​A Giant Step Forward In Forensic Science

The length of the string is important. For the purpose of the invention, and because it would be the only bullet marked for identification in the world, only one character is required to create a unique bullet. But, for the ballistic identification number to be commercially or forensically viable a longer string is required, but how long, and from what pool would the characters be drawn?

The largest character pool available would be the 94 visually printable ASCII characters. There are actually 95 printable ASCII characters, the space character is considered to be an invisible character and would be retained for its intended purpose.

The number of bullets manufactured in the United States every year is currently above ten billion. That is ten followed by nine zeros. ​10,000,000,000. This is a very large number.

While it may seem at first glance that the ballistic identification number 3^W%b7! is a random string of seven characters; it is not. It has a logical progression. 3^W%b7! is the first number in the BIN system. 3^W%b7” is the next logical number, the third number is 3^W%b7# and; 64 trillion, 847 billion, 759 million, 419 thousand, 264 BIN numbers later is 3^W%b7~  the last number in the BIN system.

Referring to Fig 9. the printable ASCII table, will make the progression clear. In row one, column one is the binary number 010 0000. Row one, column four, GLYPH is the invisible printable ASCII character "space". The BIN system starts, progresses from, and terminates here. The 3^W%b7 was indeed a random number, but the ! was intentional. Think of 3^W%b7! as the equivalent of the ordinal number 1, in a cardinal set of 94^7.

To put that large a number into perspective, from the birth of the very first human some 3.2 million years ago, up until today, there have been roughly 108 billion humans born and died.

In the ten years between 2005 and 2015, more bullets were manufactured in the United States than the total number people that have ever been born, lived and died in the history of the world. 10,000,000,000 bullets a year is a very large number. How long a character string would be needed to deal with numbers that big?​

This is where the magic of exponents comes into play.

If we have a character string of 1, and 94 possible characters to fill that position, we have 94^1 = 94. With a character string of 1, 94 bullets can be uniquely marked. A two character string 94^2, or 94 squared, will identify 8,836 bullets. 94 cubed, 94^3 will identify 830,584 individual bullets.

The expressions below show the number of bullets that can be uniquely marked as the character string lengthens.

94^1 = 94
94^2 = 8836
94^3 = 830,584
94^4 = 78,074,896
94^5 = 7,339,040,224
94^6 = 689,869,781,056
94^7 = 64,847,759,419,264

A string of five characters results in 7.3 billion unique ballistic identification numbers. This will uniquely identify all the bullets manufactured between January first, and the second week of August in any year.

A string of six characters, 94^6 = 690 billion possible character strings. Six hundred ninety billion is another one of those very large numbers. To make it easier to visualize how big a number 94^6 is, I will use something that everyone can understand. The night sky.

Estimates are that our home galaxy, the Milky Way, contains between 100 and 400 billion stars. Let’s average it out and say that our Milky Way has 200 billion stars.

Now, visualize walking out on a clear night with no moon and no city lights to haze the sky, and seeing the sky filled with three Milky Ways.

This what 94^6 looks like.

If bullet production were to remain static, a six-character string would be able to fingerprint every bullet manufactured for the next sixty-nine years.

Unfortunately, static bullet production seems unlikely.

Unless a character set larger than 94 is available, the most flexible character string length would be seven characters. A seven-character string will produce 94^7, or 65 trillion unique combinations.  Using the same Milky Way comparison, a character string of 7 produces a number bigger than all the stars in more than 324 Milky Ways. More than enough BIN numbers to last until someone comes up with a better idea.

To reduce the possibility of error in the forensic laboratory it might be advantageous to eliminate some of the characters that could be confused. But; even if the numeral 1, the uppercase letter I, the lowercase letter l, the numeral 0, the uppercase letters O, and Q were removed from the pool there would still be 41 trillion possible combinations. More than enough BIN numbers to identify every bullet produced for the next four thousand one hundred years.

This is 94^7 or 64,847,759,419,264

The Numbers Behind The Numbers

Once it was proven that a method of placing an identifying mark on an individual bullet was possible, the next question was; to make this method of identification commercially or forensically practical, how many characters would be needed in the string.

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