Day 34 in math modeling

Solar soars: Renewable energy, by the numbers

Global investment climbs to $280 billion in 2017 -- and the economies leading the charge may surprise you.

Climate change threatens rare British orchid that tricks bees into mating:

Researchers find that warmer temperatures are upsetting the seasonal relationship between the early spider orchid and pollinating bees

Shell Knew Fossil Fuels Created Climate Change Risks Back in 1980s, Internal Documents Show:

A trove of documents shows the oil company's scientists urged its leaders to heed the warnings. That could now play into lawsuits over global warming.

Internal documents show oil giant Shell had a deep understanding, dating at least to the 1980s, of the science and risks of global warming caused by fossil fuel emissions. They also detail how the company pondered its responsibility to act, and what its scientists warned could happen.

In fact, Shell produced a video in 1991 that painted a grim but honest picture of what might happen: 'Climate change "at a rate faster than at any time since the end of the ice age -- change too fast perhaps for life to adapt, without severe dislocation". That was the startling warning issued by the oil giant Shell more than a quarter of a century ago.'

• Minimum Model
• Maximum Model

• Download your city's latest, greatest data from the folder Jacob shared with you via email (if you did not hear from Jacob, please contact him);

• The Modeling Group has provided a model (model parameters) for the two temperatures, Max and Min. Let's call these the Togo temperature models.

• Your task: Evaluate the Togo temperature models for your town.

  1. Examine the new data: compare it to the original data for your town, and see if you agree with the changes the Data Quality team has made.

  2. Run the model against your town's max and min temperature data. You will need your town's elevation, and latitude and longitude.

  3. Evaluate the model, and investigate the residuals. What patterns and problems do you notice?

  4. Try some temporal oscillatory periods other than those used in the general model (other pairs of sines and cosines): are there any you wish had been included?

     If you see some periodic behavior in the residuals, that would be your guide as to period.

1. Daballe ("infancy" -- Olinick spells it "Dabella"; Hoffmann "Daballe")

2. Folle (party time! Seems like there could be some incidental fathers at this stage....)

3. Kondalla (marriage and war)

4. Luba (administration)

5. Yuba (wise counsel)

Under what conditions will the age-grade system be stable?

So Hoffmann sought to address this issue of stability with a definition, an axiom, and two different models.

• A few comments

  • Hoffmann was responding to Prins's (perhaps imaginary!:) argument that a necessary condition for stability was that procreation be confined to the last two grades (p. 115 of the paper).

  • Is having children at the age of 40 realistic? Reflect on the society's grades and responsibilities....

    Ask someone who's had a child at the age of 40....

  • From a review of Prins's 1953 thesis:

    As the author [Prins] remarks, some social recognition of growth and aging is universal. In East Africa, however, this recognition of the aging process has developed into a complex social institution that should be called a social age-class system. To a degree, actual age is ignored in favor of other criteria for entering a given age class. Thus, all the sons of a Galla man, and all the sons of his brothers, enter the same age class which is forty years behind that of their fathers. The author has coined the terms "infra-puerilization" for cases where the actual years are less than their social years and "ultra-senectation" for those individuals who are too old for their age classes. The prohibition against fatherhood for the warrior class is seen as a device that reduces ultra-senectation where, as with the Galla, the social age separating father and son is so great.

    ....Each Galla male is supposed to go through five age classes, each of eight years' duration. The first two classes are for children, the third and half of the fourth are for warriors, while the second half of the fourth and the fifth are for elders. The forty-year interval rule discussed in the previous paragraph keeps all members of a given patrilineal line of the same generation in the same age class. [my emphasis]

• "This model deals only with one-dimensional father-son links and ignores the branching of descent lines representing siblings. In other words, the model assumes that a man has only one son when, in fact, many men have several sons. Of course, some men have no sons, and this shows another weakness of the model. The model transforms every given family into points of future time when it may, in fact, no longer exist." (p. 319)

• So how might address Olinick's concern?

• Hoffmann gives a hint: "... it is not necessary that every age of parenthood equal 40, but merely that they fluctuate about a mean of 40."

  1. How do we make ages "fluctuate"?

  2. How many sons?

  3. What happens long term?