Ten (Well, Really, Eleven) Misconceptions about Infinity
The only sure-fire way to avoid having misconceptions about infinity is by not having any beliefs about it at all. Misconceptions and errors are almost inevitable once you start studying and thinking about infinity, because infinity often defies our intuitions. In addition, space probes and radio astronomy have dramatically altered our image of the universe in recent decades; as a result, much that was regarded as scientifically correct in 1980 now belongs in the category of popular misconceptions. Nonetheless, outdated conceptions still haunt many textbooks. They are as tough as leather. Well, let us hope do our small part to dispel some of them now.
1. Universe Misconception: Our universe originated from a tiny spot about 13.7 billion years ago and has since expanded at the speed of light. Thus, its radius now extends over approximately 13.7 giga-lightyears.
Fact: The universe did not originate from a spot, but has probably been of infinite dimensions from the beginning. However, only a region with a radius of about 46 giga-lightyears is visible to us. You can read up on why astronomers hold this view today under the categories ►Universe and ►Big Bang.
2. Perspective Misconception. The further an object is away from us the smaller it appears.
Fact: This is only true of relatively close objects. Extremely distant galaxies, by contrast, are illusionary giants — they appear larger the more distant they are. This paradoxical optical effect is a result of the finite speed of light and the continuous growth of all distances in the universe. You'll find more about this topic in the article on ►distance.
3. Redshift Misconception: Distant galaxies appear red to us because they have been drifting away from us since the big bang. Thus, the redshift is caused by a Doppler effect of the light waves.
Fact: As far as we know today, the galaxies are not drifting away from us, nor is a Doppler effect the cause of cosmic ►redshift. The real cause is the expansion of space itself and hence of the light waves on their way through the ► universe.
4. Parallel Worlds Misconception: Parallel worlds exist only in sci-fi novels or in hyperspaces, alternative universes, or other kinds of dimensions.
Fact: Parallel worlds resembling ours to a tee, even containing doppelgangers of you, are quite probable within our normal universe. This is a consequence of its infinity, on one hand, and of the fact that as quantum theory shows the number of possible states of the world is finite, on the other. You'll find a pointer to your doppelganger in the article on ►parallel worlds.
5. Space Travel Misconception: Einstein showed that nothing can move faster than light. This is why travel to distant galaxies is impossible, as it would take far too much time.
Fact: On the contrary, the finite speed of light considerably shortens travel time to other galaxies. In conformity with Einstein's relativity theory, you may be able to reach the Andromeda nebula in only 15 years. There is, however, another obstacle that may prevent you from traveling such distances: the unavailability of fuel. You'll find more details about the challenges of space travel under ►infinite spaces.
6a. Numbers Misconception I. There are exactly half as many even numbers (2, 4, 6, ...) as there are natural numbers (1, 2, 3, 4, ...).
Fact: Both sets of numbers contain exactly the same number of elements. The reason to think so is that you can correlate each natural number with exactly one even number and, conversely, each even number with exactly one natural number. Still not convinced? Read more about this topic under ►countability.
6b. Numbers Misconception II. Since the set of all numbers is infinite it is the largest set there can be. Nothing can be greater than infinity, and no infinitude can be greater than another (there are no degrees of infinity).
Fact: Actually, not only are there different infinite magnitudes, there are infinitely many of them. Read why mathematicians think that one infinite set can be more infinite than another and what such more infinite sets look like under ►cardinals.
7. Misconception about Immortality. Only the gods are immortal. All earthly creatures, by contrast, get older and will die at some point.
Fact: There are not only unicellular organisms but are also higher organisms whose life expectancy is, at least potentially, infinite. If you're a diving enthusiast you've probably encountered a number of them. Make sure you read the section on ►immortality before your next dive.
8. Laws of Nature Misconception. Processes in nature are governed by the laws of nature.
Fact: Nature doesn't care very much about laws of nature drawn up by human beings. What these are really good for is explained in ►laws of nature.
9. Progress Misconception. The natural sciences and mathematics have progressed so far that we now know almost everything about infinity, eternity, and the nature of the universe.
Fact: For all the dramatic developments in the natural sciences and mathematics over the last century, we still have but a faint glimpse of the whole truth about infinity. The biggest as-yet-unanswered questions about infinity are summarized in ►Ten Puzzles about Infinity.
10. Comprehensibility Misconception. The natural sciences and mathematics have progressed so far that contemporary laypersons are no longer able to understand their results. This applies especially to matters related to infinity, eternity, and the nature of the universe.
Fact: The opposite is true, which is evidenced by this very ►website.