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to calculate with a fair amount of accuracy the radius and circumference of Earth, for example. Their ability to measure length was more refined than their ability to measure time.

      In a practical sense, one of the important things that science accomplishes is making precise and accurate measurements of quantities in the physical world. When people talk about a “scientific fact” that’s truly objective, they’re usually talking about this measurement aspect of science.

      Changes in what can be measured, in turn, lead to changes in what can be talked about scientifically. The invention of devices such as the telescope, microscope, and particle accelerator has allowed for measurements and explorations of whole new realms of nature, turning things that had previously been beyond the reach of scientific inquiry into something that can be measured and, in turn, analyzed and better understood.

      Old becomes new again: Science as revolution

      The interplay between experiment and theory is never so obvious as in those realms where they fail to match up. At that point, unless the experiment contained a flaw, scientists have no choice but to adapt the existing theory to fit the new evidence. The old theory must transform into a new theory. The philosopher of science Thomas Kuhn spoke of such transformations as scientific revolutions.

      In Kuhn’s model (which not all scientists agree with), science progresses along until it accumulates a number of experimental problems that make scientists redefine the theories that science operates under. These overarching theories are scientific paradigms, and the transition from one paradigm to a new one is a period of upheaval in science. In this view, string theory would be a new scientific paradigm, and physicists would be in the middle of the scientific revolution where it gains dominance.

A scientific paradigm, as proposed by Kuhn in his 1962 work, The Structure of Scientific Revolutions, is a period of business as usual for science. A theory explains how nature works, and scientists work within this framework.

      Kuhn viewed the Baconian scientific method — regular puzzle-solving activities — as taking place within an existing scientific paradigm. The scientist gains facts and uses the rules of the scientific paradigm to explain them.

      The problem is that there always seems to be a handful of facts that the scientific paradigm can’t explain. A few pieces of data don’t seem to fit. During the periods of normal science, scientists do their best to explain this data, to incorporate it into the existing framework, but they aren’t overly concerned about these occasional anomalies.

      That’s fine when there are only a few such anomalies, but when enough of them pile up, it can pose serious problems for the prevailing theory.

      As these abnormalities begin to accumulate, the activity of normal science becomes disrupted and eventually reaches the point where a full scientific revolution takes place. In a scientific revolution, the current scientific paradigm is replaced by a new one that offers a different conceptual model of how nature functions.

      At some point, scientists can’t just proceed with business as usual anymore, and they’re forced to look for new ways to interpret the data. Initially, scientists attempt to do that with minor modifications to the existing theory. They can tack on an exception here or a special case there. But if there are enough anomalies, and if these makeshift fixes don’t resolve all the problems, scientists are forced to build a new theoretical framework.

      

In other words, during a scientific revolution, scientists are forced not only to amend their theory, but to construct an entirely new paradigm. It isn’t just that some factual details were wrong, but that their most basic assumptions were wrong. In a period of scientific revolution, scientists begin to question everything they thought they knew about nature. For example, in Chapter 10 you see that string theorists have been forced to question the number of dimensions in the universe.

      Combining forces: Science as unification

      Science can be seen as a progressive series of unifications between ideas that were, at one point, seen as separate and distinct. For example, biochemistry came about by applying the study of chemistry to systems in biology. Together with zoology, this yields genetics and neo-Darwinism — the modern theory of evolution by natural selection, the cornerstone of biology.

In this way, we know that all biological systems are fundamentally chemical systems. And all chemical systems, in turn, come from combining different atoms to form molecules that ultimately follow the assorted laws defined in the Standard Model of particle physics.

      Physics, because it studies the most fundamental aspects of nature, is the science most interested in these principles of unification. String theory, if successful, might unify all fundamental physical forces of the universe down to one fundamental object — a string.

      Galileo and Newton unified the heavens and Earth in their work in astronomy, defining the motion of heavenly bodies and firmly establishing that Earth follows exactly the same rules as all other bodies in our solar system. Michael Faraday and James Clerk Maxwell unified the concepts of electricity and magnetism into a single concept governed by uniform laws — electromagnetism. (If you want more information on gravity or electromagnetism, you’ll be attracted to Chapter 5.)

      Albert Einstein, with the help of his old teacher Hermann Minkowski, unified the notions of space and time as dimensions of space-time, through his theory of special relativity. In the same year, as part of the same theory, he unified the concepts of mass and energy as well. Years later, in his general theory of relativity, he unified gravitational force and special relativity into one theory.

      Central to quantum physics is the notion that particles and waves aren’t the separate phenomena they appear to be. Instead, particles and waves can be seen as the same unified phenomenon, viewed differently in different circumstances.

      The unification continued in the Standard Model of particle physics, when electromagnetism was ultimately unified with the “weak” nuclear force (which is responsible for radioactivity) into a single force, which, in line with physicists’ lack of imagination in naming things, was dubbed the “electroweak” force.

      

The process of unification has been astoundingly successful, because nearly everything in nature can be traced back to the Standard Model — except for gravity. String theory, if successful, will be the ultimate unification theory, finally bringing gravity into harmony with the other forces.

      What happens when you break it? Science as symmetry

A symmetry exists when you can take something and transform it in some way, and nothing seems to change about the situation. The principle of symmetry is crucial to the study of physics and has special implications for string theory in particular. Even when a symmetry used to be there, but is then broken by some other effect, physicists find it extremely useful to use it to describe the world. They call those spontaneously broken symmetries.

Symmetries are obvious in geometry. Take a circle and draw a line through its center, as in Figure 4-1. Now picture flipping the circle around that line. The resulting image is identical to the original image when it’s flipped about the line. This is reflection symmetry. If you were to spin the figure 180 degrees, you’d end up with the same image again. This is rotational symmetry. The trapezoid in Figure 4-1, on the other hand, has asymmetry (or lacks symmetry) because no rotation or reflection of the shape will yield the original shape.

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