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.

The haversine formula

What is the trust equation and what makes you trust someone in a professional context? I liked this simple equation by Charles Green, which makes it a combination of how credible, reliable, and how intimate — or how safe you feel with that person — divided by the self-orientation of the person — are they focused on their interests, or simply paying more attention to themselves vs being genuinely interested in you and your success. Depending on how you scored this abstract model, I guess that would mean that trust is either undermined by someone focusing on their own interests or strengthened the more they are focused on yours.

The trust equation

The time to a target depends on the ratio of distance to the target over it’s size. So clicking on a small target close by might take a similar time to clicking on a large target further away. It’s a simple model and there are a few little games out there to bring it home in practice.

I’m reminded however, of an observation from a mentor of mine, Darrell Mann, that just because people call it a law doesn’t mean you have to treat it like one. The example of Apple’s standard program icons at the base of the screen that expand when you mouse near them, are a simple technique that help to overcome the limitations of Fitt’s law. There are plenty more. Don’t be sucked in to laziness by a name.

Fitts’ Law

Big data + Machine learning + Cloud = Informed, intelligent decisions. As a very minor example of this I have been enjoying the Dark Sky app.

The big data equation

OK, there are probably many candidates, but it is remarkable to me how such esoteric and difficult to define numbers - derived independently - have such a simple elegant relationship.

Equation sketches