The improbability of a human birth

After many, many births and deaths one achieves the rare human form of life, which, although temporary, affords one the opportunity to attain the highest perfection. Thus a sober human being should quickly endeavor for the ultimate perfection of life as long as his body, which is always subject to death, has not fallen down and died. After all, sense gratification is available even in the most abominable species of life, whereas Kṛṣṇa consciousness is possible only for a human being.

— Srimad-Bhagavatam 11.9.29

The Srimad-Bhagavatam stresses again, again, again, again, again and again how rare and valuable a human birth is, using the word durlabham: very difficult to obtain. Unfortunately we tend to forget this and take our human bodies for granted, which is very tragic considering just how rare and valuable they are. Someone who has understood this will try to use this chance to the utmost, and not waste a second on any other endeavour than self-realization.

There is an allegory in Buddhism which gives a rough estimate of the rarity of the human form of life:

The human rebirth is said to be extremely rare. The Majjhima Nikaya (129 Balapandita Sutta) compares it to a wooden cattle-yoke floating on the waves of the sea, tossed this way and that by the winds and currents. The likelihood of a blind turtle, rising from the depths of the ocean to the surface once in a hundred years, putting its head through the hole in the yoke is considered greater than that of a being in the animal realm, hungry ghost realm or hell realm achieving rebirth as a human.

— Wikipedia

This inspired me to try to make my own estimation, based on modern science. Leaving the question of ghost and hell realms aside, we can start by asking the question: If you are born as one of the living organisms (known to science) on this planet, how likely is it that you will be born as a human?

There are roughly 5,000,000,000,000,000,000,000,000,000,000 bacteria on this planet, and the number of other organisms is negligible in comparison, so we can say that this is the total number of organisms. Now, there are roughly 7,000,000,000 humans. This gives us the ratio of 1 in 700,000,000,000,000,000,000 - that is the probability of being a human being if you live on this planet. There is no mundane analogy which our brains can digest, which even comes close to a realization of this improbability.

But we can start by comparing to the turtle analogy. The area of the world's oceans is roughly 362,000,000,000,000 square meters. If we assume that the hole in the yoke is 20 by 30 cm, the area of the hole is 0.06 square meters, and then the probability of hitting the hole is 1 in 6,000,000,000,000,000. So we can take the turtle analogy and multiply it by 100,000; the turtle most also win the first prize in the national lottery.

And even leaving bacteria aside, if we can assume that we are born with the abilities to eat, sleep, mate and defend, which the current human civilization is preoccupied with, but which insects can do as well, we find that the insects outnumber us by 700,000,000 to 1. So you could say that you have already had 700,000,000 chances to simply eat, sleep, mate and defend, and now is your one chance to develop love - are you going to take it?

Even leaving insects aside, if we can assume that we are born with the ability to love and take care of each other, like birds and mammals do, well, there are roughly 1,000,000,000,000 birds and mammals, so they outnumber us by 140 to 1. You have had 140 chances to help others with their material happiness, and now is your one chance to help others with self-realization, to help others realize that they are not these bodies, but eternal units of consciousness, with a forgotten, all-fulfilling purpose in life - are you going to take it?