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  • Since ancient times, we've looked into the night skies and wondered:

  • How far do the stars stretch out into space?

  • 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 look back to near the time of its birth.

  • They've reconstructed the course of cosmic history in astonishing detail.

  • From intensive computer modeling, and myriad close observations, they've uncovered important

  • clues to its ongoing evolution.

  • Many now conclude that what we can see, the stars and galaxies that stretch out to the

  • limits of our vision, represent only a small fraction of all there is.

  • Does the universe go on forever? Where do we fit within it?

  • And how would the great thinkers have wrapped their brains around the far-out ideas on today's

  • cutting edge?

  • 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, manuscripts, newspapers, books, and rare examples of impressively large

  • numbers.

  • From Zimbabwe comes a 100 trillion dollar note. In late 2008, with that nation battered

  • by hyperinflation, it was worth about a dollar fifty US.

  • Go up two orders of magnitude to something decidedly more useful. The fastest supercomputer

  • in history will soon hum along at 20 thousand trillion calculations per second, a twenty

  • followed by 15 zeroes.

  • You'll 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.

  • That's roughly the number of stars in the visible universe.

  • Atoms in the visible universe? That's upwards of 10 to the 78th power, a 10 with 78 zeroes.

  • Cubic centimeters? A mere ten to the 84th, a septvigintillion.

  • To go up from there, we turn to no less a source than the Guinness Book of World Records.

  • The largest named number in regular decimal notation: the Buddhist time period Asamkhyeya

  • is ten to the 140th years, or 100 quinto-quadragintillions.

  • Then there's the largest number ever used. Graham's number is a calculation of angles

  • in a type of hypercube.

  • If you divided the visible universe into the smallest units known, called Planck volumes,

  • the total of those units wouldn't get you anywhere close to Graham's number.

  • But it's still nowhere close to the ultimate ceiling: infinity.

  • For those who find infinity hard to grasp, even troubling, you're not alone. It's a concept

  • that has long tormented even the best minds.

  • Over two thousand years ago, the Greek mathematician Pythagoras and his followers saw numerical

  • relationships as the key to understanding the world around them.

  • But in their investigation of geometric shapes, they discovered that some important ratios

  • could not be expressed in simple numbers.

  • Take the circumference of a circle to its diameter, called Pi.

  • Computer scientists recently calculated Pi to 5 trillion digits, confirming what the

  • Greeks learned: there are no repeating patterns and no ending in sight.

  • The discovery of the so-called irrational numbers like Pi was so disturbing, legend

  • has it, that one member of the Pythagorian cult, Hippassus, was drowned at sea for divulging

  • their existence.

  • A century later, the philosopher Zeno brought infinity into the open with a series of paradoxes:

  • situations that are true, but strongly counter-intuitive.

  • In this modern update of one of Zeno's paradoxes, say 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 finite distance, you must take an infinite number of steps.

  • In math today, it's a given that you can subdivide any length an infinite number of times, or

  • find an infinity of points along a line.

  • What made the idea of infinity so troubling to the Greeks is that it clashed with their

  • goal of using numbers to explain the workings of 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, devoid of all form and content.

  • But if the universe is finite, what would happen if a warrior traveled to the edge and

  • tossed a spear? Where would it go?

  • It would not fly off on an infinite journey, Aristotle said. Rather, it would join the

  • motion of the stars in a crystalline sphere that encircled the Earth.

  • To preserve the idea of a limited universe, Aristotle would craft an historic distinction.

  • On the one hand, Aristotle pointed to the irrational numbers such as Pi. Each new calculation

  • results in an additional digit, but the final, final number in the string can never be specified.

  • So Aristotle called it "potentially" infinite.

  • Then there's the "actually infinite," like the total number of points or subdivisions

  • along a line. It's literally uncountable. Aristotle reserved the status of "actually

  • infinite" for the so-called "prime mover" that created the world and is beyond our capacity

  • to understand.

  • This became the basis for what's called the Cosmological, or First Cause, argument for

  • the existence of God.

  • Another century later, Archimedes incorporated "actual infinity" into measurements of curved

  • lines and volumes.

  • His method boils down to a process of summation. Place a triangle inside a circle. Turn it

  • into a square, then a pentagon, and so on. As the number of sides increases, to infinity,

  • their combined lengths equal the circumference of the circle.

  • By slicing and dicing curves into an infinite number of straight lines, he was able to compare

  • a variety of curves, areas, and volumes.

  • Archimedes anticipated techniques developed two thousand years later.

  • And yet, his ideas on infinity did not carry forward, due to what the author David Foster

  • Wallace described as a mathematical allergy to the concept that developed in response

  • to Aristotle's "potential infinity."

  • It was Aristotle's ideas that passed into the Christian era along with his cosmology,

  • with Earth seated firmly at the center.

  • That view was not universal. Islamic, Hindu, and even some western thinkers posed alternate

  • views that included infinite space.

  • In European circles, the issue of infinity resurfaced during the Renaissance.

  • In 1543, the Polish astronomer Nikolas Copernicus argued that Earth orbits the Sun, not the

  • other way around.

  • The old Greek spheres began to fall by the wayside when a distant supernova, then a comet,

  • were spotted by the astronomer Tycho Brahe. These objects seemed to behave independently

  • of the other stars.

  • 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.

  • 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 later writings, he even sought to discredit

  • the distinction between potential and actual infinity.

  • Galileo was forced to recant his views, and the old Aristotelian view held sway. Any attempt

  • to assign a value to infinity, in numbers or in nature, was doomed, for that was the

  • unique province of God.

  • Finally, at the end of the 19th century, the mathematician Georg Cantor sought once and

  • for all to divorce metaphysics from the abstract pursuit of math.

  • Infinity, he wrote, had to be studied without "arbitrariness and prejudice."

  • He became known for folding finite and infinite numbers into a unified theory of number sets,

  • considered a foundation of modern math.

  • One of his defenders used a paradox to show how infinite sets are subject to concrete

  • comparisons.

  • Say you've come to stay at this grand hotel.

  • You're in luck, because here there is an infinite number of rooms.

  • Oddly enough, you learn there are "No Vacancies."

  • Fortunately, the manager says: I can still check you in. He assigns you to room #1 and

  • directs you down the corridor. Then, he goes to work, shifting the guest in room 1 to room

  • 2 -- room 2 to 3 -- 3 to 4 -- 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, yet one is a subset of

  • the other.

  • Being able to use infinite sets of different sizes allowed mathematicians to design equations

  • describing continuous motion and change over time.

  • Echoing Aristotle, a critic of the new set theory suggested that the end of the corridor

  • is still only a potential infinity, with God representing the only actual infinity.

  • For those who pine for humble accommodations, we'll recommend an alternative later on.

  • Even as mathematicians embraced infinity, astronomers in the early 20th century still

  • saw a limited universe... centered on the galaxy, a flat disk of stars.

  • Did the limits of our vision, like the horizon at sea, conceal an infinite universe beyond?

  • Albert Einstein, for one, believed that if that were true, then the night sky would be

  • filled with dense starlight shining from every direction. We'd reel from the effects of infinite

  • gravity.

  • Arguing for a finite universe, he described a people living on the 2D surface of a sphere.

  • To them, a beam of light moving through space would appear 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.

  • Like the old Greek spheres, this view of a static and limited universe began to fall

  • by the wayside in the 1920s.

  • Edwin Hubble and Milt Humason used the new 100" telescope on Mt. Wilson 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.

  • What's more, they found that most are moving away from us. In fact, the farther out they

  • looked, the faster the galaxies are moving.

  • This fact, known as Hubble's law, led to an inescapable conclusion: that the universe

  • is expanding. Furthermore, if you run the clock back on this expansion, it appears that

  • it all began in one singular moment.

  • That moment has traditionally been described as an explosion... a "Big Bang."

  • How large the universe has gotten since then depends on how long it's been growing, and

  • how quickly.

  • Using an array of modern telescopes, astronomers have recently narrowed the beginning to 13.7

  • billion years ago. Taking into account the expansion of space ever since, the radius

  • of the visible universe, the part we can see, has expanded out to 46 billion light years.

  • These measurements have raised anew the ancient questions: What's beyond our cosmic horizons?

  • Is there an edge? Or does it somehow go on forever?

  • A new set of answers has emerged from a theory designed to address 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, near the edge of our cosmic horizons.

  • By the time one of those galaxies reached maturity, it would have moved far, 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.

  • Astronomers believe that whatever process flung the universe outward, 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.

  • The idea is that in primordial times, an energy field embedded in this so-called quantum vacuum

  • suddenly moved into a higher energy state, causing space and time to literally inflate,

  • and our universe to burst forth.

  • If this theory is right, then our universe is incomprehensibly large. Its author, the

  • scientist Alan Guth, wrote that the universe as a whole would have grown to at least ten

  • billion trillion times the size of our visible patch. That's a ten followed by 23 zeroes.

  • If you think that's big.

  • A variation on the theory describes the origin of our universe as a physical process that

  • exists far beyond it, out into the seemingly infinite void that had confounded Aristotle

  • and other Greek thinkers.

  • In that case, our universe would have inflated like a bubble, and joined a stream of other

  • bubble universes frothing up and expanding across an endless ocean of time and space.

  • A related idea theorizes a cosmic landscape unfolding in vast fractal patterns.

  • These new, more expansive, visions of the cosmos are not without their paradoxes.

  • Logically speaking, with infinite stars, infinite planets, infinite universes, you will also

  • have infinite possibilities.

  • The so-called infinite monkey theorum has its roots in Aristotle's attempts to illustrate

  • the perils of thinking about 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, some how, you'll get the full text

  • of Shakespeare's Hamlet.

  • It's clearly absurd.

  • Then again, consider the increasingly strange nature of our universe, as suggested by some

  • new observations.

  • This is where we draw your attention from the famous Hotel Infinity -- to a less well-appointed

  • alternative.

  • You're sure to get a big welcome at the old Hall of Mirrors.

  • This ramshackle place would have thrown even the great thinkers for a loop.

  • It represents a kind of optical illusion that may be present in our view of deep space,

  • according to a new interpretation of data 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.

  • It revealed an intricate pattern of hot and cold spots, now thought to represent the seeds

  • of galaxy filaments and walls seen on large scales. The pattern was laid down by pressure waves

  • that ricocheted through the expanding gas of the early universe.

  • One group of scientists, looking at the sizes of these waves, suggested that some are actually

  • mirror images of themselves. From this, they argue that the universe could be much smaller

  • than we think.

  • That's not the only strange new line of evidence.

  • Tracking the movement of distant galaxies, astronomers found huge clusters moving at

  • about two million miles per hour in the direction of the Constellation Centaurus.

  • With the results published in a top scientific journal, the astronomers describe an immense

  • gravitational presence that may loom beyond our visible horizon, perhaps another universe

  • that inflated near our own.

  • Ideas like these may well have led to imprisonment or death in centuries past. Now, they are

  • part of a field of study that is bursting with data and ideas.

  • Cosmology, the study of the universe as a whole, has long been infused with metaphysics

  • and philosophy. Today, it's steadily merging into the physical sciences.

  • So is the universe infinite?

  • Scientists will continue to look for evidence of what lies beyond our horizons and test

  • theories on the nature of time and space. But like the room at the end of an endless

  • corridor, the final final answer will always elude us.

  • 1

Since ancient times, we've looked into the night skies and wondered:

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宇宙是無限的嗎? (Is the Universe Infinite?)

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    Wonderful 發佈於 2021 年 01 月 14 日