Tuesday, September 27, 2011

Exercise 2.3 - Wizzles and Woozles

This is exercise 3.3 from the text, which is 2.2 online, and 2.3 in my nomenclature.

1. Consider a population of wizzles, which unlike woozles can multiply only when their numbers are larger than a certain minimal value a. If there are less byukies than a, they cannot find a partner for mating and the population dies off. The carrying capacity of the island where wizzles live is also A. Obviously A > a. What model would describe the population dynamics of wizzles on this island?

2. What are the equilibria in the byukies model? Are they stable? 
The solution that comes to mind isn't very satisfying, but it works. I've added an IF statement to the growth rate, such that if the A > a, the growth rate is positive, and if A < a, the growth rate is negative. The first image shows the model still works when the Ao > a; the second image shows the stable equilibrium at zero if the Ao < a.

Exercise 2.2 - Modeling a Toilet

A note on my nomenclature: This is exercise 3.2 from the text; it also happens to be 3.2 online, but online it's part of the art of modeling chapter, and in the text it's part of the math chapter. Following the online order, I'm calling the math chapter ch. 2, but since I'm working from the text for the math chapter (and only the math chapter) I'm calling this ex. 2.2. Whatever.

The model, as I downloaded it, needed to be broken before it could be fixed. First, I deleted the "/dt" from the outflow equation. Second, I changed the flush's if statement to be "if Use>0.995..." because I wasn't getting many flushes with the 0.999 threshold. Third, I deleted the seed from the random function ["RANDOM(0,1,14)" -> "RANDOM(0,1)"] in the parameter "use" to get different random flushings on each run. Doing that gives the following with dt = 0.5:

Q: Can you reformulate the model in such a way that the stock would be drained out properly under any computational method and any time step DT? As you may have noticed, when we switch to other methods, the outflow starts to deplete the stock, but then, apparently, does not have enough time to take it all out. How can this be fixed?

To get the tank to empty no matter what the dt, I just cranked up the outflow. Since tank is defined as a non-negative reservoir, this has no consequences. I made the outflow 1000 x tank, which should work up to a dt of 0.001. The result is:

Math! Simluation Modeling Exercises 2.1

1. Consider a population [in] which cells divide into 3 every time step. What mathematical model will describe this population? 
x(n) = 3x(n - 1)
= 3[3x(n-2)]
= 3{3[3x(n - 3)]} ...
= a3^n
2. Formulate the model with triple growth in terms of a differential equation and solve it. Is the difference between the discrete and continuous models larger or smaller than in the double growth model?
 x(t + dt) = x(t) + 2x(t)dt
[x(t + dt) - x(t)] / dt = 2x(t)
dx/dt = 2x
dx/x = 2dt ... Integrating gives:
ln x = 2t + C
x(t) = ae^(2t)

Now that we have the continuous and discrete models (ie., continuously compounded vs. compounded once per "t"), I plugged the equations into Excel to see how different they are. And they're hugely different! And the difference is much greater for the tripling equations: there's a million-fold difference between the two computation methods by the 16th generation!

time 2x discrete 2x cont. 3x discrete 3x cont. 2x ratio 3x ratio
1 2.00E+00 2.72E+00 3.00E+00 7.39E+00 1.36E+00 2.46E+00
2 4.00E+00 7.39E+00 9.00E+00 5.46E+01 1.85E+00 6.07E+00
3 8.00E+00 2.01E+01 2.70E+01 4.03E+02 2.51E+00 1.49E+01
4 1.60E+01 5.46E+01 8.10E+01 2.98E+03 3.41E+00 3.68E+01
5 3.20E+01 1.48E+02 2.43E+02 2.20E+04 4.64E+00 9.06E+01
6 6.40E+01 4.03E+02 7.29E+02 1.63E+05 6.30E+00 2.23E+02
7 1.28E+02 1.10E+03 2.19E+03 1.20E+06 8.57E+00 5.50E+02
8 2.56E+02 2.98E+03 6.56E+03 8.89E+06 1.16E+01 1.35E+03
9 5.12E+02 8.10E+03 1.97E+04 6.57E+07 1.58E+01 3.34E+03
10 1.02E+03 2.20E+04 5.90E+04 4.85E+08 2.15E+01 8.22E+03
11 2.05E+03 5.99E+04 1.77E+05 3.58E+09 2.92E+01 2.02E+04
12 4.10E+03 1.63E+05 5.31E+05 2.65E+10 3.97E+01 4.98E+04
13 8.19E+03 4.42E+05 1.59E+06 1.96E+11 5.40E+01 1.23E+05
14 1.64E+04 1.20E+06 4.78E+06 1.45E+12 7.34E+01 3.02E+05
15 3.28E+04 3.27E+06 1.43E+07 1.07E+13 9.98E+01 7.45E+05
16 6.55E+04 8.89E+06 4.30E+07 7.90E+13 1.36E+02 1.83E+06
17 1.31E+05 2.42E+07 1.29E+08 5.83E+14 1.84E+02 4.52E+06
18 2.62E+05 6.57E+07 3.87E+08 4.31E+15 2.50E+02 1.11E+07
19 5.24E+05 1.78E+08 1.16E+09 3.19E+16 3.40E+02 2.74E+07
20 1.05E+06 4.85E+08 3.49E+09 2.35E+17 4.63E+02 6.75E+07

3. Suppose you have $10,000 on your savings bank account with an annual interest rate of 3%. Build a model to calculate your interest earnings in 5 years. What will be the difference in your earnings if the interest is calculated monthly instead of annually? How much does the bank make on your account by calculating the interest monthly, instead of doing it continuously?

Continuous interest accumulates by the formula:
A = Ao x e^(rt)
Where A is the final amount, Ao is the initial amount, r is the interest rate, and t is time elapsed.

So after five years:
A5 = $10,000 x e^(0.03 x 5) = $11,618.34
If the interest is compounded in discrete steps, the operative formula is:

  (thanks, Wikipedia!)
where n is the number of compounding periods per year, in this case 12, so:
A5 = $10,000 x (1 + 0.03/12)^(12 x 5) = $11,616.17
So the bank pockets $2.17 every five years by compounding interest monthly rather than continuously.

Is this discrepancy so much smaller than for the doubling and tripling functions because of the low interest rate? If, instead of a savings account, this were a delinquent credit account that accumulated interest at 28%, after five years, the $10k would be:
Monthly compounding: $39.904.99
Continuous compounding: $40,552.00
Indeed, the difference after five years at 28% (~$550) is about 5% of the initial amount, where the difference after five years at 3% (~$2) is about 0.02% of the initial amount. Since these are exponential functions, as more time elapses, the difference will become more pronounced, as it did in the doubling and tripling exercises.

So the take home message from these exercises seems to be: the greater the rate of change, the more important the time increment.

Monday, September 26, 2011

Simulation Modeling Exercises 3.1

Finally got Stella installed! $129 for a perpetual student license. A good deal, but no upgrades, and they're set to upgrade in a few months. Did a quick tutorial from Voinov's online course, now on to the first exercises that actually involve playing with models. Yippie!

1. A model of a car dealership. The number of customers is random and sales occur with a certain probability. New stock is delivered with a delay. At given model parameters the stock goes to zero at certain times. How to avoid this if:
a) the delivery time is no less than 10 days?
b) or the size of the warehouse is limited by 100 units?
c) or both of the above? Can you change the dealership operation in such a way, that the average number of units sold daily will be above 10, while the stock size will be maintained below 50?

Stock (blue) and # deals/day (red) using either
a moving average or 10, whichever is greater.
This took a long time (and dinged my modeling confidence, but hey, I'm a beginner, right?), but I found something that works. I made two changes to the number of deliveries: to smooth things out, I use a moving average of the past 10 days (which is 10 to 20 days ago when the cars get delivered). In addition to using the moving average, I also set a minimum number of deliveries for each day of 10. That way, if the dealership had a bad day 10 days ago, we still get 10 cars 10 days later, so the inventory never collapses.

2. A simple population growth model, that has a certain growth rate and mortality rate. At this time it shows exponential growth with the population increasing to infinity. Modify the model in such a way that the population would grow to 400 and stabilize at about that size. Can this be achieved by changing parameter values only or the functions that describe flows need be modified? 
Booyah! #2 came much easier and more elegantly, if I may say so myself. All I did was modify the birthrate to be a function of the ratio of the population to the target population relative to the death rate. So my birthrate equation became
and the model and output ended up looking like this. Notice that now we can stabilize the population at whatever target we want.
3. The system describes a human population, which growth also depends upon the level of "development". The larger the population, the higher level of development it can reach. The development in turn stimulates population growth. As development grows, more babies are born, therefore the higher the population. Is there anything wrong with this conceptual model? What modifications could make the system "sustainable"? (That is, keep both variables within certain limits, avoiding extinction and runaway growth to infinity)

One way this model differs from the real world is that natality is linearly influenced by development, while in the real world, natality is inversely influenced by development; that is, as development increases, family size goes down. Making just that one change to the model, stabilizes the population at 30 and development at 1.5.

4. A model of CO2 and biomass on this planet. CO2 is released into the atmosphere. It is consumed by the forests. The forests are cut at a certain rate. They also decompose adding to the pool of CO2. Currently the model displays infinite growth of forests. How to modify the system to stabilize it?
Deforestation = Biomass / 100
I suspect there are many ways to stabilize this system, and I'd rather have done this by adjusting photosynthesis rate so that it's not linearly affected by CO2 (it's not, and in the climate change debate, that matters. If we assume, as Dr. Voinov seems to here, that as we pump more CO2 into the atmosphere, forests will be proportionally stimulated, then we'd have much less to be concerned with than we do). Nevertheless, one easy solution is to make the deforestation rate proportional to the amount of forest. Since the deforestation was originally set to 1 and biomass to 100, I used deforestation = biomass/100 to keep the initial deforestation rate the same, and the simulation stabilizes nicely.

5. Model of body weight. You gain weight because you eat. You loose weight due to exercising. However the more you exercise, the higher your appetite. Also the more you weigh the higher the appetite. So the weight grows and grows. Can this pattern be changed? 

Well, I suppose it's as good a time as any to show how ridiculous an exercise modeling can be if you're not careful. I solved this one analytical and managed to stabilize the weight right at 120 ... with -48.5 hours of exercise a day! Hmm... back to the drawing board.

There's another solution, which I also hit on analytically, which stabilizes weight with a positive value for exercise. All I did was set the equations for food intake and weight loss equal, decided that calorie content and exercise efficiency should be static parameters (so I substituted the values from the original model), and then solved for exercise in terms of body weight, which ends up being body weight * .07/2.3, and the model ends up looking like that to the left.

6. A river is represented by 5 identical reaches. The water collected from the catchment area drains into the river reach N5 and then travels down the river. The precipitation pattern is random and results in sharp oscillations in the river stage in the reaches. What changes to parameters and/or functions are necessary to stabilize the system so that
1) there is no accumulation of water in the river;
2) the oscillations in the water depth are smoothed out.
Modify the model to describe the travel of one pulse of water through the river system. 

I don't completely understand this model. I don't get what the parameter M is. However, by unclogging the plug at the bottom of the model, I accomplished the two goals. I increased the outflow rate from 0.1 to 1, which drains the system so that water no longer accumulates, but doesn't drain it so fast that the each precipitation event flashes through all five reaches.

Fun with modeling! I really love this stuff and am glad to have moved from the theoretical part of the course to the hands on part. Can't wait until we're building our own models. First, "Essential Math."

Thursday, September 15, 2011

Expect very slow recovery of jobs lost

I just found a graph that I think is telling about the depth and unique nature of our current economic predicament. This is as of April 2010, and it assumes that the depth of unemployment was reached then. We now know that to be false, so the situation is actually quite a bit worse than the already dismal picture presented here.

Click here for full size image

The first thing to notice is the severe depth of this recession.

The second thing, the one germane to the theme of this blog, is the shapes of the curves. Notice that the longer-ago the recession, the more sharp the losses and rebounds. The more recent recessions, in contrast, have long, deep troughs. I suspect that the slower rebounds of recent years are due to lack of easily exploitable resources. If there are virgin forests and gushing oil fields for the taking, jobs will be quick to be reborn. The less that is true, the more difficult it is to regenerate jobs.

Notice the long arcs of recovery of the '01, '90, and '81 recessions. We can now tack 17 more months onto the red curve at deep unemployment, and if we use the shape of the three most recent recessions' curves to extrapolate our current recession, we may well be looking at a decade-plus of dire unemployment.

Friday, September 9, 2011

Article: Peak Concetration of Power

To date, I've only posted my own writings here. But I read an article this morning that is so important, relevant, and quality, I couldn't not post it. It is about the real and metaphorical connections between the concentration of power in a barrel of oil and the concentration of power in a society such as ours. The author points out that our whole money/economic system is going to (have to) change as we cross peak-oil, peak-debt, peak-power-concentration, peak-civilization. It is truly an excellent synthesis.

The article is reproduced in full below, or you can read it on its original site, here.

Peak Oil, Peak Debt, and the Concentration of Power

by Charles Eisenstein, an author and faculty member at Goddard College in Vermont.

When theorists approach the peak oil problem from the perspective of finding a substitute that will allow us to maintain our present energy infrastructure, their conclusion is one of despair. There may be many substitutes for oil as a concentrated form of storable energy, but none of them are nearly as good as oil itself. Those invested in the status quo would, quite understandably, like to maintain it, but it is becoming apparent even to the most highly invested that the status quo is doomed; that it can be maintained only temporarily, and at a rapidly accelerating environmental cost. The transition before us is not merely a transition in fuel types. It is also a transition in the whole energy infrastructure, both physical and psychological; a transition away from big power plants, distribution lines, and metered consumers; away from capital-intensive drilling, refining, distribution, and consumer fueling stations. More broadly, it is a transition away from centralization, concentration, and all the social institutions that go along with it.

Both the energy system and the money system are based on accumulation and the concentration of power. Not only our energy infrastructure, but our dominant yet invisible way of thinking about energy, presupposes a centralized system of distribution based on a highly concentrated energy source. Many alternative energy technologies have made little headway, not because they are technologically unfeasible, but because they don't fit into our present physical, financial, and psychological infrastructure.

There is a causal as well as a metaphorical parallel between the concentration of power in oil and in money. A concentrated power source that can be stored allows social and political power to concentrate in the hands of those who control it. It generates very different social dynamics from an energy source that is universally distributed and constantly renewed. For one thing, the profit potential of the latter is intrinsically less. Once you have sold the geothermal pump or the PV array, the buyer is self-sufficient, unlike the electrical power consumer who has to pay the metered rate in perpetuity. Energy dependency and economic dependency are closely linked.

A similar pattern holds in other fields as well. In medicine, for instance, the universal, endogenous medical knowledge of several centuries ago that employed common weeds as medicine has given way to a system in which both knowledge and pharmaceutical medicines have been purified, abstracted, and concentrated in an exclusive domain. There is little profit potential in dandelion or burdock, nor did the village herbalist or country doctor of yesteryear make much money. We might apply the same analysis to the migration of legal power from informal community-based mechanisms of dispute resolution to the centralized, codified, and therefore in a sense concentrated mechanisms of the law. So also for education, entertainment, and news.

In all these realms though, the trend toward increasing concentration is nearing its peak, or has peaked already. The peak manifests in many different ways. In some areas it reflects resource depletion; in others, demand saturation; in others, it is due to technology. For example, thanks in large part to the Internet, a tide of decentralization and disintermediation is erasing the producer/consumer divide in the areas of news and entertainment. That more and more of our time is spent watching "content" produced by amateurs suggests that we are approaching "peak Hollywood," in parallel with peak healthcare, peak pollution, peak advertising, peak fisheries, and peak oil.

It should not be surprising, since the profit motive has been the primary driver towards these peaks, that we should be approaching a peak in the realm of money as well, a peak that we might call "peak debt." The crisis in money is ineluctably related to the crisis in everything else, because the viability of our money system depends on growth: the conversion of nature into goods, and relationships into services. This conversion cannot proceed much farther, due to resource depletion and the inability of society and biosphere to sustain more damage. While one may dispute that economic growth depends on petroleum, it does depend on increasing consumption of something. For decades or centuries, we have maintained growth first by meeting needs, then by creating new needs, then by bringing non-monetized cultures and non-monetized domains of our lives into the money domain. Community, for example, can be stripmined just as coal can: turn the functions of story-telling, dispute resolution, child care, elderly care, recreation, entertainment, into paid services. But in either case, material or social, this process is reaching its limit. We are indeed entering a time of Peak Everything.
The crisis in money is related to the crisis in energy, the environment, and everything else. The difficulty in finding a substitute for oil, for example, is born of economics. Imagine what we could have accomplished if the millions of scientific careers and hundreds of billions of dollars that have been devoted to petroleum and nuclear power over the last fifty years had gone instead into developing "alternative" energy technologies. Imagine if, at the dawn of the environmental movement in the 1960s, we had launched a global scientific effort exceeding that devoted to the space race to create a pollution-free society. It did not happen, and with good reason: there was no money in it (given the kind of money system we have had). Compared to the technologies of Big Energy, there is little profit to be made in the alternatives. The alternatives are not conducive to economic growth, and will never flourish in a money system that compels and depends on growth.

Sunlight, wind, conservation, geothermal energy, and more controversial technologies like cold fusion, Bedini/Bearden devices, and so forth share an important characteristic in common. Their energy source is more or less ubiquitous, so that users needn't be dependent on an ongoing supply of scarce fuel. They are, in an important sense, abundant. This feature puts them at odds with our money system, which depends on the creation and maintenance of scarcity. To profit from something, say energy, it must be scarce: high-tech pharmaceuticals, for example, rather than ubiquitous weeds and folk medicine.

The same is true of information; hence the strenuous efforts of music, book, and film publishers to create artificial scarcity in digital content through copy protections and intellectual property law. They are fighting a losing battle: when the marginal cost of production for any product approaches zero, the natural price point tends toward zero as well. The first copy of Microsoft Word costs hundreds of millions of dollars to produce, but each subsequent copy costs virtually nothing.

Alternative energy sources are similar: the initial cost may (or may not) be high, but once the installation is complete, ongoing costs are extremely low or zero. By returning energy to a non-monetary realm, they actually contribute to economic de-growth. Think about that next time you read economic arguments about how to "stimulate demand" and "reignite economic growth." In the present system, in the absence of growth, unemployment, poverty, and the polarization of wealth intensify. In the present system, economic well-being is incompatible with post-carbon energy technologies.

A cynical observer, looking at the history of the suppression of alternative energy technologies, might conclude the same attempt to create artificial scarcity is happening in energy as it has in digital content. However, there is no need to resort to conspiracy theories to explain it; mere economics will suffice. Let's consider an example.

It is not too difficult to build houses that require almost no external power source for heating and cooling. By using construction materials of large thermal mass, geothermal wells, and passive solar principles, a house could, with sufficient PV (photo voltaic) power, be comfortably independent of the energy grid. Why aren't they being built this way?

One reason is certainly the habits and culture of the building industry, but the main reasons are financial. (1) For starters, future energy savings are generally not fully capitalized in a real estate value appraisal. (2) But even if they were, our interest-based system, with discounting of future cash flows, only motivates the initial investment if it generates savings above the rate of interest. (3) Finally, the existing energy system enjoys a high level of hidden subsidy due to the externalization of its environmental and social costs.

The first point is easy to explain: assuming a 2.5% interest rate, the net present value (NPV) of $1,000 in annual electricity savings is $40,000. Rarely, however, does that modest level of energy efficiency contribute nearly that much to a house's value.

As for the second point, what is more economically rational: to buy a house for $200,000 and pay $2,000 a year for power, or to buy a house for $300,000 and pay $200 a year for power? Assuming your mortgage loan is at 5% interest, it is much more rational to pay $2,000 a year for power, forever and ever. Even if you don't need to borrow, you can earn more than 2% interest on that extra $100,000.

Thirdly, the price of gasoline, oil, electrical power is artificially cheap. The costs of pollution, war, oil spills, nuclear accidents, and so forth are not reflected in the price of a gallon of gasoline or a KWH of electricity. They are offloaded onto society and future generations. For example, because the government will have to pay the costs of any truly catastrophic oil spill or nuclear accident, the companies are operating with free insurance. It is no coincidence that massive risks accompany centralized energy installations. Big Energy comes with big risks, as well as the political power to socialize the costs of those risks. People complain that solar and wind power are only competitive because of subsidies, but conventional energy enjoys far greater subsidies.

These subsidies are not the result of mere political influence. They are built into our money system. Unless and until we have a money system that forces the internalization of costs and eliminates the discounting of future cash flows, Big Energy will always enjoy an advantage. That advantage can be mitigated through moral suasion and various kinds of subsidies, but wouldn't it be better to align the money system with the kind of energy system we would like to see, and indeed the kind of planet we would like to see, so that goodness and profit need not be opposed?

What would a money system like this look like? Perhaps it would model the common feature of alternative energy systems that I have described. Rather than originating at a monopoly source, perhaps it would be universally distributed in its genesis. Rather than being storable in concentrated form, maybe it would require constant regeneration. Rather than requiring payment for its continuing supply (i.e. via interest), maybe it would be generated at no cost.

In fact, money systems bearing some or all of these features have been proposed, and if implemented, they would create conditions far more salubrious than at present for the development of a new energy infrastructure. These systems internalize social and environmental costs, restore the commons, build community, reverse the discounting of future cash flows, are compatible with a steady-state or de-growth economy, eliminate economic rents, and systemically discourage the concentration of wealth.

My book, Sacred Economics, lays out one such system, or rather a synthesis of several of them. The key ideas are not new, however, and are even slowly making inroads into the mainstream dialog as the inescapability of Peak Debt becomes undeniable. A central idea is negative interest (also known as demurrage), which discourages accumulation, allows money to circulate in the absence of growth, and encourages long-term thinking.

Other important pieces of the puzzle include commons-backed currency, local and bioregional currency, mutual credit and P2P banking, gift economics, shifting taxation away from income and onto resource and pollution, and a social dividend. Today, most of these proposals seem very radical, although they are entering the public discourse in covert forms. Interest rates, for example, are nearing zero and look to stay there for the foreseeable future, making investments with very long payback periods more feasible. Some economists, among them Willem Buiter, Greg Mankiw, and Robert Hall, have even dared propose taking rates (namely the Fed Funds Rate) negative.

As old certainties break down, what was once radical becomes common sense. However dogged our denial, the present energy infrastructure is doomed to obsolescence. The same is true of our financial infrastructure; indeed, the two are inextricably linked. They will fail together, yet on the other hand, while they remain, each props up the other. The money system exerts an irresistible pressure to convert everything and anything into money – for example, the Alaskan National Wildlife Refuge, the Alberta tar sands, the capacity of the atmosphere to absorb waste – and with each successful conversion, the money system gets a brief reprieve. By the same token, any bit of nature that we can protect from exploitation hastens the demise of the money machine.

This is why efforts to reform the energy system must go hand in hand with efforts at financial reform. Neither is prior to the other; each, rather, is a different facet of the same thing. The collapse of each is part of the collapse of an entire mode of civilization, and an entire way of being that underlies it, clearing the way for the emergence of a new, in accordance with universal dynamics of birth, death, and transcendence.

We might call this way of being, this mode of civilization, the "Ascent of Humanity." It was an age of growth, of domination, of taming the wild and expanding the human realm; of becoming the lords and possessors of nature. That age is ending, and a new era of co-creative partnership with nature is beginning, in which we understand that we are interdependent, not separate. The energy system, and money system, of the future must embody this new relationship.

Thursday, September 8, 2011

Simulation Modeling Exercises Module 1

Exercise 1.1

Can you think of 3 other examples of models? What is the spatial/ temporal resolution in your models?

1. An engineer’s diagram of a circuit board. Spatial resolution is on the order of microns, no temporal resolution.

2. An architect’s blueprint. Spatial resolution is on the order of cm, no temporal resolution.

3. A timeline of the history of an invasion. Spatial resolution is on the order of km, temporal resolution on the order of months.
Model of Napoleon’s ill-fated 1812 invasion of Russia. Thickness of the line represents troop numbers, brown on the advance, black on the retreat. Troop size, location, date, and temperature are all captured in the model. Edward Tufte called this “probably the best statistical graphic ever drawn.”
Can you use an electric lamp as a model of the sun? What goals could such a model meet?

You could use a lamp as a model of the sun to show how light radiates out from a sphere. If your goal were to demonstrate how eclipses are generated by different states of the sun-earth-moon system, this would make an excellent model.

Exercise 1.2

Think of examples of 3 systems. How would you describe these systems?

The human body is a complex system made up of scores of organs, each of which with unique and interacting functions. An organ is a system composed of one or more types of cellular tissue. Cells within tissue interact to produce a function such as nutrient absorption or hormone secretion. Cells are complex systems comprised of proteins, membranes, and genetic material, each of which could again be described as a system.

Describe chicken noodle soup as a system. What are the elements? What is the function? What makes it a system?

Chicken noodle soup could be thought of a system comprised of water, soluble chicken elements, chicken meat, noodles, and spices. My functions for chicken soup are warmth, nourishment, and feelings of comfort, but the function of chicken soup for a chicken may be quite different, and the function for, say, Lipton, different still. It can be thought of as a system because it has multiple components which, when combined, produce a function greater than the sum of its parts. I would not derive the same satisfaction as from eating  a bowl of chicken soup by eating a chicken, drinking a glass of water, swallowing a bunch of garlic and black pepper, and then sitting on the stove for an hour.

Exercise 1.3

List five elements for each of the following systems:

I.        steam engine
1.       Fuel
2.       Combustion chamber
3.       Boiler
4.       Water pump
5.       Water

II.      oak tree
1.       Roots
2.       Xylem
3.       Phloem
4.       Leaves
5.       Acorns

III.    Thanksgiving turkey
1.       Skin
2.       Flesh
3.       Bones
4.       Gravy
5.       Stuffing

IV.    city
1.       Roads
2.       Buildings
3.       Public officials
4.       Merchants
5.       Sewers

What is the system that has the following elements: water, gravel, 3 fish, fish feed, aquatic plants?

One such system is an aquarium.

What if we add a scuba diver to this list? Can elements entirely describe a system?

Then it’s either an ecologically poor lake or sea or a very large aquarium with a scuba diver that needs a new hobby.

Elements cannot describe a system completely for at least two reasons; one is that we have defined a system as having emergent properties that are greater than the sum of its components, and another is that we cannot ever fully describe the elements of a system; there is always another level of detail to which we could appeal (eg., human body, organs, tissues, cells, proteins, atoms, quarks, strings…).

Exercise 1.4

Look at a tree in a forest and describe the relevant hierarchy.

The immediate super-system of the tree is the forest ecosystem, composed of a population of that species of tree, a community of trees and other plants, a collection of animals, fungi, etc.. Moving further up the hierarchy, the forest ecosystem fits within the global ecosystem. In the other direction, the tree’s organs—leaves, xylem, roots, etc.—are subsystems of the tree. Each of those contain tissues and within those cells, proteins, atoms, etc..

Think of an example when a system is affected by a system 3 levels above in the hierarchy, but is not affected by the system 2 levels above in the hierarchy. Is this possible?

I am going to assume that the question intends the meaning “is not being affected by the system 2 levels above in the hierarchy at the moment” because, by definition, a system can be affected by any super-system. With that caveat, using Alexi’s example of a student as a system and the class as the immediate supersystem, the department could be a system 2 levels up, and the university a system 3 levels up. If the university instituted new degree requirements, that could affect the student directly, while the interaction between the student and the department remained the same.

If a system collapses (dies off) can subsystems survive?

Sure. When an animal dies, the proteins within them survive for a time. They will eventually decay, but the sub-er-system of atoms will ultimately survive.

Friday, September 2, 2011

Nature of Human Altruism

Some thoughts I jotted down as I was reading a fascinating evolutionary psychology and behavioral economics article on human altruism: Fehr and Fischbacher, 2003. The nature of human altruism. Nature 425, 785–791.
In the abstract, the authors say that “current gene-based evolutionary theories cannot explain important patterns of human altruism,” and that gene-culture co-evolution will be invoked as an alternative explanation.
I am excited to see the explanation they deliver. I tend to be skeptical of this sort of thing because, well, evolution operates at the level of the gene. It is simply the nature of the process. In a given environment, a gene that has properties that lead to increased copies of itself will proliferate, and a gene that has properties that cause it to become less abundant in the gene pool will decline. That is the primary level on which evolution operates; anything else is secondary. That is not to say that other levels are ineffectual, simply that they are emergent from, and constrained by, that primary level of evolution.
An analogy: suppose that instead of looking to evolution to explain how altruism came to be, you wish to look at the movement of matter to explain how a bunch of sycamore branches and leaves got to be hundreds of feet up in the air. Gravity is the primary governor of how matter moves. Matter will always move toward other massive objects, so if you observe a case in which objects are not moving toward a massive object (like our sycamore leaves), you must search for a more powerful countering force that still operates within the confines of gravity. In this case, the explanation required for the phenomenon that appears to have bested gravity requires invoking the capillary action of xylem cells and water potential gradients from the soil to the leaves. Gravity is still operating on those leaves, but for the moment, the other forces are stronger, so the leaves remain in the air.
Cultural evolution is not impossible, and if we observe behavior that cannot be explained at the level of the gene (just as we couldn’t explain how the sycamore was up in the sky by looking to gravity alone), we should seek levels of evolution that emerge out of the gene level. However, we must always keep in mind that, just as gravity is always acting on matter, gene-based evolution is always acting on our bodies, behaviors, and societies.
Early-on, the authors say that there exists evidence for “strong reciprocity” among humans, which is the rewarding of “cooperative, norm-abiding behaviors” and punishing of norm-violating behavior, even when the rewarder/punisher gains no benefit whatsoever from rewarding/punishing. The problem with this is that rewarding/punishing must impose some cost on the rewarder/punisher, and if they truly gain nothing, then the genes that encode for that behavior decrease the fitness of any individual in whom they occur. Thus, if there is a group of people, all of whom have the rewarder/punisher genes, a mutation that inactivates those genes would produce an individual that is fitter than the rest of the group*, which would cause the inactive genes to increase in frequency, thus eliminating strong reciprocity. I don’t mean to state categorically that strong reciprocity is impossible, and indeed if it is observed, we ought to search for a mechanism for its evolutionary stability. However, I hope I have illustrated how difficult it is for such a trait to become evolutionarily stable and thus the challenge that any evolutionary biologist faces in trying to explain its occurrence.
* Upon rereading this, it occurs to me that this is not necessarily true. If punishments were also dolled out to those who don’t altruistically punish (or altruistic rewards to those who do), then an individual who received the non-rewarder/punisher gene would be punished by their group and could thus be made less fit.
** And lo-and-behold, this is precisely the conclusion the article reaches, nicely summarized the following figure. The red line is the possibility that only occurred to me upon rereading what I had originally written.

Evidence for altruistic punishing/rewarding
The ultimatum game provides a simple example of self-harming behavior to enforce a social norm. An offerer is given some amount of money, of which they offer some fraction to a responder. If the responder accepts the offer, they both keep their fractions; if the responder rejects the offer, they both keep nothing. Apparently, proposals offering less than 25% are very likely to be rejected across cultures and across monetary stakes. I wonder, though, how high those monetary stakes get. If I were the responder and were offered $2.50 of $10, I’d be very likely to forgo the $2.50 to teach the offerer a lesson. That teaching opportunity would be worth $2.50 to me. However, if the offer were $250 of an offerer’s $1,000, I would almost certainly accept the offer because $250, well, I suppose because I believe that $250 would significantly increase my fitness. So I suspect that the decision of whether to punish or not is the result of an analysis of the detriment to one’s own fitness imposed by punishment, the effectiveness of the punishment, and other factors.
The ultimatum game provides an opportunity for the person who is harmed (the responder) to punish the person who harmed them. However, in the real world, social norms are often enforced by a third-party, one who isn’t directly harmed. This sort of scenario has been simulated in a game with three players: an allocator, a recipient, and a third-party. The allocator is given 100 monetary units (MU) and is allowed to give any fraction of the 100 MU to the recipient. The third-party is given 50 MU, from which they can spend any number to punish the allocator. Every MU spent by the third-party as punishment results in a 3 MU penalty to the allocator. Since the third-party gains nothing by punishing, the economically-rational, purely self-interested punisher (i.e. Homo economicus) would never punish and would simply keep all 50 MU. However, the third-party often does punish allocators who offer less than half their MU.
Interestingly, while 55% of third-parties punish unfair offers, 70-80% of recipients expect unfair offers to be punished. So perhaps we expect more fairness than we are willing bring about.
In an altruistic rewarding game, a player can give money to another, then the players are shuffled and there is another round of giving, and the shuffling and giving are repeated. A recent experiment enacted such an experiment with half the players being able to develop a reputation (for giving or not) and the other half was anonymized so that they couldn’t develop a reputation. Those who were reputation-enabled helped on average in 74% of exchanges, while those who were reputation disabled helped in 37% of cases. This suggests that the possibility of developing and benefiting from a reputation of generosity may drive some altruistic behavior, but some baseline generosity (37%) exists beyond that.
Here’s an interesting tad-bit from a neurobiology study. Two groups played prisoners’ dilemma games, one group with another human; the other with a computer program. When the human-interacting group achieved a result of mutual cooperation, their neural reward circuitry was activated relative to the computer-interacting group achieving the same result.