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 ----------------------------------------------------------------- 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! --------------------------------------------------------------- Subscribe to THE TRANS TIMES! Please begin my subscription to THE TRANS TIMES. I enclose ___ $12.00 for one year (six issues) ___ $22.00 for two years ___ $31.00 for three years. (Add $4.00 per year if you reside outside North America.) I may cancel my subscription at any time for a pro rata refund. Name______________________________ Phone________________________ Address__________________________________________________________ City,State,Zip___________________________________________________ Send to: TRANS TIME, INC., 10208 Pearmain Street, Oakland, CA 94603. (510) 639-1955 Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=5414