Part 13 (1/2)
These speeds, when combined with the stars' distance from the center of the galaxy, are a direct measure of the total ma.s.s contained within their orbits. Armed with these data, we can use the back of an envelope to calculate whether the attracting central ma.s.s is, indeed, concentrated enough to be a black hole. The largest known black holes are typically a billion solar ma.s.ses, such as what lurks within the t.i.tanic elliptical galaxy M87, the largest in the Virgo Cl.u.s.ter of galaxies. Far down the list, but still large, is the 30-million solar ma.s.s black hole in the center of the Andromeda galaxy, our near neighbor in s.p.a.ce.
Beginning to feel ”black hole envy”? You are entirely justified: the one in the Milky Way's center checks in at a mere 4-million solar ma.s.ses. But no matter the ma.s.s, death and destruction are their business.
SECTION 6.
SCIENCE AND CULTURE.
THE RUFFLED INTERFACE BETWEEN COSMIC DISCOVERY AND THE PUBLIC'S REACTION TO IT
THIRTY-FOUR.
THINGS PEOPLE SAY.
Aristotle once declared that while the planets moved against the background stars, and while shooting stars, comets, and eclipses represented intermittent variability in the atmosphere and the heavens, the stars themselves were fixed and unchanging on the sky and that Earth was the center of all motion in the universe. From our enlightened perch, 25 centuries later, we chuckle at the folly of these ideas, but the claims were the consequence of legitimate, albeit simple, observations of the natural world.
Aristotle also made other kinds of claims. He said that heavy things fall faster than light things. Who could argue against that? Rocks obviously fall to the ground faster than tree leaves. But Aristotle went further and declared that heavy things fall faster than light things in direct proportion to their own weight, so that a 10-pound object would fall ten times faster than a 1-pound object.
Aristotle was badly mistaken.
To test him, simply release a small rock and a big rock simultaneously from the same height. Unlike fluttering leaves, neither rock will be much influenced by air resistance and both will hit the ground at the same time. This experiment does not require a grant from the National Science Foundation to execute. Aristotle could have performed it but didn't. Aristotle's teachings were later adopted into the doctrines of the Catholic Church. And through the Church's power and influence Aristotelian philosophies became lodged in the common knowledge of the Western world, blindly believed and repeated. Not only did people repeat to others that which was not true, but they also ignored things that clearly happened but were not supposed to be true.
When scientifically investigating the natural world, the only thing worse than a blind believer is a seeing denier. In A.D A.D. 1054, a star in the constellation Taurus abruptly increased in brightness by a factor of a million. The Chinese astronomers wrote about it. Middle Eastern astronomers wrote about it. Native Americans of what is now the southwestern United States made rock engravings of it. The star became bright enough to be plainly visible in the daytime for weeks, yet we have no record of anybody in all of Europe recording the event. (The bright new star in the sky was actually a supernova explosion that occurred in s.p.a.ce some 7,000 years earlier but its light had only just reached Earth.) True, Europe was in the Dark Ages, so we cannot expect that acute data-taking skills were common, but cosmic events that were ”allowed” to happen were routinely recorded. For example, 12 years later, in 1066, what ultimately became known as Halley's comet was seen and duly depicted-complete with agape onlookers-in a section of the famous Bayeux tapestry, circa 1100. An exception indeed. The Bible says the stars don't change. Aristotle said the stars don't change. The Church, with its unmatched authority, declares the stars don't change. The population then falls victim to a collective delusion that was stronger than its members' own powers of observation.
We all carry some blindly believed knowledge because we cannot realistically test every statement uttered by others. When I tell you that the proton has an antimatter counterpart (the antiproton), you would need $1 billion worth of laboratory apparatus to verify my statement. So it's easier to just believe me and trust that, at least most of the time, and at least with regard to the astrophysical world, I know what I am talking about. I don't mind if you remain skeptical. In fact, I encourage it. Feel free to visit your nearest particle accelerator to see antimatter for yourself. But how about all those statements that don't require fancy apparatus to prove? One would think that in our modern and enlightened culture, popular knowledge would be immune from falsehoods that were easily testable.
It is not.
Consider the following declarations. The North Star is the brightest star in the nighttime sky. The Sun is a yellow star. What goes up must come down. On a dark night you can see millions of stars with the unaided eye. In s.p.a.ce there is no gravity. A compa.s.s points north. Days get shorter in the winter and longer in the summer. Total solar eclipses are rare.
Every statement in the above paragraph is false.
Many people (perhaps most people) believe one or more of these statements and spread them to others even when a firsthand demonstration of falsehood is trivial to deduce or obtain. Welcome to my things-people-say rant: The North Star is not the brightest star in the nighttime sky. It's not even bright enough to earn a spot in the celestial top 40. Perhaps people equate popularity with brightness. But when gazing upon the northern sky, three of the seven stars of the Big Dipper, including its ”pointer” star, are brighter than the North Star, which is parked just three fist-widths away. There is no excuse.
And I don't care what else anyone has ever told you, the Sun is white, not yellow. Human color perception is a complicated business, but if the Sun were yellow, like a yellow lightbulb, then white stuff such as snow would reflect this light and appear yellow-a snow condition confirmed to happen only near fire hydrants. What could lead people to say that the Sun is yellow? In the middle of the day, a glance at the Sun can damage your eyes. Near sunset, however, with the Sun low on the horizon and when the atmospheric scattering of blue light is at its greatest, the Sun's intensity is significantly diminished. The blue light from the Sun's spectrum, lost to the twilight sky, leaves behind a yellow-orange-red hue for the Sun's disk. When people glance at this color-corrupted setting Sun, their misconceptions are fueled.
What goes up need not come down. All manner of golf b.a.l.l.s, flags, automobiles, and crashed s.p.a.ce probes litter the lunar surface. Unless somebody goes up there to bring them back, they will never return to Earth. Not ever. If you want to go up and not come down, all you need to do is travel at any speed faster than about seven miles per second. Earth's gravity will gradually slow you down but it will never succeed in reversing your motion and forcing you back to Earth.
Unless your eyes have pupils the size of binocular lenses, no matter your seeing conditions and no matter your location on Earth, you will not resolve any more than about five or six thousand stars in the entire sky out of the 100 billion (or so) stars of our Milky Way galaxy. Try it one night. Things get much, much worse when the Moon is out. And if the Moon happens to be full, it will wash out the light of all but the brightest few hundred stars.
During the Apollo s.p.a.ce program, while one of the missions was en route to the Moon, a noted television news anchor announced the exact moment when the ”astronauts left the gravitational field of Earth.” Since the astronauts were still on their way to the Moon, and since the Moon orbits Earth, then Earth's gravity must extend into s.p.a.ce at least as far as the Moon at least as far as the Moon. Indeed, Earth's gravity, and the gravity of every other object in the universe, extends without limit-albeit with ever-diminis.h.i.+ng strength. Every spot in s.p.a.ce is teeming with countless gravitational tugs in the direction of every other object in the universe. What the announcer meant was that the astronauts crossed the point in s.p.a.ce where the force of the Moon's gravity exceeds the force of Earth's gravity. The whole job of the mighty three-stage Saturn V Saturn V rocket was to endow the command module with enough initial speed to just reach this point in s.p.a.ce because thereafter you can pa.s.sively accelerate toward the Moon-and they did. Gravity is everywhere. rocket was to endow the command module with enough initial speed to just reach this point in s.p.a.ce because thereafter you can pa.s.sively accelerate toward the Moon-and they did. Gravity is everywhere.
Everybody knows that when it comes to magnets, opposite poles attract while similar poles repel. But a compa.s.s needle is designed so that the half that has been magnetized ”North” points to Earth's magnetic north pole. The only way a magnetized object can align its north half to Earth's magnetic north pole is if Earth's magnetic north pole is actually in the south and the magnetic south pole is actually in the north. Furthermore, there is no particular law of the universe that requires the precise alignment of an object's magnetic poles with its geographic poles. On Earth the two are separated by about 800 miles, which makes navigation by compa.s.s a futile exercise in northern Canada.
Since the first day of winter is the shortest ”day” of the year, then every succeeding day in the winter season must get longer and longer. Similarly, since the first day of summer is the longest ”day” of the year, then every succeeding day in the summer must get shorter and shorter. This is, of course, the opposite of what is told and retold.
On average, every couple years, somewhere on Earth's surface, the Moon pa.s.ses completely in front of the Sun to create a total solar eclipse. This event is more common than the Olympics, yet you don't read newspaper headlines declaring ”a rare Olympics will take place this year.” The perceived rarity of eclipses may derive from a simple fact: for any chosen spot on Earth, you can wait up to a half-millennium before you see a total solar eclipse. True, but lame as an argument because there are spots on Earth (like the middle of the Sahara Desert or any region of Antarctica) that have never, and will not likely ever, host the Olympics.
Want a few more? At high noon, the Sun is directly overhead. The Sun rises in the east and sets in the west. The Moon comes out at night. On the equinox there are 12 hours of day and 12 hours of night. The Southern Cross is a beautiful constellation. All of these statements are wrong too.
There is no time of day, nor day of the year, nor place in the continental United States where the Sun ascends to directly overhead. At ”high noon,” straight vertical objects cast no shadow. The only people on the planet who see this live between 23.5 degrees south lat.i.tude and 23.5 degrees north lat.i.tude. And even in that zone, the Sun reaches directly overhead on only two days per year. The concept of high noon, like the brightness of the North Star and the color of the Sun, is a collective delusion.
For every person on Earth, the Sun rises due east and sets due west on only two days of the year: the first day of spring and the first day of fall. For every other day of the year, and for every person on Earth, the Sun rises and sets someplace else on the horizon. On the equator, sunrise varies by 47 degrees across the eastern horizon. From the lat.i.tude of New York City (41 degrees north-the same as that of Madrid and Beijing) the sunrise spans more than 60 degrees. From the lat.i.tude of London (51 degrees north) the sunrise spans nearly 80 degrees. And when viewed from either the Arctic or Antarctic circles, the Sun can rise due north and due south, spanning a full 180 degrees.
The Moon also ”comes out” with the Sun in the sky. By invoking a small extra investment in your skyward viewing (like looking up in broad daylight) you will notice that the Moon is visible in the daytime nearly as often as it is visible at night.
The equinox does not contain exactly 12 hours of day and 12 hours of night. Look at the sunrise and sunset times in the newspaper on the first day of either spring or fall. They do not split the day into two equal 12-hour blocks. In all cases, daytime wins. Depending on your lat.i.tude, it can win by as few as seven minutes at the equator up to nearly half an hour at the Arctic and Antarctic circles. Who or what do we blame? Refraction of sunlight as it pa.s.ses from the vacuum of interplanetary s.p.a.ce to Earth's atmosphere enables an image of the Sun to appear above the horizon several minutes before the actual Sun has actually risen. Equivalently, the actual Sun has set several minutes before the Sun that you see. The convention is to measure sunrise by using the upper edge of the Sun's disk as it peeks above the horizon; similarly, sunset is measured by using the upper edge of the Sun's disk as it sinks below the horizon. The problem is that these two ”upper edges” are on opposite halves of the Sun thereby providing an extra solar width of light in the sunrise/sunset calculation.
The Southern Cross gets the award for the greatest hype among all eighty-eight constellations. By listening to Southern Hemisphere people talk about this constellation, and by listening to songs written about it, and by noticing it on the national flags of Australia, New Zealand, Western Samoa, and Papua New Guinea, you would think we in the North were somehow deprived. Nope. Firstly, one needn't travel to the Southern Hemisphere to see the Southern Cross. It's plainly visible (although low in the sky) from as far north as Miami, Florida. This diminutive constellation is the smallest in the sky-your fist at arm's length would eclipse it completely. Its shape isn't very interesting either. If you were to draw a rectangle using a connect-the-dots method you would use four stars. And if you were to draw a cross you would presumably include a fifth star in the middle to indicate the cross-point of the two beams. But the Southern Cross is composed of only four stars, which more accurately resemble a kite or a crooked box. The constellation lore of Western cultures owes its origin and richness to centuries of Babylonian, Chaldean, Greek, and Roman imaginations. Remember, these are the same imaginations that gave rise to the endless dysfunctional social lives of the G.o.ds and G.o.ddesses. Of course, these were all Northern Hemisphere civilizations, which means the constellations of the southern sky (many of which were named only within the last 250 years) are mythologically impoverished. In the North we have the Northern Cross, which is composed of all five stars that a cross deserves. It forms a subset of the larger constellation Cygnus the swan, which is flying across the sky along the Milky Way. Cygnus is nearly twelve times larger than the Southern Cross.
When people believe a tale that conflicts with self-checkable evidence it tells me that people undervalue the role of evidence in formulating an internal belief system. Why this is so is not clear, but it enables many people to hold fast to ideas and notions based purely on supposition. But all hope is not lost. Occasionally, people say things that are simply true no matter what. One of my favorites is, ”Wherever you go, there you are” and its Zen corollary, ”If we are all here, then we must not be all there.”
THIRTY-FIVE.
FEAR OF NUMBERS.
We may never know the circuit diagram for all the electrochemical pathways within the human brain. But one thing is for certain, we are not wired for logical thinking. If we were, then mathematics would be the average person's easiest subject in school.
In this alternate universe, mathematics might not be taught at all because its foundations and principles would be self-evident even to slow-achieving students. But nowhere in the real world is this true. You can, of course, train most humans to be logical some of the time, and some humans to be logical all of the time; the brain is a marvellously flexible organ in this regard. But people hardly ever need training to be emotional. We are born crying, and we laugh early in life.
We do not emerge from the womb enumerating objects around us. The familiar number line, for example, is not writ on our gray matter. People had to invent the number line and build upon it when new needs arose from the growing complexities of life and of society. In a world of countable objects, we will all agree that 2 + 3 = 5, but what does 23 equal? To answer this question without saying, ”It has no meaning,” required that somebody invent a new part of the number line-negative numbers. Continuing: We all know that half of 10 is 5, but what is half of 5? To give meaning to this question, somebody had to invent fractions, yet another cla.s.s of numbers on the number line. As this ascent through numberdom progressed, many more kinds of numbers would be invented: imaginary, irrational, transcendental, and complex, to name a few. They each have specific and sometimes unique applications to the physical world that we have discovered around us from the dawn of civilization.
Those who study the universe have been around from the beginning. As a member of this (second) oldest profession, I can attest that we have adopted, and actively use, all parts of the number line for all manner of heavenly a.n.a.lysis. We also routinely invoke some of the smallest and, of course, largest numbers of any profession. This state of mind has even influenced common parlance. When something in society seems immeasurably large, like the national debt, it's not called biological or chemical. It's called astronomical. And so one could argue strongly that astrophysicists do not fear numbers.
With thousands of years of culture behind us, what has society earned on its math report card? More specifically, what grade do we give Americans, members of the most technologically advanced culture the world has ever known?
Let's start with airplanes. Whoever lays out the seats on Continental Airlines seems to suffer from Medieval fears of the number 13. I have yet to see a row 13 on any flight I have taken with them. The rows simply go from 12 to 14. How about buildings? Seventy percent of all high-rises along a three-mile stretch of Broadway in Manhattan have no thirteenth floor. While I have not compiled detailed statistics for everywhere else in the nation, my experience walking in and out of buildings tells me it's more than half. If you've ridden the elevator of these guilty high-rises you've probably noticed that the 14th floor directly follows the 12th. This trend exists for old buildings as well as new. Some buildings are self-conscious and try to conceal their superst.i.tious ways by providing two separate elevator banks: one that goes from 1 to 12 and another that goes upward from 14. The 22-story apartment building in which I was raised (in the Bronx) had two separate banks of elevators, but in this case, one bank accessed only the even floors while the other bank accessed the odd. One of the mysteries of my childhood was why the odd bank of elevators went from floor 11 directly to floor 15, and the even bank went from 12 to 16. Apparently, for my building, a single odd floor could not be skipped without throwing off the entire odd-even scheme. Hence the blatant omission of any reference to either the 13th or or the 14th floor. Of course, all this meant that the building was actually only 20 stories high and not 22. the 14th floor. Of course, all this meant that the building was actually only 20 stories high and not 22.
In another building, which harbored an extensive subterranean world, the levels below the first floor were B, SB, P, LB, and LL. Perhaps this is done to give you something to think about while you are otherwise standing in the elevator doing nothing. These floors are begging to become negative numbers. For the uninitiated, these abbreviations stood for Bas.e.m.e.nt, Sub-Bas.e.m.e.nt, Parking, Lower Bas.e.m.e.nt, and Lower Level. We surely do not use such lingo to name normal floors. Imagine a building not with floors labelled 1, 2, 3, 4, 5, but G, AG, HG, VHG, SR, R, which obviously stand for Ground, Above Ground, High Ground, Very High Ground, Sub-Roof, and Roof. In principle, one should not fear negative floors-they don't in the Hotel de Rhone in Geneva, Switzerland, which has floors-1 and-2, nor are they afraid at the National Hotel in Moscow, which had no hesitation naming floors 0 and-1.
America's implicit denial of all that is less than zero shows up in many places. A mild case of this syndrome exists among car dealers, where instead of saying they will subtract $1,000 from the price of your car, they say you will receive $1,000 ”cash back.” In corporate accounting reports, we find that fear of the negative sign is pervasive. Here, it's common practice to enclose negative numbers in parentheses and not to display the negative symbol anywhere on the spreadsheet. Even the successful 1985 Bret Easton Ellis book (and 1987 film) Less Than Zero Less Than Zero, which tracks the falling from grace of wealthy Los Angeles teens, could not be imagined with the logically equivalent t.i.tle: Negative Negative.