Tag Archives: Ronald Giere

Scientific Revolutions and Relativism

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Recently, Facebook CEO Mark Zuckerberg chose Thomas Kuhn’s classic The Structure of Scientific Revolutions for his book discussion group. And although I don’t usually try to update this blog with the most recent controversy of the day, this time I can’t resist jumping on the Internet bandwagon and delving into this difficult, challenging book.

To briefly summarize, Kuhn disputes the traditional notion of science as one of cumulative growth, in which Galileo and Kepler build upon Copernicus, Newton builds upon Galileo and Kepler, and Einstein builds upon Newton. This picture of cumulative growth may be accurate for periods of “normal science,” Kuhn writes, when the community of scientists are working from the same general picture of the universe. But there are periods when the common picture of the universe (which Kuhn refers to as a “paradigm”) undergoes a revolutionary change. A radically new picture of the universe emerges in the community of scientists, old words and concepts obtain new meanings, and scientific consensus is challenged by conflict between traditionalists and adherents of the new paradigm. If the new paradigm is generally successful in solving new puzzles AND solving older puzzles that the previous paradigm solved, the community of scientists gradually moves to accept the new paradigm — though this often requires that stubborn traditionalists eventually die off.

According to Kuhn, science as a whole progressed cumulatively in the sense that science became better and better at solving puzzles and predicting things, such as the motions of the planets and stars. But the notion that scientific progress was bringing us closer and closer to the Truth, was in Kuhn’s view highly problematic. He felt there was no theory-independent way of saying what was really “out there” — conceptions of reality were inextricably linked to the human mind and its methods of perceiving, selecting, and organizing information. Rather than seeing science as evolving closer and closer to an ultimate goal, Kuhn made an analogy to biological evolution, noting that life evolves into higher forms, but there is no evidence of a final goal toward which life is heading. According to Kuhn,

I do not doubt, for example, that Newton’s mechanics improves on Aristotle’s and that Einstein’s improves on Newton’s as instruments for puzzle-solving. But I can see in their succession no coherent direction of ontological development. On the contrary, in some important respects, though by no means all, Einstein’s general theory of relativity is closer to Aristotle’s than either of them is to Newton’s. (Structure of Scientific Revolutions, postscript, pp. 206-7.)

This claim has bothered many. In the view of Kuhn’s critics, if a theory solves more puzzles, predicts more phenomena to a greater degree of accuracy, the theory must be a more accurate picture of reality, bringing us closer and closer to the Truth. This is a “common sense” conclusion that would seem to be irrefutable. One writer in Scientific American comments on Kuhn’s appeal to “relativists,” and argues:

Kuhn’s insight forced him to take the untenable position that because all scientific theories fall short of absolute, mystical truth, they are all equally untrue. Because we cannot discover The Answer, we cannot find any answers. His mysticism led him to a position as absurd as that of the literary sophists who argue that all texts — from The Tempest to an ad for a new brand of vodka — are equally meaningless, or meaningful. (“What Thomas Kuhn Really Thought About Scientific ‘Truth’“)

Many others have also charged Kuhn with relativism, so it is important to take some time to examine this charge.

What people seem to have a hard time grasping is what scientific theories actually accomplish. Scientific theories or models can in fact be very good at solving puzzles or predicting outcomes without being an accurate reflection of reality — in fact, in many cases theories have to be unrealistic in order to be useful! Why? A theory must accomplish several goals, but some of these goals are incompatible, requiring a tradeoff of values. For example, the best theories generalize as much as possible, but since there are exceptions to almost every generalization, there is a tradeoff between generalizability and accuracy. As Nancy Cartwright and Ronald Giere have pointed out, the “laws of physics” have many exceptions when matched to actual phenomena; but we cherish the laws of physics because of their wide scope: they subsume millions of observations under a small number of general principles, even though specific cases usually don’t exactly match the predictions of any one law.

There is also a tradeoff between accuracy and simplicity. Complete accuracy in many cases may require dozens of complex calculations; but most of the time, complete accuracy is not required, so scientists go with the simplest possible principles and calculations. For example, when dealing with gravity, Newton’s theory is much simpler than Einstein’s, so scientists use Newton’s equations until circumstances require them to use Einstein’s equations. (For more on theoretical flexibility, see this post.)

Finally, there is a tradeoff between explanation and prediction. Many people assume that explanation and prediction are two sides of the same coin, but in fact it is not only possible to predict outcomes without having a good causal model, sometimes focusing on causation gets in the way of developing a good predictive model. Why? Sometimes it’s difficult to observe or measure causal variables, so you build your model using variables that are observable and measurable even if those variables are merely associated with certain outcomes and may not cause those outcomes. To choose a very simple example, a model that posits that a rooster crowing leads to the rising of the sun can be a very good predictive model while saying nothing about causation. And there are actually many examples of this in contemporary scientific practice. Scientists working for the Netflix corporation on improving the prediction of customers’ movie preferences have built a highly valuable predictive model using associations between certain data points, even though they don’t have a true causal model. (See Galit Shmueli, “To Explain or Predict” in Statistical Science, 2010, vol. 25, no. 3)

Not only is there no single, correct way to make these value tradeoffs, it is often the case that one can end up with multiple, incompatible theories that deal with the same phenomena, and there is no obvious choice as to which theory is best. As Kuhn has pointed out, new theories become widely accepted among the community of scientists only when the new theory can account for anomalies in the old theory AND yet also conserve at least most of the predictions of the old theory. Even so, it is not long before even newer theories come along that also seem to account for the same phenomena equally well. Is it relativism to recognize this fact? Not really. Does the reality of multiple, incompatible theories mean that every person’s opinion is equally valid? No. There are still firm standards in science. But there can be more than one answer to a problem. The square root of 1,000,000 can be 1000 or -1000. That doesn’t mean that any answer to the square root of 1,000,000 is valid!

Physicist Stephen Hawking and philosopher Ronald Giere have made the analogy between scientific theories and maps. A map is an attempt to reduce a very large, approximately spherical, three dimensional object — the earth — to a flat surface. There is no single correct way to make a map, and all maps involve some level of inaccuracy and distortion. If you want accurate distances, the areas of the land masses will be inaccurate, and vice versa. With a small scale, you can depict large areas but lose detail. If you want to depict great detail, you will have to make a map with a larger scale. If you want to depict all geographic features, your map may become so cluttered with detail it is not useful, so you have to choose which details are important — roads, rivers, trees, buildings, elevation, agricultural areas, etc. North can be “up” on your map, but it does not have to be. In fact, it’s possible to make an infinite number of valid maps, as long as they are useful for some purpose. That does not mean that anyone can make a good map, that there are no standards. Making good maps requires knowledge and great skill.

As I noted above, physicists tend to prefer Newton’s theory of gravity rather than Einstein’s to predict the motion of celestial objects because it is simpler. There’s nothing wrong with this, but it is worth pointing out that Einstein’s picture of gravity is completely different from Newton’s. In Newton’s view, space and time are separate, absolute entities, space is flat, and gravity is a force that pulls objects away from the straight lines that the law of inertia would normally make them follow. In Einstein’s view, space and time are combined into one entity, spacetime, space and time are relative, not absolute, spacetime is curved in the presence of mass, and when objects orbit a planet it is not because the force of gravity is overcoming inertia (gravity is in fact a “fictitious force“), but because objects are obeying the law of inertia by following the curved paths of spacetime! In terms of prediction, Einstein’s view of gravity offers an incremental improvement to Newton’s, but Einstein’s picture of gravity is so radically different, Kuhn was right in seeing Einstein’s theory as a revolution. But scientists continue to use Newton’s theory, because it mostly retains the value of prediction while excelling in the value of simplicity.

Stephen Hawking explains why science is not likely to progress to a single, “correct” picture of the universe:

[O]our brains interpret the input from our sensory organs by making a model of the world. When such a model is successful at explaining events, we tend to attribute to it, and the elements and concepts that constitute it, the quality of reality or absolute truth. But there may be different ways in which one could model the same physical situation, with each employing different fundamental elements and concepts. If two such physical theories or models accurately predict the same events, one cannot be said to be more real than the other; rather we are free to use whichever model is more convenient.  (The Grand Design, p. 7)

I don’t think this is “relativism,” but if people insist that it is relativism, it’s not Kuhn who is the guilty party. Kuhn is simply exposing what scientists do.

What Are the Laws of Nature? – Part Two

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In a previous post, I discussed the mysterious status of the “laws of nature,” pointing out that these laws seem to be eternal, omnipresent, and possessing enormous power to shape the universe, although they have no mass and no energy.

There is, however, an alternative view of the laws of nature proposed by thinkers such as Ronald Giere and Nancy Cartwright, among others. In this view, it is a fallacy to suppose that the laws of nature exist as objectively real entities — rather, what we call the laws of nature are simplified models that the human mind creates to explain and predict the operations of the universe. The laws were created by human beings to organize information about the cosmos. As such, the laws are not fully accurate descriptions of how the universe actually works, but generalizations; and like nearly all generalizations, there are numerous exceptions when the laws are applied to particular circumstances. We retain the generalizations because they excel at organizing and summarizing vast amounts of information, but we should never make the mistake of assuming that the generalizations are real entities. (See Science Without Laws and How the Laws of Physics Lie.)

Consider one of the most famous laws of nature, Isaac Newton’s law of universal gravitation. According to this law, the gravitational relationship between any two bodies in the universe is determined by the size (mass) of the two bodies and their distance from each other. More specifically, any two bodies in the universe attract each other with a force that is (1) directly proportional to the product of their masses and (2) inversely proportional to the square of the distance between them.  The equation is quite simple:

F = G \frac{m_1 m_2}{r^2}\

where F is the force between two masses, G is a gravitational constant, m1 and m2 are the masses of the two bodies and r is the distance between the center of the two bodies.

Newton’s law was quite valuable in helping predict the motions of the planets in our solar system, but in some cases the formula did not quite match to astronomical observations. The orbit of the planet Mercury in particular never fit Newton’s law, no matter how much astronomers tried to fiddle with the law to get the right results. It was only when Einstein introduced his theory of relativity that astronomers could correctly predict the motions of all the planets, including Mercury. Why did Einstein’s theory work better for Mercury? Because as the planet closest to the sun, Mercury is most affected by the massive gravitation of the sun, and Newton’s law becomes less accurate under the conditions of massive gravitation.

Einstein’s equations for gravity are known as the “field equations,” and although they are better at predicting the motions of the planets, they are extremely complex — too complex really for many situations. In fact, physicist Stephen Hawking has noted that scientists still often use Newton’s law of gravity because it is much simpler and a good enough approximation in most cases.

So what does this imply about the reality of Newton’s law of universal gravitation? Does Newton’s law float around in space or in some transcendent realm directing the motions of the planets, until the gravitation becomes too large, and then it hands off its duties to the Einstein field equations? No, of course not. Newton’s law is an approximation that works for many, but not all cases. Physicists use it because it is simple and “good enough” for most purposes. When the approximations become less and less accurate, a physicist may switch to the Einstein field equations, but this is a human value judgment, not the voice of nature making a decision to switch equations.

One other fact is worth noting: in Newton’s theory, gravity is a force between two bodies. In Einstein’s theory, gravity is not a real force — what we call a gravitational force is simply how we perceive the distortion of the space-time fabric caused by massive objects. Physicists today refer to gravity as a “fictitious force.” So why do professors of physics continue to use Newton’s law and teach this “fictitious force” law to their students? Because it is simpler to use and still a good enough approximation for most cases. Newton’s law can’t possibly be objectively real — if it is, Einstein is wrong.

The school of thought known as “scientific realism” would dispute these claims, arguing that even if the laws of nature as we know them are approximations, there are still real, objective laws underneath these approximations, and as science progresses, we are getting closer and closer to knowing what these laws really are. In addition, they argue that it would be absurd to suppose that we can possibly make progress in technology unless we are getting better and better in knowing what the true laws are really like.

The response of Ronald Giere and Nancy Cartwright to the realists is as follows: it’s a mistake to assume that if our laws are approximations and our approximations are getting better and better that therefore there must be real laws underneath. What if nature is inherently so complex in its causal variables and sequences that there is no objectively real law underneath it all? Nancy Cartwright notes that engineers who must build and maintain technological devices never apply the “laws of nature” directly to their work without a great deal of tinkering and modifications to get their mental models to match the specific details of their device. The final blueprint that engineers may create is a highly specific and highly complex model that is a precise match for the device, but of very limited generalizability to the universe as a whole. In other words, there is an inherent and unavoidable tradeoff between explanatory power and accuracy. The laws of nature are valued by us because they have very high explanatory power, but specific circumstances are always going to involve a mix of causal forces that refute the predictions of the general law. In order to understand how two bodies behave, you not only need to know gravity, you need to know the electric charge of the two bodies, the nuclear force, any chemical forces, the temperature, the speed of the objects, and additional factors, some of which can never be calculated precisely. According to Cartwright,

. . . theorists tend to think that nature is well-regulated; in the extreme, that there is a law to cover every case. I do not. I imagine that natural objects are much like people in societies. Their behavior is constrained by some specific laws and by a handful of general principles, but it is not determined in detail, even statistically. What happens on most occasions is dictated by no law at all. . . . God may have written just a few laws and grown tired. We do not know whether we are living in a tidy universe or an untidy one. (How the Laws of Physics Lie, p. 49)

Cartwright makes it clear that she believes in causal powers in nature — it’s just that causal powers are not the same as laws, which are simply general principles for organizing information.

Some philosophers and scientists would go even further. They argue that science is able to develop and improve models for predicting phenomena, but the underlying nature of reality cannot be grasped directly, even if our models are quite excellent at predicting. This is because there are always going to be aspects of nature that are non-observable and there are often multiple theories that can explain the same phenomenon. This school of thought is known as instrumentalism.

Stephen Hawking appears to be sympathetic to such a view. In a discussion of his use of “imaginary time” to model how the universe developed, Hawking stated “a scientific theory is just a mathematical model we make to describe our observations: it exists only in our minds. So it is meaningless to ask: which is real, “real” or “imaginary” time? It is simply a matter of which is the more useful description.” (A Brief History of Time, p. 144) In a later essay, Hawking made the case for what he calls “model-dependent realism.” He argues:

it is pointless to ask whether a model is real, only whether it agrees with observation. If two models agree with observation, neither one can be considered more real than the other. A person can use whichever model is more convenient in the situation under consideration. . . . Each theory may have its own version of reality, but according to model-dependent realism, that diversity is acceptable, and none of the versions can be said to be more real than any other.

Hawking concludes that given these facts, it may well be impossible to develop a unified theory of everything, that we may have to settle for a diversity of models. (It’s not clear to me how Hawking’s “model-dependent realism” differs from instrumentalism, since they seem to share many aspects.)

Intuitively, we are apt to conclude that our progress in technology is proof enough that we are understanding reality better and better, getting closer and closer to the Truth. But it’s actually quite possible for science to develop better and better predictive models while still retaining very serious doubts and disputes about many fundamental aspects of reality. Among physicists and cosmologists today, there is still disagreement on the following issues: are there really such things as subatomic particles, or are these entities actually fields, or something else entirely?; is the flow of time an illusion, or is time the chief fundamental reality?; are there an infinite number of universes in a wider multiverse, with infinite versions of you, or is this multiverse theory a mistaken interpretation of uncertainty at the quantum level?; are the constants of the universe really constant, or do they sometimes change?; are mathematical objects themselves the ultimate reality, or do they exist only in the mind? A number of philosophers of science have concluded that science does indeed progress by creating more and better models for predicting, but they make an analogy to evolution: life forms may be advancing and improving, but that doesn’t mean they are getting closer and closer to some final goal.

Referring back to my previous post, I discussed the view that the “laws of nature” appear to exist everywhere and have the awesome power to shape the universe and direct the motions of the stars and planets, despite the fact that the laws themselves have no matter and no energy. But if the laws of nature are creations of our minds, what then? I can’t prove that there are no real laws behind the mental models that we create. It seems likely that there must be some such laws, but perhaps they are so complex that the best we can do is create simplified models of them. Or perhaps we must acknowledge that the precise nature of the cosmological order is mysterious, and any attempt to understand and describe this order must use a variety of concepts, analogies, and stories created by our minds. Some of these concepts, analogies, and stories are clearly better than others, but we will never find one mental model that is a perfect fit for all aspects of reality.