As doth eternity: Cold Pastoral!
When old age shall this generation waste,
Thou shalt remain, in midst of other woe
Than ours, a friend to man, to whom thou say'st,
"Beauty is truth, truth beauty," - that is all
Ye know on earth, and all ye need to know.
John Keats' famous poem, "Ode on a Grecian Urn," ends with these beautiful lines. What does he mean when he proclaims that "beauty is truth," and what does it have to do with mathematics?
The Math of Beauty
Mathematicians at the University of Bergen in Norway, including Rolf Reben and Karoline Mitterndorfer, recently completed a study of beauty in mathematics which provides the very first solid, empirical evidence which suggests that, when it comes to math, science and related fields, humans respond far more clearly to concepts deemed "beautiful."
More precisely, the findings showed, as Science Daily (online edition, November 24, 2008) reported in "Beauty is Truth in Mathematical Intuition: First Empirical Edition" that, "stimuli processed with greater ease elicit more positive affect and statements that participants can read more easily are more likely to be judged as being true." The more simple a concept is, the more pleasing to the mind, and the more beautiful it seems, the more likely it will be perceived to be truth.
In their study, the researchers showed that their test subjects, when faced with such simple tasks as judging the truth of simple additions using patterns of dots, were far more likely to assume the truth of a given addition when the dots were placed in a symmetrical pattern. Thus, when a problem was given such as: 12 dots plus 20 dots equals 34 dots, the subjects were more likely to say that this statement was true (even though it clearly is not) when the dots were placed in certain patterns with greater beauty.
The Effects of Beauty and Truth in the Human Consciousness
The results of tests such as these showed that the human mind, regardless of its stored knowledge, is far more likely to respond positively to beauty when forced to choose between options. If a problem is given where more than one solution may be possible and the clues given are not sufficient to fully solve it, a person will be more likely to choose the more beautiful, symmetric, or easily "digestible" answer.
Fortunately, this may very well not be a negative thing. While surely this natural reaction may lead at times to incorrect assumptions, more often than not it very well reflect a very real aspect of nature - for the universe itself, both in science and in mathematics, seems to be built, at least to a certain extent, on a very symmetrical, beautiful foundation.
Mathematicians throughout the centuries have marveled at the fact that their equations and methods possess remarkably symmetrical features, and can be performed in surprisingly beautiful methods. In fact, Albert Einstein once quipped that, "The most incomprehensible thing about the world is that it is comprehensible." The truth of this statement stems, it seems, from a natural beauty - an order which tends toward the human perception of beauty.
So, in an experiment such as the one above where participants are given patterns of dots to add up, it does stand to reason that with little time to actually add them up sufficiently, their answers would tend toward those which seems more beautiful, as this seems to be the tendency of science and mathematics.
This is how the human mind tends to work, and now there is real evidence to back up this claim.
Isaac M. McPhee - Isaac McPhee was born as a human child in Mt. Vernon, WA, c. 1982; he currently resides in the bustling heart of New York City where he ...
