Preface
Typical statements involving concepts and degrees of complexity
          Don't mind the math
Introduction to Measuring Complexity
Measuring the complexity of something very complex ( Windows XT )
Measuring the complexity of something that seems relatively simple (but surprisingly, is not)
          Flip how many times to get a match ?
          If we flip once a second, how long would it take ?
          Introducing the maximum bit compression into the 7-letter word "example" analysis
Increasing the complexity by adding "bits of information"  ( Formulas )
Human DNA has 3 billion DNA base pairs, that include 20,000 protein-coding genes
Conclusions
"Complexity"  to  "Number of Tries / Attempts / Times"  conversion  TABLE
Introducing the maximum bit compression into the 7-letter word "example" analysis

We are all familiar with the idea that "if we keep on trying" we may eventually "get it right."

Or maybe, if accidents just keep on happening, then such-and-such is bound to happen.

Of course, with no intelligence in the universe, these accidents would keep on happening, even today, regardless of the produced results.  Our planet would be littered, throughout history and now, with the failed attempts of accidental creation "trying to get it right."  Exactly how many attempts (tries) would it take to get something complex "right," is the subject of this web page.
     ( An observation:  We see lots of births, lives, and deaths from beings that are alive,
        but seemingly nothing from endless random attempts at accidental creation. )

What are the Mathematical Probabilities of Random / Accidental Creation -vs- Complexity ?

What would it take to Create Something Complex from Random Accidents ?

What are the odds that Something Complex comes into being, as the result of Random Accidents ?

What are the probabilities (chances) of creating useful complexity either randomly or accidentally ?

Complexity .. Measuring Complexity .. Quantifying Complexity .. Mathematics that describes Complexity

From a "theory of evolution" perspective, everything that happens must be a truly random event or accident (with no plan, rhyme, or reason, or help, or intelligence from God).  So let's rely on a purely mathematical analysis of what happens.  (i.e. Let's rely on pure science; nothing religious about it.)

Something created (something that comes into being) in the universe is typically measured by its complexity.  We say that something simple has very little complexity, whereas something very intricate is described as being very complex.

An easy place to start is to measure the complexity of something very complex like the Windows XT operating system.

By doing a right-click on C:\WINDOWS and selecting "Properties", my PC tells me that my Windows XT operating system has a size of about 2.5 GB.  Since each byte contains 8 "bits of information", we can say that about 20 billion "bits of information" is required to describe the complexity of this Windows XT operating system.  ( 2.5 GB = 2.5 GigaBytes =~ 2.5 Billion Bytes.  2.5 Billion Bytes times 8 bits per byte = 20 billion "bits of information." )

At this point we should reflect on how vastly more complex the human brain is, as compared to the Windows XT operating system.

We can conclude, with as close to absolute certainty as we can imagine, that this 20 billion "bits of information" is not going to be randomly or accidentally duplicated (or come into being that way).

As we mentioned before, the human brain is vastly more complex, so we can also state that the human brain is not going to be randomly or accidentally created.

( Question to ponder:  Why is it that we can believe that there is no way that Windows XP could be created by random accidents, but some of the same individuals can believe that the human brain "evolved" via a series of random accidents ??? )

Now, using a very simple example, let's explore how difficult it would be to accidentally, or randomly, create something that has any significant degree of complexity.

Say we want to accidentally, or randomly, create the 7-letter word "example".

Therefore, the 7-letter word "example" can be represented by 56 "bits of information."
          ( 7 letters = 7 bytes.  7 bytes times 8 bits per byte = 56 "bits of information." )

The table below describes this structure, as well as the value of each of the 56 "bits of information" needed to represent our 7-letter word "example".

Each "bit of information" has a required value of 0 or 1, shown in the table above.

One way to represent these 56 "bits of information" is to lay out 56 pennies in a line (one penny for each "bit of information").  Lets say "heads/h" represents a value = 1, and "tails/t" represents a value = 0.

Our next question is likely to be:  On the average, how many times do we have to flip all 56 pennies to get a match?

The answer is:  "2" raised to a power equal to the "number" of "bits of information."
The answer may also be described as:  "2" with an exponent equal to the "number" of "bits of information"
The answer has the following formula:  2^(# of bits of information)

2^56 times = 72,057,594,037,927,900 times =
7.2 E+16 (i.e. 7.2 times 10 to the 16th power (7.2 x 10^16) ) times.
( Note:  10^16 = 1 followed by 16 zeros. )

Another way of expressing this is "the odds of getting a match on the next try is
    1 in 72,057,594,037,927,900."

Let's ask still another question.
If the 56 pennies were all flipped once every second, on the average, how long would elapse between matches?  (i.e. How long would it take, on the average, to get a match ?)

The answer is:  72,057,594,037,927,900 times, and at once per second = 72,057,594,037,927,900 seconds.

Then, divide by 60 seconds per minute to get 1,200,959,900,632,130 minutes.
Then, divide by 60 minutes per hour to get 20,015,998,343,869 hours.
Then, divide by 24 hours per day to get 833,999,930,995 days.

Then, divide by 365.25 days per year to get 2,283,367,368 years.
    ( That's 2.28 billion years. )  (2.28 E+9 years)

Now we can begin to understand why the "theory of evolution" needs all the billions of years it can fabricate.

Therefore in either analysis, our conclusions would be the same.  ( end of this web page ) )

What if we want to increase the complexity of what is going to be randomly (accidentally) created?

A simple of rule of thumb is:  For each 10 "bits of information" we start with or add to the complexity of something, we must add 3 more zeros to the number of times all the pennies have to be flipped to get a match.

In our case, adding 10 more "bits of information" to the 56 above, would have the following results:
    2^(56+10) times = 7.2 E+(16+3) times = 2^66 times = 7.2 E+19 times
    2.28 billion years x 1000 = 2.28 E+(9+3) years = 2.28 E+12 years
    ( Notice that we are now at 2.28 trillion years ( = 2.28 billion years + 3 more zeros). )

( Note:  To be exact, instead of adding 3 more zeros (which is the same as multiplying by 1,000), we must multiply by 1,024 (because 2^10 is exactly = 1,024). )

What are the chances that human DNA came into being by random accidents?

According to Wikipedia, the human genome is the genome of Homo sapiens, which is stored on 23 chromosome pairs.  The haploid human genome occupies a total of just over 3 billion DNA base pairs, and has a data size of approximately 750,000,000 bytes.

750,000,000 bytes x 8 bits per byte / 2 bits per DNA base pair = 3,000,000,000 DNA base pairs

750,000,000 bytes x 8 bits per byte x .015 = 90,000,000 "bits of information" for protein-coding genes

2^(90,000,000 bits) = 1 followed by 90,000,000 x 0.301029995664 zeros =

1 followed by 27,092,700 zeros = 1 E+27,092,700

( Note:  Above, we have been focusing on "bits of information" that represent the genetic code for all human beings.  However, in DNA detective work, we would focus on the differences in the human genetic code that would give us a unique DNA match or signature for each individual.

The reliability of these DNA matches is claimed to be about "1 in a billion."
          ( 2^(30 bits) =~ 1 billion = 1,000,000,000 = 1 E+9 = 1 followed by 9 zeros )

By taking our original results of 1 in "1 followed by 27,092,700 zeros", and subtracting the exponents of 1 in "1 followed by 9 zeros", we would wind up with 1 in "1 followed by 27,092,691 zeros" (i.e. with 9 fewer zeros).

Consequently, we can easily see that the DNA differences between humans are very, very small when compared to the DNA similarities between humans.  Therefore, our original conclusions are unaffected by these DNA differences. )

As shown in the various analyses above, mathematically speaking, the probability of something very complex being randomly (accidentally) created is as improbable as we can imagine or fathom.

Stated another way:  It is mathematically totally improbable that anything very complex ever came into being by accident or by any other random happening.

A belief in the "theory of evolution" merely means that one has chosen to believe the opinions of "experts", rather than thinking it through for oneself.

The reason for "evolutionists" wanting to state that the "theory of evolution" is no longer a "theory," but a "fact," is so no one needs to concern themselves with thinking it through for themselves.  Everyone would just accept it as "fact," without thinking.

This would also apply to any "theory" that includes random or accidental creation of anything that has any degree of complexity.

Conclusion:  As shown in the various analyses above, mathematically speaking, the probability of something very complex being randomly (accidentally) created is as improbable as we can imagine or fathom.
 
A Final Question:  With the mathematical probabilities of it (something very complex being randomly or accidentally created) being so low (odds so low, the possibilities being so improbable), can you make the statement that

          " I would not bet any money on it,
                 nor my future,
                     nor my eternity " ?

The table below enables us to quickly convert the complexity of something (measured in "bits of information") to the average number of tries / attempts needed to randomly (accidentally) create something of that complexity.     In this table, binary (computer) terminology is used where:

a terabyte (aka tebibyte TiB)=1024^4 or 2^40 bytes,  a gigabyte (aka gibibyte GiB)=1024^3 or 2^30 bytes,
a megabyte (aka mebibyte MiB)=1024^2 or 2^20 bytes,  a kilobyte (aka kibibyte KiB)=1024 or 2^10 bytes.

For those of you who are familiar with using an 8-bit byte to represent 256 (2^8 = 256) printer symbols, you may be thinking that we should eliminate (compress out) many or all of the 256 printer symbols that are not letters of the English alphabet.

For instance, we could eliminate the 128 special characters that have a leading "1" bit, digits 0-9, the distinction between upper case and lower case letters, and the remaining special characters.  With only the 26 symbols a-z or A-Z, we would only need enough bits to fit the following equation:

          2^(# bits) = 26 = 2^(4.700439718 bits) =~ 2^(4.7 bits)

If we define a compression factor for 26 symbols (CF = .587 554 964 767 637), it fits the following equations:

log10( 2^(8x7) ) =~ 16 zeros    (for 8x7=56 uncompressed bits in our 7-letter word called "example")

log10( 2^(8x7) ) x CF = log10( 2^( 4.7x7) ) =~ 9 zeros    (for 4.7x7=32.9 compressed bits in our 7-letter "example")

16 zeros x CF =~ 9 zeros   (where CF = 0.587 554 964 767 637)

log10( 2^( 4.7x12) ) =~ 16 zeros (for 4.7x12=56.4 compressed bits in our 12-letter word called "conventional")

log10( 2^(8x7) ) =~ 16 zeros    (for 8x7=56 uncompressed bits in our 7-letter word called "example")

Most "bits of information" representations have already been reasonably compressed.