One of the great challenges in this course, and in all of science, is to think and transmit information in many dimensions.
For example, x-ray experiments and quantum mechanics tell us about electron density in 3-D space. To graph this in any simple way would seem to require 4 axes and 4-dimensional space, one each for x, y, z, and electron density.
An even worse example is graphing the potential energy of a molecule as the atoms move around. Here we need x, y, and z for each of the N atoms plus a final coordinate to denote energy. Plotting a 3N+1 dimensional graph is quite a challenge when we use 2-D paper!
To catch on quickly to the techniques and concepts we will need to address such problems, you should have thought carefully about what is going on in familiar plots that convey 3-D information in 2-D. Here are four examples and a few questions to tune up with.
I. Topographic maps use contours to show altitude for various 2-D (EW and NS) positions. Here is an example:
On this map locate a local maximum of altitude (hilltop), a local minimum of altitude, a valley, a steep hillside, and a pass between two valleys.
Does Leskinen Creek flow Northeast or Southwest?
How do you know?
II. Weather maps use contours to show pressure for various 2-D (EW and NS) positions. Here is an example (you can find an updated one by clicking here):
The white numbers denote atmospheric pressure in millibars (1000 mbar = 1 atmosphere)
On this map use the contours to locate a local maximum of pressure, a local minimum of pressure, a "valley", a "steep hillside" (where winds should be high), and a "pass" (or "saddle-point" or "potato chip") joining two regions of low pressure.
What do you think of the positioning of H and L ?
III. There are alternatives to contour lines for coding electron density, or vegetation cover, or annual rainfall, or altitude, or whatever:
How is the 3rd dimension coded in this graph?
Might there even be a 4th dimension? What is it? (This should make you appreciate clear identification of coordinates in a graph)
On this map locate a local maximum, a local minimum, a valley, a steep hillside, and a pass between two valleys.
IV. Here is a very different kind of 3-D graph.
What are the dimensions?
How is the 3-Dness conveyed?
How might you use a different method to present the same information?
Which presentation is simpler?
Which is clearer?
Comments on this page are welcomed by the author.
J. Michael McBride
Department of Chemistry, Yale University
Box 208107, New Haven, CT 06520-8107
text copyright © 2000,2003 J.M.McBride