Large Numbers and Small Odds

Evolutionists claim that given enough time, anything can happen. This is very misleading. At first, it sounds convincing because we have a difficult time grasping large numbers. When we do some calculations, however, the argument falls apart. Below is a reference of numbers and odds to keep everything in perspective.

A Quick Math Reminder

A brief refresher from math: Adding 1 to the exponent in base 10 makes the number ten times larger. Adding 6 makes the number a million times larger. And so, for example, $10^{100}$ is a million times smaller than $10^{106}$ . Also, while a googol is $10^{100}$ (“1” followed by a hundred zeros), half of a googol is $5 \times 100^{99}$ (5 followed by 99 zeros), not $10^{50}$ , though it may be tempting to think this way. We are dealing with extremely large numbers.

Large Numbers

Number	Examples
$7\times10^{9}$	Earth’s population today
$10^{19}$	Total insect population alive today (estimated) ¹
$4.3 \times 10^{20}$	Milliseconds since the beginning of the universe, according to evolutionists
$2.6 \times 10^{23}$	Total teaspoons of water in all the oceans (including bays and seas) ²
$10^{24}$	The estimated number of stars in the universe ³
$2.5 \times 10^{28}$	The length in centimeters from one end of the known universe to the other
$10^{80}$	The estimated number of atoms in the known universe ⁴

Small Odds

Number	Scenario
$2.8 \times 10^{5}$	Odds of lightning striking the average person
$1.2 \times 10^{30}$	Flipping an honest coin 100 heads in a row
$8.1 \times 10^{67}$	Arriving at a predetermined order of playing cards by randomly shuffling
$5\times10^{579}$	The odds of randomly typing the 12-line poem “The Arrow and the Song” (without punctuation, capitalization, or line breaks) ⁵
$1.8\times10^{746}$	The odds of randomly typing “The Arrow and the Song” as written (with punctuation, capitalization, and line breaks) ⁶

Odds Illustrated

Flipping a Coin

The odds of flipping an honest coin “heads” 100 times in a row is 1 in $1.2\times10^{30}$ . Suppose someone flipped coins as a full-time job (about 2,000 hours per year), and each flip took three seconds (to flip the coin and write down the result). It would take this person on average $5\times10^{23}$ years before he flipped one hundred straight heads.

Suppose instead the entire earth population (7 billion people) flipped coins around the clock at one flip per second. At this rate they could flip $2.2\times10^{17}$ coins per year. On average, this would take $5.5\times10^{12}$ years (5.5 trillion years) before any of them flip one hundred straight heads. This is about four thousand times longer than the age of the universe according to evolutionists.

Deck of Cards

If we randomly shuffle a deck of cards, how many more decks would we have to shuffle before we could expect to have an identical deck? On average we would need $8.1 \times 10^{67}$ more decks to get an identical one to our original. Since each deck of cards weighs on average 94 grams, the weight of all these would be $7.6\times10^{66}$ kilograms. The earth weighs $6\times10^{24}$ kilograms. This means that all the decks would weigh $1.3\times10^{42}$ times the weight of the earth.

The Arrow and the Song

The chance of typing “The Arrow and the Song” as written (with punctuation, capitalization, spaces, and line breaks) by random processes is one in $2.6\times10^{723}$ . Although the universe could not contain them, assume that for each atom in the known universe, there is one Tianhe-2 supercomputer. The Tianhe-2 can calculate at 33.86 petaflops (a thousand trillion calculations per second, or $3.386\times10^{16}$ calculations/second). Let’s say each of these calculations represents one typed letter for each of these supercomputers.

At this speed, all $10^{80}$ supercomputers could type $3.386\times10^{96}$ letters every second. The age of the universe, according to evolutionists, is 13.8 billion years, or $4.4\times10^{17}$ seconds. If these supercomputers were running for all this time, they could produce $1.5\times10^{114}$ attempts. While a very large number, this is not nearly enough attempts to approach the $2.6\times10^{723}$ average required. This 13.8 billion-year scenario would need to be repeated $1.7\times10^{609}$ times on average to produce “The Arrow and the Song” randomly, making the scenario impossible by all observations.

Conclusion

When you hear that “given enough time, anything can happen”, remember that this argument is very deceptive. While it sounds true, when we look at the numbers we realize that even with our enormous universe, and even with the estimated billions of years by evolutionists, there is not enough time to account for the random development of a simple 12-line poem. Even if we imagined a trillion other universes each a trillion times older than ours (according to evolutionists), this is still not enough time to randomly generate “The Arrow and the Song”. Thus, the claim is not true.

Notes

http://www.bigsiteofamazingfacts.com/how-many-insects-are-therefor-every-person-on-earth
http://water.usgs.gov/edu/earthhowmuch.html
http://www.universetoday.com/102630/how-many-stars-are-there-in-the-universe/
http://www.universetoday.com/36302/atoms-in-the-universe/, http://en.wikipedia.org/wiki/Observable_universe
“The Arrow and the Song” contains 405 characters. With no punctuation, capitalization, or line breaks (spaces instead), we are left with 27 characters (26 letters plus the space). This yields a probability of $27^{405}$ , or $5\times10^{579}$ .
Including punctuation and line breaks, “The Arrow and the Song” (just the poem, not the author information) contains 425 characters. Assuming 26 letters uppercase and lowercase (52 total), the spacebar, the line break, and three punctuation symbols “.;,”, we have 57 characters total. This yields a calculation of $57^{425}$ , or $1.8\times10^{746}$ .