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.
I am compiling a list of the different ways I can think of to be creative. Here’s what I’ve come up with:
1. Be 100% New
In the description of their history, El Bulli, one of the highest-rated restaurants in the world, quotes French chef Jacques Maximin who said “Creativity means not copying“.
Everything is a Remix is an excellent video series on the importance of derivative works and recombinations in the creative process.
3. Copy, But Modify
This is how evolution works.
4. Copy Perfectly
Adam Savage from Mythbusters gave a great talk on making a copy of the statuette from The Maltese Falcon and it shows how much creativity there is in trying to produce a specific, well-established end goal.
by Olivia DeLane
What seems like a lifetime ago (actually, for a chicken it was about a lifetime ago) I started looking at a simple model of predator-prey dynamics and found that it might be better for Lions to stop eating Gazelle kids.
Just as people tend to throw back young fish, perhaps excluding young Gazelle from the food supply would be better for both Lions and Gazelle.
The basic model looked like below, where K is the number of Kids, A is Adults, L is Lions and the rest are parameters.
The two values of the s-parameter that I looked at were the case where Lions eat Kids (s=1) and where Lions refrain from eating Kids (s=0).
I noticed that the ratio of Adults-to-Kids tends to converge on the Golden Ratio (approximately 1.618) when s=1 and that this ratio (A/K) tends to go to 1 when s=0. I am curious about other values of s, so that only a portion of Lions eat Kids.
What has made me curious about this is the idea that these equations might not be just a model of Lions and Gazelle, but also of the rate at which new companies are formed. Every venture starts small (like a Kid Gazelle) and then might either die out or grow to be a mature enterprise. These established companies (like Adult Gazelle) help to spawn new small enterprises, through intentional spin-offs (like when Microsoft spun-off Expedia) or by serving as a meeting place where entrepreneurs then strike out on their own (like the famous Traitorous Eight who started Fairchild).
The ‘predators’ in this example would be investors and the general business environment, which seek to tear apart companies when the number of Lions is high and are relatively weaker in power when their numbers are low. Likewise, conditions are best for established firms when s is high and best for startups when it is low.
Apparently, I am not the only one who has thought of this analogy, since I received this message via Twitter:
@bradd_libby can’t help but wonder if start up activity (prey) and VC activity (predictor) follow the same cycles
— MobCon (@excapite) August 4, 2013
The graph below shows the ratio of Adult (or, Established firms) to Kids (Startups), for differing values of the s-parameter. For values of s up to about 0.25, the ratio of Adults to Kids remains constant, being a little over 1. When s = 1, as I mentioned before, the A/K ratio also tends toward a constant, the Golden Ratio.
But for intermediate s values, the A/K ratio steadily oscillates between two different values. My thinking is that since we tend to see times that favor established firms and times that favor startups (similar in concept to the ‘business cycle’), then this simple model of predator-prey dynamics might be useful for studying startup dynamics in the economy as a whole, or perhaps in just one industry, especially if the value of s itself varies over time.
At this point, I don’t know if this model is actually useful, or if it just an analogy, but I hope to be able to put a little more time into studying it before this lifetime is over.
Olivia DeLane has a Master’s certificate in normative ethology from Gallus College, a non-accredited online institution. Her writings are for entertainment purposes only and should not be misconstrued as being for any other use. Olivia’s new book “50 Simple Tips to Turn Your Chicken Shack into a Hen House” will soon be available.