Like Neo in "The Matrix," we can visualize the earth’s topography as a matrix of zeros and ones. Every location on and around Earth can be specified on a grid by a matrix of three numbers.
The three numbers represent the three dimensions in which we perceive space. On a small scale they are a Cartesian grid (x, y, z). On a large scale they become the rounded sphere of Earth where the planar coordinates become too small to consider and the distance from Earth is what matters.
As seen from Earth, pasting a grid on the black sphere of night that encircles the earth forms the celestial grid.
Using Earth as the center of the universe is geocentric and sounds medieval, but it is not. It is merely convenient and easier to use.
Most data sets for earthly measurements use either a latitude/longitude (GPS) system, Universal Transverse Mercator coordinate system or Military Grid Reference System, which is the geocoordinate standard used by NATO militaries for locating points on the earth.
In any case, the first two numbers represent a location on the imaginary flat earth.
Earth’s sphere may be flattened in various ways by many different map projections, one of which is the old standard Mercator. Two modern equal-area projections — the Mollweide and the Robinson — each take a unique approach to solving the difficult problem of making a sphere look flat.
For small-scale maps, the projection does not matter. From where we see it the horizon looks perfectly flat, but for mapping purposes the scale of the map does not have to become very large before the vertical lines on the map grid begin to converge noticeably due to the poleward curvature.
The first two numbers in the matrix represent the position on the flat Earth grid. By tradition and now formalized: North is up, south is down, east is positive and west is negative.
In the real world the two flat-space coordinates are not enough. We live in a three-dimensional universe. To map this we need to add to the data one more number, which represents the elevation of a point on the surface.
Adding that one number to the matrix allows every hill, valley, ridge and stream to be digitized. The size of the point can be large or infinitely small. The denser the data, the higher the resolution of the screen image created from the data.
Digital elevation models are available for Earth, the moon and Mars, the only heavenly bodies on which we have been able to measure the topography. A digital model of these data displayed on the computer screen takes on the shape of the topography.
The viewer can then look at the model landscape and rotate it and change its scale to gain different perspectives. Sometimes these new perspectives lead to new scientific theories or add support to theories in process.
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Richard Brill is a professor of science at Honolulu Community College. His column runs on the first and third Friday of the month. Email questions and comments to brill@hawaii.edu.
