far from its sun as does Mercury. The planet of 47 Ursae Majoris is calculated to be 3.5 times Jupiter's mass, lies further away, as far as our asteroid belt, with an orbit of 1,100 days. The hope of finding extraterrestrial life is more compelling than reading science fiction novels.

The U.S. Naval Observatory will launch a satellite in 2004, Full-sky Astrometric Mapping Explorer (FAME). This device will determine the distance to all of the suns on this side of Milky Way and detect many of the associated large planets. We will have the capability to record the positions, motions, parallaxes and photometry of nearly all 40 million suns. Then it will be time for another 'Wow!'

42) The last word on Astrology: The ancient Hebrews, like the Babylonians, Egyptians, and Greeks, were impressed by Astrology. In The Bible, the Hebrew word 'mazel' referred to a planet or a constellation of the zodiac, and the word was invoked when 'fate' was involved. Later, Talmudic sages sternly warned the Jews to eschew soothsaying and diviners...the Midrash teaches: "The Holy One forbade astrology in Israel," and it is said that God made Abraham "a prophet, not an astrologer."

Nevertheless, Jews continue to utter "Mazl tov!" The supernatural or divination aspects are forgotten and mazel has become 'luck,' "Mazl tov!": 'Congratulations.'

Maimonides (Hilhoth Tshuvah) taught: "Do not believe the astrologers...our Torah [holds] that a man's conduct is in his own hands, that no external compulsion prevents a man from being virtuous or vicious -- except as he may be so constituted, by nature, and finds it easy or hard to do a certain thing. But that a man must do, or refrain from doing, something [because of the stars] is entirely untrue...Astrology is a disease, not a science." (Laws of Repentance)

A 1986 Gallup poll reports that 52 percent of American teenagers believe in Astrology, and of course many adults too. If people will believe in astrologers and Astrology, it's frightening to consider whom or what else they'll believe.

43) Reading each year the new discoveries of Astronomy is better entertainment than keeping track of major league baseball for some. Have we learned enough about Universe to free us from our superstitious nature? Not that we have all the answers; we may not even have all the questions; so we must have the attitude of a good student: we must not only want and feel the need to learn more, we must also approach this study with an open mind and with all the talent we can muster. As we do that, we should hold to the notion that many of the answers are found when we look 'in here' instead of 'out there,' especially those answers of a moral and spiritual nature that are still in dispute. Universe contains its own answers; however, it does not contain the answers to our legitimate questions of how to form better societies. Why are we here on Earth? What should we live for? How can we find meaning in life? and so on. It remains to the balance of Frame of Reference to disclose these answers, carefully.

44) The rest of Universe: "In actuality, we can see only those galaxies that lie close enough to us for their light to have reached us at the present time: These galaxies, the ones at 'lookback times' less than the age of the universe, inhabit the observable universe. In all feasible expanding-universe models, the observable universe is but a fraction of the whole. An inflationary universe would be incredibly large today, and the observable universe an incredibly small part of it. If the entirety of an inflationary universe were the surface of the earth, the observable part would be smaller than a proton. The inflationary universe might be globally spherical or globally hyperbolic, but to all observers it would look locally flat. So if we do live in an inflationary universe it will be very difficult, perhaps impossible, to determine the overall shape of space, just as it is hard to discern the radius of the earth [which is pear-shaped] by measuring only a tiny patch of soil." (Timothy Ferris, The Whole Shebang, 1997) Earth is the next subject of our inquiry.