Archive for the ‘Uncategorized’ Category

Two Futures

I found this article from 1998 online, ‘The Simple Economics of Easter Island‘, by James Brander and M. Scott Taylor.

The authors consider some small South Pacific islands, especially Easter Island, and have built a simple mathematical model that they claim helps explains the island’s growth and decline in human population from its settlement around the year 400 AD until the arrival of Europeans in the 18th Century.

The model is a version of a predator-prey system with people as the hunter and forest as the prey. The forest would naturally grow exponentially at a rate of about 4% per decade, but its actual growth rate is constrained by a ‘carrying capacity’, the maximum area of trees the island can sustain when it is completely covered in forest. As the forest cover increases toward the island’s carrying capacity, the growth rate of additional forest slows down.

People harvest the forest as one of their resources. In the absence of any harvesting, the human population would decline 10% per decade. Population is gained in proportion to the amount of resource harvesting.

The equations in the model are shown below

‘Resource’ is the number of (acres of) trees on the island and ‘Population’ is the number of people on the island. ‘b’ is the fraction of people involved in harvesting trees (so, ‘b x Population’ is the number of people involved in harvesting trees) and ‘a’ is their ‘harvesting productivity’, according to the authors.

Why does the harvesting rate depend on the number of trees? One reason is that the higher the number of trees, the easier it is to harvest them (and vice-versa). As the number of trees drops, workers must go further from their homes to access the remaining trees and use more time to bring the wood back to the village.

The authors suggest that 40% of the population is involved in harvesting resources. “Various pieces of evidence suggest that the resource sector probably absorbed somewhat less than half the available labor supply. A value of 0.4 for B is probably in the reasonable range.”

These equations and parameter values reproduce what the authors claim was the basic population dynamic over 1500 years of Easter Island history. A small population grew to about 10,000 people by the year 1200 and then slowly declined to around 3000 people by the time of first contact with Europeans.

I am interested in the values of Population, Resources and ‘harvesting Resources’ if we run the simulation for a long time. For the case of b=40%, the Population will eventually settle down to around 4790 people and the resource reaches about 6250 acres of trees (just over half the carrying capacity) if we run the calculations long enough. Thus, there are about 1.3 acres of trees per person. The long-term harvesting rate is about 0.025 acres (about 10 meters by 10 meters) per person per year.

What if the value of ‘b’ (the portion of the population involved in resource harvesting) was some other value, like 20% or 80% or 100%? What would happen to the Population, and Resources per person?

The graph below shows the long-term (that is, ‘equilibrium’) Population for various values of ‘b’.

If ‘b’, the fraction of people who are involved in harvesting resources, is less than about 20%, the population eventually falls to 0, as the rate of losing population always exceeds the rate of gaining population. For this model, the largest sustainable population is about 4800 people when ‘b’ is 42% and it falls to about 3166 as ‘b’ rises to 100%.

One measure of the prosperity of the Easter Island society is the number of acres of forest per person (that is, the quantity ‘Resources’ divided by ‘Population’). The forest serves not only as a source of wood, but also as a habitat for birds and nuts the islanders can eat, so more trees per person is, in itself, a measure of how prosperous the society is.

The graph below shows the long-term (‘equilibrium’) ratio of Resources / Population for various values of the ‘b’ parameter. When 40% of the population is involved in harvesting resources, the Population eventually reaches its largest possible long-term value. That point is marked with a dark blue dot on the graph.

Raising the portion of the population harvesting resources above 42% causes the equilibrium population to decrease and also causes the Resources/Population to decrease. When 100% of the population is involved in harvesting resources, the population settles down to about 3166 and the Resources/Population to about 0.8. (That point is marked with an open circle.)

There is another value of ‘b’ that also results in a long-term population of 3166 and that is when the portion of people harvesting resources is around 26.3%. In that case, the Resources/Person is about 3.

Another measure of the prosperity of the society is the per-person rate of harvesting resources (‘harvesting Resources’ / Population). The forest is a source of wood, which is useful for making houses, canoes, tools and fire. So, the amount of forest cut down per time tells how much wood is available per person. Interestingly, for all of the different ‘b’ values above 20%, the long-term ‘Harvesting per Person’ is exactly the same: 0.025 acres per person per year.

So, depending on the value of ‘b’, two different Easter Islands are possible. In one, the portion of the population harvesting resources is at or below 40%, the resources per person is 1.3 or more, and the forest covers at least half of the island.

In the other version, the portion of the population harvesting resources is above 40%, the resources per person is below 1.25, and the forest covers less than half of the island.

Which version of the island would you rather live on?

The good news is that, in this model, is it possible to reversibly switch from one version of Easter Island to the other, although it can take several hundred years for the system to settle down and the population can change (read: drop) dramatically during the transition.

The most efficient organization is not necessarily the most effective. It might sound crazy, but it is straightforward to show that it’s true.

Think about a charity run entirely by volunteers that provides meals to hungry people. This charity receives $1000 per month in donations, which they use to buy meals for hungry people. Food is literally their only expense. They wish to increase the monthly money available for buying meals, so they decide to start advertising to bring in more donations. They find that when spending no money on advertising, they got no advertising-driven donations (obviously). By spending $100, they can get $300 in advertising-driven donations. By spending $225, they can get $450. And by spending $400, get they can get $600. How much advertising should they do?

The first $100 in spending will bring in $300. These donations, minus the $100 in advertising cost, leaves $200 extra to provide meals. Spending $225 brings in $450, leaving $225 extra to provide meals. And spending $400 generates only $200 extra after the advertising cost is paid. So, of the three, the maximum amount of money to provide meals comes from spending $225 per month. This is the optimal amount of money for this charity to spend on advertising.

[These numbers follow the ‘square root rule of advertising’ by the way, specifically REVENUE = 30 x SQRT(SPENDING). If you are inclined, you can check for yourself in Microsoft Excel that, for this particular case, the extra money for meals (donations minus advertising spending) is the highest when advertising spending is $225.]

By spending $225, they can take in $450, giving $225 more than they would have had otherwise. By advertising, they have $1225 rather than $1000. But, charity organizations are often judged by the portion of their donation that goes toward “The Cause”, the purpose for which they exist, as opposed to business expenses like office space, staff salaries and marketing. If they do not advertise, 100% of their income goes to food. If they do advertise, then only $1225/1450 = 84% of their income goes to food.

By increasing the amount of service delivered, the charity reduces its efficiency.

Let’s say our charity makes an effort to get better at advertising, to better understand potential donors and get more bang for its advertising dollar. Now, its ad-driven donations are equal to REVENUE = 40 x SQRT(SPENDING). So, if the organization spends $100 on advertising, they receive $400 in ad-driven donations (on top of the $1000 they get automatically). If they do $225 in advertising, they get $600 in donations. And if they do $400 in advertising, they get $800 in donations. (Remember, the equivalent values for the previous charity were $300, $450 and $600. So, the second charity is simply better at advertising regardless of how much it spends.) So, this organization simply gets more revenue per advertising dollar spent, for all possible levels of advertising spend. It is simple a more-effective organization at advertising.

charity-before-after
How much advertising should the charity do now?

We can check different values and see that to maximize the amount of money left over to deliver meals after advertising costs, they should spend $400 per month on advertising and receive $800 in ad-driven donations. This takes in a total of $1800 per month ($1000 from regular donations, plus $800 from advertising-driven donations), leaving $1400 per month to provide meals. For this more-effective charity, the amount of money spent on meals relative to their total revenue would be $1400 / $1800 = 78%.

The charity is now undeniably better at advertising and therefore spends more on advertising. But the result is that the more-effective charity’s advertising spending is higher (22% compared to 15%), which means that the charity looks more wasteful and less efficient when in fact it is simply better at getting results from advertising.

I recently participated in two separate ‘startup incubator’ brainstorming programs, in the same city, a couple of days apart, with two different high-tech companies operating independently of each other. It was surprising to see how different was the quality of their results (by my own estimation), despite only a few apparent small differences in how they were run.

Both programs had 70-80 motivated and well-educated adults from diverse national and cultural backgrounds. They divided up into 10 teams of roughly equal size. Each team worked intensely over the course of a day or two to generate one new business concept for a product or service that could be offered to the marketplace. At the end, each team gave a 3-minute ‘pitch’ presentation describing the idea they had generated, there was a short question-and-answer period after each presentation, and a winner was selected from the 10 pitches.

Both programs had comfortable conference areas with tables and chairs, food, fizzy drinks, electricity and internet access, large pieces of paper and colorful pens and little more than that. No big piles of cash were dropped into anyone’s lap.

Both program organizers offered their teams a list of questions to help guide the idea formation. In one case, this was in the form of Osterwalder’s Business Model Canvas, which you can see below. In the other, essentially the same topics were covered, but as a list of questions starting with Who…, What…, Where…, How…, etc.

business-model-canvas

Having seen all of final business ideas, in my opinion the results of one of the programs seemed greatly superior to the other, both in the slickness of the presentations and in the quality of the underlying ideas. This got me thinking about what differences there were in this ‘Star’ program that might have made the results be (or maybe just seem) better than in the ‘Regular’ program. Here are a few things I noticed:

1. In the Star program, the teams were formed according self-expressed interest
The Star program started with 10 self-selected people making one-minute presentations about what their basic business idea or topic was. After this pitching session, these 10 team leaders scattered around the room and the remainder of the participants came to find out more about the ideas that intrigued them. The participants each wore sticky notes briefly describing their background and skills. The team leaders got final say in selecting who would be on their team.

In the Regular program, the team leaders and each team’s members were selected by the overall program organizer. Each participant was told a couple of weeks before the program day which team they would be on, the leader was selected by the program organizer, and the team was asked to begin brainstorming a business idea topic that they would develop on the program day.

2. In the Star program, there was a strong emphasis on validation, validation, validation
At the beginning of the Star program, participants were given an explicit list of criteria on which their idea would be judged. One-third of these criteria involved the extent to which the team had demonstrated that (1) their idea will actually work and (2) that there exists a market for it. The teams consisted of both experts in topic and non-experts, and all of the teams had intermediate appointments scheduled with outside coaches, some of whom were experts in the team’s idea’s general industry and some were not.

In addition to ‘sanity checking’ their ideas with experts and non-experts, the teams in the Star program were asked to contact potential customers. Several teams put surveys out on SurveyMonkey and Facebook. One got more than 50 replies from within their city between the hours of 10:00 in the evening one day and 8:00 the next morning. One went out to meet with prospective customers and another went out to shoot a demo video. Another set up a functional website that described the team’s idea and provided a box for website visitors to enter their e-mail address if they wished to learn more. (5 prospective customers signed up.) Several contacted support staff from different companies that might be key suppliers or partners. One even set up an in-person meeting with a key partner.

All of the teams provided basic financial estimates of unit cost and unit revenue (and therefore, unit profit) and market size. In the Regular program, the teams were not asked to estimated market size or the profit potential, and so none of them did.

In the Star program there was a strong emphasis on results and action over talk and deliberation. The participants were even told “less talk, more action”. In the Regular program, to the best of my knowledge none of the teams spoke with outside experts, contact potential customers, or even left the building to get fresh air.

3. In the Star program, teams were told what to do, not how to do it
The Star program had no template for the final presentation: as a result, every presentation was unique, some with very high quality graphics, professional looking logos, creative videos, working iPhone app prototypes, a functional website. In the Regular program, the teams were given template presentations where the teams had to ‘fill in the boxes’. Most teams used this template with little modification, and some added additional slides of nice-looking photos to demonstrate their ideas.

4. The Star program had significant outside involvement
In addition to the already mentioned outside coaches, the Star program’s judging was done a panel of 9 people, including local business founders, a city politician and a professional venture capitalist, none of whom were involved in the coaching. In the Regular program, the judging was entirely by the program participants and program organizer, with no one even from within the wider company.

5. The Star program’s ideas went through a larger number of iterations
The final difference that I think might have been important was the duration of the programs and the emphasis on iterating through ideas. The Star program ran for 48 hours, while the Regular program was a single business day. In the Star program, participants were encouraged to ‘Build, Measure, Learn’. The results of the online survey indicated that one team’s initial idea might not have a market interest. The results from the survey were used to ‘pivot’ to a related, but distinctly different, idea. The final presentation was a third idea.

There might have been other important differences, or maybe I am wrong in my assessment of the quality of the final ideas, but if I were in charge of a similar business concept brainstorming day, I would work to make the day more like the Star program and less like the other one.

Delft Earrings

delft-earrings

Blue and white glass beads. Sterling silver findings.

Pearl Ring

A friend found a pearl in an oyster from the supermarket. I made a ring from it by attaching a short segment of sterling silver tubing to a sterling silver band I made. The tubing acts as a bezel cup to hold the pearl.
pearl-ringSterling silver (3 g), pearl.

Previously I looked at the number of times different 4-digit sequences of numbers starting with ‘1’ appear in English-language books published in the year 2000. I took statistics from Google and looked at the number of times the digits ‘1491’ appeared versus ‘1492’. Obviously not all 4-digit numbers are references to years, so I simply dropped numbers that are evenly divisible by 10.

Google offers statistics for books published in a variety of languages, so I have repeated my analysis using values from the German-language books that Google has scanned.

The graph below shows the frequency of 4-digit numbers in German-language works. Number after 1700 are much more frequent than those before 1700, so to make things easy to read, I have put the y-axis on a logarithmic scale.

 

German-4-digit-numbers
(click image to enlarge)

As in the case with English-language books, some values make a little blip on the graph. ‘1648’ is more common than ‘1647’ or ‘1649’, probably because that was the year that The Thirty Years’ War ended. (The number ‘1618’ is more common than ‘1617’, but for some reason ‘1619’ is more common than either ‘1618’ or ‘1617’.)

I have marked some other numbers that look interesting. Some are easy to explain, but others are not.

For example, we see ‘1492’ again, though it is much less prominent than was the case for English-language books. Some other numbers that are common in English-language books are also hard to see here – ‘1066’, for example’, and ‘1776’. Some others that I would expect, like ‘1517’, the year that Martin Luther started the Protestant Reformation, and ‘1989’, the fall of the Berlin Wall, do not stand out either.

Some of the values are difficult to understand their importance, like ‘1408’ and ‘1711’. I don’t know anything important that happened in central Europe in those years. In fact, all of the 1700s seem to be a time when nothing important happened in German-speaking lands, which I find strange given that it was the time of Bach, Mozart, Euler and Goethe. But ‘1848’, a year of revolutions in much of Europe, including Germany, is easy to see, as are ‘1789’ and ‘1815’.

In numbers that start with ’19’, important ones obviously include ‘1914’ and ‘1918’, which were the start and end of the First World War, ‘1933’, the year that the Nazis came to power and of course Germans are interested in ‘1945’, which is famous for being the last year that the Cubs made it to the World Series.

Overall though, I find it rather depressing how many of the references, like with English-language texts, seem to be to wars and revolutions.