X-Message-Number: 5414
From:
Date: Wed, 13 Dec 1995 04:49:31 -0800 (PST)
Subject: Trans Time Newsletter SCI.CRYONICS
THE TRANS TIMES
Life Extension through Cryonic Suspension
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Volume 4 Number 6 December 1995
[SECOND HALF OF NEWSLETTER]
If you would like the printed version of this newsletter, please
send me your street address by e-mail.
Fighting the Odds
by Art Quaife, Ph.D.
I have been involved in cryonics for more than 30 years. When I
got involved in my flaming youth, I figured I had another 50
years or so of life under normal expectancy.
Over the first 15 years or so of my involvement, hardly any of my
colleagues in cryonics died. It appeared that making
arrangements to be frozen by TRANS TIME might provide a guarantee
of immortality without need for cryonics! However, over the last
five years, I have seen all too many of my friends and colleagues
die and be suspended. As many of them were my age, I could be
next.
Last July I began feeling abdominal pain, which was soon
diagnosed as colon cancer. On September 14 I had surgery to
remove most of the colon. Although the risk of death in surgery
was very low, we carried out a standby alert. Paul Hirsch drove a
van loaded with our portable ice bath, 300 pounds of ice, and the
heart-lung resuscitator to the hospital. I obtained agreement
from my surgeon and from the hospital administration that they
would follow my emergency instructions if I died, and indeed
they added my instructions to my chart. Fortunately none of these
preparations were necessary, as I came out of surgery nicely.
Since then I have begun chemotherapy to try to kill the remaining
cancer in my system. My experience with the chemotherapy has so
far been rocky.
I hope and intend to beat this cancer and live out a "normal"
lifespan. But at this point my *expected* lifespan has dropped
considerably, and has refocused my attention to immediate
preparedness here.
My special thanks to my colleagues at Trans Time, who have been
very supportive during this trying time.
[CARTOON OMITTED]
*The Brighter Side of Death*
The Logarithmic Spiral
by Art Quaife, Ph.D.
Eadem mutata resurgo
(Though changed, I shall arise the same)
-- from the tombstone of Jakob Bernoulli
Mathematics offers a variety of symbols that could be used in an
immortalist logo. The lazy eight, oo, is a well-known symbol for
infinity. Mathematicians have developed a very elaborate theory
of infinite sets, with symbols for the various sizes of infinity.
The first infinite ordinal number is w (omega). If everything
works right, your lifespan will have "w" years.
The logarithmic spiral has many features that make it a nice
symbol for cryonics goals. For any point (x, y) in the plane,
draw the line from the origin (0, 0) to the point. Let the length
of that line be r, and its angle with the x-axis be A. Then (r,
A) are the *polar coordinates* of (x, y).
*Basic Properties*
The logarithmic spiral is defined by the equation
log(r) = aA + b,
or equivalently
r = exp(aA + b).
The growth rate of the spiral is a. During each revolution, the
spiral grows by the same factor exp(2 pi a). If *a* is positive,
we get a left-handed spiral. If *a* is negative, we get a right-
handed spiral, which is the mirror image of a left-hand spiral.
When *a* is zero, we get the circle as a special case of the
spiral.
If we start at any point on the spiral and trace it inward, we
will go through an infinite number of turns and never reach the
origin (although we come arbitrarily close). Even though we
circle the origin infinitely many times, the distance we cover is
finite! If instead we spiral outward, we approach infinity,
although we never actually get there. Thus, the logarithmic
spiral has no beginning and no end.
The logarithmic spiral is the preferred growth pattern of many
natural forms, such as shells, horns, tusks, sunflowers, and even
spiral galaxies. It is closely connected to the "golden
rectangle", the rectangle that allegedly has the most pleasing
proportions. The artist M.C. Escher embodied two systems of
logarithmic spirals in his print "Whirlpools".
*Invariance*
Cryonicists expect to undergo substantial changes in their
physical self, through freezing, reanimation, and extensive
reconstruction, yet fervently hope that throughout these
transformations their *identity* survives.
The collection of logarithmic spirals (for different a and b) is
a hardy beast that embodies such hopesDit remains unchanged under
many transformations. Let us look at a few simple ones. If we
dilate a spiral, by multiplying each distance from the origin by
the same positive factor c, we get another spiral, which could
also be obtained by rotating the spiral though an angle --log(c)/a.
For another example, if we perform the inversion in the
unit circle that replaces each point (r, A) by (1/r, A), a
logarithmic spiral is mapped into its mirror image spiral,
rotated by an angle 2b.
The *evolute* of a logarithmic spiral, the *pedal curve* of a
logarithmic spiral, the *caustic by reflection* and the *caustic
by refraction* of a logarithmic spiral, are all again logarithmic
spirals. Some of these invariance properties follow directly from
the invariance of the exponential function under differentiation:
d(exp(x))/dx = exp(x).
Bernoulli's Fate
Jakob Bernoulli was the first to investigate the properties of
the logarithmic spiral, in the late 1600s. He was moved to say
"Since this marvelous spiral, by such a singular and wonderful
peculiarity . . . always produces a spiral similar to itself,
indeed precisely the same spiral, however it may be involved or
evolved, or reflected or refracted . . . it may be used as a
symbol, either of fortitude and constancy in adversity, or of the
human body, which after all its changes, even after death, will
be restored to its exact and perfect self." He called it the
*spira mirabilis* (the marvelous spiral), and had it engraved on
his tombstone.
This story has a sad ending, as do all stories that end in the
grave. The mason inscribed Bernoulli's tombstone with the
Archimedean spiral, which has much different properties than his
beloved logarithmic spiral. Rumor has it that this error set
Jacob spiraling in his grave; we have no word that he was ever
resurrected to his perfect self.
*Reference*
Maor, E. e: The story of a number. Princeton: Princeton
University Press (1994).
*Postscript*
I have requested that my cryocapsule be labeled with
Cryono ergo ero
(I am frozen, therefore I will be)
[GRAPH OMITTED]
Emergency Responsibility
Have you completed your arrangements for cryonic suspension?
Without advance suspension arrangements, you will not be
suspended. Arrangements can hardly ever be made at the last
minute.
The first step is to enroll for our Emergency Responsibility
service. We enclose an application form with this issue.
Have Something to Say?
We invite our readers to submit cryonics-related articles for
possible publication in this newsletter. The best way to submit
is to send us the article in WordPerfect, on an MS DOS diskette.
Call us about other electronic formats you may use. We will also
consider typed or handwritten submissions.
Upcoming Meetings
Trans Time holds bimonthly business meetings at which visitors
are welcome. The next meeting will be held Sunday, December 17,
1:00 p.m. at:
The Home of Judy and Paul Segall
1003 Middlefield Road
Berkeley, CA 94708
(510) 644-3153
This meeting will be followed by the annual Cryonics Holiday
Party, from 4:00 8:00 p.m. All are invited!
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