All contingent events (i.e. they don't have to occur) are brought about either by chance or by design. (See previous blog.)
We infer design as the cause when an event is both:
- Complex, i.e. has an extremely low probability of occurring "by chance", and
- Specified, i.e. it matches a specific, recognizable pattern or structure.
But what is considered "an extremely low probability" of chance? At what probability should we conclude that "chance" is implausible (i.e. unbelievable, dubious, untenable) as an explanation for something?
How low must the probability get before we can be comfortable dismissing random chance as the cause of something, and instead inferring design as the cause?
When "Chance" Becomes Implausible
What's Implausible to Most Of Us
If you're 32 years old, you've lived for 1 billion seconds. That's 1,000,000,000, a number so big it's hard for us to fully grasp. But clearly "1 chance in a billion" is pretty small. It's the equivalent of identifying one specific second out of your entire 32-year-old life. For most of us, a chance of 1 in a billion is a very small probability, too low for us to consider random "chance" as the cause of something.
Even smaller is 1 chance in a trillion (which is 1,000 billion). Here are some examples of things with a "1 in a trillion" chance of happening:
- Flip "heads" 40 times in a row, using a fair coin. (Just try to flip "heads" even 10 times in a row.)
- Spin a "24" on the roulette wheel 8 times in a row.
- Winning your state's million-dollar lottery jackpot not just once, but two times in a row.
Pragmatically, we know these things are never going to occur in our lifetime. We would never plan on, or expect, something with a "1 in a trillion" probability to occur "by chance"; it is implausible.
Even so, if we wanted to be super conservative, we might consider 1 chance in a trillion trillion (that's a "1" with 24 zeroes after it) to be the level or probability at which we exclude random "chance" as the cause of an event.
But how low would probability have to be before scientists exclude "chance" as a cause?
Before we go farther, we need to review our high school algebra regarding exponents, because that’s the only way to represent extremely large numbers and extremely small probabilities.
- For powers of 10, the exponent tells how many zeroes to put after the 1, or how many times to multiply 10 by itself:
- so 103 = 10^3 = 10 x 10 x 10 = a "one" with 3 "zeroes" after it, or 1,000.
- and 1012 = 10^12 = a "one" with 12 "zeroes" after it, or 1,000,000,000,000, which is one trillion.
- For powers of 2, the exponent tells how many times to mulitply 2 by itself:
- so 23 = 2^3 = 2 x 2 x 2 = 8
- and 210 = 2^10 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 1,024
- Similarly, (1/2)3 = 1/2 x 1/2 x 1/2 = 1/8.
- When multiplying numbers, ADD the exponents: 1012 = 109 x 103
Really Big Numbers
When exponents get large, i.e. once we get beyond, say, one trillion (1012, which equals a million million) we have hard time grasping the enormity of the number. Here are some figures just for reference.
- 106 = one million, 109 = one billion, and 1012 = one trillion = a million million
- A million seconds is 12 days. A billion seconds is 31 years.
- A trillion seconds is 317 centuries (or 31,700 years). Jesus lived on the earth just 20 centuries ago!
- 2 x 109 = 2 billion = number of seconds that a 70--year-old has lived
- 14 x 109 = 14 billion = age of the universe in years
- 1.5 x 1011 = distance from earth to sun in meters
- 4 x 1017 = age of the universe in seconds
- 2 x 1018 = 2 billion billion = number of pennies required to cover the surface of the earth
- 6 x 1023 = number of atoms contained in 12 grams of pure carbon-12 (12C) = Avogadro's Number
- 1023 = more blood cells than contained in all living humans
- 1023 = enough marshmallows to cover the entire face of the earth to a depth of 12 miles
- 1024 = one trillion trillion
- 1036 = one trillion trillion trillion, etc.
- 1080 = number of elementary particles (e.g. quarks, leptons, bosons, etc.) in the universe
- 10100 is called a Googol (not Google)
Science and Implausibility
Imagine someone flipping a coin, and each time before they flip, they predict whether it will be heads or tails.
How many flips do you think you could correctly predict in a row?
Go ahead and try it. Grab a coin and see how many consecutive flips you can accurately predict. You probably won't even get to 10 (unless you're willing to invest a whole day or two, and repeatedly try the experiment).
- The probability that you accurately predict 10 flips in a row in only 1 in 1024 (i.e. 2^10), or roughly one in a thousand.
- The probability that you accurately predict 20 successive flips is about one in a million.
- And the odds of predicting 40 flips in a row is about one in a trillion, i.e. 1,000,000,000,000. That means it can't be done in a typical human lifetime, which is only 2 billion seconds long.
Universal Probability Bound
Scientists suggest that there is a probability cutoff, i.e. a level of probability so extremely small that "chance" becomes an unacceptable explanation. When the probability of an event is less than this cutoff value, called the universal probability bound, the event is considered impossible to occur by chance.
For most of us, a "1 in a trillion" chance seems very unlikely. But scientists are extremely conservative when it comes to ruling out "chance" as a cause, and instead saying it was caused "by design." They have proposed various, extremely low levels of probability as a cutoff or universal probability bound.
One of the most conservative (i.e. small) cutoffs that has been proposed is from mathematician Michael Dembski. He suggested a universal probability bound of 1 chance in 10150.
10150 is a 1 with 150 zeroes after it! That's not a number we comprehend at all. --- It looks like this:
1,000,000,000,000,000,000, 000,000,000,000,000,000, 000,000,000,000,000,000, 000,000,000,000,000,000, 000,000,000,000,000,000, 000,000,000,000,000,000, 000,000,000,000,000,000, 000,000,000,000,000,000,000,000.
Dembski derived this cutoff value based upon three figures:
- The total number of elementary particles in the universe (1080 particles)
- The entire length of time, in seconds, that our universe will be in existence from start (“big bang”) to finish (“heat death”) (1025 seconds)
- The number of transitions that can occur from one physical state to another in one second (1045, based upon Planck time, the smallest unit of time we can measure).
Dembski multiplied these three figures together, i.e. 1080 x 1025 x 1045. (Remember we add the exponents.)
1 chance in 10150 is equal to the probability that an individual accurately predicts 500 coin tosses in a row! This is NEVER GOING TO OCCUR! After all, how much success did you have trying to predict just 10 coin tosses in a row?
Design and the Movies
The 1997 science fiction movie Contact, starring Jodie Foster, popularized the idea of searching the skies for communications from alien civilizations. In the movie, Foster works as a scientist involved with SETI, the Search for Extra-Terrestrial Intelligence. She and her team continually search radio signals from space for signs of intelligence.
At one point in the film, Foster and her team detect this binary signal (i.e. just zeroes and ones):
The signal is quite lengthy, and it repeats itself.
The team's analysis reveals the following: The zeroes are "spaces," and when the ones situated between two zeroes are summed, the "ones" represent the sequence of all prime numbers from 0 to 100. The signal can be broken apart into pieces, like this:
110 = 2 ( = the sum of the ones)
1110 = 3
111110 = 5
11111110 = 7
111111111110 = 11
11111111111110 = 13, etc.
In the movie, after verifying the signal and their analysis, the team concludes that they have received a signal that must have been designed (by an alien intelligence).
Why did this team of scientists conclude that the signal was designed? Why not conclude it was a random event caused by chance, rather than a communication from an intelligent alien civilization?
Because we know that signals or events or outcomes that are complex, specified and implausible, must be caused by design.
- Specified: The signal matches a specific pattern that we recognize, i.e. the sequence of all prime numbers between zero and 100.
- Complex: The signal is complex, consisting of 1,085 binary characters (i.e. zeroes and ones):
- Since there are 25 prime numbers between zero and 100, there are 25 "zeroes", i.e. spaces, in the sequence.
- The 25 prime numbers between zero and 100, when added together, sum to 1,060. So there are 1,060 "ones" in the sequence.
- Implausible: Given 1,085 binary characters in this sequence, the probability that the sequence was generated at random, or "by chance," is only 1 chance in 2^1085, which equals 1 chance in 10^319.
- Dembski's proposed cutoff threshold is 1 chance in 10^150, an immensely small figure.
- The probability of the prime number sequence from the movie occurring is 1 chance in 10^319, which equals 1 chance in 10^150 x 10^169. It could never occur by chance.
Thus, the scientific team in the movie, and we as viewers, are all correct to conclude this signal was designed (by an alien intelligence) and not caused "by chance." The probability of random "chance" as the cause is too eminently small to be a plausible option.
We infer design when a specified event or outcome (i.e. one that matches a specific recognizable pattern) is so complex (e.g. lengthy) that the probability it occurred by random chance is too low to be a plausible explanation.
For everyday events, 1 chance in a trillion might be sufficiently implausible to infer design. That's the probability of successfully predicting "heads" or "tails" for 40 successive flips of a coin.
But for scientists, the implausibility cutoff, or universal probability bound, must be much lower. One of the most conservative probability bounds proposed is 1 chance in 10^150. That's equivalent to the probability of predicting "heads" or "tails" for 500 successive flips of a coin. When the probability of an event is less than this cutoff value, the event is considered impossible to occur by chance.