Outer Limits of Reason (48 page)

Many people scoff at such thoughts. They say that the end of physics has been “just around the corner” many times before. All those previous predictions turned out to be false and so will this one. For some two centuries after Newton's work was done, physicists also believed that only the details remained to be finished. When the twentieth century hit, quantum mechanics and relativity theory showed them that they were wrong and that there were many new phenomena that needed explanations. Perhaps there will be many new phenomena in the years to come.

This argument is not foolproof. Just because people predicted in the past that science will soon end, and these predictions turned out false, does not mean that the current predictions will also fail. For thousands of years mankind was looking for the source of the Nile and failed at finding it. Then, one day, we did find the source of the Nile.
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Similarly, there was the boy who cried “wolf” many times when there was, in fact, no wolf. Eventually, however, the wolf did come. Similarly, thinkers can predict that the end of science is near many times, but now it could really be true. The reason why it failed in the past is that the solutions were simply not found. There were new phenomena that had to be discovered and new explanations that had to be revealed. Now, perhaps, all the phenomena are known and all the explanations are understood. Or maybe not.

There are many reasons to believe that the end of science is very close. We really are closer than before in describing many forces. Our knowledge of the subatomic world is far superior to our earlier knowledge. As time goes on, we have combined more and more forces and shown that they are really the same. This shows much economy in our theories that Occam would have appreciated. String theory and other theories seem to be legitimate Grand Unified Theories that have combined all the others. Also, our theories seem more mathematical than ever.

Similarly, there are many reasons to believe that science has a long way to go and might never end. If science were ending very soon, one would think that some parts of science would have already ended. And yet, we do not see any major field of science complain of a lack of work or even close up shop. Every field still asks and sometimes answers good questions, so why believe that eventually all of science will end? Immanuel Kant described another problem with the end of science being near: “Every answer given on principles of experience begets a fresh question, which likewise requires its answer and thereby clearly shows the insufficiency of all physical modes of explanation to satisfy reason.”
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In other words, even if we have all the answers to the questions that we have today, in the future we will have many more questions. Science is, in a sense, self-perpetuating.

Whether science will end depends, in part, on some of the answers that one accepts for the questions posed in this section. Do you have enough observational evidence to inductively come up with a theory that is a final theory? If we accept Popper's falsification scheme, then science might have ended and we will never know about it since the theory that we have cannot be absolutely verified. We simply must wait for eternity until we know that our theory has never been falsified. In contrast, if Popper is wrong, then we might come to the end of science and know that we are there. If Kuhn's paradigm view is correct and paradigms must continually change, then we will never get a final theory.

But the answer to whether science will end also depends on the very structure of the universe. Is there some type of final explanation that exists and that scientists are trying to find it? Or, in contrast, is there simply no deepest level of explanation?

There do not seem to be any knockdown answers to any of these questions. No side of the argument is more attractive than the other.

There are many different possibilities for the end-of-science questions, including the following:

• Science can, in fact, end very soon and we will know and understand all the mysteries of the universe.
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• Science can end and there will be no new answers, but we simply do not understand all the mysteries. That is, there are no essential new results in science, but we still do not have the answers to all our questions. As I have stressed many times in this book, the ultimate nature of our physical universe might simply be beyond the limits of human reason.

• Science can go on forever and we will still not arrive at the ultimate answer. There is simply an infinite chain of explanations, one after another. Each explanation will be deeper than the previous one.

• Science can go on and we will not know that we already have all the answers to the important questions. That is, science could be working on the unimportant questions and we simply do not realize it. Every scientist thinks that she is working on the most important question in the world, no matter how trivial or unimportant it seems to most other people. That is simply the nature of the profession. Perhaps we are all under an illusion about the contemporary status of science.

• Science can never end, but its progress gets slower and slower.

• Science could have already ended and we are now only dealing with the small problems, but we just do not know it.

There is no doubt that this list of possible scenarios for science can be extended indefinitely. I am sure there are many other plausible developments that we cannot even imagine. It is impossible to even make a complete list of the possibilities for the end of science, let alone to determine which of the possibilities will happen. It is hard to predict the future. Just 100 years ago we did not have anything like computers, the World Wide Web, microwaves, televisions, nuclear submarines, and so on. There is no way we could have predicted what science and technology had in store for us. Similarly, it is impossible to predict what will happen in the century to come. We cannot tell if or how science will end.
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This topic clearly has implications for our limits-of-reason theme. If science will never end or if science will end, but we still will not know all the answers to the big questions, then those answers are necessarily beyond the limits of reason. In contrast, if one day the universe does reveal all of its mysteries to its human inquisitors, then the limits of reason are not so severe.

All the different topics in the philosophy of science that we have discussed have one theme in common: they show that science is a human activity. It is created by finite, flawed human beings attempting to search for the ultimate truth. The data sets that we examine are limited, the theories that we come up with are tentative, and the equations that we find are incomplete. We are not promoting some type of silly postmodernist belief that science is not real. Rather, what we are saying is that the ways human beings find and describe these laws of nature are simply human. We do not have access to magic oracles or time machines that will help us peek into the future. Rather we are looking at the evidence we have and trying to make sense of the world we live in.
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8.2  Science and Mathematics

There is a rather deep puzzle at the heart of the scientific endeavor. As anyone who has ever studied the sciences knows, a large amount of mathematics is needed to understand the physical world. Science uses mathematics as a language to express itself, and without that language science is impossible. This can be seen by looking at the course prerequisites for college science classes. Physics and engineering majors need several semesters of advanced calculus. Computer scientists must study discrete mathematics, linear algebra, probability, and statistics. Modern chemists have to know a fair amount of topology, graph theory, and group theory. The necessity of studying mathematics was described nicely almost four hundred years ago by one of the greatest scientists of all time, Galileo Galilei:

Philosophy is written in that great book which continually lies open before us (I mean the Universe). But one cannot understand this book until one has learned to understand the language and to know the letters in which it is written. It is written in the language of mathematics, and the letters are triangles, circles and other geometric figures. Without these means it is impossible for mankind to understand a single word; without these means there is only vain stumbling in a dark labyrinth.
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This leads to the obvious question: Why is mathematics so essential to an understanding of the physical world? Why does math work so well? Why does the physical world obey mathematics? These simple questions have been asked by the greatest scientists and thinkers in every generation. Paul Dirac (1902–1984) wrote:

It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that it is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better.
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In 1960, the physicist Eugene Wigner published “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” This paper posed interesting questions about the relationship between mathematics and the natural sciences. These questions now go under the name of “Wigner's unreasonable effectiveness.” Wigner did not come to any definitive answers to his questions. He wrote that “the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and . . . there is no rational explanation for it.” He concludes the paper with these words:

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.

The mystery was stated perfectly by Albert Einstein, who wrote:

At this point an enigma presents itself, which in all ages has agitated inquiring minds. How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? Is human reason, then, without experience, merely by taking thought, able to fathom the properties of real things?
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The power of mathematics can be seen by looking at some historical vignettes where mathematics has made amazing predictions about the physical world.

The Discovery of Neptune

On March 13, 1781, the English astronomer William Herschel (1738–1822) pointed his telescope to the heavens and found a new planet, which came to be called Uranus. The motion of this new planet had certain unexplained irregularities. The French mathematician Urbain Leverrier realized that another planet must be influencing the orbit of Uranus. He sat down and used Newton's laws to calculate the exact position of this heretofore unseen planet. Leverrier sent a letter to the German astronomer Johann Galle (1812–1910) telling him about this planet and exactly where to look for it. The letter arrived on September 23, 1846, and on that very night, Galle aimed his telescope at the exact place he was told and found a planet. Galle immediately wrote to Leverrier: “The planet whose place you have [computed]
really exists.
” This planet was named Neptune. Nothing but pure mathematics was used to find it.

The Discovery of the Positrons

In 1928, Paul Dirac jotted down an equation to describe some of the properties of an electron. This work was remarkable because it took into account both quantum mechanics and special relativity theory. With the usual way of thinking about the Dirac equation, one arrives at the properties of the electron. One of the properties of this subatomic particle is that it has a negative charge. Dirac wondered what would happen if you played with other solutions to this equation. This is similar to considering solutions to the simple equation
x
²
= 4. The obvious solution is that
x
= 2. There is, however, another not so trivial solution where
x
= –2. From a simple contemplation of the equation and the possible solutions, Dirac posited that there might be another particle with similar properties to an electron but with a positive charge. In 1932, Carl Anderson (1905–1991) did some experiments that showed that such a particle actually existed. This particle was called the positron. Anderson won the Nobel Prize for this work in 1936.

So by simply following mathematics, one finds out things about the physical world. Dirac wrote:

A good deal of my research in physics has consisted in not setting out to solve some particular problem, but simply examining mathematical equations of a kind that physicists use and trying to fit them together in an interesting way, regardless of any application that the work may have. It is simply a search for pretty mathematics. It may turn out later to have an application.
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Dirac added, “As time goes on, it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen.”
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String Theory

A purported Theory of Everything that will unite quantum mechanics and relativity theory is string theory. This is the theory that takes as the basic building blocks of the universe minute strings that wiggle around. These strings shake, rattle, and roll while combining and separating to make up all the quarks, protons, electrons, and other particles of everyday life. By just looking at the different properties of these strings and the way they interact, theoretical physicists have successfully predicted most of the properties of the physical world. This theory can be used to describe all the forces of quantum mechanics as well as the gravity force of general relativity. There is only one small problem: there is no empirical evidence that shows that string theory is correct. It is a purely mathematical theory derived from looking at the geometry of strings interacting. No one has ever “seen” a string or shown that they exist. Detractors of string theory declare that it is “just mathematics” and has nothing to do with the physical world. Defenders point to other branches of mathematics that have made correct predictions about the physical world. To them, this theory will also be proved true in the future. They say, too, that string theory is one of the few theories that successfully unite quantum mechanics and general relativity. Whether the world is made out of little strings or not, it is still amazing that pure mathematics can describe all the properties of the physical universe.