Fascinating results from an effort by the Gapminder Foundation called ‘The Ignorance Project‘. Gapminder provides a software tool for studying global health statistics and the foundation’s Dr. Hans Rosling speaks widely on related topics, like demographics and economic development.

Gapminder has conducted a survey in the US, UK and Sweden probing adults’ knowledge of the state of global health.

For example, the survey asked “**In the last 30 years the proportion of the World population living in extreme poverty has…**” and then gave three options: ‘**almost doubled**‘, ‘**more or less stayed the same**‘, and ‘**almost halved**‘. (Actually, in the UK the options were ‘increased’ and ‘decreased’ instead of ‘almost doubled’ and ‘almost halved’.)

23% of the people in Sweden knew that global poverty has decreased dramatically. In the UK, 10% of people knew that (12% of UK university graduates). And in the US, only 5% of people knew that. Results like these were the basis for new articles like: ‘United States Scores Poorly on Global Ignorance Test‘.

But on questions like ‘**What is the life expectancy in the world as a whole today?**‘, the results were the opposite. In that case, 56% of Americans knew that the answer was about 70 years. 30% of Brits knew that. And 22% of Swedes knew.

Interestingly, the percentage of university-educated Brits who knew the world average life expectancy was only 20%, *lower* than the British population as a whole.

With the Olympics starting soon, I thought it would be fun to compare the results to see which of these three countries is actually the best informed and which is the least. Unfortunately, the survey did not ask all the same questions, or offer the same choice of responses, in all three countries. But five questions were the same, including the two above. Another was, ‘**What % of adults in the world today are literate, i.e. can read and write?**‘

OK, first of all, I think if you need the interviewer to define the word ‘literate’ for you, maybe you are not the best person to ask about statistical trends in global demographics. For this question, the Swedes and Americans were given three options: 40%, 60% or 80%. The Brits were also given the choice of 20%. Twenty-two percent of Americans chose the correct answer (80% literacy). 20% of Swedes did, and only 8% of Brits did (with only 4% of university-educated Brits knowing the right answer).

Two things to note here: One is that the survey did not talk to every Swede and every Brit – it only asked a little over 1000 of each (including 400 Brits with university educations). So, we do not know if slightly more Americans actually knew the correct answer than Swedes. With a sample size of about 1000 people, the margin of error is somewhere around 3%. So, it is not fair to give the US the ‘gold medal’ for this question since, statistically speaking, the Swedes did just as well.

Secondly, the Brits were given 4 options instead of three, so it is understandable that people did not do as well. Nevertheless, a 4% correct response rate from university-educated Brits to me seems appalling. Even the proverbial chimpanzees throwing darts at a dartboard would select the right answer from four choices 25% of the time.

So, I think it’s fair to compare countries’ responses to Chimpanzees (that is, to how choosing randomly would have performed). For this question, the Chimps would get the Gold medal, the US and Sweden (who answered about the same) shared a Silver medal, and the UK got the Bronze.

For the questions about Literacy and Extreme Poverty, the Chimps also win the gold medal. And the US wins the gold for the question about Life Expectancy. The other two questions were ‘**How many [babies] do UN experts estimate there will be by the year 2100?**‘ where 11% of Swedes (and 33% of Chimps) knew the answer was 2 billion, and ‘**What % of total world energy generated comes from solar and wind power?**‘ In that case, 56% of Swedes, 46% of Americans, and 33% of Chimps knew the right answer. (Again, the UK was given more options, so the comparison is not entirely fair, but 30% of Brits and 37% of university-educated Brits knew the right answer, so I said that Brits and Chimps shared the Bronze on this one.)

Additionally, Americans and Swedes were asked 5 questions that were not posed to the Brits.

One asked how many babies are born to each woman, worldwide, on average. 49% of Americans knew the answer was 2.5, but only 29% of Swedes did. When asked to choose which population distribution was correct from a set of maps, Americans, Swedes and Chimps all answered about the same.

On the last three questions, How many years of formal education women get worldwide, the percentage of children vaccinated against measles, and the worldwide income distribution, the Chimps all win, with Americans coming in second place and Swedes last.

Of these ten questions (of which the UK only participated in 5 and were generally given more options than the Americans or Swedes) the finally tally of results looks like:

It turns out that Chimps answered best on 7 of the 10 questions. I would say that the performance in the US and Sweden was essentially the same. And the UK seems to lag, though to be fair they only participated in half the questions and, even then, had more options to choose from.

Most surprising to me was that, in questions that were posed to Brits, the general population performed better than university graduates on most of them, which makes me think that maybe we should all be sending our children to Monkey College instead.

Here is an interesting little recipe I found in an old notebook. Unfortunately, I did not write down where I got it from, or if I just thought it up, or what.

Start with “0″. At each step, if a character is a “0″, replace it with “1″. If “1″, replace it with “10″.

So, the results are:

Step 1. **0**

Replace the “0″ with “1″, so we get:

Step 2. **1**

If a character is a “1″, replace it with “10″, so we get:

Step 3. **10**

If a character is a “0″, replace it with “1″. If “1″, replace it with “10″. So, the “1″ becomes “10″ and the “0″ becomes “1″, to give us:

Step 4. **101**

(Do you see what happened there? The “1″ was replaced by “10″ and then the “0″ at the end was replaced with a “1″.) Repeat again: “0″ -> “1″ and “1″ -> “10″. This gives us:

Step 4. **10110**

Step 5. **10110101**

Step 6. **10110101 10110**

And so on and so on.

Two interesting things: One is that each step (Step 6) is simply the text from the previous step (Step 5) with the text from the step before that (Step 4) added to the end. So:

Step 7. **10110101 1011010110101**

Also, the ratio of 1′s to 0′s in each step approaches **phi**, the Golden Ratio.

In Step 4 there are three 1′s and two 0′s. 3/2 = 1.5

In Step 5: the ratio is 5/3 = 1.6667

In Step 6: the ratio is 8/5 = 1.6

In Step 7: the ratio is 13/8 = 1.625

These are all Fibonacci Numbers: 2, 3, 5, 8, 13, and the ratio of one Fibonacci Number to the previous one approaches the Golden Ratio, which is the ratio of Adults to Kids in an extended Lotka-Volterra model of predator-prey dynamics.

It seems exceedingly strange to me that the ratio of 1′s to 0′s approaches an *irrational* number even though the recipe only involves swapping each “0″ with “1″ and each “1″ with “10″.

Now I really wish I had written down where I got this recipe from.

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*This post from BoingBoing says that the aspect ratio of human eye’s field is about 16:10 width-to-height (or 1.6, which is maybe why people find the Golden Rectangle aesthetically pleasing). In some previous photo posts of mine, including this picture of an insect and this one of a car, I used a photo size of 550 x 170, which is 2 times Phi.*

Sometimes, focusing on solving one set of problems causes another set to pop up. Call it ‘firefighting’. By treating the worst-off patients, the slightly better off become neglected. By only taking care of the most severe issues, we draw time and resources away from issues that are becoming severe. Things tend to get better in the short run, but worse in the long run.

Here is a visual representation of a mathematical model of this issue. Each box (or ‘bathtub’) represents the number of issues in each category: some are Non-issues, some are Mild Issues and some are Severe Issues.

An issue moves from one category to the next by way of one of the pipes that connect the bathtubs. Each of these pipes contains a mathematical equation that governs how quickly issues pass through it from one bathtub to the next. In each of the green-colored pipes, the rate that issues move is simply a fraction of the number of issues upstream. So, we say for example that 5% of Mild Issues become Severe Issues each month and, say, 10% of Severe Issues become Mild Issues.

The only pipeline that works differently from this is the orange one – the rate at which Nonissues become Mild Issues. In that case, let us say that rate is some fraction (again, 10% works) of the number of Nonissues (just like the other flow rates, so far), but multiplied by the number of Mild Issues squared. So, instead of ’10% x Nonissues’, the equation is ’10% x Nonissues x MildIssues^2′. Some diseases and health problems work this way. If you are a nonsmoker who lives with a smoker, you might have a 10% chance of becoming a smoker each year, but if you live with *two* smokers, your chance goes up to 40% each year and if you live with *three* smokers, it goes up to 90%. The idea is that mild problems recruit new mild problems. Neglecting that slow oil leak in your car’s engine might mean a 10% chance of an engine problem this month, but neglecting both the oil leak and the dirty filter might make that chance go up to 40%.

We can choose these percentages so that the number of issues in each category is constant – one Non-issue becomes a Mild Issue for each Mild Issue that becomes a Non-issue. What happens to the number of Severe Issues as we increase the rate at which Severe Issues are moved into the Mild Issue category?

The graph above show what happens to the number of Severe Issues when we increase the fraction of Severe Issues that are turned into Mild Issues each month from 10% to 15% (starting midway through the first time period). In the short run, the number of Severe Issues drops, since we are treating 15% of them, rather than 10%. But in the long run, this causes the number of Severe Issues to increase.

What is happening here is that, by moving Severe Issues into the Mild Issue category, we are increasing the rate at which Non-issues become Mild Issues. For example, by treating someone’s acute respiratory infection, we get them back on the street sooner to infect more people.

I am not saying that we should neglect Severe Issues or not treat them at all. One lesson from this model is that by increasing the acute care without following through and also increasing the rate of Mild Issues becoming Nonissues makes the problem worse in the long run than it would have been by not increasing acute care at all. It would be especially perverse if things played out slowly enough that the person who made the decision to focus more on treating Severe Issues had gotten all the credit for the short-term improvement and then moved on, or retired, before the next person stepped into the position to take the blame just as the negative consequences of that decision just started to appear.

It is interesting to see this ‘better-before-worse’ behavior in such a simple model. I might spend some time whenever I can trying to find even simpler structures that show similar behavior.

There’s an old parable about blind men trying to figure out what an elephant looks like. One man feels its trunk and says an elephant is like a snake. Another feels the leg and says an elephant is like a tree. And so on.

Likewise, a lot of different behavior patterns are commonplace in the world. There’s **Exponential Growth** and the **S-Shaped Plateau**, **“Peak” Behavior** (like Peak Oil) and slow **Stagnation**. Economists and ecologists and epidemiologists, etc, have come up with mathematical descriptions for each separately.

All of these, though, I think can be thought of manifestations of the same underlying process – different behaviors of the same elephant. This is what I think that elephant looks like: A **Non-Renewable Resource** gets converted into a **Usable Good**, which can then be used up or destroyed. Visually, this can be represented as:

Think about ‘Crude Oil’ being converted into ‘Gasoline’, or ‘Potential Buyers’ of a product being converted into ‘Current Owners’.

There are actually several ways I have found that S-shaped growth can happen – and ways it can look like **Exponential Growth**, **Stagnation** and so forth – and all are derivatives of the diagram above.

When the Non-Renewable Resource is available in essentially unlimited supply and the growth is restricted by some ‘carrying capacity’, then the structure above reduces to the following:

One way to represent ‘effect of remaining capacity’ is simply ’1 – (Yeast Cells / max Yeast Cells)’. The growth rate is some constant (say, 0.05) multiplied by this effect. Thus, when the number of yeast cells is small, the growth rate is highest (near 5%, in this case) and as the population grows, the growth rate declines.

If cells can die, and the death rate goes up as the population goes up, this also gives S-shaped growth.

This is similar in concept to the birth rate declining as the population grows, but instead affecting the death rate.

A delay in a system can sometimes be thought of as similar to riding on a conveyor belt. You get on the conveyor, ride for a while, and then get off. For example, a house is built in one year, exists for 30 or 40 or 50 years, and is then pulled down to be replaced by a bigger, newer building.

If there is growth in the number of houses being built, it will take 30 or 40 or 50 years for the number of houses being replaced to catch up. In the intervening time, the number of houses in existence can be an S-shaped profile.

Finally, when there is a Non-renewable Resource and the Good it generates can decay, the system can exhibit and S-shaped profile. In the example below, the rate of buying (the rate at which Nonowners become Owners is simply ‘f * Nonowners * Owners’, where ‘f’ is a small fraction.

If Owners can never become former Owners, then the number of Owners will show a S-shaped profile. If a small portion of Owners disappear each time period, then then S-shaped profile will be followed by a long period of perpetual stagnation, like what is shown in the figure below – a simulation of the model above with f = 0.00005 and ‘becoming former Owners’ being 0.001 of the number of Owners.

In this graph, we can see all of the parts of the elephant: initially Exponential Growth, followed by S-Shaped Growth, followed by a peak, followed by a long period of Stagnation. Modeling the behavior of the system simply a matter of finding the variation of the models above that most closely resemble the structure of the real system. I think that many physical, social and economic patterns fit this profile in the long run – stock prices of companies, populations of countries – but we often only see a small selection of the overall behavior profile and mistake the elephant for being just a trunk or a leg.