On the Importance of Perspective

On the Importance of Perspective

Whether in observing things or explaining them, different people may see matters differently. Should one support a welfare reform proposal put forward by a politician? Should one buy a new front-loading washing machine? Should one collect an antique ceramic bowl? Faced with the questions before them, people respond in different ways. Everyone sees things in their own way. We usually call the way people “encode” things a perspective. But if we really ask what a perspective is, most people probably have only a vague idea. A very famous example of perspective is Mendeleev’s periodic table of the elements.

In the periodic table, each element has a unique numerical designation. These numbers organize all the elements in an orderly way. In other words, they provide a structure. Compare this perspective with everyday names such as oxygen, carbon, and copper. Generally speaking, we know what these names mean—for example, copper is a relatively soft, conductive, brown metal. But the names themselves do not produce any meaningful structure; they are just names. If we wished, we could just as well call copper “Kamisha.” Mendeleev’s periodic table, by contrast, provided a meaningful structure. Achieving such a perspective required painstaking effort. To explore the structure of the elements, Mendeleev made a card for each of the 63 known elements. Each card represented information about one element, including its chemical and physical properties. He then spent a great deal of time studying and arranging these cards, turning the problem he wanted to investigate into a representative “puzzle.” In the end, Mendeleev pinned the cards to a wall in seven columns, arranged from the lightest to the heaviest—you can imagine paper cards pinned to a wall with thumbtacks. When he completed that “puzzle,” he saw a structure, but it was not until 30 years later, with the introduction of the concept of atomic weight, that people fully understood it. Before Mendeleev, people believed that atomic weight had nothing to do with how the elements should be arranged. Scientists could order the elements by atomic weight from lightest to heaviest, alphabetically, or even by the number of letters in their names, and it seemed not to matter.

Because some elements had not yet been discovered at the time, Mendeleev’s table contained blank spaces. Soon, newly discovered elements filled those gaps. In this way, Mendeleev transformed the information he had into “puzzle pieces” and showed what earlier thinkers had missed. Unlike a problem such as determining the chemical composition of salt, Mendeleev’s “puzzle” had no real analogue in physics. He was not searching for an already existing structure; rather, he created one. This structure revealed the order underlying matter itself. Mendeleev’s story is not unique. We can find many similar examples in the history of science, such as Copernicus’s heliocentric theory and Einstein’s theory of relativity. In these cases, scientists viewed the world differently from their predecessors—for example, Einstein linked time and space together. These new ways of seeing made things that had once been vague, chaotic, or invisible become clear.

Scholars in many fields have studied the question of how individuals and teams achieve major breakthroughs. They have arrived at a common answer: different perspectives. As the philosopher of science Stephen Toulmin pointed out, “At the heart of all major discoveries in the physical sciences is the discovery of novel methods of representation.” Toulmin called new perspectives “novel methods of representation,” and these are often metaphorical in nature. For example, standard earthquake models often include tectonic plates connected by springs so that they can be analyzed rigorously with mathematics. Although we know that diverse perspectives produce breakthroughs, their precise origins are still shrouded in mystery. The necessary ingredients seem to be extraordinary effort and a willingness to take seriously what others overlook—another recurring theme. But we should not forget that relevant diversity is often hard to achieve, whereas irrelevant diversity is easy. At this point, we can give perspective a formal definition. A perspective is a method of representation used to encode objects, events, or situations so that each has its own unique name. No two chairs or two people may be represented in exactly the same way. Mathematicians call this a one-to-one mapping, or bijection. This is a compelling assumption, and a necessary one as well. The names assigned to objects through a perspective must be able to capture their underlying structure. If they cannot, then the perspective is of little use.

Cases like these show that the right perspective can make problems easier to solve. History shows that most scientific breakthroughs and business innovations begin when someone starts looking at a problem differently. The germ theory of disease transformed a mass of confusing and seemingly incoherent data into a coherent set of facts. Thanks to Adam Smith, we all know the story of the pin factory and its efficiency. What many people may not know, however, is that the first pin factory originally produced stiff steel brushes. When someone realized that the steel bristles could be cut down and made into pins, the factory began producing pins. A diversity of perspectives sees each brush as a bundle of pins. Viewing the world from different perspectives provides the “seeds” of innovation.