An average car, sat idling, can produce exhaust emissions to fill 150 balloons. That's a lot of balloons to imagine puffing away out of the cars idling outside a school for a pickup, say. Other tests have found (pdf) that for any time over 10s fuel use and emissions are always greater when idling than turning off the engine and restarting. Spread the word.

Of course, if you have an electric car this won't apply.

I did draw 150 balloons, but a few of them didn't fit on the page.

Idling

Intuitively, we can relate to this: as we get closer to completing a goal we can feel more motivation to complete it. Getting close to the last piece of a puzzle, the last clue of a murder mystery or escape room, the final chapter of your book (perhaps), the final kilometre of a marathon, or as you find you need just one more stamp to get a free coffee, being so close to our goal can give us a motivation lift to get to the end. It has a name:  the goal-gradient effect*.

In the example in the sketch, Oleg Urminksy and coauthors found that as people approached the final stamp towards a free coffee they were more likely to pick up the rate of buying coffees. And when issued with the new card, the coffee buying rate went back down again. They also found that it wasn't so much the absolute 'distance' from a goal, but the perception of distance. So, people who started out on a 12 stamp card with 2 stamps already complete tended to complete the card faster than the people who had a 10 stamp card starting empty even though it was the same number of stamps to the goal.

Read more in Katy Milkman and Kassie Brabaw's Scientific American article, Why Feeling Close to the Finish Line Makes You Push Harder.

Katy Milkman also educated me about the fresh start effect.

*The goal-gradient effect is also known as the goal-gradient hypothesis

The goal-gradient effect

It might seem straightforward to pull out a map and measure the distance between two distant points, however, the larger the distance the bigger the distortion caused by traveling on the curved surface of the Earth as opposed to flat 2D space. So while the distance you measure to your neighbouring town won't be too bad, if you're measuring between London and Rio the curvature of the Earth will make a big difference to the distance that you'll travel. To help figure out the correct distance there's the haversine formula.

The haversine formula allows you to calculate the shortest distance between two points on a sphere using their latitudes and longitudes — this will be the arc between them on the great circle that includes both points. A great circle is a circle on a sphere with the same centre as the sphere, like the Equator. The haversine formula isn't perfect in practice, as Earth isn't a perfect sphere — see the 3 tallest mountains.

It was invented around two hundred years ago, together with tables to speed any calculations, to help sailors navigate.

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The haversine formula