Watching the trailer for "28 weeks later" I have raised a question:
If you wake up the dead from their graves, could with them?. Ie: How many people have inhabited Earth
The realization of such calculations is not that easy, we must take many things that inevitably will lead to errors. But at least we will get an idea where the shots go, but not for us to publish in Nature .
To make these estimates, we need a mathematical model. This is a little formula math will tell us how to evolve a variable to others based on certain parameters and conditions. In our case, the population over time. Here we begin with the first assumption. Assume that everyone will have a certain number of children, and that the number of children is going to stay constant over time (a man of the Middle Ages have as many children as one of the industrial revolution). So if we have 2 people going to be about three children, a generation after we 3 / 2 of what we had before. This 3 / 2 is what we consider constant, and we call k (3 / 2 only serves as my example, after which it will calculate k in our example). Another assumption that exponential growth means that the population will grow without limitation, this means that there will be famine, disease and war. Naturally, this is not true, but is used to calculate what we know. Moreover, as we use real data, the k reflected in part these famines, wars and other (to be somewhat less than a k solely dependent on our ability to reproduce). As we are looking at the data on a global level, there is no migration phenomena, no one is leaving the planet, and nobody will come to the planet.
The population growth rate is proportional to the population at a given time. I mean, that a population of 5000 individuals, the next generation will grown much faster than another of only 50 individuals. This equation is written:
growth rate of population = Number of Individuals x constant growth
more Since simple: dP / dt = k * P (t)
Where dP / dt is the rate of growth (something like that as change when we change the time P (t))
k is the constant growth that we had discussed before
and P (t) is population.
This is a differential equation. For those who do not know how to solve it, I put the solution here:
P (t) = P or * e kt
where P (t ) is the population at time t, P or is the initial population, and is the constant (2.71 and it is widely used in mathematics) k is the constant growth we talked about earlier, and t is time.
A typical example of exponential growth is the story of rice and a chessboard. If you put a pimple in the first box, twice in the second, twice second in the third ... there will be enough rice in the world to fill the board.
Returning to the subject that interests us. Humans are animals Especialito. We have been able to overcome adversity, we can consider that there is no limitation on our growth. Same thing happens with bacteria and viruses (but be careful, in special conditions). If we take the look back we see that it all started with the ability to change the environment. That is, in the Neolithic with the development of agriculture. Since then mankind has grown more or less like an exponential curve. Sure, there have been population declines, and during
In this image we see is the growth of humanity over time, from 1750 until 2150. It is a sort of plateau when you get 2100 or so, because it is estimated that by then the population balance (so-called logistic curve), but today, in 2007 we can still consider the model as exponential.
The way to know how many people have lived in total would add that has lived in every time. It is like saying that to know how heavy a sausage, cut it into different pieces, which weighed separately and then add. In mathematics this operation chorizo \u200b\u200bis what is called integral.
The integral will give us the area below the curve, which amounts to the total population at all times. But leave us not to infinity (we do not know how many people live in the year 40,000) going to set limits. As mentioned, we consider the exponential growth of humans from the Neolithic. The Wikipedia
But miss one thing, if in our operation chorizo \u200b\u200bcut too thin, we run the risk of double counting people, so we divide the total time the average length the life of a person. Here we put another assumption, since I do not know exactly as is. Today, in developed countries, is around 70, but for thousands of years was significantly lower. Still, I'm going to get wet and put some 50 years (although it is true that would be something minor, so I go round numbers)
7000 years / 50 years of average per person = 140 generations
That is, consider that happen every 50 years to different generations (as I said before, is an approximation). In the Neolithic we have t = 0 and currently offer t = 140.
now lack one thing to know: how much is k?. The easy way to estimate it in the little formula for exponential growth in the values \u200b\u200bwe know.
According
P (t) = P or * e kt
P (140) = 10 * e 140 * k = 7000
Solving k us provides that:
And we have the data we need for the operation of the integral chorizo. We integrate from t = 0 to t = 140, ie, we see how valuable the integral at t = 0 and t = 140 and subtract.
∫ (P or * e kt) dt = (P or / k) * e kt + C
Where is the symbol of the integral, dt (time difference) is to know about which axis cut our sausage and that C is a constant, which is now irrelevant because the subtraction we will (if you want, I can explain the basics of the integral in another time.)
Now with this equation that has left us, we replace t by 0 and 140 and subtract.
[(10/0.04679) * e 0.04679 * 140] - [(10/0.04679) * e 0.04679 * 0] =
[( 10/0.04679) * e 0.04679 * 140] - [(10/0.04679) * e 0 ] =
[(10/0.04679) * e 0.04679 * 140] - [(10/0.04679) * 1]
If we solve this leaves us the total People who have lived throughout the history of humanity have been: 147,730 million people!
words, from the Neolithic to now have lived about 147,730 million people. Almost nothing.
This means that if given to get up, we would have to face against an army of 147,730 million hungry zombies human livers.
With 147,730 million dead, I am surprised has not yet met a ghost ...
For each live about 21 dead have been about. When I reached the end of the world, and rise from their graves, will you be able to defend yourself?
Again, this is a comment that simple model, so you can make many mistakes, may be more or less. To begin with we assume that everything that happened before the Neolithic period does not count, that there have been people who have not had children, there has been no war or famine, and that the average life of humanity is 50 years (when they are certainly less), but not bad for an idea.