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Draft Script: "Is the Universe Infinite?"
How far do the stars stretch? And what’s beyond them?
In modern times, we built giant telescopes that have allowed us to cast our gaze deep into the universe. Astronomers have been able to pinpoint the time of its birth. They’ve reconstructed the course of cosmic history…. And found clues to its ongoing evolution.
Now, they are beginning to conclude that what we can see… the stars and galaxies on out to the limits of our vision… may represent only a tiny fraction of all there is.
A concept discovered in ancient times… infinity… has reemerged from a long debate about the limits of knowledge...
How far do the stars stretch? And what’s beyond them?
In modern times, we built giant telescopes that have allowed us to cast our gaze deep into the universe. Astronomers have been able to pinpoint the time of its birth. They’ve reconstructed the course of cosmic history…. And found clues to its ongoing evolution.
Now, they are beginning to conclude that what we can see… the stars and galaxies on out to the limits of our vision… may represent only a tiny fraction of all there is.
A concept discovered in ancient times… infinity… has reemerged from a long debate about the limits of knowledge...
To challenge long-held views of the cosmos… and of our own place within it.
To begin to get a handle on infinity, we’re going to need some perspective on the numbers and scales that define our universe.
One place to start is a narrow side street in Charles Dickens’ London. A Curiosity Shop, fictional to be sure. Here you can find an unparalleled collection of stuff.
Old shrunken heads, Russian manuscripts, Persian rug designs, crumbling newspapers, and odd bits and pieces too numerous to count. Some can be counted, to a degree.
From Zimbabwe comes this 100 trillion note. In late 2008, with that nation battered by hyperinflation, it was worth about a dollar fifty US.[1]
Go up two orders of magnitude to something a little more useful. The fastest supercomputer in history, due out in 2011, will hum along at 20,000 trillion calculations per second… a twenty followed by 15 zeroes.[2]
You have to run it about a day and a half for your calculations to equal the number of grains of sand on all the world’s beaches. That’s around a sextillion… a ten followed by 22 zeroes.[3] That’s approximately the number of stars in the visible universe… depending on what assumptions you make.
Atoms in the visible universe? That’s upwards of 10 followed by 78 zeroes, or 10 to the 78th power. [4] [5]
Cubic centimeters? A ten with 84 zeroes, a number that goes by the name of septvigintillion. [6] Subdivide the visible universe into the smallest units known… called Planck volumes. That’s just over a sexagintillion, a 10 with 185 zeroes.
Even that’s downright tiny compared to the largest number considered to be mathematically useful, according to the Guinness Book of Records. A calculation of angles in a cube, Graham’s number is so large it doesn’t yield to conventional notation.
Take that number, and square it. Then square the answer.
Now you have a number that’s incomprehensibly large. It’s still nowhere near the ultimate ceiling: infinity.
Today, the idea of infinity is part of a growing link between the physical sciences and cosmology… the study of the universe as a whole that has long been infused with metaphysics and philosophy.
It was the Greeks, over two thousand years ago, who first grappled with the implications of infinity.
The mathematician Pythagoras and his followers saw numerical relationships as the key to understanding the world around them.
Few relationships seemed more fundamental than the ratio of a circle’s circumference to its diameter… called Pi.
3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196 [7]
But in probing this geometric ratio, and others, Pythagoras and his group found something disturbing. They found no repeating patterns, and no ending in sight.
Computer scientists recently confirmed this by calculating Pi out to 5 trillion digits… on desktop computers no less. [8]
Legend has it that one member of the Pythagorian cult, Hippassus, was drowned at sea for divulging this discovery. [9]
A century later, the philosopher Zeno brought the problem of infinity into the open in a series of paradoxes: situations that are true, but strongly counter-intuitive.
In this modern update of one of Zeno’s paradoxes, you have arrived at an intersection. But you are only allowed to cross the street in increments of half the distance to the other side. So to cross this finitedistance, you must take an infinite number of steps.
In math, you can subdivide any given length an infinite number of times. In the real world, of course, you’d get down below the point, about 10–35 meters, when quantum effects make space and time indiscernible.[10]
What made the idea of infinity troubling to Greek mathematicians is that it took them far beyond their goal of explaining the real world.
To the philosopher Aristotle, a century after Zeno…
Infinity evoked the formless chaos from which the world was thought to have emerged… a primordial state with no natural laws or limits, one devoid of all form and content.[11] Aristotle debated with rivals who asked: what would happen if a warrior tossed a spear out into space? [12]
It would not fly off on an infinite journey, he said. Rather, it would join the motion of the stars in a crystalline sphere that encircled the Earth.
To preserve this idea of a limited universe, one that made sense, Aristotle crafted an historic distinction.
On the one hand there are the irrational numbers such as Pi. Each time you calculate one, you get a finite result. But since the final, final result can never be reached, Aristotle called it potentially infinite. [13]
Then there’s the “actually infinite.” In the physical realm, Aristotle reserved actual infinity status for the so-called “prime mover” that created the world and is beyond our capacity to understand.[14]
This became the basis for what’s called the Cosmological, or First Cause, argument for the existence of God.[15]
Another century later, Archimedes found ways to fold infinity into rigorous mathematical proofs. He did this by comparing the relative number of points on lines of different length, or lines within cubes versus pyramids, cones versus spheres.
All these sets of numbers are infinite. And yet some are just larger than others.
Archimedes has been described as one of the greatest mathematicians of all time. His use of infinity, however, did not carry forward.
The author David Foster Wallace describes a kind of allergy that developed in math in response to “the metaphysical shadow land” of Aristotle’s potential infinity concept. [16]
Aristotle’s view of the cosmos held sway in the Christian era, with Earth at the center, finite in space, but infinite in time.
That view was not universal. Islamic, Hindu and even some western thinkers posed a range of alternate views that included infinite space.
The issue resurfaced during the intellectual flowering of the Renaissance.
Just before his death in 1543, the Polish astronomer Nicolaus Copernicus argued that Earth orbits around the Sun, not the other way around.
The old Greek spheres then began to fall away when Tycho Brahe spotted a comet and a distant supernova that seemed to behave independently.
A monk named Giordanno Bruno inflamed the issue by traveling Europe at the height of the Inquisition to proclaim an infinite universe. In the year 1600, he was burned at the stake for this and other heresies in what’s now a pleasant Roman piazza, Campo dei Fiori.[17]
Just nine years later, in 1609, Galileo Galilee used the first astronomical telescope to show that the universe is much larger than we thought. In his later writings he took on the Aristotelian view of the universe, including the division between potential and actual infinities. [18]
Galileo was forced to recant his heliocentric views, but change was in the air.
Math began to evolve from empirical study of the world to a purely abstract pursuit with a whole new sense of rigor. Ironically, it began to anchor the Scientific Revolution, in disciplines from astronomy to mechanics, engineering, and geography.[19]
In the 1880s, the mathematician Georg Cantor set out to resolve the issue of infinity, by folding Archimedes’ ideas on infinitely large number sets, including both rational and irrational numbers, into a singular mathematical theory.
He endured years of attacks. One of his defenders, the German mathematician David Hilbert used a modern paradox to made a case that infinity is a multi-faceted concept. Say you’d like to check in at this grand hotel.[20]
As advertised, there is an infinite number of rooms. And yet, you hear there are “No Vacancies.” So you visit the front desk.
The manager says… Let’s see what we can do. No problem, I can open up room #1 by shifting that guest to room 2, and the guest in room 2 to room 3, and so on. So in this hotel, there’s a number set that includes an infinite number of guests and rooms. Then there’s that same set plus you… two infinite sets, but not the same size.
Echoing Aristotle, one of Hilbert’s critics suggested that the end of the corridor is still only a potential infinity… that God still represents the only actual infinity.
Later on, we’ll recommend other accommodations for those who still aren’t sure.
Even as mathematicians embraced infinity, astronomers in the early 20th century saw the universe as the galaxy, as flat disk of stars. What, if anything, they asked, lay beyond it?
Albert Einstein, for one, believed that if the universe did extend into infinity, then the night sky would be filled with dense starlight shining from every direction and we’d feel the effects of infinite gravity. Arguing for a finite universe…
He described a people living on the 2D surface of a sphere. To those folks, a beam of light moving through space appears to go straight, on an infinite journey. In fact, it follows a path determined by the overall gravity of the universe, and curves back around.[21] Thus, he said, the universe is finite, yet “unbounded.”
In the 1920s Edwin Hubble and Milt Humason showed that the universe was more dynamic, and far larger, than anyone assumed.
They used the new 100” Hooker Telescope in California to look at mysterious fuzzy patches of sky called “nebulae.” They found that these patches were galaxies like our own… and that some were very far away.
But that’s not all. They discovered that most of these galaxies are moving away from us. The farther out they looked, the faster they were receding.[22]
This fact, now known as Hubble’s law, led to an inescapable conclusion: the universe is expanding. Furthermore, if you run the clock back on this expansion, it appears it all began in one place.
That time… when our universe sprung forth… has come to be called the Big Bang. [23] How large it has gotten since then depends on how long it’s been growing… and its expansion rate.
Using an array of modern telescopes, cosmologists have recently narrowed that beginning to a time 13.7 billion years ago. Taking into account the expansion of space in that time, the radius of the visible universe, the part we can see, has expanded out to 46 billion light years. [24]
These measurements have raised anew questions posed by the ancient Greeks: What’s beyond our cosmic horizons? How far does the universe extend? And is it infinite?
A new set of answers has emerged from a theory designed to answer questions that arose from the original model of the Big Bang.
For one… how did the universe get so large? The Hubble Deep field contains images of infant galaxies at less than 10% of the age of the universe. With the universe expanding, by the time those galaxies reached maturity they would have moved far beyond our horizon.
And what of all the galaxies visible at its horizons?
For another… how did the universe get so smooth? In every direction you look, the density of galaxies is the same on large scales. [25]
Astronomers believe that whatever process flung the universe out to immense size, must have also blended it in its earliest moments.
The theory that addresses these questions was based on the discovery that energy is constantly welling up from the vacuum of space in the form of particles of opposite charge… matter and anti-matter.
No one knows exactly why, but the idea is that in primordial times, an energy field embedded in this so-called quantum vacuum suddenly tipped into a higher energy state causing space and time to literally “inflate.”
The universe went from atomic size… to cosmological size within an incredibly small fraction of a second. From the energy unleashed, the energy and matter content of our universe took shape.
The originator of cosmic inflation, Alan Guth, wrote that the entire universe would have grown by now to at least ten billion trillion times the size of the observable universe. That’s a ten followed by 23 zeroes. [26]
If you think that’s big…
The theory places the origin of our universe in the context of a physical process that’s spread over a far larger cosmic patch… like the seemingly infinite void that had confounded Aristotle and other Greek thinkers.
One variation on the theory suggests that as our universe inflated like a bubble... It joined a stream of other bubbles frothing up and expanding across an endless ocean of time and space. This new, more expansive vision of the universe is not without its paradoxes.
Logically speaking, with infinite stars, infinite planets, infinite universes, you will also have a set of infinite possibilities.
The so-called infinite monkey theorum has its roots in Aristotle’s attempts to show the absurdity of infinity. Ask a monkey to type, or ask an infinite number of monkeys to type, for an infinite amount of time. You’re sure to get a lot of random letters.
But there is a chance, however small, that somewhere, somehow, you’ll get the full text of Shakespeare’s Hamlet.
It’s clearly absurd.
Then again, new observations are taking the search for infinity into rather strange new directions. Just up the road from the famous Hotel Infinity, you’ll find a less well-appointed alternative.
You’ll get a big welcome at the old Hall of Mirrors. It’s the hallways that give visitors trouble. It can be tough to find your room. This is what the universe is like, according to the way recent evidence is being interpreted by some cosmologists.
The evidence comes from one of the most important space satellites ever launched. WMAP was sent out to make precision measurements of radiation left over from a period about 300,000 years after the Big Bang.
WMAP revealed an intricate pattern of hot and cold spots, caused by pressure waves that rickocheted through the expanding gas of early universe.
These variations are thought to mirror the structure of galaxies arrayed across the universe on large scales. One group of scientists, looking at the sizes of these waves, believes they show a universe that’s on the small side.
This view redraws the universe not as a simple sphere, but more oblong. What’s more its authors suggest that some structures seen in the data may well be mirror images of themselves. That there’s more to it than we know is born out by this recent scrap of evidence.
Tracking the movement of galaxies across a broad region to the north, a group of astronomers found huge clusters moving along at about two million miles per hour toward an unseen presence in the Constellation Centaurus. [27]
With the results published in a top scientific journal, the team describes an attractor that may well sit beyond our visible horizon … perhaps another universe that inflated near our our own.
The ideas that define cutting edge science today may well have led to imprisonment or death in centuries back. That includes today’s fervent quest to understand the limits of our universe.
So is the universe infinite?
Because our expectations for knowledge are boundless, the search for infinity is bound to disappoint. Like the room at the end of an endless corridor, the final final answer will always elude us.
You can give us feedback in the comment section or more privately by emailing us at info@spacerip.com!
[1] http://en.wikipedia.org/wiki/Zimbabwean_dollar
[2] http://technology.timesonline.co.uk/tol/news/tech_and_web/article5649731.ece
[3] http://www.newton.dep.anl.gov/askasci/ast99/ast99215.htm
[4] http://www.universetoday.com/36302/atoms-in-the-universe/
[5] http://g42.org/MiscInfo/numbers.html
[6] http://spacemath.gsfc.nasa.gov/weekly/2page9.pdf
[7] http://www.math.com/tables/constants/pi.htm
[8] http://www.numberworld.org/misc_runs/pi-5t/details.html
[9] Aczel, Amir, “The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity,” p. 5.
[10] http://physics.nist.gov/cgi-bin/cuu/Value?plkl
[11] Wallace, David Foster, “Everything and More: A Compact History of Infinity” p. 44
[12] http://www.jb.man.ac.uk/~jpl/cosmo/infinity.html#[1]
[13] Wallace, David Foster, “Everything and More: A Compact History of Infinity” p. 65
[14] http://csep10.phys.utk.edu/astr161/lect/retrograde/aristotle.html
[15] http://www.allaboutphilosophy.org/cosmological-argument.htm
[16] Wallace, David Foster, “Everything and More: A Compact History of Infinity” p. 68
[17] http://www.theosophy-nw.org/theosnw/world/modeur/ph-holli.htm
[18] Wallace, David Foster, “Everything and More: A Compact History of Infinity” p. 99
[19] Wallace, David Foster, “Everything and More: A Compact History of Infinity” p. 106
[20] Pickover, Clifford A., “The Math Book: From Pythagoras to the 57th Dimension” p. 354
[21] Isaacson, Walter, “Einstein: his life and universe” p. 252.
[24] Lineweaver, Charles H. and Davis, Tamara M. “Misconceptions About the Big Bang,” Scientific American: March 2005.
[26] Guth, Alan. The Inflationary Universe, Perseus Publishing: 1997, p. 186
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