Quotes of the Day

A few years ago the city council of Monza, Italy, barred pet owners from keeping goldfish in curved bowls. The measure's sponsor explained the measure in part by saying that it is cruel to keep a fish in a bowl with curved sides because, gazing out, the fish would have a distorted view of reality. But how do we know we have the true, undistorted picture of reality?

The goldfish view is not the same as our own, but goldfish could still formulate scientific laws governing the motion of the objects they observe outside their bowl. For example, due to the distortion, a freely moving object would be observed by the goldfish to move along a curved path. Nevertheless, the goldfish could formulate laws from their distorted frame of reference that would always hold true. Their laws would be more complicated than the laws in our frame, but simplicity is a matter of taste.

A famous example of different pictures of reality is the model introduced around A.D. 150 by Ptolemy (ca. 85–ca. 165) to describe the motion of the celestial bodies. Ptolemy published his work in a treatise explaining reasons for thinking that the earth is spherical, motionless, positioned at the center of the universe, and negligibly small in comparison to the distance of the heavens.

This model seemed natural because we don't feel the earth under our feet moving (except in earthquakes or moments of passion). Ptolemy's model of the cosmos was adopted by the Catholic Church and held as official doctrine for fourteen hundred years. It was not until 1543 that an alternative model was put forward by Copernicus. So which is real? Although it is not uncommon for people to say Copernicus proved Ptolemy wrong, that is not true. As in the case of the goldfish, one can use either picture as a model of the universe. The real advantage of the Copernican system is that the mathematics is much simpler in the frame of reference in which the sun is at rest.

These examples bring us to a conclusion: There is no picture- or theory-independent concept of reality. Instead we adopt a view that we call model-dependent realism: the idea that a physical theory or world picture is a model (generally of a mathematical nature) and a set of rules that connect the elements of the model to observations. This provides a framework with which to interpret modern science.

Though realism may be a tempting viewpoint, what we know about modern physics makes it a difficult one to defend. For example, according to the principles of quantum physics, which is an accurate description of nature, a particle has neither a definite position nor a definite velocity unless and until those quantities are measured by an observer. In fact, in some cases individual objects don't even have an independent existence but rather exist only as part of an ensemble of many.

Electrons are a useful model that explains observations like tracks in a cloud chamber and the spots of light on a television tube. Quarks, which we also cannot see, are a model to explain the properties of the protons and neutrons in the nucleus of an atom. Though protons and neutrons are said to be made of quarks, we will never observe a quark because the binding force between quarks increases with separation, and hence isolated, free quarks cannot exist in nature.

Model-dependent realism can provide a framework to discuss questions such as: If the world was created a finite time ago, what happened before that? Some people support a model in which time goes back even further than the big bang. It is not yet clear whether a model in which time continued back beyond the big bang would be better at explaining present observations because it seems the laws of the evolution of the universe may break down at the big bang. If they do, it would make no sense to create a model that encompasses time before the big bang, because what existed then would have no observable consequences for the present, and so we might as well stick with the idea that the big bang was the creation of the world.

A model is a good model if it:
1. Is elegant
2. Contains few arbitrary or adjustable elements
3. Agrees with and explains all existing observations
4. Makes detailed predictions about future observations that can disprove or falsify the model if they are not borne out.

The above criteria are obviously subjective. Elegance refers to the form of a theory, but it is closely related to a lack of adjustable elements, since a theory jammed with fudge factors is not very elegant. To paraphrase Einstein, a theory should be as simple as possible, but not simpler. As for the fourth point, scientists are always impressed when new and stunning predictions prove correct. On the other hand, when a model is found lacking, people still often don't abandon the model but instead attempt to save it through modifications. Although physicists are indeed tenacious in their attempts to rescue theories they admire, the tendency to modify a theory fades to the degree that the alterations become artificial or cumbersome, and therefore "inelegant."

In our quest to find the laws that govern the universe we have formulated a number of theories or models, such as the four-element theory, the Ptolemaic model, the phlogiston theory, the big bang theory, and so on. Regarding the laws that govern the universe, what we can say is this: There seems to be no single mathematical model or theory that can describe every aspect of the universe. Instead, there seems to be the network of theories, With each theory or model, our concepts of reality and of the fundamental constituents of the universe have changed.

Excerpted from the book The Grand Design
Copyright 2010 by Stephen Hawking and Leonard Mlodinow
Posted by arrangement with Bantam Books, an imprint of the Random House Publishing Group, a division of Random House Inc.

• Stephen Hawking and Leonard Mlodinow
• In an exclusive excerpt from his new book, 'The Grand Design,' physicist Stephen Hawking ponders the limitations of the models we use to explain the universe