This post evaluates the complexity (in terms of bits of information) of a single human being. The evaluation is performed from an reductionistic viewpoint. The same methodology is then extended to evaluate the complexity of two human beings. Further extension enables evaluation of the complexity of a million, a billion and then finally all 6 billion or so human beings on earth.

Bit: A bit is a quantity that is capable of two values, or states, e.g., 0 or 1.

Information: Can be expressed in bits.

DNA: A DNA base pair can take four states, A,C,T, G, and so can hold 2 bits of information.

Complexity: One measure of how complex an object is, is how much information (in bits) is needed to specify the object.

Complexity of a human: In the case of a human being, the information in the person's genes can be used as a lower-bound measure of the person's complexity. This does not include the complexity of the person's brain (that is likely to be the subject of a future post).

Engineering Notation: Large numbers can be expressed as follows.

1E0 = 1 x 1 = 1
1E1 = 1 x 10 = 10
1E2 = 1 x 100 = 100
1E3 = 1 x 1000 = 1000
2E3 = 2 x 1000 = 2000
1E5 = 1 x 10000 = 10000
3.6E7 = 3.6 x 10,000,000 = 36,000,000

One human = 3 billion DNA base-pairs (4 states per DNA base-pair, i.e., A, C,T, G) = 6 billion bits = 6E9 bits.

Any two human beings are 0.1 % genetically different from each other (Source: National Human Genome Research Institute, National Institutes of Health – a US Government Institute).

Average 0.1% genetic difference between any two humans = 30 million base-pairs = 3E7 base-pairs = 6E7 bits.

So, 1 human (complexity-measured in bits of information) = 6E9 bits.

Now, to estimate the complexity of 2 humans we use the base complexity of one human (6E9 bits) and add the differential-complexity between the two humans (6E7 bits). Doing this, we obtain …

Complexity of 2 humans = 6E9 bits + 6E7 bits = 6.06E9 bits.

Complexity of 3 humans = 6E9 bits + 2*(6E7 bits) = 6.12E9 bits.

Complexity of 101 humans = 6E9 bits + 100*(6E7 bits) = 12E9 bits = 1.2E10 bits.

Complexity of 1001 humans = 6E9 bits + 1000*(6E7 bits) = 6E9 bits + 6E10 bits = 6.6E10 bits.

Complexity of 1,000,001 humans = 6E9 bits +1,000,000*(6E7 bits) = 6E9 bits + 6E13 bits = 6.0006E13 bits = 6E13 bits.

Complexity of 10 million and one (10,000,001) humans = 6E9 bits +10,000,000*(6E7 bits) = 6E9 bits + 6E14 bits = 6.00006E14 bits = 6E14 bits.

For ease of calculation, I am going to drop the one extra human (this will drop the 0.00006 value in the sentence above).

Complexity of 10 million (10,000,000) humans = 10,000,000*(6E7 bits) = 6E14 bits.

Complexity of 100 million (100,000,000) humans = 100,000,000*(6E7 bits) = 6E15 bits.

Complexity of 300 million humans = 300,000,000*(6E7 bits) = 18E15 bits = 1.8E16 bits.

Assuming the population of the USA to be about 300 million human beings, this means that the complexity of the human-inhabitants of the USA = 1.8E16 bits.

Assuming that the population of China to be about 1 billion human beings: complexity of the1 billion humans in China = 1,000,000,000*(6E7 bits) = 6E16 bits.

Assuming that the population of planet earth to be about 6 billion human beings: complexity of 6 billion humans = 6,000,000,000*(6E7 bits) = 36E16 bits = 3.6E17 bits.

In summary, we found that the complexity of a single-human being, as measured by the information in her genes, is 6E7 bits (i.e., 60,000,000 bits).