I have enjoyed immensely your lecture about the exponential function. Your web site states you have given this lecture 1600 times. This is an incalculable contribution to the world.
The version I saw was a YouTube video that you gave perhaps 15 or 20 years ago: http://www.youtube.com/watch?
At the end of the video, you asked for corrections for any calculations that might be in error. I only know of one such--your discussion of population in that lecture is misleading. Perhaps you have already corrected it :-)
At about the 9 minute mark of part 2 you said the following: "I have to realize that anything that just lowers the death rate makes the problem worse." Consequently, you say that the items on the left hand side of the Table of Options (shown , Medicine, Public Health, Sanitation and Peace "makes the problem worse".
While strictly true (almost by definition), nevertheless your statement is highly misleading. Perhaps even tragically misleading. Indeed, Medicine, Public Health, Sanitation and Peace do not just lower the death rate. They also tend (in the long run) to lower the birth rate even more! Indeed, disease, famine and war typically tend to increase population. The best (perhaps the only) way to control population is the increase the well-being of mothers and infants.
This was the message of the late, great James Grant of UNICEF. Imo, every person who talks about population issues really must understand this counter-intuitive fact if they are to avoid uttering nonsense.
To see the truth of Grant's assertion, it pays to study
very closely the statistics at the back of every edition of UNICEF's
State of the World's Children reports. The 2013 report is at http://www.unicef.org/
As you will see, as death rates decline, birth rates decline more. This is why many countries in the world have total fertility rates below the replacement rate.
The correlation between U-5 mortality rates and total fertility rates holds true both "horizontally" and "vertically". That is, the correlation holds at any particular time when comparing different countries. Countries with lower U-5 mortality rates have lower fertility rates. But the correlation also holds in any single country over time. As death rates decline, fertility rates decline even more, in any country you choose to study.
Although correlation does not necessarily imply causation, it is fairly easy to see what is leading to reduced fertility rates. As death rates decline, there is no need for mothers to raise "extra" children to replace those expected to be lost to disease, wars and famines.
There are, of course, other factors at work. I highly recommend this report: http://www.un.org/esa/
1. You will not be surprised to learn that seemingly minor changes in projected fertility rates have huge consequences when "multiplied" over many years. In a sense, this report merely illustrates the properties of the exponential function.
2. The essay in part 2 of the report are fascinating. Population experts can interesting and important things despite massive uncertainties.
Again, many thanks for the enormous contributions you have made to the world. I trust you will come to agree that the best way to reduce world population is to reduce the death rates among infants and children everywhere.
As you will see, as death rates decline, birth rates decline more. This is why many countries in the world have total fertility rates below the replacement rate.
The correlation between U-5 mortality rates and total fertility rates holds true both "horizontally" and "vertically". That is, the correlation holds at any particular time when comparing different countries. Countries with lower U-5 mortality rates have lower fertility rates. But the correlation also holds in any single country over time. As death rates decline, fertility rates decline even more, in any country you choose to study.
Although correlation does not necessarily imply causation, it is fairly easy to see what is leading to reduced fertility rates. As death rates decline, there is no need for mothers to raise "extra" children to replace those expected to be lost to disease, wars and famines.
There are, of course, other factors at work. I highly recommend this report: http://www.un.org/esa/
1. You will not be surprised to learn that seemingly minor changes in projected fertility rates have huge consequences when "multiplied" over many years. In a sense, this report merely illustrates the properties of the exponential function.
2. The essay in part 2 of the report are fascinating. Population experts can interesting and important things despite massive uncertainties.
Again, many thanks for the enormous contributions you have made to the world. I trust you will come to agree that the best way to reduce world population is to reduce the death rates among infants and children everywhere.
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