The S Curve

Imagine setting fire to a very large field of dry grass. The shape of the field does not matter too much as long as you start small fires in different locations. Initially the small fires are burning, and start consuming the grass right next to it. The beginning is a little slow, because the perimeter of the fire is very small. But as the fire grows, the rate at which it starts burning increases, because there is more and more fuel available at the edge - as the small circles spread into larger ones. After a point when half or more of the grass is burned out, the fire starts slowing down. Burning continues, but the rates start becoming smaller. This happens because different circles merge, and the perimeter actually decreases. What starts out with islands of fire, becomes islands of grass. These islands shrink further and further, reducing the strength of the fire. Ultimately everything dies down when the whole field burns out.


If you took a picture of the fire at different times, and measured the area burned down, first few intervals will show slow rise. However, the growth acceslerate rapidly, almost exponentially till the halfway point. At halfway point, the rate of rise is steep, and in the later half when most of the field has burned down, the rate of rise is slow. This is the classic S curve.


Why is the S curve important? Well, to begin with, it applies to population. Population, too increases like the bushfire to increase rapidly at first and then settle down. Technically speaking the S curve may not exactly describe the human population, because unlike the fire example with the fixed space conditions by which the human population increases, and the causes by which it ceases to increase are not constant. For example, we may discover another planet on which to grow human race in future. Or the sociological changes will actually cause the population to decrease. Nevertheless, conceptually the curve is still valid. For a fairly foreseeable future - the next 100 years or so - we can safely assume that the population will plataue at around 9 to 10 billion.



The exact number is not really important. But what it tells us is that the doomsday scenarios that were common in 1970s about the population explosion were obviously incorrect. Those looked at the halfway point, fast burning, rapidly rising S curve, and blindly interpolated to go for some years. The math was not incorrect, it never is for typical scaremonger statistics. The error was in assumptions that the population growth will continue at the same vigorous rates.


The other extremely important aspect of S curves is that it approximates how a particular life improvement spreads through the world. The bottom part of the S curve represents the initial period of very low pervailance and slow growth. Typically in this period a particular item or freedom is available to only the cream of the society. The growth is slow, but it picks up. The second part is when the spread is very rapid, and in no time most of the society gets that item. This is the period when the item changes from luxury available to only the top 5 to 10% to a necessity that eventually 90% people possess. The last bit is little difficult, again because of various reasons. So sometimes the last 10% takes as much time as covering the middle 80%. But eventually almost everyone has it and the world starts taking it for granted.


If you take the "safty from predetors" like lions, tigers, hyenas etc as your variable and charted what percentage of population had this "luxury" you will see a similar trend. The stone age people and their ancestors did not have this luxury. Very few people were protected because they either were rulers of tribes could afford to live protected by others who faced the risk. As the civilization spread through, and the agricultural societies thrived, the villages grew (just like bushfires). The inner people were protected. Now we have completed the S curve (almost) and less than 1% are actually exposed to it. We have forgotten that it was a problem once, and that it killed large number of people every year.


Another example is the spread of the cellphone. This can be illustrated with numbers. [need a plot]. Before 1900, the conept just wasn't there beyond somebody's imagination. I am sure people must have sat around a campfires and wondered what wonderful life it would be if everyone could talk to their dear ones, friends at a press of a button, no matter where they were. Probably they had a good laugh about it and forgot. But the dream lived on and now it's reality. In late 80's there were very few people who could afford car phones or new fangled mobile phones that weighed a ton. That was the less than 1% phase. As of now, there are around 3 billion (need to confirm the numbers) equivalent to about 60% of the population that could use cell phones. We have quickly reached from a mobile phone becoming a necessity from extreme luxury. And only a 100 years ago it was science fiction.


The S curve for cell phone population is much steeper than the S curve for the safty from predators. It took a few thousand years for human beings to achieve the second, whereas it will take only 50 odd years for the cell phone being available to every human being. This is a new feature of modern times, the progress takes place right under our noses. The reaction time is fast. On the face of it, the difference looks like the difference between sociological change to a technological change. I personally have never taken much liking to lables. Ultimately they are the structures that get formed either to thwart predators, or transmit phone signals. Nevertheless, by the 20th century there have been enough changes, so that a thing like cellphone can be invented, and more importantly spread through amazingly quickly. So if you draw a meta S curve, we are on the rise - long time ago all S curves were very slow, now they are fast.


The progress is spreading like a wild fire...