Tag Archive | "overpopulation"

Footprints on the Pale Blue Dot


Can Everyone Be A Texan?

Many opponents of the RH Bill and of population management in general deny that the world is overpopulated. To support their denial of overpopulation, conservatives usually claim that everyone alive today can fit inside the state of Texas, leaving the rest of the planet blissfully empty of humans. A moment’s thought is enough to come up with definitive arguments against this everyone-can-be-a-Texan scenario. Unfortunately, the said scenario keeps on getting parroted, and by no less than our own anti-RH senators like Tito Sotto.

So how do we elegantly debunk the we-can-all-fit-in-Texas scenario and other similar baloney “arguments” commonly used by RH Bill opponents? The answer comes from the environmental sciences.

 

My Very Own Patch of Earth

How does your lifestyle affect the environment? To answer this question, environmental scientists William Reese and Mathis Wackernal invented the simple but powerful concept of ecological footprint. Your ecological footprint is the total area of bioproductive land and sea needed to sustain your lifestyle. The name ecological footprint is therefore well chosen because it essentially measures how heavily you tread on planet Earth.

The Energy Library gives the following definition of a bioproductive patch of Earth:

 1. able to produce and sustain living organisms

2. specifically, describing land area that is capable of providing natural substances that support human activities; e.g., land used for growing food crops

In other words, a bioproductive patch of Earth is an area that produces goods and performs services that have economic value to humans.

Now, let us get back to ecological footprint. I wanted to know what my ecological footprint was, so I went here to take a test that gives me a rough estimate of its value. After taking the test (I tried my best to give the most accurate and honest answers possible) I found out that my ecological footprint is around 1.8 hectares. That’s 18,000 square meters of the Earth’s sea and land that’s dedicated to support my lifestyle. (I tried other tests, and they gave me answers ranging from 0.90 hectares to 5.5 hectares. I think 1.8 hectares is the most accurate. I encourage the reader to take other tests, for example this or this.)

How do I make sense of my 1.8-hectare footprint? To make it easier to explain my ecological footprint, I tried splitting it into several divisions. (The divisions that follow are mine. Environmental scientists have yet to reach a consensus on how to divide the ecological footprint.)

A meat-eating diet translates to a large dietary footprint.

One portion of my 1.8-hectare footprint consists of the total land and sea area needed to grow and process everything I eat. This is called my dietary footprint. You can think of my dietary footprint as the total area of all the farmland, orchards and fishing areas where the things I eat are grown or caught.

Of course, I need water too. A good fraction of my ecological footprint consists of my freshwater footprint. This is the area covered by all the freshwater sources tapped to give me water for drinking, bathing, washing my clothes, flushing the toilet and many more.

The Angat Dam and Reservoir is part of our freshwater footprint.

Another part of my ecological footprint is the patch of forest and shallow seas needed to absorb my yearly carbon emission. My carbon emission is the total amount of carbon dioxide I directly or indirectly add to the atmosphere every year. For example, when I commute from home to work, I use buses, cars, and trains that run on the burning of fossil fuels. Carbon dioxide is one byproduct of the burning of fossil fuels. The area needed to absorb my carbon emission is the now well-known carbon footprint. Notice that your carbon footprint is only a subset of your ecological footprint. Reducing one’s carbon footprint is good, but it’s not good enough. (Carbon footprint is more naturally measured in metric tons.)

Stanford Kay's carbon footprint infographic.

And yes, let us not forget all the waste products I produce. The area in the landfill taken up by all the non-biodegradable garbage I produce in a year can be lumped under my waste footprint. Other parts of my waste footprint include the total area required to recycle my recyclable waste and decompose my biodegradable waste.

What you throw away is still here to stay. And it becomes part of your garbage footprint.

In my day-to-day life I also need go to school, to work or to some places of leisure. To do all of this, I need to use roads, railways, airports and seaports. The said places I mostly share with other people. My share in all these built-up areas I want to call my built-up footprint. Also included in my built-up footprint are my shares in government buildings and other public structures such as shopping malls and places of recreation.

My energy footprint is my share in the area taken up by all the power plants, refineries and LPG factories built to produce the energy I consume in a year.

Ecological footprint is a measure of how heavily we tread on planet Earth.

The connections in the web of nature are delicate and intricate. Just because an area in the Amazon Rainforest remains “untouched” by humans does not mean that it is unaffected by human activities. Similarly, when we overfish one species, we are not affecting only that species but are affecting an entire food web. Overfishing tuna, for example, may greatly affect countless other marine species. My share in the human impact on habitats I’d like to call my biodiversity footprint. Biodiversity is a measure of the richness of life. There are several ways to measure biodiversity. One way is to count the number of unique species living in an ecosystem. Another measure called the Simpson index takes into account the percentage of each subspecies or breed in a given habitat. Sometimes, the number of unique habitats in a given region is also used to measure biodiversity.

What else can one find in my 1.8-hectare ecological footprint? Let me see. How about that patch of forest cleared to supply me all the paper and other wood products I use in a year? And how about that patch of mountain quarried to mine the minerals required to supply me all my metallic needs? The area needed to produce the raw materials and the goods I use in a year I’d like to lump under my goods footprint.

The foregoing breakdown of a person’s ecological footprint is far from exhaustive (and even farther from authoritative). However, I tried to outline the major components of an average person’s ecological footprint to provide the issue some perspective.

Other environmental scientists have other ways of dividing the ecological footprint.

According to estimates published by the Global Footprint Network in the National Footprints Account 2010 Edition, the ecological footprint of the average Filipino is 1.3 hectares. This is a bit higher than India’s 0.90 hectares and nearly five times lower than the Netherlands’ 6.2 hectares. The United States’ average footprint is a whopping 8.0 hectares. (Other estimates peg the average Dutch footprint at 5.9 hectares and the average American footprint at an unbelievable 9.7 hectares.)

The average citizen of the world has a footprint of 2.7 hectares. However, the average citizen of a developed country has a 6.1-hectare footprint while the average citizen of a developing country only has a 1.2-hectare footprint. This disparity comes from the differences in lifestyle and available technologies. People living in poor countries don’t have a small footprint by choice. If you barely have enough money to feed yourself, then you cannot consume much. This translates to a small footprint. However, it is known that as a developing country makes its way out of poverty, the average footprint of its citizens sees a dramatic increase.

 

How Many Earths Are We Gonna Need?

If everyone on Earth lived like me, how many Earths would we need? How about if everyone on Earth lived like the average Dutch? What if everyone lived like the average American? And is it true that everyone alive today can live comfortably as Texans? Before we can answer that, let’s go through some preliminaries.

It is first important to understand the concept of biocapacity. The biocapacity of a region is a measure of the population it can support. In more technical terms, biocapacity is a weighted total of the area of bioproductive land and sea in a given region. Being a weighted total, when we count the biocapacity of the world, the Sahara Desert will not contribute much even though its area is quite large. On the other hand, the biocapacity of the seas in the Philippines would be exceedingly high even though their total area is less than that of the Sahara Desert. In terms of biocapacity, two of the biggest giants are the Amazon Rainforest and the Great Barrier Reef system. The Philippine seas are not far behind.

The Philippines has a relatively high biocapacity.

Biocapacity is measured in global hectares (gha.). The global hectare unit of measurement was invented to accommodate the fact that not all patches of Earth are equally productive or capable of sustaining life. However, on average, 1 global hectare is equal to 1 normal hectare. Therefore, when I say 1.30 global hectares, you can simply think of it as 1.30 normal hectares. (As a matter of fact, I have been using this simplifying assumption in the previous paragraphs.)

The total biocapacity of the Earth is estimated to be 12 billion global hectares. That is, the Earth has 12 billion hectares of land and sea that is capable of sustaining human life. If human civilization uses less than 12 billion hectares, then it can exist for an indefinite period of time. Humans can exist for very long if they use up less than 12 billion hectares of Earth because nature has the ability to repair itself even after human damage has been done. A civilization that uses less than 12 billion hectares of the Earth has a sustainable existence.

Recall, however, that the average person on Earth has an ecological footprint of 2.7 hectares. There are more than 7 billion people alive today. If every one of them has a footprint of 2.7 hectares, this puts total footprint of humanity at around 19 billion hectares. In other words, human civilization is currently exploiting around 19 billion hectares of the Earth’s land and sea for all of its operations.

But wait, something seems wrong. Didn’t I just say that the Earth has only 12 billion hectares of sustainably useful land and sea? But why is human civilization using 19 billion hectares? What’s going on here?

The discrepancy in the Earth’s total biocapacity and human civilization’s total ecological footprint results in what is called unsustainable existence. At present, human civilization is degrading the Earth’s capacity to support life by operating with a deficit of 7 billion hectares.

If you divide 19 billion hectares by 12 billion hectares, you’d get something close to 1.5. This means that to sustainably support human civilization’s current operation, we’re going to need 1.5 Earths – that is, 1½ Earths. But we’ve only got one planet. This doesn’t sound good.

And it only gets worse. Remember that the world’s population is growing at an alarming rate. The human population growth rate in the year 2011 was estimated to be 1.8%. If this does not decrease significantly, then by the year 2016 the world population will be at 7.4 billion! Assuming the average ecological footprint per person remains at 2.7 hectares, by 2016 the total ecological footprint of human civilization is already 20 billion hectares. By then we’ll need 1 and 2/3 Earths!

But the assumption that the average ecological footprint per person remains at 2.7 hectares is unrealistic. All indicators show that as Third World countries emerge out of poverty, their ecological footprint will increase by as much as 400%. Assuming a steady rate of development in the Third World, the ecological footprint of the average person in the year 2016 will increase to 2.9 hectares. If 7.4 billion people each have a footprint of 2.9 hectares, this means that by 2016, humanity’s total footprint will reach 21.5 billion hectares. By that time, we’re going to need 1 and ¾ Earths to sustain such an operation!

One and three quarters Earths is hardly the size of the state of Texas. There goes the everyone-can-be-a-Texan scenario down the drain!

Here’s another way to play the game. It is widely known that for most people living in the developing world, the American lifestyle is the paragon of progress. For example, middle and upper class Filipinos show all the signs of wanting to live like Americans. But what does the American lifestyle cost planet Earth? Recall that the average American has an ecological footprint of 8.0 hectares. If all the 7 billion people alive today were to live like Americans, the total ecological footprint of human civilization would be a gargantuan 56 billion hectares! To support such a footprint, we’re going to need 4 and 2/3 Earths!

But what if we live like Western Europeans? They’re not as consumerist and wasteful as the Americans, after all. If we all live like the average Dutch, then our footprint per person will be 6.2 hectares (this will include the area of all the cannabis farms, oh yeah). If all the 7 billion people alive today were to live like the Dutch, then our total footprint as a civilization will be 43 billion hectares. We’ll be still running a huge deficit since the Earth has only 12 billion hectares to offer. To support 7 billion people living like the average Dutch, we’ll need 3 ½ Earths. It’s not as bad as the 4 2/3 needed when we’re going to live like Americans. However, 3 ½ Earths is still something we don’t have.

We have but one planet Earth. We have but one Pale Blue Dot.

That pale blue dot is all we have for now. And we are overtaxing it.

 

How Many Philippines Are We Gonna Need?

Now let us take the numbers game to the local level. Recall that the average Filipino footprint is 1.3 hectares. That is in fact a small number. If all of the 7 billion people alive today were to have a footprint that size, we’re going to need less than one Earth.

Sounds great? Nope. Here are the reasons why.

First, the fact that you are reading this implies that your footprint is probably larger than 1.3 hectares. How do I know this? Well, you have Internet connection at home, don’t you? If you don’t, at least you have money to spend on computer rental. Either way, the fact that you are reading this implies that you are more affluent that the average Filipino. As of November 2011, there are 101 million Filipinos alive. A person who can go online and read this essay is certainly in the upper quartile of that 101 million and even probably part of its upper 10%. (Yes, you don’t have to be rich to be part of the Philippine’s most affluent 10%. After all, ten percent of 101 million is more than 10 million.)

So yes, to have a 1.3-hectare ecological footprint you have to live like the average Filipino, which means you have to be really poor. Of course, Mr. or Ms. Average Filipino does not exist in real life, but if you take a quick look at the standard of living of most Filipinos, you will get an idea of how our hypothetical Average Filipino will live if he were alive.

Second, even with the seemingly small 1.3-hectare ecological footprint, we are already over taxing our beautiful country. According to the National Footprints Account, the Philippine islands and its surroundings seas have a total biocapacity exceeding 115 million hectares. That’s pretty big for a country the size of the Philippines. As a matter of fact, the Philippines contains nearly 1% of the world’s total biocapacity. This should be a small wonder given that the Philippine seas are among the richest in the world. However, all this richness is being degraded because we are running on an ecological deficit. If all the 101 million Filipinos alive today were to have a 1.3-hectare footprint, the national footprint of the Philippines will be 131 million hectares. This is obviously larger than the 115 million hectares we have. The difference between our national footprint and our national biocapacity translates to environmental degradation. Environmental degradation includes but is not limited to deforestation, land and water pollution, habitat and biodiversity loss and resource depletion. Also, because of our current economic set-up, this also translates to social inequity.

The Philippines is 3rd best in the world. In terms of deforestation, that is.

 

How Can We Save the Earth? How Can We Save the Philippines?

There is an umbrella answer to the questions above: We must reduce our ecological footprint. But how doe we do that? Now that is the subject for another post.

For now, the lesson I want all of you readers to take home is this: We can all fit in Texas, but we can’t all live in Texas. Since one obvious way to reduce our ecological footprint as a nation and as a civilization is to curb the population explosion, population management measures like the RH Bill are both important and urgent. Anyone familiar with the quadrants of priorities knows that such important and urgent bills must be top priority. Unfortunately, many people in power have very skewed sense of priorities. For those of you who know how to prioritize properly, I urge you to keep on supporting the RH Bill. The fight for the RH Bill is a fight not only for the Filipina mothers, it is also a fight for Mother Earth.

 

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The Most Powerful Force in the Universe (Part 2)


The RH Bill and Exponential Growth

In my article What the Debate on the RH Bill Should Not be About, I argued that overpopulation is a non-issue in debates over the passage of the RH Bill. There I reasoned that the battle over the RH Bill is a women’s rights battle and that overpopulation has little if anything to do with it. While I am still convinced that the RH Bill is a women’s rights issue, the following observations forced me to reconsider the relationship between the bill and the Philippine population problem:

  • The world population has exceeded 7 billion. What’s worse is that it shows no signs of stabilizing on its own anytime in the foreseeable future (contrary to the claims of the laissez-faire advocates).
  • The successful population management measures in many countries around the world, particularly in neighboring Thailand and Vietnam, have yielded very positive effects. In fact, the said countries have already overtaken the Philippines in terms of social and economic progress.
  • Our legislators, particularly Senator Sotto, continue to use overpopulation denial myths as arguments against the passage of the RH Bill.
  • Conservative estimates have pegged the Philippine population at 101 million as of July 2011.[1]
  • The Philippine population grew by 1.904% in the year 2011.[1]

The above observations should be enough to convince any rational person that the RH Bill is not only important but is urgently needed. Sadly, many of our politicians aren’t really of the rational sort.

 

Seven billion. That's a pretty big number, dontcha think?

 

Sotto Voce?

On a Senate interpellation on the RH Bill held last December 5, Senator Tito Sotto parroted the same old ridiculous arguments that supposedly prove that the world is not overpopulated. Worse still, Sotto went as far as to claim that the world would never experience overpopulation. In his own (?) words, “These people think that they are smarter than God. Sa tingin ba nila gagawa ba ang Diyos ng mundo na mapupuno? [Do they think God will create a world that will be overpopulated?]”

"Dapat bang maging senador 'to?" "HINDE!!!!11!!!1!!"

Sotto’s argument is blatantly invalid in two ways. First, it is legally invalid; such a theological argument has no place in a secular interpellation (and that goes for you too, Senator Miriam Santiago). The fact that such a theological argument can be used in a Senate interpellation without drawing any objections from the other senators is enough to give any secularist a conniption. Second and perhaps worse, Sotto’s argument is logically invalid; it does not follow that if there is a god, then that god will create a world that will never be overpopulated.

Setting aside the invalidity of his arguments, Sotto’s claim that the Philippines will never be overpopulated is also demonstrably, disturbingly and dangerously false. The key to debunking Sotto’s absurd claim is contained in just two words: exponential growth.

 

Three Chinas in a Philippines

This year, the Philippine population experienced a growth of 1.904%. If this population growth rate is maintained, the Philippine population will double in a mere 36 years and 9 months – around 37 years.[2] If there are 101 million Filipinos alive today, that means there will be 202 million Filipinos alive 37 years from now. Give another 37 years (that’s 74 years from now) and there will be 404 million Filipinos alive. Fast-forward to another 37 years (111 years from now) and our population is already at 808 million; by then our population is rapidly speeding toward the 1 billion mark. Does this pattern sound familiar? Why of course, it is nothing but the geometric progression that we’ve met in Part 1 of this article. By now you should know that if our population keeps on growing in such a pattern, then we’re in for a lot of trouble.

Shown below is a table of the projected population of the Philippines in the next two centuries under the assumption that our population growth rate remains steady at 1.904%.

Table 1
Year Population
2011 101 million
2048 202 million
2085 404 million
2122 808 million
2159 1.616 billion
2196 3.232 billion

 

Under this steady growth rate scenario, the Philippine population would exceed 1 billion somewhere around the year 2130. Our great grandchildren, perhaps even some of our grandchildren, would still be alive at that time and would be among the 1 billion Filipinos trying to fit inside a country 32 times smaller than China. By the end of the 22nd century, the number of people trying to fit inside the Philippines is more than thrice the number of people living in China today. By the year 2500 the Philippine population is already, quite simply, astronomical. Now matter how look at it, the Philippines can be overpopulated and it will be overpopulated if we will do nothing about our population growth rate. Take that, Tito Sotto.

 

The Philippine Population Growth Rate: Good News and Bad News

Three objections can be leveled against the previous hypothetical scenario. The first one goes like this: Malayo pa naman ang taong 2196 ah, bakit natin po-problemahin yun? [The year 2196 is still many, many years away, why should we bother about what’s going to happen then?] The degree of myopia implied by this objection is, sad to say, exhibited by many of our politicians and citizens. This can be remedied only by good moral education. But this remedy takes a long time, perhaps several generations. We need to act on the problem now. The only way to expedite the solution is to replace our myopic politicians with wise, far-seeing leaders. For this purpose we have the democratic process of voting our future leaders.

The second objection is worse than the first: Malapit namang magugunaw ang mudo. Bakit pa tayo magpapakahirap sa pag-ayos nito? [The world is going to end soon anyway. Why waste your effort making it a better place?] Unfortunately, many people, some of them even intelligent, sincerely hold this view that the world is ending soon. It is our job as freethinkers and as people who love the earth to think of creative ways to convince these people to care for the future of our planet. We might need to convert them to freethought or to more liberal versions of their religion. We might also try to convince them that if they believe that the god they love created this world, then they should do everything to take care of it. Whatever our strategy is, we must do everything we can to decrease the number of people who believe the world will end soon because if we don’t, then it surely will.

The third objection is a rational one: The steady growth rate scenario is an oversimplification because the Philippine population growth rate isn’t really constant but is in fact decreasing. This objection is in fact valid. (It does not, however, negate the fact that the scenario in the previous section disproves Tito Sotto’s claim that the world will never be overpopulated.) Official records show that the Philippine population growth rate has been on a general trend of decline over the past decades. The Philippine population growth rate over the past few years is shown in the table below. [3]

Table 2
Year Population Growth Rate
1970 3.08%
1980 2.71%
1990 2.35%
2000 2.36%
2007 2.04%

 

There is good news and bad news in the trend of the population growth rate.

Let’s begin with the good news. The decline in our population’s growth rate is either an effect or an indicator of the following:

  • Our government’s previous family planning programs have been, to a certain extent, effective.
  • Filipino women have been slowly gaining empowerment over the past decades.
  • The Filipino youth have been slowly gaining accurate RH information in recent years.
  • Philippine cultural values have shifted from the valuing the quantity of life to valuing the quality of life.
  • The Church’s anti-contraceptives stance is quickly losing support among Filipinos.

Now off to the bad news. I will first state them in somewhat technical language. Later I will unload them in layman’s language. Here they go:

  • While fertility rates have been steadily declining in middle- to high-income families, the fertility rates in low-income families have not dropped; in fact, studies show that they have increased in the period between 1997 and 2000(see Reference [7]).
  • The disparity between our country’s fertility rate (somewhere between 2.79 and 3.19[4]) and population growth rate (1.904%) is an indication that there remains a high infant mortality rate in the Philippines.
  • The decline in our population growth rate is better modeled by a decreasing exponential and not a decreasing linear plot.[5]

Now let us explain the bad news in layman’s language one by one.

First bad news: Families with means voluntarily undergo family planning while poor families continue to have more babies than they can feed. (But who doesn’t know this already? Apparently the anti-RH camp.) So even though the population growth rate of the Philippines is declining on average, the decline is not uniform across all income levels.  This causes the top of the social pyramid to become thinner and the base to become wider. If this keeps on going, this means that in the near future our society will be composed of fewer and fewer people with means and more and more people who cannot feed their families. (Wait, am I describing the future here or the present?) An economist of any feather will tell you that this is really bad news.

A Philippine porridge line. (AP Photo/Aaron Favila)

Second bad news: If there are many children born for every woman in the Philippines, then why is our population not growing as rapidly as it should? Surely this is not because of an increased natural death rate; our natural death rate is in fact declining. The only explanation available is that many infants are dying. High infant mortality rate is an indication of high birth rates among low-income families. That brings us back to bad news number one.

Third bad news: Yes, our population growth rate is decreasing, but its rate of decrease is slowing down over time. This means that as years go by, it won’t decrease fast enough to curb our growing population. For example, by year 2100, our population growth has decreased but is still at 1.52%. That’s 89 years from now when our population growth rate is at 1.904%! End story: our population will keep on growing exponentially if we do nothing about it. The decline in population growth rate is not enough to curb the exponential population growth that has been going on for decades now.

The graph below shows the projected Philippine population in the coming decades as assessed by the U.S. Census Bureau. According to the graph, the Philippine population will be at 150 million in the year 2050. Note that this projection is around 75% of the value projected in Table 1 for the year 2048.

Projected growth in Philippine population. From the U.S. Census Bureau.

 

Lessons From the Losing CEO

If we learned anything from Part 1 of this article, then it is that one should never underestimate the power of exponential growth. We are therefore faced with the following fact: Our population is already at 101 million and it continues to grow exponentially. Even if our population growth rate is declining, it is not declining fast enough to curb the dangerous rise in our numbers. Worse still, studies show that while families with means tend to have fewer children, poor families tend to have many.

But we’ve seen that there’s good news. As long as you give families and especially women the freedom to choose, they will choose to keep their family size manageable. This is shown by the significant decrease in the fertility rates among middle to upper class women over the past decades. Poor families and poor women in particular, however, still do not have the means and the freedom to choose the family planning method that suits them best. This explains why the fertility rate among low-income families remain dangerously high. All the facts indicate, however, that if we give them the power to choose, low-income families will voluntarily plan families of manageable sizes (1-4 children). Note that they will do this for their own good without knowing that they are, in effect, helping to solve a national problem.

Herein lies the magic of the RH Bill: It solves two different problems in one stroke. On the one hand, it will give poor families the power of options in planning their family. On the other hand, its end effect will be the curbing of our population growth. The RH Bill will do these and more. At the most basic level, the RH Bill will give women their basic rights to family planning services and it will give the youth their basic rights to scientific and age-appropriate education.

 

The RH Bill: An Urgent National Concern

Never forget that one does not kid with exponential growth. If we are to secure our future as a country, then we must manage our population now. In fact, we should have started decades ago.

Congress and Senate must pass the RH Bill by January of next year, or else it will be too late. Remember, we are racing against time in our battle against the most powerful force in the universe.

Reproductive Health = our Republic's Health.

* * *

 

Notes:

[1] Taken from the webpage of index mundi, Reference [4]. See also References [5] and [6] for official data.

[2] The equation for any kind of exponential growth is similar to that of compound interest: FV = PV(1 + i)n. Here, FV is the future value (of an investment or of a population), PV is the present value, i is the rate of increase and n is the number of times the value is increased. In our case, PV is 101 million, the present population of the Philippines. If it doubles, this means that FV is 202 million. Meanwhile, i is 1.904% = 0.01904, the population growth rate. We want to solve for n, the number of years it takes for PV = 101 million to become FV = 202 million. This is accomplished by dividing both sides of the compound interest equation by PV, then taking the logarithm of both sides and then finally using the properties of logarithms. The solution is going to be n = 36.75.

[3] See References [5] and [6] for the official estimates. Reference [4] provides more recent, unofficial estimates. Reference [8] provides projections based on UN studies.

[4] The high estimate is from Reference [4], the low estimate is from Reference [8].

[5] The best fit exponential curve in the population growth rate has an equation of f(x) = (2×10-7)e-0.01x with coefficient of determination R2 = 0.935. I tried the best-fit linear curve, and its coefficient of determination is only at R2 = 0.932; even then, the slope of the linear trend line is negligibly small so that difference between the predictions of the linear plot and those of the exponential plot will not be very great.

* * *

References:

[1] Miller, G. Environmental Science, 10th ed, 2005.

[2] Campbell, N.A., Reese, J.B. and Mitchell, L.G., Biology, 5th ed, 1999.

[4] Index Mundi. <http://www.indexmundi.com/philippines/population_growth_rate.html>, accessed 15 December 2011.

[5] National Statistics Coordination Board. <http://www.nscb.gov.ph/secstat/d_popn.asp>, accessed 15 December 2011.

[6] National Census Data via the National Statistics Office. <http://www.census.gov.ph/data/sectordata/popproj_tab1r.html>

[7] Asian Development Bank, Poverty in the Philippines: Income, Assets and Access. 2005.

[8] Costello, M.P. and Casterline, J.B., Fertility Rate Decline in the Philippines: Current Status, Future Prospects. 2005

 

 


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The Most Powerful Force in the Universe (Part 1)


A Tale of the Two CEOs

One day, two bold CEOs decided to play a game of chess where the winner gets to ask anything he wants from the loser. After the game, the winning CEO asked the losing CEO to choose between two payments. The first payment involves the losing CEO giving half of his company’s assets to the winning CEO. The second payment involves placing 1¢ in the first square of the chessboard, 2¢ in the second square, 4¢ in the third, 8¢ in the fourth and so on until all the 64 squares of the chessboard are filled. Thinking that it will allow him to get off easy, the losing CEO agreed to the pay the winning CEO the second reward. But the losing CEO made a very serious mistake. In the process of trying to pay the winning CEO the reward, the losing CEO ended up going bankrupt and buried in debt. In fact, the losing CEO may never be able to give the reward money even if he spends his whole life working for it.[1]

 

Double, Double, Double….Jeopardy!

Human intuition evolved to understand linear progressions and patterns only. For many everyday purposes, this intuition is a quick and effective tool in assessing odds and projecting future values. The losing CEO’s big mistake is that he used the said intuition on an example where it is not applicable, an example that involved not a linear progression but a geometrical one.[2]

When you add up the terms of an increasing geometric progression, what you get is exponential growth.[3] As with geometric progressions, the human brain is notoriously ill equipped in understanding the power of exponential growth. This is shown by the fact that, without the aid of mathematics, almost all of us find it difficult to understand why the losing CEO made such a grave error. In order to comprehend the gravity of the losing CEO’s mistake in choosing the second payment option, let us get rid of our intuition for the moment and let us turn to mathematics.

Imagine starting with x of something. If you double that number, it becomes twice the original, 2x. If you double the previous result, you get four times the original, 4x. If you keep on doubling the most recent result, you’d successively get 8x, 16x, 32x, 64x and so on. Notice that doubling once gives you 2x or 21x while doubling twice gives you 4x or 22x. Meanwhile, doubling thrice gives you 8x or 23x and doubling four times gives you 16x or 24x. Following this pattern, we can see that doubling x an n number of times gives you 2nx.

 

Paal Paysam's chessboard.

Recall that the losing CEO started with a mere 1¢ (that is, x = 1¢). By the 8th  square (the last square in the first row) he is required to double the original 1¢ seven times. This means that he must place 27 times 1¢ on the 8th square. Using a simple calculator, one can easily confirm that 27 = 128. This means that the 8th square must contain 128¢ or $1.28. So far, the losing CEO still feels he’s having it easy. However, when he reaches halfway through the chessboard (the 32nd square), he would have doubled the original value 31 times. This means that the 32nd square must contain 231 times 1¢. Using a calculator, one can compute that this amounts to 2 147 483 648¢ or around 21.5 million dollars! But the tragedy of the losing CEO is only beginning; even though at this point he is halfway through the chessboard, the losing CEO is still very far from paying half his due. By the time he reaches the last chess square, he is going to need a whopping 92 million billion dollars! But wait, there’s more. The said 92 million billion dollars is for the last square only. Adding up the amount of money he must place on all 64 squares of the chessboard, the total amount of money the losing CEO owes the winner is approximately 184 million billion dollars![4]

 

The Curious Case of Exponential Growth

Here’s another example of how wildly counter-intuitive exponential growth is. Imagine starting with a piece of paper (of thickness 1.0 mm). Fold that paper into two halves so that its new thickness is twice the original. Now fold it again so that its thickness is four times the original. If you repeat this process just 42 times,[5] you end up with a piece of paper that will extend from the surface of the earth of the surface of the moon!

 

Going expo.

 

A very peculiar aspect of exponential growth that the human brain finds so hard to understand is the fact that if something grows exponentially then the present value is greater than all the previous values combined. For example, notice that the amount of money the losing CEO must place on the 5th square, for example, is greater than the total amount of money he must place on the 1st, 2nd, 3rd and 4th squares. This is true even for the 64th square – the amount of money it must contain is greater than the sum of the contents of the remaining 63 squares.

 

Exponential Crises

Albert Einstein once said, “The most powerful force in the universe is compound interest.” Since the mechanism behind compound interest is exponential growth, the previous example shows that Einstein’s humorous hyperbole is only partly so.

Big companies, especially banks, tap into the power of exponential growth to get rich. But big companies pay decent sums to their actuaries and analysts to deal with the number shuffling involved in compound interests (in the interest of compounding their profit and compounding your debt). In the absence of such expertise, unaided human intuition will more often than not fail in assessing problems involving exponential growth.

An individual’s failure to appreciate the power of exponential growth usually leads to debt crises.  The losing CEO is just one (rather fantastic) example of the victims of the human brain’s inability to grasp exponential growth. To give a more common example, the many people who are buried in credit card debts are similarly victims of the failure of human intuition to grasp the full force of compound interest and the mechanism behind it, exponential growth.

In many ways, the losing CEO represents human civilization. Many of the problems we face today as a society stems from our failure to assess the power of exponentially growing quantities around us. Like the losing CEO, we use our linear human intuition to analyze situations involving geometric progressions and we end up engulfed by the problems this wrong judgment caused.

Three of the greatest problems caused by our failure to grasp exponential growth are:

  • the human population explosion
  • the rapid (or should I say rabid) increase in human demand for resources leading to the even more rapid depletion of natural capital
  • the rapid increase in industrial activity leading to uncontrolled increase in the generation of pollution and waste

I will write about the other two global problems in future articles. In Part 2 of this article, however, I will concentrate on the first and perhaps most important the three – human population explosion. I say it is the most important because it is the key to solving the other two problems; the problems of resource depletion and environmental degradation cannot be fully addressed without addressing population explosion. Finally, it is the human population explosion that I will write about in Part 2 because it is an urgent national issue that is intimately related to the debates regarding the passage of the RH Bill.

 

Click here to read Part 2.

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Notes:

[1] Adapted from a version of the legend of Paal Paysam told on Reference [1].

[2] An arithmetic progression is a sequence of numbers in which the next number in the sequence is just the previous number plus a constant. Examples are the sequence {1, 2, 3, 4, 5, …} and the sequence {4, 7, 10, 13, 16, …}. In the first progression, the constant being added is 1 while in the second it is 3. A geometric progression, on the other hand, is a sequence of numbers in which the next number in the sequence is just the previous number times a constant. Examples would be {5, 15, 45, 135, 405, …} and {2, 4, 8, 16, 32, 64, …}. In the first sequence, the constant being multiplied is 5 while in the second it is 2. Notice that the second progression is simply the progression our losing CEO is having a problem with. Geometric progressions, however, can also be decreasing, just like the sequence {4, 2, 1, ½, ¼, …}.

[3] The sum of the terms of an increasing geometric progression increases exponentially as you increase the number of terms being summed up. For those who know their math jargon, this can be expressed by saying that the partial sum of a monotonically increasing geometric series diverges. The result for a decreasing geometric progression is similarly tricky to the human intuition and is at the root of Zeno’s Paradox. The apparent Paradox is resolved if one understands that a sum of infinitely many numbers can be finite if the numbers being summed up form a decreasing geometric progression. That is why 4 + 2 + 1 + ½ + ¼ + … = 8, even though you are adding infinitely many numbers.

[4] For those who recall their college calculus, the formula for the nth partial sum of a geometrical series with 1 as its first term and 2 as the common ratio is given by the formula sn = (rn – 1)/(r – 1). Here, r = 2 and n = 64. The total amount of money the losing CEO must place in all the 64 squares of the chessboard is just equal to the partial sum sn.

[5] Douglas Adams is God.

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References:

[1] Miller, G. Environmental Science, 10th ed, 2005.

[2] Arfken, G. B. and Weber, H. J., Mathematical Methods for Physicists, 5th ed, 2001.

 

 

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