# Mathematical Formulas With Dance Notation

First, let's look at the work of data visualization expert Edward Tufte, who featured the following example of a music score with dance notation in his book Envisioning Information:

Now, let's look at a number of mathematical functions expressed in dance notation (via Kottke):

And now, an actual performance of mathematics-inspired dance....

After seeing that, we're really looking forward to seeing what a professional choreographer like Twyla Tharp can do with the choreography for the Standard Model Lagrangian Density Equation:

# Is Marijuana Sucking California Dry?

In March 2015, environmental scientists employed by California Department of Fish and Wildlife published a study examining the impact of diverting surface water to sustain marijuana cultivation upon four northwestern California watersheds. For a state that has been experiencing an extreme drought, the researchers were alarmed to find that marijuana growers were diverting up to 100% of the water flowing in a number of small streams in Humboldt, Mendocino and Trinity Counties during dry periods for the purpose of irrigating their pot farms.

California’s Mediterranean climate provides negligible precipitation during the May—September growing season. In Northern California, 90–95% of precipitation falls between October and April [14]. Marijuana is a high water-use plant [2,15], consuming up to 22.7 liters of water per day. In comparison, the widely cultivated wine grape, also grown throughout much of Northwestern California, uses approximately 12.64 liters of water per day [16]. Given the lack of precipitation during the growing season, marijuana cultivation generally requires a substantial amount of irrigation water. Consequently, MCSs are often situated on land with reliable year-round surface water sources to provide for irrigation throughout the hot, dry summer growing season [7,8,12]. Diverting springs and headwater streams are some of the most common means for MCSs to acquire irrigation water, though the authors have also documented the use of groundwater wells and importing water by truck.

Converting liters to gallons, a single marijuana plant can consume up to 6 gallons per day.

TakePart summarizes the California Department of Fish and Wildlife scientists' research and findings:

They chose four areas, all surrounded by forests, and all with streams containing endangered salmon. The scientists estimated that the growing operations were using between 138,200 and 191,265 gallons of water a day. People in Northern California, for comparison, use an average 172 gallons of water per day per person.

Marijuana growers were taking 100 percent from three of the streams studied and 25 percent of a fourth stream.

Those streams aren’t just picturesque—they’re critical to the survival of the coho and Chinook salmon and steelhead trout.

Doing some more quick math, the estimated cultivation of 23,033 to 31,878 marijuana plants in these regions was consuming the same amount of water per day as somewhere between 803 and 1,112 people. Or rather, 28 plants consume the same amount of water as the average northern Californian.

But that's just that small region. To find out how much water is being diverted to grow marijuana in California, we need to know how many plants are being grown throughout the state.

To determine that, we're going to use the same methodology that was done in a study by the U.S. Department of Justice's National Drug Intelligence Center for its 2010 drug market analysis of the High Intensity Drug Trafficking Area in Central Valley California. Here's how they described it:

California Produced More Outdoor Grown Marijuana in 2009 than Mexico: (Method 1-Seizure Based): Mexico’s 29,025 MT production was eclipsed by California’s cannabis output of 49,105 Metric Tons in 2009. How was the California output computed? To determine the California output potential we used different (published) methods in an attempt to determine the accuracy of these estimations.

First we began with the 2009 DC/SEP actual seizures of outdoor marijuana, 7,365,760 plants which weighed 5,140 MTxii We applied the WDR median percentage (15%) and calculated that 49,104,576 marijuana plants was the production potential for California in 2009. Applying the Gaffney formula to determine metric tonsxiii, this equates to a gross weight of 49,105 MT of marijuana possibly produced in California during 2009.

We found the number of marijuana plants seized by law enforcement in California in 2014 and an estimate of the total crop that was seized compared to previous years in the Washington Post:

The number of marijuana plants seized and destroyed by the Drug Enforcement Administration fell slightly last year and remained sharply lower than the record numbers seen at the dawn of the Obama administration. According to the DEA's records, 4.3 million marijuana plants were destroyed last year, down from 4.4 million the year before and 10.4 million in 2009.

With 2.7 million plants destroyed, California alone contributed 63 percent of the total haul last year. But California's numbers have fallen sharply during the Obama administration, taking the national numbers down with them. "Coinciding largely with the downsizing of, and then ultimately the disbanding of, the state's nearly 30-year-old Campaign Against Marijuana Planting (CAMP) program, DEA-assisted annual marijuana seizures in California have fallen over 60 percent percent since 2010," said Paul Armentano, deputy director of NORML, in an email.

Those numbers give us what we need to estimate the number of marijuana plants grown in California in 2014. Since the number of plants seized by law enforcement has dropped only because of the Obama administration's changes to federal drug enforcement policies, all we need to know is by how much those enforcement efforts have declined. Since those seizures have fallen by 60% from 2009's levels, we just need to multiply 2009's 15% of plants seized figure and to reduce it by 60%. Doing that math:

15%*(100% - 60%) = 6%

We find that law enforcement authorities believe that they seized about 6% of the number of marijuana plants grown in California in 2014. To find the total number of marijuana plants being grown in the state that year, we just need to divide the number of plants seized in 2014 (2.7 million) and divide it by 6%. The result of that math puts the estimated number of marijuana plants currently been grown in California at 45 million.

Multiplying those 45 million plants by 6 gallons of water per day puts the total water consumed by pot farmers at 270 million gallons a day - the same amount of water that would be consumed by 1,569,767 northern Californians. With the average time to grow a mature plant being about 105 days (or 3.5 months) long, providing enough time for two full crops per year, that works out to be 56.7 billion gallons a year, which works out to be 174,006 acre feet of water consumed per year.

That puts marijuana cultivation at a little over double California's strawberry crop when it comes to annual water consumption.

From the numbers presented in the chart above, it is pretty clear that marijuana cultivation is a smaller contributor to California's overall water shortage problems compared to other commercial crops, even though it would rank in the top 10 of California's thirstiest crops. However, the irrigation practices of marijuana growers in a number of the state's watersheds is causing considerable ecological damage, as the growers who unlawfully divert any portion of the water flowing in natural streams to irrigate their pot crops during California's dry seasons would appear to be little more than environmental rapists who are facing too few consequences under the Obama administration's politically selective law enforcement policies.

### References

Bauer S, Olson J, Cockrill A, van Hattem M, Miller L, et al. (2015) Impacts of Surface Water Diversions for Marijuana Cultivation on Aquatic Habitat in Four Northwestern California Watersheds. PLoS ONE 10(3): e0120016. doi:10.1371/journal.pone.0120016.

Holthaus, Eric. Stop Vilifying Almonds. Slate. [Online Article]. 17 April 2015.

Ingraham, Christopher. Facing budget pressures, the DEA is pulling up less weed. Washington Post Wonkblog. [Online Article]. 24 March 2015.

U.S. Department of Justice. Central Valley California High Intensity Drug Trafficking Area. Marijuana Production in California. [PDF Document]. 4 June 2010.

# The Four Dimensional Cube

Last week, we explored the history of the right triangle. This week, we're going to add an extra side and two extra dimensions as we consider the four dimensional cube!

Or, as Phys.org would describe it: "A rotating two-dimensional projection of the four-dimensional tesseract. The projection appears to change as it rotates even though the four-dimensional polytope is symmetrical because it is warped by the loss of two dimension[s]. [Image] Credit: Wikimedia Commons."

Here's hoping we all don't lose two dimensions and become asymmetrically warped this weekend!

# An Almost Perfect Correlation

Now that we've established both how to calculate Irving Fisher's consumption-based measure of the size of the nation's economy as it matters to ordinary Americans (the national dividend) and compared that result with the alternative production-based measure of the national income of Gross Domestic Product (GDP) developed by other economists, the next question we'll address is how well does the national dividend line up with the incomes earned by the ultimate end consumers?

We'll do that as simply as possible, in nominal terms, by determining the correlation of the average annual total expenditures per consumer unit, which is the near equivalent of a U.S. household, with median household income over the thirty year span for which we have data for both series. The chart below shows the result of that very simple linear regression analysis.

What we find is an almost perfect correlation for the years from 1984 through 2013, where the relatively small deviations from the otherwise nearly 1:1 linear trend are easily explained by the following factors:

• The Dot-Com Stock Market Bubble (1997-2003)
• The First U.S. Housing Bubble (2001-2007)
• The Second U.S. Housing Bubble (2012-Present)

Otherwise, with such an almost perfect 1:1 correlation, we confirm that our consumption-based national dividend for the U.S. almost perfectly represents the national economy as experienced by its most typical and ultimate end consumer representative: the median U.S. household.

### Data Sources

U.S. Bureau of Labor Statistics. Consumer Expenditure Survey. Total Average Annual Expenditures. 1984-2013. [Online Database]. Accessed 14 March 2015.

U.S. Census Bureau. Income, Poverty, and Health Insurance in the United States: 2013 (P60-249). Current Population Survey. Annual Social and Economic Supplement (ASEC). Table H-5. Race and Hispanic Origin of Householder -- Households by Median and Mean Income. [Excel Spreadsheet]. 16 September 2014. Accessed 21 March 2015.

### Previously on Political Calculations

Once upon a time, last Wednesday, we solved a problem that had stymied economists since 1906. And we made it look easy!

# The Right Triangle

The YouTube video is one that high school math teacher Mr. D put together for his class that provides a brief history of the Pythagorean Theorem:

Just in case you were ever curious about how long math students have been having to learn about the Pythagorean Theorem because of how long people have been using it. And as a bonus, there's an ancient religious cult involved!