# Why Visualisation?

## Some data

Take a look at the following data, measuring the speed of my laptops over a period:

 Date Speed 10/06/88 800 02/04/90 1600 06/05/93 2083 05/05/94 16666 19/06/96 118175 22/01/99 268212 24/03/00 527093 16/04/02 1183152 17/03/06 1250000 19/02/09 2630000 24/04/11 7837000

If I told you one of those computers was seriously underpowered for its time, would you be able to tell which one?

## A graph of the data

This graph suggests that the 2006 computer is underpowered, but the problem is computer power over time is an exponential function, so to see the detail at the lower end, we need to use a logarithmic scale.

## A Different Graph of the Data

Now we can see that the 1993 laptop is under-powered, but something looks wrong with the last three as well. In fact, this graph revealed the problem: the speed measured was the speed of one core. All machines except the last three were single-core machines. The figures for the last three should be multiplied by the number of cores.

## Why can we see these things in a graph?

But not from the data?

Because we are putting another independent processor to work.

Time yourself on the following three examples.

## How many of these numbers are in the range 25:35?

 37 17 85 67 61 80 74 24 96 27 21 54 68 87 49 69 28 11 78 51 79 81 43 68 46 16 83 23

## Why?

(The audience took 18, 8 and 2 seconds for these tasks, and by the way got progressively better results, with no errors on the last example)

Note that usability is about making tasks faster, error-free and more enjoyable. By visualising data, you make the data more usable.

## Beware of illusions

You may have heard references to "passing the knee in the exponential curve" or similar. In the above graph the knee appears at about the 15th doubling.

## Illusions

However, if we take a larger range, the knee appears around the 30th doubling. The knee is an optical illusion caused by using the wrong sort of graph. Exponential functions should use a logarithmic scale.

## Illusions

Using a logarithmic scale you see a straight line; there is no knee.

## What exponential growth really means to you and me

Often people don't understand the true effects of exponential growth.

A BBC reporter recently: "Your current PC is more powerful than the computer they had on board the first flight to the moon". Right, but oh so wrong (Closer to the truth: your current computer is several times more powerful than all the computers they used to land a man on the moon put together.)

To demonstrate this, take a piece of paper, divide it in two, and write this year's date in one half:

## Paper

2011

Now divide the other half in two vertically, and write the date 18 months ago in one half:

## Paper

2011
2009

Now divide the remaining space in half, and write the date 18 months earlier (or in other words 3 years ago) in one half:

## Paper

2011
2009
2008

Repeat until your pen is thicker than the space you have to divide in two:

## Paper

2011
2009
2008
2006
2005
2003
2002
2000
99
97
96
94
93
91

This demonstrates that your current computer is more powerful than all other computers you have had put together (and way more powerful than the computer they had on board the first moonshot).

This is just another visualisation of an exponential, but with more relevance to the point being demonstrated.

## Tufte

Anyone who wants to do anything with data visualisation should make sure they have read Edward Tufte's books, such as Envisioning Information.

## Colour

A and B are physically the same colour (they really are), but our visual systems interpret them differently

## Tufte

Contrast helps our visual system see detail

## Conclusion

This short introduction was intended to sensitise you to the whys and some of the pitfalls of visualising data.