Author’s Musings
These Notes as I see them, relate not to lectures but to feeling. I’m sure my readers differ from me on many things, hut I hope that we share the essence of wonder and longing for what we may never quite understand. —Piers Anthony, 1991, Virtual Mode |
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Piers Anthony, one of science fiction and fantasy’s most prolific talented writers, established the interesting practice of placing an “Author’s Note” section at the end of some of his books. In these notes, he gives that slice of his life occurring during the writing of a current novel, complete with discussions of social issues and unfinished thoughts. In keeping with Piers (with whom I collaborated on a recent science fiction novel), I started this practice in my book Chaos and Wonderland and continue it here by providing you a slice of some of the mail I have received while writing The Loom of God. Also included are miscellaneous recent thoughts, and reader responses to subjects in my previous books.
If one was able to replay the whole evolution of animals, starting at the Cambrian and, to satisfy Laplace, move one animal two feet to its left, there is no likelihood that the result would be the same. There might be no conquest of land, no emergence of mammals, certainly no human beings.
—Evolutionist John Maynard Smith
In Chapters 10 and 21, I discuss theories relating the demise of the dinosaurs to an impact of a huge comet or asteroid. The January 9, 1995, issue of Time presents a recent view on this subject. One new theory holds that clouds of sulfuric acid, formed from the debris thrown into the atmosphere by the impact, were the primary cause of extinctions. Another theory suggests that impact also caused extreme volcanic activity on the opposite side of the Earth, creating a double whammy that killed the dinosaurs. Jon Hagstrum of the U.S. Geological Survey says, “This would be the best way to trigger worldwide mass extinctions because you have both Earth hemispheres affected.”
The likely site of the impact is centered below the town of Chicxulub on the northern tip of Mexico’s Yucatan peninsula. The Yucatan rock around Chicxulub contains large quantities of sulfur. The impact 65 million years ago would have vaporized the sulfur and spewed 100 billion tons of it into the air where it mixed with moisture to form drops of sulfuric acid. These drops reflected sunlight back into space to drop temperatures to near freezing for decades. Kevin Baines of the Jet Propulsion Laboratory comments, “If the asteroid had struck almost any other place on Earth, it wouldn’t have generated this tremendous amount of sulfur. Dinosaurs would still be roaming the Earth.”
How could debris from the impact have traveled high enough into the stratosphere to block out the sun or destroy the ozone layer? Computer simulations suggest that a large asteroid or comet slamming into the ocean floor is capable of producing produce a “hypercane”—the mother of all hurricanes—20 miles high and with winds approaching 500 miles an hour. This would have been sufficiently strong to spread debris all over the Earth. For more information, see: Svitil, K. (1995) Hurricane from Hell. Discover April 16(4): 26.
The period of history which is commonly called “modern” has a mental outlook which differs from that of the medieval period in many ways. Of these, two are the most important: the diminishing authority of the Church, and the increasing authority of science.
—Bertrand Russell
In Chapter 10, I mentioned that a Death Star companion to our Sun was once hypothesized as the cause for recurring extinctions in the history of life. Another kind of Death Star is described in the January 20, 1995, issue of Science 267(5196): 334.
Could a nearby supernova have caused the mass extinction on Earth 251 million years ago—way before the dinosaurs? Researchers suggest a supernova exploding within 30 light-years of Earth is expected to occur once every 240 million years. Even at this distance, the exploding star could bombard the Earth with enough radiation to destroy the ozone layer, thereby exposing photosynthetic creatures at the low end of the food chain to lethal doses of ultraviolet radiation. Currently, scientists debate whether the biological effects of the ozone loss would be sufficient to kill 90% of Earth’s species—as happened at the end of the Permian period 251 million years ago.
In May 1995, a group of astronomers, physicists, and engineers met at Lawrence Livermore National Laboratory to discuss the risks of asteroids and comet crashes. Many methods for protecting the Earth were discussed including non-nuclear schemes for breaking asteroids into little pieces or for forcing them off course. Other “spaceguard” suggestions included: automated charge-coupled devices mounted on telescopes for precise asteroid detection, the use of high-velocity projectiles strung together with strong fibers Musings (“kinetic energy cookie cutters”), the use of rockets to crash into asteroids, the use of solar collectors for heating asteroids’ surfaces, and various methods for shoving small asteroids into larger ones.
One of the scariest predictions advanced at the meeting was the Earth should experience a major asteroid-triggered tsunami every 4000 years. For more information, see: Hill, D. (1995) Gathering airs schemes for averting asteroid doom. Science. June 268(5217): 1562.
Robert Schloss of Yorktown Heights, New York, has brought several interesting facts to my attention regarding virtual reality. In my book Mazes for the Mind, I discuss computers allowing us to enter lifelike, computer-generated realities. Strap on a pair of goggles and you gaze into a three-dimensional world limited only by the speed with which your computer can change the images in response to your eye and head motions. Some call this sense of actually being present within a new reality a “virtual reality” or cyberspace.
On August 20, 1994, 25-year-old Monika G. Liston and 33-year-old Hugh H. Jo were married in the world’s first virtual reality wedding. The couple and their minister donned computerized headgear in pods at CyberMind Virtual Reality Center in San Francisco. They immediately became immersed in a recreation of the lost city of Atlantis containing a palace, chariots, carousels, and doves. The bride, a CyberMind executive assistant, told BusinessWeek: “We’ve been married in our ultimate dream palace.”
Two other interesting factoids. In the 1980s, a new religious denomination was formed every week (source: Newsweek), 52% of 3000 11-year-olds interviewed in New York state would prefer to be without their father rather than without their televisions (source: Minty, L. (1992) Television Viewing and Your Brain)
Michael Seargant writes to me:
I was captivated by the “Latööcarfian Dream” images in your book Chaos in Wonderland: Visual Adventures in a Fractal World (St. Martin’s Press, NY). I therefore was compelled to write a program for IBM PCs to reproduce the images.
Mike says that the free programs are available by anonymous ftp:spanky.triumf.ca [pub.fractals.programs.ibmpc]. By WWW, the url is: http://spanky.triumf.ca/pub/fractals/programs/ibmpc/ganymede.zip. For additional information, contact: Mike Sargent, University of Vermont Student Health Center, 425 Pearl St., Burlington, VT, 05401 or e-mail him at msargent@moose.uvm.edu.
In this book’s Introduction, I wrote: “Imagine a universe called JUMBLE where Kepler looks up into the heavens and finds that most planetary orbits cannot be approximated by ellipses …” You should know that although most orbiting bodies follow elliptical orbits, a few confound scientists with their strangeness. For example, Miranda, a moon of Uranus, once spent millions of years in a chaotic orbit, tumbling erratically like a trapeze artist high on LSD. Hyperion, a moon of Saturn, is now tumbling chaotically, and chaotic orbits explain how asteroids reach Earth in the form of meteors. Many other satellites of the outer planets may have orbited chaotically before ending up in their present, predictable orbits.
Some of you will be interested in Underwood Dudley’s Mathematical Cranks (1992, Mathematical Association of America: Washington, D.C.). In it are the musings of slightly mad mathematicians. One favorite formula relates the value of π to various physical constants such as the speed of light (c) and Planck’s constant (h):
Another relates the golden ratio Φ with π in a compact formula:
Is there anything wrong with this formula?
My favorite chapter is on Matrix Prayers designed by a priest of the Church of England. The priest regularly prayed to God in mathematical terms using matrices, and he taught the children in his church to pray and think of God in matrices. The book goes into great detail regarding “revelation matrices,” “Polite Request Operators,” and the like. The priest finally derives a beautiful prayer which he succinctly writes as:
P < R{S} → {U}, all r > 0 >
He says, “This prayer should be sufficiently concise to be acceptable to Christ, yet every single Christian inhabitant of Northern Ireland has been separately included.” The chapter concludes with information regarding the geometry of heaven.
The null set is also a set; the absence of a god is also a god.
—A. Moreira
Many physicists have been excited about the possibility of establishing units for time, mass, and length which are independent of specific bodies and which would have a meaning for all time and civilizations. The units would even have a meaning for extraterrestrial civilizations. By combining the velocity of light c with the gravitational constant G and Planck’s constant h, physicists compute:
Planck length = (Gh/c3)1/2 = 10–33 cm
Planck time = (G/c5)1/2 = 10–43 s
Planck mass = (hc/G)1/2 = 10–5 g
Notice that the values have enormously different size scales, and this disparity has intrigued physicists for a century. Physicists have also wondered if the fundamental constants of nature—such as the mass of the electron, velocity of light, charge of an electron, gravitational constant, and Planck’s constant—are connected in some subtle way. I believe the current thinking is that the constants are independent entities. (Source: Klotz, I. (1995) Number mysticism in scientific thinking. Mathematical Intelligencer 17(1):43—51)
One unusual paper in a prestigious chemical journal reported that many products and quotients of fundamental constants have values very close to the number 3:
Function |
Numerical Value |
c |
2.9976 × 10 l0 |
(∈/m0)1/2 |
2 2.9995 × 101 |
m0/(2π∈) |
3.0009 × 109 |
|
2.9990 × 10–14 |
2π∈ |
2.9971 × 10–9 |
3Gc/2 |
2.9967 × 103 |
Author J. E. Mills claims that the high occurrence of values extremely close to the number 3 is “amazing.” (Do you think it is amazing?) In the table, m0 is the mass of an electron, and e the electronic charge. (Source: Mills, J. E. (1932) Relations between fundamental physical constants. J. Physical Chemistry 36:1089–1107.)
If we are to believe best-selling novelist Anne Rice, vampires resemble humans in many respects, but live secret lives hidden among the rest of us mortals. In Keys to Infinity I asked readers to consider a numerical metaphor for vampires. I call numbers like 2187 “vampire numbers” because they’re formed when two progenitor numbers 27 and 81 are multiplied together (27 × 81 = 2187). Note that the vampire, 2187, contains the same digits as both parents, except that these digits are subtly hidden, scrambled in some fashion. Similarly, 1435 is a vampire number because it contains the digits of its progenitors, 35 and 41, since (35 × 41 = 1435). These vampire numbers secretly inhabit our number system, but most have been undetected so far. John Childs wrote to me of a 40-digit vampire number he discovered using a Pascal program on a 486 personal computer. His amazing vampire number is 98765432198765432198 × 98765432198830604534 = 9754610597415368368844499268390128385732.
I conclude these “Author’s Musings” with “Satan is a Mathematician,” a poem from Keith Allen Daniels.
The tattoo demon laughed.
“I shall inscribe you with pi—
a pi whose digits are fractal glyphs
of transcendental agony, whose serifs
are influorescent with infinities.
And I shall render it with all
the panache of a pointillist
creating continua from the discrete.
But where to begin? The umbilicus
or the anus? The alpha or the omega?”
“Hey, wait a minute!” cried
the mathematician, and the demon
raised an eyebrow. “Pi’s an irrational number
with a nonrepeating decimal.
Such a task would take an eternity!”
“Imagine that,” said the demon,
and smiling smugly, it poised a talon
tapering to a single atom, plucked lint
from the navel of its flinching victim.
Playing his last card, the mathematician
rose up on his elbow. “Have you really
thought about this? When the flesh
of one man emblazoned subsumes the infinite,
you will have modeled God from numbers
and I will destroy you!”
The other eyebrow twitched. “Well, then,
I shall adorn you with the closest
rational approximation of pi.”
“Shit!” said the mathematician.
“As you wish,” replied the demon,
and began with the anus.
