Conference hydra::dejavu

    Yes, they say it will be an oasis for those seeking refuge during
    the "closing of the door" of this world and the "opening" of the
    next.

    	Please forgive me, but I am very skeptical of all those "The
    world will end on THIS date" books.
    
    	How many such "prophets" and religions have said in the past
    that the world will end on such-and-such a date, only to have
    everything go on in its usual boring/violent fashion, with those
    who claimed it saying that their prayers saved the world, or even
    going as far as making a NEW date!
    
    	Astrologers in India said that the world would end on August
    8, 1962; pounding my foot on the ground, I think we're still here;
    and let us not forget the Jupiter effect of 1982, in which the
    so-called lining up of the planets in the Sol system would wreack
    havok on Earth, yet life went on.
    
    	Please understand that I am NOT putting down the Hopi Amerind
    culture - I happen to admire the Amerinds and their ways very much.
    I am just skeptical about all this End of the World predictions.
    
    	For my money, I'll go with the cosmologists who predict that
    Earth will be ddestroyed in about 5-10 billion years from now, when
    the Sun swells into a red giant star and consumes Earth in its
    expansion.
                                                           
    	Larry
    

    Remember when Exidor told Mork that the end_of_the_world was the
    second Saturday of every month? :-)

    Re .3:
    
    I tend to agree.  However "end of the world" can be figurative as
    well as literal.
    
    Re .*:
    
    The "creative energy" released can permit others to _prevent_ the
    end of the world.  See how nature balances? :-)
    
    Steve Kallis, Jr.
    

    Sigh.. So many ends of the world and I can't seem to get my laundry
    done on Thursdays.  
    
    It has been an outstanding discovery for me to see just how many
    different and varied "Ends of the World" come from unjustly oppressed
    cultures.
    
    To me these prophecies do not fortell anything other than the time
    which an oppressed culture will give up the ghost, so to say. That
    seems to be the general trend when an oppressed cultures shamans,
    mystics, or prophets predict an end to the oppression.  When the
    end doesn't come the oppressed ones lose faith and join with the
    oppressors (or at least learn to live with them better).
    
    Personaly I don't see their or our culture changing drasticly in
    the next year or so.  When the prophecy doesn't come true some will
    say "Well, the Shamans were just a few years off."  I guess we'll
    find out won't we. B^)                                  
    
      Mikie?    (World without end... Until the Sun munchs us.)

    Don't dismiss the Hopi prematurely though.  In many ways their culture,
    philosophy, and belief-systems are far more advanced than some of
    our own.  They seem to have an intuitive understanding and cosmic
    awareness that many technically advanced societies lack.  Their
    prophesy is based on very ancient, religious beliefs that have been
    handed down by cermony and tablet through countless generations.
    They are very secretive and resistant to outside influence and so
    the old beliefs have retained a kind of purity.  From a historical
    perspective the accounts of the Hopi people are facinating.  From
    a spiritual perspective, the Hopi beliefs are well worth investigation.
                                                                           

    Reply to .7;
    
    I have not dismissed the Hopi as a culture in any manner under
    any circumstance.  I merely stated that prophecies that fortell
    the freeing of the oppressed ones are generated (in my opinion)
    by the emotionaly felt need to be free of the oppression and have
    no direct correlation to reality.
    
    You know there are some AmerIndian nations that seem to be doing
    better than others.  Could it be becuase they are willing to work
    with the white man as equals and not as antagonists?
    
    I love AmerIndian culture and take my first set of priorities from
    them.  Just look at my personal name.  Still the AmerIndian cultures,
    which possibly lasted for some 18,000 years are over and togather
    we are creating a new future that hopefully will include all races
    and their cultures.
    
      Mikie?

    FWIW, the date August 1987 appears in several places throughout
    the world as the end of calendars, predicted dates of destruction.
    This date exists in the Egyptian pyramids and in the South and Central
    American Indian ruins.  
    
    Wait and see...
    
    Elizabeth
    

    I live and work in Tucson, Arizona. I have a friend, Willy
    Whitefeather, who says he is half Hopi and half Mexican, and claims
    to have lived on the Hopi reservation until he was drafted to go
    to Korea.
    
    I asked him about Frank Waters and he said that people would make
    up 'traditions' just to see him get excited and start scribbling
    in his notebook... 
    
    Although apparently it IS true that a Hopi tradition says that as
    long as they stay near Shiprock (four corners area), they will be
    safe. There has been an incredible stink recently, as the BLM 
    (Bureau of Land MisManagement) has been opening this sacred area 
    to mining concerns.
    
    karl moeller

    
    
    Re:  .9
    
    I received a flyer in the mail from a group called Sunray Meditation
    Society (with no return address) announcing a special evening on
    Friday, May 1 at the New England Life Hall at 7:30 P.M. called
    "Voices of Our Ancestors: Echoes Through Time".
    
    The total content of the flyer follows:
    
                   "SUNRAY MEDITATION SOCIETY PRESENTS
                   
               VOICES OF OUR ANCESTORS: ECHOES THROUGH TIME
               An Evening with Dhyani Ywahoo and Tony Shearer
    
     According to the prophecies of the ancient ones of this hemisphere,
     August 17, 1987 is a crucial time.  The ancient Mayan Calendar
     shows that the Fifth Sun will die and the Sixth Sun will be born.
     At this most significant point in planetary evolution, we can make
     the choice to bring forth a peaceful world.
    
     Please join us for this special evening of music, story, slides
     and lecture.  Together we will evoke the wisdom of our ancestors
     - echoes around the spiral of life calling us to remember we are
     all Earth's children, one family.
    
        Friday, May 1                                7:30 PM
        New England Life Hall        225 Clarendon St, Boston
        Tickets         $8.00 in advance - $10.00 at the door
    
     Dhyani Ywahoo is the spiritual director of Sunray Meditation
     Society.  She is a 27th generation lineage holder of the Ywahoo
     lineage of the Etawa Band of the eastern Tsalagi (Cherokee)
     nation.  The Ywahoo lineage originated with the teachings of
     the Pale One.
    
     Tony Shearer of the Lakota Nation, noted author, lecturer, scholar
     and performer, is well known for his translation of the Central
     American Ceremonial Calendar and his study of the ancient Mexican
     god, Quetzalcoatl.
    
                      Tickets on sale at: Sagada, Harvard Sq.
                      Horai-San Crystal Shop, Brookline Village"
    
    
     So it seems that this date is mentioned by a different culture,
     in addition to the Hopis.
    
     Is anyone familiar with this Society?  Or the individuals mentioned?
     Or the Mayan Calendar (i.e. how old is it?)?
    
     Carole
    

    
    Mesoamerican calendrics are/were based on two permutating cycles. One is
    of 260 days, interpolating a numerical sequence of 1-13 with 20
    days, each having its own omens and portents. The second is/was a 365 
    day calendar, which includes 18 named time periods of 20 days each,
    with a five day 'unlucky' period at the end.
    
    For the Maya, the year began with 1 Pop although, interestingly
    enough, the final day of a 'month' was not the 20th, but a separate
    sign that foreshadowed the time period to come. This concept seems
    to have echoed the Maya philosophy (borne out by ethnohistorical
    study) that the influence of a period of time is felt -before- it
    begins, and lingers on after its apparent end.
    
    So, a day in the 260 day calendar also had a position in the 365
    day year, and the complete cycle was made in 52 years. For example,
    if we were starting a new cycle on January 1, 1987 of our time,
    August 17, the second day of the 34th week (or the 233rd day) would
    correspond to the Maya date 13 Auac in the 260 day calendar, and
    13 Ceh in the 365 day cycle.  13 Auac 13 Ceh would not recur until
    another 18,980 days (52 years) had passed.
    
    But it's difficult to say exactly when the calendar dates from.
    When I was in graduate school studying the Maya and their neighbors,
    speculation was that the Maya Preclassic period dated from around
    2500 BC, plus or minus. And of course Maya cosmologies spoke of
    a time far earlier than that. 
    
    And there were earlier civilizations than the Maya - the Olmec,
    for example - who were certainly keeping time somehow.
    
    By the way, the combination of the two cycles is known as the
    Calendar Round, and is the circular sun-centered depiction that
    the later Aztec civilization used.
    
    I'm curious about the way that August 17 has been arrived at
    as a date based on the calendrics and cosmologies of the Maya -
    as I remember, dates were always subject to reassessment in 
    the world of archaeology.
    
    But then, if enough of us agreed that it's so, is that enough?
    
    
    Gloria Bates
    

    Ref .12

    Someone once told me that the Mayans units of time that ranged from
    microseconds to thousands of years.  His theory was that the Mayans
    would not have units like these unless they had a practical need
    for them and that the practical need was for keeping track of
    radioactive half lives.  He thought that the Mayans were aware of
    nuclear physics.  (While the Mayans may have been advanced in some
    areas, I have a little trouble swallowing the nuclear physics stuff.)

    Anyway, I've also heard that they had the length of the year timed
    correctly down to the second way before the Europeans figured it out.
    Any truth to this?

    Mike

    
    And I'll check my Mickey Mouse cartoons - they are more likely to
    be right than EvD
    
    /Bevin

RE: .13
    
    I could be wrong (though I don't think so in this case) but no one
    anywhere had a concept of precise short periods of time (e.g., seconds)
    until Galileo discovered the principle of the pendulum.  You can
    get fairly accurate estimates using the time it takes for water
    to run out of a container or the time for a candle to burn but you
    are measuring things in units closer to an hour than to a second.
    
    They may have had names for units of time down to milleseconds but
    I've never heard that they or anyone else was able to measure time
    more accurately than to say, within 10 minutes.  (For example, we've
    had units of time defined down to femtoseconds for years, but we've
    only recently been able to measure the length of events measured
    in femtoseconds -- and even now we can't measure the time of day that
    accurately only short differences in time).
    
    To put it another way if I define the borg to be a unit of time
    which is 1/100,000th of the length of a day, I can truthfully say
    that I know the length of the day in borgs (which is of the same
    scale as milleseconds) but that doesn't mean a whole lot.
    
    					Topher

    
    Re .13: When you're dealing with archaeological evidence alone,
            there's nothing I know of that points to the existence
            of seconds/microseconds in the Maya system of defining
            time.  Even ethnohistorically, there exists nothing -
            although one might argue that by the time Western contacts
            were identifying and recording the Maya and their way of
            life (beginning at the time of the Spanish conquest and
            thereafter) they were already dealing with a remnant of
            a civilisation, one much in decline, for whom only the
            most basic elements of the culture survived.
    
            As an archaelogist, I have read VonDaniken's book, and others
            like it. Von Daniken is so eager to find material to reinforce
            his hypothesis that he ignores simple, logical explanations
            for certain prehistorical phenomena, in favor of some very
            convoluted concepts. 
    
            I do not deny that there is much, very much that we don't
            know about a number of civilisations that have preceded
            us. And what's more, we're trying to interpret the material
            they've left behind through a number of veneers of prejudice
            (and I mean that in the non-pejorative sense of the word)
            based on who we are, what our values and those of our culture
            may be, and whatver other agenda we bring to the process
            of trying to understand people who were far more different from
            us than we think. 
    
            I'd enjoy discussing Von Daniken, the Maya and their
            civilisation in greater detail with anyone interested...
            since we've strayed from the topic of the Book of the Hopi,
            who are quite specially something else!!   
    
    
    -Gloria

    
    
                                 ;-)
    
    karl

    Re 17 August:
    
    In the 23 June issue of _The Wall Street Journal_, there's a front-page
    story on the Event.  Actually, it doesn't say much beyond discussing
    some of the personalities who are stirring up talk about 17 August
    (more accurately, 16-17 August, asccording to the WSJ).  Various
    predictions, from catastrophe [or averting same] to UFO arrivals
    and "some people ... going off into the fourth dimension" are covered.
    One feature is there's supposed to be a series of Gatherings at
    sacred spots like Machu Piku on those dates to focus energies, says
    Jose Arguelles, a Millenialist.
    
    Steve Kallis, Jr.
    

NEW AGE WILL DAWN IN AUGUST, SEERS SAY, AND MALIBU IS READY

Whether Earth will survive, by one theory, depends on 
turnout at Sacred Sites.

By Meg Sullivan

(Reprinted without permission, consent, or even a hint of knowledge from
THE WALL STREET JOURNAL: Tuesday June 23, 1987)

MALIBU, Calf.- Vijali Hamilton sits cross-legged in a sandstone cave high
above the rugged Malibu coast.  She is naked from the waist up, and the
branches of a small bush rise from Her disheveled hair like antlers.  Ms.
Hamilton, a 48-year-old environmental artist, is rehearsing her role as
Earth Mother, which she will play in an elaborate two-day rite scheduled
for the days following the ideas of August.  That's when a bright new era
for mankind will be ushered in.  Either that or nuclear annihilation.

At that time, when the earth starts to slip out of its "time beam,"
ordinary mortals are going to feel a bit disoriented.  the metaphysically
inclined will experience recurring deja vu.  Coincidences will proliferate.
So will UFOs.

MEET AT MACHU PICCHU

So says Joe Arguelles from Bolder, Colo., an art historian by training but
a "millennialist" by inclination, by divine direction, be the dictates of
reincarnation --actually, it all depends on how you view these things.

Mr.  Arguelles says the choice between a "new age" and all out destruction
is ours, and we had better decide within the next eight weeks.  A new
beginning can be assured only if enough people gather at sacred spots
around the global like Machu Picchu, Peru --on August 16 and 17. (!)

If the attendance is sparse, he warns, we lose our chance at joining a
federation of extraterrestrials.  It is Mr.  Agruelles's hope that the
United Nations will rouse and support this drive.

Mr.  Arguelles's new age, however captivating, is only one new age in what
has become an age of new ages.  Or, for those who recall the "Age of
Aquarius" from the 1960s rock musical "hair," a _new_ age of new ages.

In California, there are plenty of "millennialists" predicting various new
eras on the horizon.  (There are, or course, very many more whose new ages
never arrived.)  There is new age music --quite hard to dance to --new age
dating services, new age travel agencies, highly inventive new age media
and in Beverly Hills, there is even a new age attorney.

"New age" is a highly commodious term, applied equally to upcoming epochs
and such diverse disciplines as pop psychology and Eastern philosophy, not
to mention mainstream trends as consumerism and health food.

Anyway, only the hardest cynic here on the West Coast could deny that a new
age has dawned, is dawning or will dawn sooner or later.  You can smell it
in the air (especially when people "sage smudge," a ritual purification
using burning sage), you can discover it underground (where people bury
expensive, magic crystals) and you can feel it in the Los Angeles seminars
of Ellen Jo Dorfman and David Ramsdale, who offer lessons in "tantra sex,"
or, as they tantalizingly describe it, "psychic and mystical experiences
through sex."  Their customers, the couple maintains, are perfect proof
that Middle America is pining and paying for a new age.

"We get some very regular people with kids and dogs and motor homes," says
Miss Dorfman.  "They eat meat, have regular jobs and don't meditate."

"People en masse are looking toward this whole realm of relatively
unexplored territory," says Marilyn Ferguson, a new age writer, "That one
was only for a minority of spiritual seekers."  Chicago's sober National
Opinions Research Council recently found that 42% of the Americans surveyed
believed that that have been in contact with the dead, up from only 27% in
1973.

What has prompted the search for the new age isn't known, although Shirley
MacLaine's otherworldly book and television movie "Out on a Limb," have
been influential. "You have these periods of religious upheaval," says Carl
Raschke, a humanities professor at the University of Denver, "whenever a
society is making a transformation from one underlying social and economic
structure to another."

How long the masses will have to wait for a new age is yet another
troubling uncertainty.  Technically, "new age" continues to refer to
astrological theory that the Earth is moving into the halcyon Age of
Aquarius from the contentious Age of Pisces.  According to one Los Angeles
astrologer, the dawning of the Age of Aquarius has been predicted for
decades and was due at any time between the years 1800 and 2600.

In the meantime, Miss MacLaine is offering "Higher Self" seminars around
the country at a cost of up to $150 per person per day.  In long beach,
Calf., Carole Carbone leader a $55 daylong seminar in past life regression,
and her conference room is packed.  Miss Carbone, who says she is
clairvoyant, plays scratchy recording of music from various continents, as
her customers close their eyes and drift off to live past--or to sleep.
Afterward, several say that have recollected lives led in India, Egypt, and
Europe.  One, with dismay, has recalled a past life in New Jersey.

And up and down the coast, people are going crazy over crystals.

A $35,000 CRYSTAL

Crystals, according to gurus like Miss MacLaine, enhance spiritual powers.
In addition, they act as magnets for the greater energies of the planet.
(Miss MacLaine adheres to a theory, originally devised by a British
scientist, that the Earth is a living entity that exudes energy, which can
be channeled.)  The crystals, pieces of rock and quart, are sole in new age
bookstores or by crystal peddlers employing a variety of mystical stage
props, including venerable dowsing rods.  One 75-pound piece of quartz was
sold in Seattle for $35,000, "Flawless and water clear," according to its
happy vendor.

But quartz crystals aren't enough for Mr.  Arguelles, the guru who is
counting the days until the new age dawns on Aug.  16.  Mr.  Arguelles wants
people --144,000 of them --to go to places like the pyramids, Machu Picchu
and even Idaho.  Once there, they should "resonate."  This will usher in
the new age and prevent catastrophe, which explains why the new age press
is hailing his plan as "Armageddon Averted."  (Its official name is
"Harmonic Convergence.")

Mr.  Arguelles is the author of the paperback cult book "The Mayan Factor,"
and he says he get is intelligence from the Mayan calendar --that "Galactic
calling card," as he describes it, left behind centuries ago by highly
intelligent aliens in the form of Mayans.  he believes the Mayans were
"called home" to a galactic federation, after leaving clues on how earth
could join the club when the calendar concludes in 2012.  he expects some
of those clues to be revealed in eight weeks, 25 years ahead of time.  the
exact dates for the harmonic convergence came to Mr.  Arguelles when he was
climbing a Mayan pyramid and then again on Dec.  4, 1983, as he motored
down Wilshire Boulevard in Los Angeles.

INTO THE FOURTH DIMENSION

"Some people are predicting earthquakes," says Susan Levin, a 42-year-old
former operator of a singles club who now runs a new age club and
newsletter in Los Angeles.  Miss Levin doesn't worry about the earthquakes,
however, because she believes that on Aug. 16 and 17 "we're going to begin
to communicate telepathically."  Foster Perry, a 26-year-old medium,
predicts that some people "will enter the fourth dimension."  Jade
Windwoman, a 51-year-old Apache medicine woman of German ancestry, says she
is expecting something like the biblical Pentecost.

Other "new agers" scoff at Mr.  Arguelles's predictions. "No one knows when
[the new age] is coming," scolds Patricia Takusm a minister at the New Age
Bible and Philosophy center in Santa Monica, Calif.  And when it does,
points out George Leonard, a renowned and reasonable new age writer, it may
not be all crystals and rainbows.

It involves economic change," he says from his Mill Valley, Calif.  home,
"and that's painful."

But Ms.  Ferguson, the new age writer doesn't see any problem with the
mystic license of the new age movement.

"If all these Second Coming scenarios are nothing but metaphorical spurs to
get us to live as though that were true," she proclaims, "they can be the
inspiration to get our act together."

    	    	    	THE ESSENCE OF HOPI PROPHECY
    	Extract from The Glastonbury Communicator, Issue 13, June 1987
		    
    The entire Hopi prophecy usually takes many days to tell, and many lifetimes
to fully understand.  This is a short summary of some essential points.
    As caretakers of life we affect the balance of nature to such a degree that
our own actions determine whether the great cycles of nature brings prosperity
or disease.  Our present world is the unfoldment of a pattern we set in motion.
    Our divergence from the natural balance is traced to a point proceeding
existence of our present physical form.  Once we were able to appear and
disappear at will, but through our own arrogance we took our procreative
powers for granted and neglected the plan of the creator.  As a consequence
we became stuck in our physical form, dominated by a continual struggle
between our left and our right sides, the left being wise but clumsy, and
the right being clever and powerful but unwise, forgetful of our original
purpose.

THE CYCLE OF WORLDS
    This suicidal split was to govern the entire course of our history
through world after world.  As life resources diminished in accord with
the cycles of nature, we would try to better our situation through our
own inventions, believing that any mistakes can be corrected through
further inventions.  In our cleverness most of us would lose sight of our
original purpose, become involved in a world of our own design, and
ultimately oppose the order of the universe itself, becoming the mindless
enemy of the few who would still hold the key to survival.
    In several previous worlds the majority have advanced their technology
in this way, even beyond what you know today.  The consequent violations
against nature and fellow humans caused severe imbalances which were resolved
in the form of war, social disintegration and natural catastrophy.
    As each world reached the brink of annihilation, there remained a small
minority who had managed to live in nearly complete accord with the infinite
plan, as implied in the name Hopi.  Towards the final stages they would find
themselves beset with signs of disintegration within, as well as enticing
offers and severe threats from without, aimed towards forcing them to join
the rest of the world.

OUR PRESENT WORLD
    Our common ancestors were among the small group who miraculously emerged
from the last world as it reached its destruction, though they were tainted
with corruption.  The seeds of the crisis we face today were brought with us
when we first set foot in this world.
    Upon reaching our present world our ancestors set out on a long migration
to meet the great spirit in the form of Maasauu, the caretaker of this land
and all that lives upon it.  They followed a special pattern, however a very
serious omen made a seperate journey necessary in order to balance the extreme
disorder anticipated for the latter days.

THE TRUE WHITE BROTHER
    A Hopi of light complexion, now known as the "true white brother", left
the group and travelled in the direction of the rising sun, taking with him
a stone tablet which matches a similar tablet held by one of those who went
to meet Maasauu at a place called Oraibi, where the present Hopi villages
were established according to his instructions.
    The Hopi anticipated the arrival of a race of light-skinned people from
the east, predicting many of their inventions, which would serve as signs
indicating certain stages in the unfoldment of the pattern the Hopi had
studied from antiquity.  It was clearly forseen that the visitors, in their
cleverness, might lose sight of their original purpose, in which case they
would be very dangerous.  Still the Hopi were to watch for one who has not
left the spiritual path, and carries the actual stone tablet.

THE SWASTIKA AND THE SUN
    Through countless centuries the Hopi have recalled in their ceremonies
the previous worlds, our emergence to the present world, and our purpose in
coming here.  Periodically they have renewed their vow with Massauu to live
the simple, humble way of life he laid out for them, and to preserve the
balance of nature for the sake of all living things.  The knowledge of world
events has been handed down in secret religious societies who keep watch as
each stage unfolds.
    The leaders watched especially for a series of three world-shaking events,
accompanied by the appearance of certain symbols that describe the pri-mordial
forces that govern all life from the sprouting of a seed to global movements
such as weather, earthquakes, migrations and wars.
    The gourd rattle is a key symbol.  A gourd signifies seed force.  The
shaking of a gourd rattle in ceremonies means the stirring of life forces.
On the rattle are drawn the ancient symbol of the swastika, showing the
spirals of force sprouting from a seed in four directions, surrounded by
a ring of red fire, showing the encircling penetration of the suns warmth
which causes the seed to sprout and grow.
    The first two world-shaking events would involve the forces portrayed
by the swastika and the sun.  Out of the violence and destruction of the
first, the strongest elements would emerge with still greater force to
produce the second event.  When the actual symbols appear it would be clear
that this stage of the prophecy was being fulfilled.

THE GOURD FULL OF ASHES
    Eventually, a 'gourd full of ashes' would be invented, which if dropped
from the sky would boil the oceans and burn the land causing nothing to grow
there for years.  This would be the signal for a certain Hopi to bring out
his teachings in order to warn the world that the third and final event would
happen soon, and that it could bring an end to all life unless people correct
themselves and their leaders in time.
    Hopi leaders now believe that the first two events were the first and
second world wars, and that the gourd full of ashes is the atomic bomb.  After
the bombing of Hiroshima and Nagasaki, teachings formally kept secret were
compared and released.

THE DAY OF PURIFICATION
    The final stage, called the great day of purification has also been
described as a mystery egg in which the forces of the swastika and the sun,
plus a third force symbolized by the colour red, culminate either in total
rebirth or total annihilation - we don't yet know which, but the choice is
ours.  War and natural catastrophe are involved.  The degree of violence
will be determined by the degree of inequity caused among the peoples of the
world and in the balance of nature.  In this crisis rich and poor will be
forced to struggle as equals to survive.
    That it will be very violent is now almost taken for granted among
traditional Hopi but man may still lessen the violence by correcting his
treatment of nature and fellow man.  Ancient spiritually-based communities,
such as the Hopi must especially be preserved and not forced to abandon their
wise way of life and the natural resources they have vowed to protect.

THE FATE OF MANKIND
    The Hopi play a key role in the survival of the human race, through
their vital communion with the unseen forces that holds nature in balance,
as an example of a practical alternative to the suicidal man-made system,
and as a fulcrum of world events.  The patten is simple.  The whole world
will shake and turn red and turn against those who are hindering the Hopi.
    The man-made system now destroying Hopi is deeply involved in similar
violations throughout the world.  The devastating reversal predicted in
these prophecies is part of the natural order.  If those who thrive from that
system, its money and its laws, can manage to stop it from destroying the
Hopi, then many may be able to survive the day of purification and enter a
new age of peace.  But if no-one is left to continue the Hopi way, then the
hope for such an age is in vain.
    The forces we must face are formidable, but the only alternative is
annihilation.  Still the man-made system cannot be corrected by any means
that requires ones will to be forced upon another, for that is the source
of the problem.  If people are to correct themselves and their leaders, the
gulf between the two must disappear.  To accomplish this one can only rely on
the energy of the truth itself.
    This approach, which is the foundation of the Hopi way of life, is the
greatest challenge a mortal can face.  Few are likely to accept it.  But
once peace is established on this basis, and our original way of life is
allowed to flourish, we will be able to use our inventive capacity wisely,
to encourage rather than threaten life, and benefit everyone rather than
giving advantage to a few at the expense of others.  Concern for all living
things will far surpass personal concerns, bringing greater happiness than
could formerly be realised.  Then all living things shall enjoy lasting harmony.

I came across the following in a book about Indians I have, printed about
16 years ago.  It is a letter sent to President Nixon as a result of strip
mining on Hopi Land.

I hope the modem doesn't munge my typing....



"We, the true and traditional religious leaders, recognized as such by the
Hopi People, maintain full authority over all land and life contained within
the Western Hemisphere.  We are granted our stewardship by virtue of our
instruction as to the meaning of Nature, Peace, and Harmony as spoken to
our people by Him, known to us as Massau'u, the Great Spirit, who long
ago provided for us the sacred stone tablets which we preserve to this
day.  For many generations before the coming of the white man, for many
generations before the coming of the Navajo, the Hopi People have lived in
the sacred place known to you as the Southwest and known to us to be the
spiritual center of our continent.  Those of us of the Hopi Nation who have
followed the path of the Great Spirit without compromise have a message
which we are committed, through our prophecy, to convey to you.

The white man, through his insensitivity to the way of Nature, has desecrated
the face of Mother Earth.  The white man's advanced technological capacity
has occurred as a result of his lack of regard for the spiritual path
and for the way of all living things.  The white man's desire for material
possessions and power has blinded him to the pain he has caused Mother Earth
by his quest for what he calls natural resources.  And the path of the Great
Spirit has become difficult to see by almost all men, even by many Indians
who have chosen instead to follow the path of the white man...

Today the sacred lands where the Hopi live are being desecrated by men who
seek coal and water from our soil that they may create more power for the
white man's cities.  This must not be allowed to continue for if it does,
Mother Nature will react in such a way that almost all men will suffer the
end of life as they now know it.  The Great Spirit said not to allow this
to happen even as it was prophesied to our ancestors.  The Great Spirit
said not to take from the Earth--not to destroy living things.  The Great
Spirit, Massau'u, said that man was to live in harmony and maintain a good
clean land for all children to come.  All Hopi people and other Indian Brothers
are standing on this religious principle and the Traditional Spiritual Unity
Movement today is endeavoring to reawaken the spiritual nature in Indian
people throughout this land.  Your government has almost destroyed our basic
religion which actually is a way of life for all our people in this land
of the Great Spirit.  We feel that to survive the coming Purification Day,
we must return to the basic religious principles and to meet together on
this basis as leaders of our people.

Today almost all the prophecies have come to pass.  Great roads like rivers
pass across the landscape; man talks to man through the cobwebs of telephone
lines; man travels along the roads in the sky in his airplanes; two great
wars have been waged by those bearing the swastika or the rising sun; man
is tampering with the Moon and the stars.  Most men have strayed from the
path shown us by the Great Spirit.  For Massau'u alone is great enough to
portray the way back to Him.

It is said by the Great Spirit that if a gourd of ashes is dropped upon
the Earth, that many men will die and that the end of this way of life is
near at hand.  We interpret this as the dropping of atomic bombs on Hiroshima
and Nagasaki.  We do not want to see this happen to any place or nation
again, but instead we should turn all this energy for peaceful uses, not
for war.

We, the religious leaders and rightful spokesmen for the Hopi independent
Nation, have been instructed by the Great Spirit to express the invitation
to the President of the United States and all spiritual leaders everywhere
to meet with us and discuss the welfare of mankind so that Peace, Unity
and Brotherhood will become part of all men everywhere.

Sincerely, Thomas Banyacya, for the Hopi Traditional Village Leaders: Mrs.
Mina Lansa, Oraibi Claude Kawangyawma,  Shungopavy Starlie Lomayaktewa,
Mushongnovi Dan Katchongva, Hotevilla"


I find several things about this letter interesting.  It has a remarkably
peaceful tone, for one.  And "Purification Day" (August 17th ?) doesn't
exactly sound like a time of "harmonic convergence!"  Another interesting
thing:  If the gourd-of-ashes prophecy is about the atomic bomb, it could
be incorrect:  A-bombs are exploded *above* the ground, not on the ground.

Oh well, interesting reading.

John M.

    	A-bombs may explode above the ground, but it IS the surface
    which receives the destruction.
                                                       
    	It's unfortunate that such a beautiful piece of prose had to
    go to Richard Nixon of all people.
    
    	Larry
    

    This base note discusses the Hopi prophesy that "a blue star will
    announce the time".  I've been watching for the discovery of a 
    blue star for some time now and last night I saw this in the paper.
    I don't know if it is our omen but it looks like it to me.
    
    The following was taken from the Fitchburg Sentinel:
    
    AUSTIN, Texas  (AP) -  Two astronomers have photographed a blue
    star they believe to be a gamma ray source so elusive it has been
    called Geminga, which means "does not exist."  
    
    Jules P. Halpern, an assistant professor of physics at Columbia
    University, says in a paper for presentation today that the source
    is an extremely faint star optically located with the 200-inch Hale
    telescope on Mount Palomar in California.
    
    The star, says Halpern, is one of the most powerful gamma ray sources
    in the universe, and astronomers had tried for years to locate it.

    	I guess my fondness for astronomy makes me react like this,
    but there are literally *billions* of blue stars in the Universe,
    and the one you are referring to cannot even be seen by people on
    Earth without special instruments!
    
    	Surely the Hopis would have been referring to a "blue star"
    which could be seen by the naked eye, as they did not even have
    crude optical telescopes in their time.
    
    	And just to stir the "metaphysical" pot a little - just to show
    that I can give other views their "due" - the star which supernoved 
    last year (Supernova 1987A), and could be seen in the Southern 
    Hemisphere with the unaided eye, was a blue star.
    
    	Larry
    

    I'll get my book and look it up Larry, but if I remember correctly
    the prophesy spoke of the star as being new, unseen, or undiscovered
    yet... something like that anyway.  An existing star that can be seen 
    with the naked eye wouldn't seem to qualify but this star appears
    to qualify as it has existed even though undiscovered.
    
    I'll see what else I can find on it.

    	Well, the word "nova" is Latin for "new", as the ancients
    considered a supernova in the sky to be a "new" star which had not 
    been seen before.  That's why if you want to attach the Hopi legend 
    to a "blue star", Supernova 1987A would be a much better candidate
    than the Genima blue star, as it was a blue star which was visible
    to the unaided eye, and had not been seen before by people on Earth.
    
    	BTW - Supernova 1987A is not a "new" star, or even a recent
    stellar explosion:  The blue star exploded in the Large Magellenic
    Cloud (A satellite galaxy of our Milky Way Galaxy) over 150,000
    years ago, and the light of the explosion traveled 150,000 years
    to reach Earth in 1987, as the LMC is over 150,000 light years from
    our planet (light has a velocity of 186,000 miles per second, and 
    travels roughly 6 trillion miles in one year).
                                                                        
    	Larry
            

    That might be the one then.  I'm attending a lecture at Interface
    on Friday by Sun Bear of the Bear Tribe who will speak on Indian
    Prophesy... maybe he will give some additional information on the
    Blue Star.  I'll post it here if he does.

    	But I ask you - how can a star over 150,000 light years away
    in another galaxy have any effect on Earth and its inhabitants,
    other than increase our scientific knowledge of supernovas?
    
    	I would say Supernova 1987A was of probably much greater concern
    to the fates any unfortunate race of inhabitants who lived on planets 
    relatively near the star.
         
    	Larry
                                                              

    re: 348.30
    
    Well, one way the supernova effected Earth was an increase in neutrino
    radiation, anything else is up to speculation.
    
    Dave

    	And what effect does neutrino radiation have on humans?
    
    	Larry
    

    Could be used as a clock - "When you see SN 1987A, X, Y, and Z will
    happen".  It could have been predicted 150,000 years in advance
    that this light would hit us when it did (by an omniscient being,
    or by someone who was there, and had faster-than-light travel).
    
    Elizabeth
    

    	Oh no, I'm not getting into the PROVEN impossibility of faster
    than light travel in THIS Conference...
    
    	Larry
    

RE: .30
    
    Straw man, Larry.
    
    If I predict that when my watch says 5PM that the doors to this
    building will open and people will come pouring out, you would not
    deny the possibility because my watch couldn't possibly cause people
    to leave the building.  If I told you that to get to my house, that
    when coming down one road that you should turn right when you reach
    a speed limit sign, you would not refuse to believe me because the
    speed limit sign couldn't possibly help transport you to my house.
    
    The appearance of a "blue star" is a sign -- a temporal landmark
    so to speak -- not, as far as I know, predicted to be an agent.
    
    And, of course, the supernova *has* had quite a bit of affect here
    on Earth, though none of it, as far as we know, terribly significant
    in the long term.  Budgets have been shifted, careers have been
    effected both positively and negatively, huge amounts (in absolute,
    though not in relative, terms) of resources have been spent in
    discussions, popular writing, technical writing, etc.  And yes,
    our scientific knowledge (of quite a bit more than simply supernovas)
    has been increased.  Very few people, over the course of their
    entire lives, have had as much influence on the world as a whole
    than 1987A has had in the past year.
    
    					Topher
    
    (By the way, I find neither "event" particularly significant to
    the prediction.  Given a large enough time slot, this prediction
    was bound to find something which corresponds to it; as evidenced
    by us having 2 candidates).

    Re .34  (Larry)
    
    Proven impossible, with current understanding of the universe and
    physics.  It may not actally be impossible.  Regardless, it was
    only being used as a (admittedly slim) possibility.
    
    Elizabeth

    	Now I *will* buy the fact that people will take the Hopi legend
    and Supernova 1987A and work it into their own purposes, though
    I doubt the supernova itself was worried over the fate of Earth
    at the time it exploded.
    
    	Larry
    

RE: .34
    
    Larry, as someone who is interested in these things and who has
    a fair (though not deep) understanding of this, let me assure you
    that no such thing has been proven.
    
    What has been proven is that the Special and General Theories of
    Relativity are very good approximations to reality, and that it
    is very unlikely that a theory will be produced which agrees as
    well with the experimental tests and yet differ significantly
    in the aspects we are discussing (actually, such theories have
    been constructed but they are *highly* contrived, and thus, unlikely):
    in other words, we may assume that Relativity Theory is true.
    
    What has been proven then, about superluminal velocities, is that
    travel faster than light is equivalent from another viewpoint to
    "travel" back in time.  Inverted causality is very difficult to
    deal with, and essentially requires, as has been discussed elsewhere
    a more complex view of time than the simply linear time generally
    assumed in physics.  However, it has not been proven in any meaningful
    sense that it does not occur.  Many choose to *assume* that and
    from that a proof of the impossibility of superluminous travel
    follows, but it does depend on that (reasonable but not necessary)
    assumption.
    
    Why should we consider the possibility of inverted causality (including
    travel back in time)?  Three things I know of encourage us, as
    scientists, to consider it, though none of them, in my opinion,
    are strong enough to force us to accept its existence:
    
    	1) There is a large body of evidence in parapsychology whose
    	   most straightforward interpretation includes inverted causality.
    	   This includes both the traditional evidence for precognition
    	   and the relatively new, but fairly extensive, evidence for
    	   retroactive PK.
    
    	2) Certain problems in General Relativity result in solutions
    	   involving inverted causality.  By the nature of the difficulty
      	   of finding exact solutions to the equations of GR, all of
    	   these involve either approximations, which might introduce
    	   errors or rather idealized situations which could not occur
    	   in reality.  (For example, if I haven't misremembered it,
    	   a point particle which loops around an infinitely long
    	   massive cylinder, which is rotating on its axis with its
    	   surface traveling a significant fraction of the speed of
    	   light will emerge, from some points of reference sufficiently
    	   far from the cylinder, before it enters the region close
    	   to the cylinder).  Can these "really" exist, or is there
    	   a "cosmic censorship" principle (as it is called) which
    	   disallow such systems from ever coming into existence?
    
    	3) I have a citation to this one (in a legitimate refereed journal)
    	   but have not yet checked it out, so this one needs a large
    	   grain of salt.  The Aspect experiment, which has gotten
    	   quite a bit of attention, seems to show the propogation of
    	   influence at faster than the speed of light as a consequence
    	   of Quantum Mechanics.  It has frequently been pointed out,
    	   however, that while the experiment can be interpretted as
    	   the superluminal propogation of *influence*, it cannot be
    	   interpretted as the superluminal propogation of *information*
    	   in any meaningful way (its as if a code were propogated at
    	   FTL but the key to figuring out the code still had to propogate
    	   STL.  In a sense you "have" the information but you can't
    	   make any use of it at all until you get the key -- in reality
    	   you don't really know that have it, until the key gets there).
    
    	   A variation of the experiment has been proposed, however,
    	   using, I believe, the rule-breaking Kaons (they are unusual
    	   in that various reactions involving them don't follow rules
    	   (symmetries) which are followed in virtually all other
    	   subatomic reactions) which it is claimed *does* allow
    	   information to be transfered superluminally, according to
    	   the same intepretation of QM which the Aspect Experiment
    	   is claimed to have confirmed (the Copenhagen Interpretation).
    	   The authors may, of course, be mistaken about this, or the
    	   experiment when conducted may fail thus disproving the
    	   Copenhagen Interpretation, but the issue is, scientifically
    	   up in the air.
    
    You are thus, I think, justified (though perhaps not correct) in
    claiming that FTL travel is unlikely.  You are within the bounds
    of reason to proclaim a personal conviction (personal convictions
    being an important feature of the development of science) to its
    non-existence, but scientific proof (and even "proof" in science is
    always tentative) cannot be claimed.
    
    						Topher

    Re: .34 & -.1
    
    We may as well be precise about this.  The proposition that FTL
    velocity is impossible comes from one simple equation in *Special*
    Relativity, viz.,
    
        m =             m0
                 ------------------
                 SQRT(1 - v**2/c**2)
    
    where m0 is the mass of the "travler" at rest, v is its velocity,
    and c is the speed of light in a vacuum.  What this equation states
    is that anything *with mass* that had velocity c (as seen from some
    frame of reference) would have infinite mass (v = c => v**2 = c**2
    => v**2/c**2 = 1 => denominator = 0).  Since, infinity is not a
    real number (or complex number either), this is generally stated
    by means of limits: as v -> c, m -> infinity.  There is more that
    can be deduced from this.  If acceleration is continuous (not unreasonable
    but perhaps not required under some interpretation) then to get to the
    speed of light would require an infinite amount of energy (for the
    acceleration to take place).  Also, if we allow for some sensible
    interpretation of a complex mass (I have no clue if this is a
    "reasonable, but it certainly isn't *logically* impossible) the
    above equation doesn't disallow FTL velocity for an object with
    mass - just one with velocity v = c.  In fact there have been proposals
    expounded that essentially postulate the existence of a whole other
    class(es) of objects with superluminal velocities.  So, the speed
    of light acts "like an inpenetrable wall".  However, if we can give
    a coherent interpretation of a non continuous acceleration, then
    going FTL would be possible, but getting there would have to
    be some sort of discrete event (analogous to energy level quantum
    jumps for atoms).
    

>    	3) I have a citation to this one (in a legitimate refereed journal)
>    	   but have not yet checked it out, so this one needs a large
>    	   grain of salt.  The Aspect experiment, which has gotten
>    	   quite a bit of attention, seems to show the propogation of
>    	   influence at faster than the speed of light as a consequence
>    	   of Quantum Mechanics.  It has frequently been pointed out,
    
    I think this one was making the rounds early last year.  In particular
    there were a number of articles on it in a few issues of Science
    (but, I can't just now recall which issues)
    
    /Jon

    re .39...
    
    Well Jon, as long as you want to be precise,  isn't the result of
    division by zero  UNDEFINED,  rather than infinity?
    
    	Bruce

RE: .39
    
    The equation you discuss, Jon, is frequently brought up in discussions
    of the impossibility of FTL but it turns out that there is a much
    more fundamental (though more complex) argument "against" it in
    special relativity.  (By the way, many people assume, without thinking
    about it, that since time "slows down" as an object approaches the
    speed of light, becoming zero at the speed of light, that it would
    go negative if you could somehow go faster than the speed of light.
    If the equations apply to that situation (they weren't really designed
    to) than time, like mass, would become a complex quantity, so we
    also have to figure out what that means).
    
    One way of handling the mass equation, at least for FTL communication,
    if not for transportation, is called "tachyons".  The quantity you
    refer to as m0 is called the "rest mass" it is an "abstract" property
    of matter, which, for ordinary matter equals, as you said, the mass
    from the viewpoint of an observer to which the mass isn't moving.
    For photons, and probably for neutrinos, the rest mass is zero which
    would mean that they don't exist at rest, or any other speed except
    the speed of light for all observers, so the rest mass doesn't
    "really" ever exist for these particles (I could discuss this at
    more length, but its not really the point).  Anyway, you can imagine
    that there is a particle, called a tachyon, whose rest mass (which
    is abstract just like for the photon) is *imaginary*.  Then, the
    equation you presented says that, as long as the tachyon is traveling
    *faster* than light it will have a perfectly reasonable, ordinary
    mass, but it cannot travel at the speed of light or slower or its
    actual mass becomes complex (i.e., meaningless).  There has been
    some effort to look for tachyons and it was negative -- if they
    exist they are very rare in nature.
    
    The problem really comes about from some of the other equations
    which control how the universe "looks" to different observers. 
    I'm not going to go through all the equations, and work out a
    particular example for you (frankly, I would have to go look them
    up, since its been a while since I played with Special Relativity
    in detail), but I'll outline, without equations or numbers, what
    such an example looks like.
    
    Say we have a situation which looks to one observer like this:
    Something happens at location A, lets call it The Cause, the people
    at A, immediately send a FTL signal (via tachyons, hyperspace, a
    Kaon Aspect machine  or whatever, it doesn't matter) to the people at
    location B who immediately react to it, lets call the reaction
    The Effect.  Sounds harmless.
    
    But the equations of Relativity say that if this takes place we
    can find another, equally valid viewpoint, potentially a second
    observer, to which that situation looked as follows:  First,
    The Effect occurs at B, then The Cause happens at A.  That observer
    deduces that either the people at B foretold the future (precognition)
    or that the people at A effected something that happened in the
    past at B (retroactive PK).
    
    Its important to understand that this is *not* an illusion on the
    part of the second observer due to light rays arriving out of order
    or some such.  The second observer's viewpoint is absolutly as valid
    as the first, they are seeing the same thing in two different, but
    ultimately equivalent ways, just as one observer may see some "energy"
    as mass and another may see it as kinetic energy, from which E=MC^2
    from.
    
    From the second observers viewpoint, when he/she/it sees The Effect
    at B, he/she/it could send (at slower than light speeds) a message
    (say an H-bomb) to A which could prevent The Cause from taking place.
    This would result, from the second observers viewpoint in a paradox,
    and from the first observer an effect (The Effect) without a cause
    (since The Cause never took place).
    
    We can extend the example in a different direction: we can make
    The Effect include the people at B sending a signal back to the
    people at A (either at sub- or super- light speed), who then react
    to that signal with The Ultimate Effect.  Now neither observer has
    to pay any attention to location B at all.  The first observer sees
    The Cause followed by The Ultimate Effect, while the second observer
    sees The Ultimate Effect followed by The Cause, all at location
    A.
    
    Relativity really breaks down at this point, since it produces
    paradoxes.  Relativity is "complete" only if no signal can propogate
    faster than light.  If this is not true (and I gave my reasons for
    feeling that the issue was still open) then it will have to be
    extended to deal with inverse causality and the more complex structure
    to time that that implies.
    
RE: second comment
    
    I read Science (and Science News, NewScientist, and Scientific
    American) pretty closely and didn't see anything about this, which
    was, if I remember, only published about a year ago.  You may be
    thinking of the Aspect Experiment itself which has received a lot
    of attention in the science press, some of which misinterpretted
    it as demonstrating FTL communication.
    
    It's certainly not impossible, though, that I simply missed it, so if
    you have a citation, or are absolutely sure that it discussed the
    variant I mentioned and could tell me roughly when it was, I would
    very much appreciate it.
    
    					Topher 

RE: .39,.40
    
    Your both right.  Infinity has a number of different meanings in
    mathematics but the most common one (which is symbolized by the
    familiar sideways eight) is sometimes read off in English as
    indefinititely large, and is interpreted when it is a result, as
    an undefined quantity.
    
    What is meant whey we say that A/B = X.  The usual mathematical
    definition of division is that it is simply the *inverse* operation
    to multipication.  When we ask what A/B is we are "really" asking
    for a number which when multiplied by B results in A.
    
    If we ask what A/0 is, we are really asking what number multiplied
    by zero results in A.  The answer is that no number has that property
    so the question "What is A/0 equal to?" has no answer.  More
    particularly, we can look at A/B and make B closer and closer to
    zero, we would see that A/B gets larger and larger, so we can say
    that if A/0 had an answer it would have to be larger than any number,
    which is a contradiction, but we represent "a something which is
    like a number but which is larger than any number" as infinity.
    Note that infinitiy (in this sense of the word) is *not* a number,
    and so is really just a shortcut way of saying *how* the answer
    to this question is undefined.
    
    The above does *not* apply, however, if A is 0.  I can answer the
    question "0/0" (i.e., what number equals zero when multiplied by
    zero?) quite easily: "Any number, 37 if you want, or pi, or zero,
    or anything else).  Zero divided by zero is meaningless, rather
    than undefined.  This is important for the mass equation since
    if a particle has a rest-mass (m0) of zero, and if it travels
    at the speed of light (c), then the mass equation says that, as
    far as its concerned, the actual mass can be anything.  And this
    is exactly what we find: photons have a rest-mass of zero, travel
    precisely (by definition) at the speed of light and can have
    any effective mass (simply depending on their
    energy/frequency/wavelength).
    
    				Topher

    Re: .41

>    For photons, and probably for neutrinos, the rest mass is zero which
>    would mean that they don't exist at rest, or any other speed except
>    the speed of light for all observers, so the rest mass doesn't

    More or less, but photons are considered to be *massless*!!  Check it
    out...

>    actual mass becomes complex (i.e., meaningless).  There has been
>    some effort to look for tachyons and it was negative -- if they
>    exist they are very rare in nature.

    It is *impossible* for us to observe these theoretical entities as
    we are "on the down side" of the "impenetrable wall" (v = c) and they
    are "on the up side".  If you have some info. on an actual experiment
    to detect them, I would be interested in hearing it.

>    ultimately equivalent ways, just as one observer may see some "energy"
>    as mass and another may see it as kinetic energy, from which E=MC^2
>    from ...

    A nit (sorry Frederick :-)).  This is not where E = MC^2 comes from.


>    of the impossibility of FTL but it turns out that there is a much
>    more fundamental (though more complex) argument "against" it in

>    The problem really comes about from some of the other equations
>    which control how the universe "looks" to different observers. 
>    I'm not going to go through all the equations, and work out a
>    particular example for you (frankly, I would have to go look them
>    up, since its been a while since I played with Special Relativity
>    in detail), but I'll outline, without equations or numbers, what...

    Naw.  You have this a bit confused, but it is essentially the argument
    to support the first postulate of SR: the speed of light c is the same
    in all frames of reference.  The equations you refer to are the Lorenz
    (as opposed to Galilean) transformations and the Mass transformation which
    I mentioned in my previous note.  I can list them if you really want to
    see them...

    BTW, the second postulate is: that all physical laws are the same in
    every frame of reference.  *EVERYTHING* in SR is deduced from these two
    axioms (along with the other common ones) - the Lorenz and Mass
    transformations, E = mc^2, the whole ball of wax.  *VERY* impressive...


>    Relativity really breaks down at this point, since it produces
>    paradoxes.  Relativity is "complete" only if no signal can propogate

    It's not a case of breaking down, it's a case of denying the postulate(s)
    upon which it is based.  Clearly, if you change the axioms you're gonna
    get a different system...

    I think this basically is further evidence for a position that I have
    felt since I really sat down and rigorously took on SR:  Unless you're
    a genius you can't understand it without understanding the mathematical
    description.  Once, you have done this, you really see how feeble most
    attempts at describing it are.


>    I read Science (and Science News, NewScientist, and Scientific
>    American) pretty closely and didn't see anything about this, which
>    was, if I remember, only published about a year ago.  You may be...

    I'm pretty sure that's where I saw it, but not 100% certain...

>    variant I mentioned and could tell me roughly when it was, I would
>    very much appreciate it.

    I've recently moved and all my journals (and everything else *sigh*)
    are in a bunch of boxes...


    Re: .42

>    If we ask what A/0 is, we are really asking what number multiplied
>    by zero results in A.  The answer is that no number has that property
>    so the question "What is A/0 equal to?" has no answer.

    In a nutshell, division = f(x,y) has an "explosive" discontinuity at
    y = 0.  This is *the* best way of understanding this - technically,
    we say that for any x (we instantiate or fix x)

         LIM    f(x,y) = 00 (sideways "eight" which here means explosive
         y -> 0              dicontinuity => undefined)

    Notice, that since we want f to be well defined, (x,0) is *not* in the
    domain of f for *any* x.

>    that if A/0 had an answer it would have to be larger than any number,
>    which is a contradiction, but we represent "a something which is
>    like a number but which is larger than any number" as infinity.

    No, it is quite simple to patch the discontinuity, but we have to
    go "outside" the set of Reals (or complex numbers too) to do so.
    The topology which results is homeomorphic to the circle.
    
>    The above does *not* apply, however, if A is 0.  I can answer the
>    question "0/0" (i.e., what number equals zero when multiplied by
>    zero?) quite easily: "Any number, 37 if you want, or pi, or zero,
>    or anything else).  Zero divided by zero is meaningless, rather
>    than undefined.

    It's undefined, lest f not be a function!  This is very important!
    Otherwise you have f(0,0) = b and f(0,0) = c and b /= c
    => f(0,0) /= f(0,0).  A reductio argument if I ever saw one...

>    This is important for the mass equation since...

    Well, the *function*, m(m0,v) = m0/sqrt(1-v**2/c**2) is clearly meant
    to have DOM = RANGE= Reals.  Hence, it really has *nothing* to say about
    *anything* which has a velocity >= c.  My comments were simply musings
    on possibly extending it such that, at least, the RANGE = Complex.
    Another thing, to say that Special Relativity is not the whole picture
    in NOWAY implies that it is false.  My own feeling is that anything which
    purports to supercede it had better well include it as a special case
    (or at least be consistent with it); just as Newtonian Mechanics is
    completely consistent with Relativity...


    /Jon