by Yohan J. John
Attitudes toward science in the public sphere occupy an interesting spectrum. At one extreme there are the cheerleaders — those who seem to think that science is the disembodied spirit of progress itself, and will usher us into a brave new world of technological transcendence, in which we will merge with machines and upload our minds to the cloud. At the other extreme there is decidedly less exuberance. Science in its destructive avatar is often called scientism, and is seen as a hegemonic threat to religions and to the humanities, an imperial colonizer of the mind itself.
The successes of science give the impression that it has no limitations, either in outer space or inner space. But this attitude attributes to science somewhat magical powers. The discourse surrounding science might benefit from an awareness that its successes are closely tied to its limitations. The relationship between scientists and the rest of society needs mutual understanding and constructive criticism, rather than a volatile mix of reverence, fear, and mistrust. The veil of the temple of knowledge must be torn in two — or at least lifted up from time-to-time.
To this end, it might be illuminating to see scientific ideas as tools forged in workshops, rather than spells divined by wizards in ivory towers. The tool metaphor also reminds us that science is not merely an outgrowth of western philosophy — it is also the result of the painstaking work of “miners, midwives and low mechanicks” whose names rarely feature in the annals of Great Men. [1]
So what sort of toolbox is science? I'd like to argue that it's a set of lenses. These lenses allow us to magnify and clarify our perceptions of natural phenomena, setting the stage for deeper understanding. The lenses of science reveal the symmetries of nature, so we might call them the Symmetry Spectacles. The Symmetry Spectacles are normally worn by mathematicians and theoretical physicists, but I think that even laypeople interested in science might find that the world looks quite interesting when viewed through them.
So what is symmetry? Most people have an intuitive sense of what symmetry is. Symmetry connotes evenness, or balanced sameness. An asymmetrical object is skewed, off-balance, and uneven. It is easy to grasp that a scalene triangle is asymmetrical, whereas an isosceles triangle is symmetrical. To many people an equilateral triangle seems even more symmetrical than an isosceles triangle. The goal of a formal approach is to make explicit our intuitions about symmetry. Mathematicians and theoretical physicists define symmetry as follows:
Symmetry is immunity to a possible change.
How can we apply this notion of symmetry to the scalene, isosceles and equilateral triangles?