# Geodesics

What’s the shortest way to travel from London Heathrow airport (LHR) to JFK International airport (JFK)?

You’d think it would be a straight line like this:

But you’d be wrong. The shortest distance between LHR and JFK is actually a curve:

This is because the “shortest distance between two points is a straight line” rule only applies to a flat surface: normally when you use a map it covers such a small area that the curvature of the Earth isn’t noticeable, but on a map of the world it becomes important.

Because a map takes the curved spherical surface of the Earth and maps it onto a flat surface no map can accurately show the whole world – every possible map projection is cursed to distort the size and/or shape of countries and their location relative to each other. The only accurate representation is a true globe. The surface of the Earth is non-Euclidean and thus the rules of geometry that you’re used to don’t apply: parallel lines will eventually meet (e.g. lines of longitude meeting at the poles) and the angles inside a triangle can add up to more than 180°.

The shortest distance between two points, regardless of geometry is called a geodesic: on  flat 2-dimensional planes geodesics are straight lines and on the surface of 3-dimensional spheres geodesics are curved.

# Estimating energy usage and savings

There’s a fascinating paper in this week’s Proceedings of the National Academy of Sciences of the United States of America (PNAS) journal about people’s perceptions of the energy used and saved by various devices and methods.

The researchers’ conclusions are not good news, especially in the light of the energy savings that are required to reduce anthropogenic climate change:

“[P]articipants in this study exhibited relatively little knowledge regarding the comparitive energy use and potential savings related to different behaviours … [they] were also … unaware of differences for some large-scale economic activities … and everyday items.”

The researchers recruited 505 volunteers using Craigslist (which must introduce an interesting set of biases) and asked them to estimate the amount of energy used by various household devices, and to estimate the amount of energy saved by various methods.

On average the study’s participants underestimated the energy used or saved by a factor of 2.8; people estimate that a device using 1000 watts of electrical power actually only uses 350W and a method that saves 500W would be estimated to save only 180W.

Participants did understand that energy savings were possible, but underestimated the size of the saving. For example, participants knew that a laptop computer used less power than a desktop computer, but thought that the saving was less (23W) than it actually was (92W). The more energy a device/method used or saved, the less accurate participants were. Participants estimated that transporting goods by truck used about the same amount of energy as transporting by train or ship, despite the fact that trucks actually use ten times as much energy: they overestimated the use of energy by ships and trains and underestimated trucks and aeroplanes.

In this graph from the paper overestimates appear above the dashed line and underestimates below.

The activity most commonly selected in answer to a question about the single most effective thing participants could do to save energy was “turn off lights”, whereas in reality resetting the thermostat or washing clothes on a colder setting would save far, far more energy. Far more participants selected “curtailment” activities (e.g. turning off lights, not using the car) as saving more energy than “efficiency” activities (e.g. switching to compact fluorescent lightbulbs) despite the fact that the opposite is most likely correct.*

* See Gardner, G. and Stern, P. (2008) The short list: the most effective actions US households can take to curb climate change, Environment Magazine, 50, pp. 12-24. Link