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From: John Conover <>
Subject: forwarded message from
Date: Fri, 9 Jan 1998 02:33:26 -0800

Interesting "On This Day, Jan 9 ..." concerning "1st income tax
imposed, in England. (1799)". Although income tax was a British
invention, the concept of progressive income tax, (that you and I so
dearly love,) was a purely American invention. Does it make sense?
Well, that depends on who is telling the story.

If you believe-and many do, but many don't-that such things as
economic robustness in a society is fractal in nature, then income in
a society should be distributed as a 1 / (n^2) function, (at least
theoretically-the empirical evidence seems to support the
hypothesis-you can verify this for the US at for
your own edification.) If that is the case, then pushing the top end
of the spectrum down also pushes the bottom end of the spectrum down,
(ie., if you plot the distribution on log-log paper, then Bill Gates
occupies the number one position, the rest of us group, more or less,
in increasing numbers down the graph, in a 1 / (n^2) fashion.) since
the slope of the line, (ie., -0.5) can not be changed.

So, if this is true-and many believe it, and many don't-then taxing
the wealthy hurts the poor. A paradox? You will have to be your own
judge ...

(And, no, I am not presenting an argument in favor of flat tax. I try
not to believe in anything. It gets me in trouble.)


BTW, the ancient Mesopotamians and Egyptians were meticulous record
keepers. It seems that the 1 / (n^2) business has been with us for
most of the time we have done the civilization agenda. Interestingly,
the, now defunct, Soviet system exhibited the same phenomena, as did
National Socialist system in WWII Germany. So did the Maya in Central
America, as did the Plains Indians in North America. So did the
Anasazi in the American South West. So did the Ming Dynasty in
China. In point of fact, there are no known exceptions in the ten
thousand years of recorded history-at least to the numerical precision
of the data we have. Kind of an interesting argument when a 1 / (n^2)
is the hallmark signature of fractal things.

And if wealth/resources/power aligns itself in a 1 / (n^2)
arrangement, what are the implications? Well, theoretically at least,
we would expect the probable duration of a society to be the
reciprocal of the square root of time, or about 4 centuries, (if we
measure such things in centuries.) We measure about 4.6, (depending on
whose numbers we are using.)

Compelling arguments? You will have to be our own judge.

The numbers used above can be found at various places on the Internet,
in ascii text files, and you can do your own analysis, (ie., run
log-log plots.) Want a flight of fantasy? If such things really are
fractal, we should be able to project, (famous last words,) what the
growth of the stock market, (since, in some sense, it represents
wealth,) by the probability constants in the economic expansion in
this, the third century of our existence. That probability would be
somewhat lower than the reciprocal of the square root of three, or
about 0.577, (we measure 0.542.) In the last century, it should be
somewhat lower than 0.707, (we measure about 0.65, or so, depending on
whose data we are using.) An interesting, (fantasies are interesting,)

BTW, the arguments here are logic. If, (and its a big if,) such things
are fractal, then the measure of a society's wealth-perhaps via a GDP
as an arbitrary ecological metric-must obey the square root and 1 /
(n^2) business, if, and only if, the Shannon Probability is exactly
random, or 0.5. If it was greater, then we would all be
Mesopotamians. And we are not. If it was less, then civilization would
not exist. But we do. Therefore, the implication is that, during a
society's duration, the Shannon Probability will rise, and during its
demise, it will fall. And, if such things are fractal, (and its a big
if,) then most of the measures of wealth in the society should follow
the same set of rules, (by definition, a fractal is self-similar, at
all scales, and is made up of fractals, that are self-similar, at all
scales.)  Therefore, the equity markets should follow the same scheme,
which means, that the Shannon Probability, should be about the
same. So, we compute the probability that a society's wealth will
increase, and we have the "instantaneous" Shannon Probability that
should be reflected in all wealth, including the equity markets, at a
specific time.

Do I believe this? (I don't know, I'm still having trouble with
mathematical induction.) But there have been some interesting
philosophical arguments presented, (again, as a flight of fantasy.)
Here is the way the logical arguments proceed. (Note that fractals
have a random nature, that assemble their self into a probabilistic
phenomena, ie., the 1 / (n^2) and 1 / sqrt (t) kind of things.) Lets
suppose that life/civilization/equites were not that way. By
implication that would mean that there was some kind of grand equation
or logic by which such things operate, (ie., there would be no
randomness.) What would that mean? Well, it would mean that it was a
deterministic system. And what does that imply? Well, it would mean
that there was no freedom of choice, (ie., no matter how much one
pondered a decision, the decision would have been preordained, and
there would be no choice. One's decision would have been inevitable
from time zero.)

There is a lemma to this logic, (fantasy as it may be.) If one
believes that one can exercise some influence over the state of
affairs in one's life, then one must believe that one's life is not a
preordained/deterministic/predictable system, and, therefore, one must
believe life is governed by random events, that chain together-ie., a
fractal. (Many mathematical logicians, over enough beer, will admit to
believing this. Sometimes, its a lot of beer-a delightful beverage,
for which, we are ever indebted to the ancient Mesopotamians, who are
no longer with us, but made their contribution to the enduring fractal

So, if this logic has anything substantive, (fantasy as it may be,)
then the question can be raised as to why we should go to all the
bother with the trials and tribulations of civilization, and all the
things we do? The argument being that if life is a series of random
events, shouldn't we just adopt a fatalistic attitude, and concede?
The counter argument presented is, (usually,) is that it is gambling,
(gambling is where fractals were invented,) and if you don't play, you
can't win. Playing is a necessary, but insufficient, requirement for

So the story goes. And, the story continues, (fantasy-maybe a soap
opera-as it may be,) that there are rules to the game, as a
consequence of the way that random processes assemble their selves
into fractals. (A Gaussian bell curve, ie., the way random events-like
the distribution of the sum of tossing two dies assemble their selves,
for one.) The accuracy, (ie., the horizon,) of how far one can predict
life's affairs into the future decays with the reciprocal of the
square root of time, (irregardless of what unit of time is used, which
is a bit of a paradox-unless one understands what self-similar
implies.) And, as one decreases the units of time, then the statistics
of the fractal scale with the square root of time, (ie., cutting the
time units by four, one cuts the statistics by a factor of two.) And,
if one looks at the way the distribution of the way sub-fractals
assemble their selves, it is a 1 / (n^2) phenomena.

Do I believe it? I'm still wondering how mathematicians proved
mathematical induction consistent without using mathematical

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Received: (from root@localhost) by (8.6.12/8.6.12) id AAA31668 for john; Fri, 9 Jan 1998 00:05:11 -0800
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From: root <>
Subject: Reminders for Friday, January  9, 1998
Date: Fri, 9 Jan 1998 00:05:11 -0800

Reminders for Friday, 9th January, 1998 (today):

              Sunrise 07:22, Sunset 17:07, Moon 0.76 (Increasing)

Reminders for Tuesday, 13th January, 1998:

________________________ On This Day, Jan  9 ... ________________________

1st San Francisco paper, 'California Star', published. (1847)
1st balloon flight in North America. (1793)
1st commercial bank in San Francisco established. (1848)
1st income tax imposed, in England. (1799)
5.9 earthquake in New England/Canada; last one was in 1855. (1982)
Astronomer Caroline Herschel, publisher of "Herschel's Catalog of Stars" and sister of William, dies at 97 (1848)
Bill Graham born (1931)
Bob Denver, actor played Gilligan on "Gilligan's Island", is born (1935)
Chic Young, creator of the "Blondie" comic strip. (1901)
Connecticut becomes the 5th state (1788)
Day of the Martyrs (Panama)
Day of the Martyrs in Panama
Exposition (now Civic) Auditorium dedicated. (1915)
Fellowship reaches Lorien (LOTR)
First issue of the "Progressive" magazine (1909)
Gypsy Rose Lee, entertainer and author, is born (1914)
James Patrick Page (Led Zeppelin) born (Middlesex, England, 1945)
James Patrick Page (Led Zeppelin) is born in Middlesex, England, 1945
Joan Baez, folk singer, is born on Staten Island, New York (1941)
Joseph B. Strauss, civil engineer & builder of Golden Gate Bridge. (1870)
Karel Capek, Czech author and originator of the term robot, is born (1890)
Mississippi secedes from the union (1861)
Plough Monday
Richard M. Nixon, 37th President (1968-1974) (1913)
Simone de Beauvoir, feminist, born (1908)
St. Marciana is martyred by being torn to bits by a leopard and a wild bull in the Caesarea amphitheater (309)
the daguerrotype process announced at French Academy of Science (1839)
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John Conover,,

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