Reforesting Iceland

The NYT has an interesting article on the difficulties of reforesting Iceland.

This is an example of forest cover tipping points.

Iceland appears to be stuck in a state in which “no trees” is locally stable. So, the system pushes back when you try to reforest, at least until you can cross into another basin of attraction that’s forested.

Interestingly, in the Hirota et al. data above, a stable treeless state is a product of low precipitation. But Iceland is wet. So, deserts are a multidimensional thing.

Bernoulli and Poisson are in a bar …

Bernoulli asks, “how long have we been here?” Poisson replies, “I have no idea.”

Bad joke aside, memoryless behavior is a key component of a toy model of car rentals I made a while ago. I recently noticed that I was a bit lazy in my choice of RANDOM functions, so I’ve produced an update.

The difference is in the use of Poisson and Binomial distribution functions. In the original, I used the Poisson distribution everywhere to represent arrival processes. That’s reasonable in the limit, where a large number of candidate arrivals are realized with a small probability, such that the expected arrivals occur at some finite rate.

Think of a lemonade stand on a busy street – there’s a very large population of potential lemonade buyers, but only a small fraction actually stop for a drink. Normally, we don’t want to model the street and the traffic generation process, so it’s reasonable to assume independent arrivals from a large pool at some rate that we can measure, using the Poisson distribution. This is similar to using a cloud in SD to indicate a source or sink that we aren’t modeling.

In the car rental model, the arrival of customers is a good example of this. But other processes in the model are not. Consider the servicing of returned vehicles:

Here, the company is not servicing all vehicles in the universe at a finite rate, but instead they’re servicing a known queue (the stock of cars returned) with some expected time for each. If servicing time is exponentially distributed (the equivalent of the continuous stock draining process), the probability of any individual car getting serviced in the next time step is inversely proportional to the service time. So, this is a Binomial distribution, i.e. a series of Bernoulli trials with n=cars returned and p=TIME STEP/service time.

Does the difference matter? Normally, not much. As long as the arrival rate is a smallish fraction of the stock of potential arrivals, the Poisson distribution will be a close approximation of the Binomial. But the Poisson distribution fails a key reality check: it can generate an arbitrarily large number of arrivals at any time. The probability of this occurring becomes significant if the service time is short with respect to TIME STEP. The Binomial distribution, on the other hand, is properly bounded above by the number of candidate arrivals (Cars Returned).

Here’s an example. With Binomial n = 100 and p = 1/10, or equivalently Poisson arrivals of 10 per time, the distributions are practically identical:

But with n = 10 and p = 1/2 (i.e. service time = 2*TIME STEP), the similar Poisson distribution with arrivals = 5 per time yields rare instances with 11, 12 or 13 out of 10 cars arriving in this sample of 1000 times:

That’s not good!

There’s another limitation of my toy model that I haven’t addressed. The Binomial arrivals are memoryless for individual cars in the service or intercity arrival queues. That assumes that the probability that a car arrives in the next moment is independent of its residence time in the queue. That’s fine for exponential decay, but for real world processes it’s usually not quite right. There’s a certain minimum time required to service a car or drive from city A to city B.

The solution is to decompose the process into multiple steps. This is essentially the same thought process as choosing a delay order. For servicing, for example, you could represent the minimum time needed to clean and fuel a car as a pipeline delay, then add randomness to describe additional delays that occur as employees take breaks, equipment fails, etc. Similarly, for the delay between rental and return, you could modify the existing structure to treat arriving as a discrete delay (representing the time required to get from A to B), plus an additional random delay before returning, representing variation from traffic congestion and sightseeing.

See also:

This is a pretty typical example of doing discrete event simulation in Vensim. Vensim is really targeted at continuous time and values, but with minimal extra work it can handle a lot of discrete cases. There’s a video covering the basics at vensim.com.

Answer to A Bongard Problem

As a few people nearly guessed, the left side is “things a linear system can do” and the right side is “(additional) things a nonlinear system can do.”

On the left:

  • decaying oscillation
  • exponential decay
  • simple accumulation
  • equilibrium
  • exponential growth
  • 2nd order goal seeking with damped oscillation

On the right:

Bongard problems test visual pattern recognition, but there’s no reason to be strict about that. Here’s a slightly nontraditional Bongard problem:

The six on the left conform to a pattern or rule, and your task is to discover it. As an aid, the six boxes on the right do not conform to the same pattern. They might conform to a different pattern, or simply reflect the negation of the rule on the left. It’s possible that more than one rule discriminates between the sets, but the one that I have in mind is not strictly visual (that’s a hint).

The original problem was here.

A Bongard problem

Bongard problems test visual pattern recognition, but there’s no reason to be strict about that. Here’s a slightly nontraditional Bongard problem:

The six on the left conform to a pattern or rule, and your task is to discover it. As an aid, the six boxes on the right do not conform to the same pattern. They might conform to a different pattern, or simply reflect the negation of the rule on the left. It’s possible that more than one rule discriminates between the sets, but the one that I have in mind is not strictly visual (that’s a hint).

If you’re stumped, you might go read this nice article about meta-rationality instead.

I’ll post the solution in a few days. Post your guess in comments (no peeking).

Update to Path Dependence, Competition, and Succession in the Dynamics of Scientific Revolution model

For the 2017 Balaton Group meeting, I’ve updated Sterman & Wittenberg’s Path Dependence, Competition, and Succession in the Dynamics of Scientific Revolution model. The new version is far more usable, with readable variable names and improved diagrams.

This is an extremely interesting model for our current situation of clashing paradigms, fake news and filter bubbles. I encourage you to take a look at the model and paper.

This is actually much more natural as a Ventity model, so watch for another update.

Dynamics of Dictatorship

I’m preparing for a talk on the dynamics of dictatorship or authoritarianism, which touches on many other topics, like polarization, conflict, terror and insurgency, and filter bubbles. I thought I’d share a few references, in the hope of attracting more. I’m primarily interested in mathematical models, or at least conceptual models that have clearly-articulated structure->behavior relationships.

From the SDR & SD Conference Proceedings

The sociopolitical destabilization of Venezuela

The dynamics of ethnic terrorism

Rethinking the Conflict Trap (Columbia)

Farmers, Bandits and Soldiers – SDR or Conference

Other model-oriented literature

Several people have mentioned Peter Turchin’s Historical Dynamics

The logic of authoritarian bargains

Taking to the streets

The authoritarian dynamic

Authoritarian reversals and democratic consolidation

Democracy Diffusion

An informational theory of the new authoritarianism

Power sharing and leadership dynamics

Stay tuned for more on this topic.

Ad Experiment

In the near future I’ll be running an experiment with serving advertisements on this site, starting with Google AdSense.

This is motivated by a little bit of greed (to defray the costs of hosting) and a lot of curiosity.

  • What kind of ads will show up here?
  • Will it change my perception of this blog?
  • Will I feel any editorial pressure? (If so, the experiment ends.)

I’m generally wary of running society’s information system on a paid basis. (Recall the first deadly sin of complex system management.) On the other hand, there are certainly valid interests in sharing commercial information.

I plan to write about the outcome down the road, but first I’d like to get some firsthand experience.

What do you think?

Update: The experiment is over.

AI babble passes the Turing test

Here’s a nice example of how AI is killing us now. I won’t dignify this with a link, but I found it posted by a LinkedIn user.

I’d call this an example of artificial stupidity, not AI. The article starts off sounding plausible, but quickly degenerates into complete nonsense that’s either automatically generated or translated, with catastrophic results. But it was good enough to make it past someone’s cognitive filters.

For years, corporations have targeted on World Health Organization to indicate ads to and once to indicate the ads. AI permits marketers to, instead, specialize in what messages to indicate the audience, therefore, brands will produce powerful ads specific to the target market. With programmatic accounting for 67% of all international show ads in 2017, AI is required quite ever to make sure the inflated volume of ads doesn’t have an effect on the standard of ads.

One style of AI that’s showing important promise during this space is tongue process (NLP). informatics could be a psychological feature machine learning technology which will realize trends in behavior and traffic an equivalent method an individual’s brain will. mistreatment informatics during this method can match ads with people supported context, compared to only keywords within the past, thus considerably increasing click rates and conversions.

 

Meta MetaSD

I was looking at my google stats the other day, curious what posts interest people most. The answer was surprising. Guess what’s #1?

It’s not “Are Causal Loop Diagrams Useful?” (That’s #2.)

It’s not what I’d consider my best technical work, like Bathtub Statistics or Fun with 1D Vector Fields.

It’s not about something controversial, like On Limits to Growth or The alien hail Mary, and other climate policy plays.

Nor is it a hot topic, like Data science meets the bottom line.

It’s not something practical, like Writing an SD Conference Paper.

#1 is the Fibonacci sequence, How Many Pairs of Rabbits Are Created by One Pair in One Year?

Go figure.