Nearing the end of the semester I assigned this article, Galactic Scale Energy, which is a great recap of exponential growth and log scales. It comes from Tom Murphy’s blog, Do the Math (uh-oh!). The initial graphic is a beautiful display of real world data giving a near perfect fit:
In this case what appears linear is actually exponential due to the log scale. My first question on the quiz asks if this is linear or exponential, and as expected many mistakenly choose linear even though the caption clearly gives the correct answer. This quiz was the most challenging of the semester partly because of statements like:
“For a matter of convenience, we lower the energy growth rate from 2.9% to 2.3% per year so that we see a factor of ten increase every 100 years. We start the clock today, with a global rate of energy use of 12 terawatts (meaning that the average world citizen has a 2,000 W share of the total pie).”
This is awesome! The first sentence alone takes almost an entire class to unpack, covering percent change, exponential growth, growth factors, units, and estimation. In addition to requiring quantitative skills, the article requires students to exercise their critical thinking. I ask them what conclusion the author reaches and many students missed the point. Some thought that the author was a liberal espousing global warming, while others thought he was a conservative bashing renewable energies. It turns out both are wrong, Tom is making the point that sustaining exponential growth of energy use is PHYSICALLY impossible, not morally suspect. In particular, if we continue growing at 2.3% we quickly (within centuries) will be generating as much energy as the sun itself… that’s pretty hot and just plain impossible no matter what sort of hot suits we build for ourselves :O)
The last questions on the quiz come from Joel Best’s, Damned Lies and Statistics, and address the issue of race in society. This is a topic that is being discussed across the country on our campuses and my students were just as engaged as we would expect. Best does a nice job explaining how race is often used as a proxy for socioeconomic class; and controlling for class differences can make statistical differences disappear for statistics like arrests. There are subtle arguments being presented here, (involving confounding variables and spurious correlations) excellent material for those looking for a way to address societal issues in class.
Q9 Galactic Energy
- What is a watt? How many watts are in a terawatt?
- The author says this 12 TW amounts to 2 kw per average global citizen. How many such citizens is he assuming?
- How many 100 watt light bulbs could each average global citizen keep burning every second with their share of the energy usage pie?
- Write down an exponential equation for Energy Usage (E) as a function of time in years (t).
- Rewrite your equation with the input for time now being centuries not years.
- What is the doubling time?
- The author claims we currently “receive” about 7,000 TW of energy from the sun on the land mass. Plug this into your equation to determine in how many centuries we will be using this much energy ourselves.
- The Galactic Energy Scale article assumes our global rate of energy usage will grow by 2.3% per year starting at 12 terawatts (TW) right now.
- The following graphic shows the growth energy production in the United States. Would you characterize this growth as linear or exponential? Explain!
- The author claims that if we continue 2.3% annual energy growth, then in 1,350 years we will be using as much energy as the sun itself!
- How much energy is this?
- Why is using this much energy not possible according to the author?
- In the third graphic there is a point labeled “steel melts”. What does this point represent in terms of the graphic?
- What conclusion does the author reach? Do you agree or disagree? Explain!
- In DLS the author gives the proportion of blacks (12.6%) and whites (82.9%) in 1996, and then in Table 4 gives the proportion of victimization and arrests.
- Use the numbers 41.1 and 7.4 (from Table 4) in a meaningful sentence.
- Which of the statistics in Table 4 (victimization or arrests) is disproportionate relative to the percentage of blacks and whites in the country?
- What possible reason does the author give to explain this disproportion?