Many years ago, I had a poster that I bought when I visited North Cape in Norway where in summer the sun never sets.  The poster was a time-series of 24 photographs taken at hourly intervals showing the height of the sun in the sky during a summer day at North Cape, similar to the thumbnail.  We can plot the height of the sun as a function of time of day with time on the horizontal axis and height on the vertical axis to obtain a graph that would be a sine wave, part of which is apparent in the thumbnail.  However, the brightness of the sun also appears to vary during the day and so we could also conceive of a graph where the intensity of a line of symbols represented the height of the sun in the sky.  Like a string of fairy lights in which we can control the brightness of each one individually  – we would have a one-dimensional plot instead of a two-dimensional one.  If we had a flat surface covered with an array of lights – a chessboard with a fairy light in each square – then we could represent three-dimensional data, for instance the distribution of elevation over a field using the intensity of the lights – just as some maps use the intensity of a colour to illustrate elevation.  We can take this concept a couple of stages further to plot four-dimensional data in three-dimensional space, for instance, we could build a three-dimensional stack of transparent cubes each containing a fairy light to plot the variation in moisture content in the soil at depths beneath as well as across the field.  The location of the fairy lights would correspond to the location beneath the ground and their intensity the moisture content.  I chose this example because we recently used data on soil moisture in a river basin in China in our research (see ‘From strain measurements to assessing El Nino events’ on March 17^th 2021).  We can carry on adding variables and, for example if the data were available, consider the change in moisture content with time and three-dimensional location beneath the ground – that’s five-dimensional data.  We could change the intensity of the fairy lights with time to show the variation of moisture content with time.  My brain struggles to conceive how to represent six-dimensional data though mathematically it is simple to continue adding dimensions.  It is also challenging to compare datasets with so many variables or dimensions so part of our research has been focussed on elegant methods of making comparisons.  We have been able to reduce maps of data – the chessboard of fairy lights – to a feature vector (a short string of numbers) for some time now [see ‘Recognizing strain’ on October 28^th, 2015 and ‘Nudging discoveries along the innovation path’ on October 19^th, 2022]; however, very recently we have extended this capability to volumes of data – the stack of transparent cubes with fairy lights in them.  The feature vector is slightly longer but can be used track changes in condition, for instance, in a composite component using computer tomography (CT) data or to validate simulations of stress or possibly fluid flow [see ‘Reliable predictions of non-Newtonian flows of sludge’ on March 29^th, 2023].  There is no reason why we cannot extend it further to six or more dimensional data but it is challenging to find an engineering application, at least at the moment.

Photo by PCmarja2006 on Flickr