Extrapolation is how we predict the future

A blog post by Adam Mrozek, placement student with Pixalytics in October/November 2013.

I grew up in a very small village with very few inhabitants. As my father very often burned the midnight oil, my mother was the only person to look after me. But I lacked for nothing as she was both mother and father to me.

I can still see a vivid image of my mother celebrating St Andrew’s Eve. During this celebration people try to predict the future using a piece of hot wax and a bucket of cold water.

She had dipped the wax in the bucket of water and tried to interpret the shape. It was a common belief that the shape of wax reveals the future.

As I grew older I left all the superstitious beliefs behind. I practiced the subject of mathematics instead. Believe me or not, but it can help us predict the future, at least to some extent.

Let’s consider a set of points collected above a river. Each point represents a different height measured by the satellite.

Maslow's hierarchy


As the satellite orbits our planet, it provides more data.

Maslow's hierarchy

More points over time

Why do points appear in different places? Because the satellite is unable to pass over exactly the same spot twice in succession as it moves around the Earth; see polar orbits.

How is the water height going to change in the future?

I am going to show the simplest approach available. Namely, the High School approach. We can use extrapolation in order to work out this problem.

Each point can be represented by a set of three elements, i.e. x and y (position) together with height.

Let us calculate the average height at every instance in time. Therefore, we will not have to worry about the x and y coordinates any more; we represent every period of time with one value only.

It becomes easy to draw all the points on a single chart. Like this…

Maslow's hierarchy


We can now extrapolate the graph easily and tell how the height is going to change in the near future.

This is a very simple approach and will only work for small areas and short time periods.

Using this method we can predict how rivers will behave in the future. More advanced methods are used to research various areas of the Congo river letting us know whether the river will flood its surroundings or not.