An Exploration of Questions in the Ontology of Unification Thought - David Burton
The English translations of Unification Thought have a quality that is reminiscent of St. Augustine’s writings. Augustine’s writings have been of particular influence in Christianity, but at the same time have sparked centuries of debate. This is because of a certain quality of his writing that has been described as “unfinished” or “open,” where, among other things, ideas are not strictly defined throughout his work.1
Unification Thought in its current formulation has a similar “unfinished” quality, even though it strives to be completely systematic. Some of the “unfinished” quality undoubtedly arises in translation from Korean to English, resulting in a need for clearer definitions for the English terms used. There are also, however, structural and pedagogical considerations and some areas that Dr. Lee does not really address at all. Two areas important for ontology that Dr. Lee does not develop are considerations of the spirit world and an evolutionary theory.2 Furthermore, there are issues of consistency with the Divine Principle, the source upon which Dr. Lee builds his philosophical edifice.
What follows is an exploration of four of these unfinished questions, or issues, in ontology. Some suggestions for development are offered for each, but the suggestions offered, like the questions themselves, are not necessarily finished or complete.
Section one deals with some of the basic assumptions that underlie Unification Thought’s ontology, and the problems with not acknowledging them as such. Section two deals with the fundamental structure of the cosmos (both spiritual and physical), that arose from a consideration of the place of Cosmic Consciousness in the ontological structures that Dr. Lee develops. Sections three and four deal with the difficulties of applying the ontological structures developed in the Theory of the Original Image to the created realm. Section three addresses their application to the individual as a connected body, and section four deals with their application to the change and development of the universe.
In their discussions of ontology, both Unification Thought and Divine Principle have four basic assumptions:
1. God exists.
2. God created all things.
3. All things resemble God.
4. Existence (including God’s) is relational.
Divine Principle quotes Romans 1:20 as scriptural support for assumption three,3 then uses that assumption to make inferences about the nature of God’s existence from observation of all things. The logic of the argument is that since there are common characteristics discernable in all things, and all things resemble God, those common characteristics must be attributes of God. In the subsequent discussion of the common characteristics4 a case is also made for assumption four, the relational nature of existence. Support for both the relational nature of existence and the Divine Principle’s view of God therefore both rely on “observation” of existing beings.
In Unification Thought, Dr Sang Hun Lee takes a slightly different track. In the newer English translations, Explaining Unification Thought (1981) and Essentials of Unification Thought(1992), the discussion of the nature of God is separated from ontology and appears in the Theory of the Original Image. It also appears first, before the discussion of ontology. Dr. Lee, therefore, changes the logic of explanation that appears in Divine Principle. He can do this because Divine Principle is now the authoritative source of support for the concepts. Indeed in Essentials of Unification Thought he clearly implies that the Theory of Original Image is deduced from Divine Principle.5
While this approach more clearly sets out the fundamental concepts for someone to understand, the change in logic from Divine Principle creates an additional problem. At the beginning of the chapter on ontology in Essentials of Unification Thought Dr. Lee states:
Unification ontology is a theory that supports the theory of the Original Image. Further, the theory of the Original Image is a deductive theory based on the Unification Principle. It is in ontology, however, that we can ascertain whether or not the attributes of God explained in the theory of the Original Image are actually manifested in all things and, if so, how are they manifested. If it can be shown that the attributes of God are universally manifested in all things, then the truthfulness of the theory of the Original Image becomes ascertained.6
The logic implicit in Unification Thought is therefore that discussions about the nature of God can be deduced from Divine Principle. Then, because of assumption three, these concepts are confirmed by “observation” of existing beings.
The difference in logic becomes apparent when looking at the dual characteristics of principal element and subordinate element as presented in Essentials of Unification Thought. Recognizing that not all subject and object relationships are sungsang and hyungsang, or yang and yin, Dr. Lee introduces principal element and subordinate element as a third set of dual characteristics of existing beings.7 In the logic of Divine Principle these characteristics should therefore be ascribed to God also, but Dr. Lee does not do this. Instead he applies them only to existing beings.
A problem then arises when we take Divine Principle and Unification Thought together, because, when they are combined, we are faced with a circular argument: God’s attributes may be deduced from observation of existing beings in Divine Principle, then the Theory of the Original Image is deduced from Divine Principle and confirmed by observation of existing beings. There is no external point of reference unless we regard Divine Principle as revelation received through Rev. Moon. Unification Thought as it stands cannot, therefore, stand apart from Father and Divine Principle. Consequently, careful thought needs to be given to the logic inherent in the explanation of Unification Thought.
I do not believe it is possible to put forward a purely deductive argument, as both Divine Principle and Unification Thought appear to try to do. Some things will have to be just given, or explained as Father’s thought. My personal preference would be to start from a set of basic assumptions, such as those that given above, and introduce the concepts of Unification Thought in their elaboration.
In my reading of Unification Thought I have always been puzzled by Dr. Lee’s introduction of a life field or cosmic consciousness. In my perception it has always appeared rather abruptly with little or no justification or explanation. I have recently experienced what amounts to a paradigm shift in my approach to understanding how it fits into the overall structure of Unification Thought’s ontology. I will attempt to explain.
In Divine Principle and Unification Thought, God is described primarily as a being of sungsang and hyungsang. In English these are translated in several different ways, such as: internal character and external form, mind and body, or spirit and matter. Then, in the created universe, these two are manifested so that the primary distinction in the creation is also sungsang and hyungsang. In Essentials of Unification Thought Dr. Lee shows this in a diagram8 where the terms spirit and matter appear in brackets after sungsang and hyungsang respectively. In Divine Principle it is the spiritual world and physical world (invisible substantial world and visible substantial world) that are presented as the primary sungsang and hyungsang description of the creation.
Since the universe was created after the model of man, who is in the image and likeness of God’s dual essentialities, every existence, without exception, takes after man’s basic form, which consists of mind and body. Thus, in the universe there exists not only the visible substantial world, which resembles the human body, but also the invisible substantial world, which is modeled after the human mind. We call the latter the invisible substantial world, because we cannot perceive it with our five physical senses; however, we can perceive it with our five spiritual senses. The invisible world, like the visible world, is a world of reality. It is actually felt and perceived through the five spiritual senses. The two substantial worlds together are called the “macrocosm.”9
In this passage human beings are said to consist primarily of mind and body, but later in the text it is the spirit person and physical person that seem to be presented as the primary structure. This appears in the description of the position of human beings in the universe,10 and in the explanation that the perfection of the individual four-position base is the spirit person and physical person relationship. There is some ambiguity in the Divine Principle explanation because it is attempting to describe the four-fold structure of a human being in terms of dualities. Thus it fails to distinguish some types of relationship within a person. There is a description of the four-fold structure of a human being in Divine Principle,12 where a human being consists of spiritual mind, physical mind, spiritual body and physical body. This model is not consistently applied, however, when discussing sungsang and hyungsang relationships.
Unification Thought is clearer on this point. In Essentials of Unification Thought, Dr. Lee identifies the four-fold nature of a human being similarly to Divine Principle. He then takes the explanation a step further than Divine Principle when he describes several kinds of sungsang and hyungsang relationships within a human being.13 Thus a person is essentially both mind and body and spirit person and physical person (two of the kinds of sungsang and hyungsang relationships).
Since God created the universe after the model of man, it seems natural to apply this four-fold structure to the universe as an individual truth body. Neither Divine Principle nor Unification Thought take this additional step or identify the multiple types of sungsang and hyungsang relationships that would go with it. Consequently in our prevailing paradigm of the structure of the universe there is not a clear place for cosmic consciousness, and its introduction in Unification Thought seems awkward. Applying this four-fold structure to the universe as a whole (see Fig. 1) I believe helps.
Changing the paradigm, by applying this four-fold structure to the universe, changes the view of the created universe. Thus the sungsang and hyungsang structure of the universe is both spirit and matter and spiritual world and physical world. This is analogous to two of the sungsang and hyungsang relationships of a person discussed above. Matter in this view can be of the physical world or spiritual world. Spirit too would be present in both the spiritual and physical worlds as their sungsang. This is similar to the idea of Teilhard de Chardin,14 who postulates a “psychic withinness” (or spirit withinness) to matter that is the base of life and consciousness.
The idea of cosmic consciousness now naturally flows from this sungsang and hyungsang structure of the creation. Analogous to the human mind, it probably derives from the relation of the spiritual sungsang and physical sungsang. It no longer appears an awkward addition.
Additionally a clearer definition of terminology is suggested since the term “spirit” is somewhat ambiguous. It can mean something just having quality, as in traditional Christian philosophy. Or, as in common usage, it can mean a spirit, referring to a spirit person, which includes the idea of body. Additionally the equality of spirit with spiritual world is quite a common paradigm. I believe the term “spirit” should be reserved just for the quality of sungsang unless it is qualified by some other term, i.e. “spirit body,” “spiritual world,” etc., when it now has quantitative hyungsang attributes.
Fundamental to both the Theory of the Original Image and ontology are the concepts of the four-position base and give-and-receive action. These concepts are the basic ground of explanation for all areas of Unification Thought, but are particularly important for the Theory of the Original Image and Ontology.
Dr. Lee introduces the concepts in the context of the Theory of the Original Image. Here we a dealing with a single unified being outside of time. This simplifies the situation in order to describe the concepts. This approach is much like a scientific model. He identifies four basic types of four-position base15 that have inner, outer, identity maintaining and developing characteristics. Moreover the primary subject and object positions are of the sungsang and hyungsang type, where both sungsang and hyungsang have yang and yin attributes.
Since all things resemble God (see assumption 3, above) similar patterns of relationship should be found in the created universe as well. Now the situation gets more complex to describe, however, as we are dealing with a multitude of existing beings interacting over the course of time. Again, in order to simplify the situation, Dr. Lee looks at things from the perspective of a single existing being. Here the inner and outer patterns of the Original Image are seen as being manifest in the existence of the being as both an individual truth body and as a connected body.16 This does, however, modify the concept of the outer four-position base presented in the Theory of the Original Image since the outer base (connected body) is no longer of the sungsang and hyungsangtype. Additionally this outer base is now the relationship of an individual truth body with something outside of itself, i.e. another individual truth body or external field. This is in contrast to the Theory of the Original Image, where there is no “other,” as God is seen as a unified being. It is therefore necessary to look at the nature of this interaction.
In the Theory of the Original Image there are two sets of dual characteristics: sungsang and hyungsang, and yang and yin. Since this outer base of the connected body is not of the sungsang and hyungsang type, we are left with yang and yin. Yang and yin relationships, however, do not cover all the possible types of relationship between two existing beings. Recognizing this, Dr. Lee introduces another set of dual characteristics, principal element and subordinate element, in Essentials of Unification Thought.17Thus, in existing beings he describes three sets of dual characteristics.
While most relationships in the created realm can be described by these three sets of dual characteristics, there are situations where this breaks down. To illustrate the problem, let us consider two isolated bodies in space interacting through gravity.
Each object has a certain energy and motion, and the force of gravity acts in a straight line between them. If the gravitational force is sufficiently strong, the two bodies will revolve around each other to form a combined system. The combined system can be regarded as a larger entity in its own right, and the two bodies revolve around the center of mass of the combined system. In this combined system the force of gravity acts through the center of mass on each body. Additionally, if both bodies have the same mass, the center of mass lies outside of both of them.
From the perspective of Unification Thought, this interaction within the combined system looks superficially like an identity-maintaining four-position base where two existing entities combine into a larger union, or harmonized body. Looking deeper we can see problems, however. First, what kind of relationship is it? It is not sungsang and hyungsang, yang and yin, or principal element and subordinate element. Furthermore there is no discernable subject entity, and the center of the relation (center of mass) lies outside of both entities since both have the same mass. This kind of relationship does not clearly follow the kind of patterns described in Unification Thought.
In the section on the mode of existence in Essentials of Unification Thought, Dr. Lee describes the circular motion that results from give-and-receive action. In this circular motion the center of the circular motion is the center and subject of the relationship.18 In the example presented above the subject, as center of the resulting circular motion, must therefore be the center of mass of the unified body even though it lies outside both interacting entities (It does, however, lie at the center of the unified body). Neither entity is in the subject position, so they must both be objects in the interaction. It is not until one of the bodies is sufficiently larger than the other that the center of mass will lie within one of the bodies and we can clearly identify a subject entity. Additionally, when we look at interactions in the physical world mediated by gravity and electromagnetism, in all cases the subject, the center of the resulting circular motion, is defined by the center of mass of the combined system rather than from any other property of the interacting bodies. Fitting these kinds of interactions into the structures developed in Unification Thought thus requires additional explanation.
In conclusion, I believe that the problem lies in the way Unification Thought maps the pattern of the inner and outer structure of the Original Image onto the creation. Dr. Lee’s mapping of the outer four-position base in the Theory of the Original Image to the connected body in creation immediately runs into problems as it modifies the sungsang and hyungsangstructures. This in turn leads him to posit a third set of dual characteristics for the created realm. This subsequently creates more problems: First, it strains assumption 3 above (the assumption of resemblance) since this third set of dual characteristics is not found in the Original Image. Second, even three sets of dual characteristics do not cover all possible types of relationships.
This mapping of the inner and outer structure, and the two sets of dual characteristics, from the Theory of the Original Image to the creation would be more applicable to single individual truth bodies. This would allow retention of the sungsang and hyungsangstructure developed in the Theory of the Original Image without modification or requiring additional sets of dual characteristics. This still leaves the problem of explaining the relationships between individual truth bodies, which is not a problem in the Original Image, especially since they do not necessarily all follow the patterns described in Unification Thought. It is possible a separate description (not additional sets of characteristics) is needed for each type of force19 that can act between individual truth bodies. Moreover, we cannot just discard all the concepts of the connected body since they are important for the overall picture presented in Unification Thought.
In its discussion of the created realm Unification Thought tends to deal with an explanation of the universe as it is now. It does not really deal with the process of how it got to be the way it is. In other words Unification Thought does not have an evolutionary theory. By evolutionary theory I do not just mean creation and evolution of life, but also the ongoing creation and evolution of the universe as a whole, including God's connection to the process.
Traditionally this has not been a problem for philosophy, since the discussion of evolution and change has taken place against the backdrop of a static universe where changes in that background are not even considered.20 In the modern scientific worldview, however, changes in the universe as a whole are important and ongoing, and need to be taken into consideration. Taking a static approach to the universe or ignoring its changes leaves a substantial gap in any explanation of existence. Science, particularly physics, has a well developed understanding of the process of evolution of the physical universe, and this understanding is therefore important to take into account in any new ontology.
Since Dr. Lee’s explanations deal more with existence as it is now rather than how it came to be, there is this same gap or incompleteness in Unification Thought’s ontology. The evolutionary process of the universe as a whole is also perhaps one of the most difficult areas to explain clearly, since there are few philosophical precedents for it. What is needed is an ontological structure for the evolutionary process of the universe that is in accord with both scientific explanation and Unification Thought.
We can begin to approach this topic by looking at God’s act of creation described in Unification Thought. Here Dr. Lee presents what amounts to two slightly different explanations that are not completely connected. The first is most clearly presented in the structure of the Original Image in Explaining Unification Thought.21Here Dr. Lee describes a two-stage process in the creation of a bird. The first stage is in creation of a Logos for the bird in the inner developing four-position base, and the second stage is creation of the substantial bird as the multiplied body in the outer developing four-position base. To quote the text, “The actual bird is the result of give and take action between Logos and hyungsang(pre matter).”22 This seems to imply the bird is created substantially without regard for what has gone before, i.e. not by an evolutionary process.
The second explanation appears in the section about the individual image in ontology. According to Explaining Unification Thought:
In His mind God conceived the image of man first. Then He conceived the images of animals, plants, and finally minerals – taking the image of man as the standard. This is the downward process of creation of images (Logos) in the mind of God. It explains why man is the integration of all things. In the phenomenal world, however, God created everything starting from the minerals, then plants, animals and finally man. This is the upward process of creation of substantial beings.23
This second explanation is still a two stage process, but with the addition of the concept of at least the appearance of evolution in both image and substance. The upward process of creation is the closest Unification Thought comes to an evolutionary theory.
Thus the bird appears substantially in two possible ways. The first way is directly, as the multiplied body in the outer developing four-position base. This implies that all the matter of the bird is created at the same time. In the second way, the upward process, God creates the bird using matter that already exists and subsequently adding something new to it. This gives the appearance that created beings have a layered structure and that change is evolutionary, even though individual images do not have layers and the idea or concept of each being has prior existence within God. While both explanations may just be different views of the same thing, Dr. Lee does not clearly explain their structural connection in Explaining Unification Thought.
In Essentials of Unification Thought Dr. Lee steps back somewhat from the clear dichotomy presented in Explaining Unification Thought and gives greater emphasis to the upward process. The dichotomy is less apparent because in this text Dr. Lee does not explicitly explain that individual things (such as a bird) are formed directly as a multiplied body in the outer developing four-position base. For example, in the discussion about the creation of the bird, the creation of the Logos of the bird is discussed, but the explanation of its substantial creation in the outer developing four-position base has been dropped.24 He also adds additional explanation of the upward process in the section on the structure of the Original Image:
Through the activity of the Original sungsang over the Original hyungsang, God was able to generate energy and elementary particles. He then formed atoms by combining elementary particles; formed molecules by combining atoms; formed cells from atoms and molecules; and formed living organisms by causing the cells to multiply.25
The dichotomy is still present, however, in the underlying structure that is presented. This is because all things still appear as the multiplied body in the outer developing four-position base.26
The problem arises not necessarily because there are two explanations, but because Dr. Lee does not explicitly connect them structurally. The direct substantial appearance of things as the multiplied body in the outer developing four-position base fits most closely with the structure of the Original Image. However, since it lacks the appearance of evolutionary change, it is unsatisfactory from the perspective of the modern understanding of the evolution of the universe. The upward process of creation of the substantial world is better from this regard. Indeed the changes in explanation from Explaining Unification Thought to Essentials of Unification Thought lead me to suspect that Dr. Lee favored this explanation. The difficulty comes in trying to explain the upward process on the basis of the structures he presents.
In order to begin to address this problem, let us look again at the types of four-position base described in Unification Thought. As mentioned above, Unification Thought describes four basic types of four-position base. We looked at the inner and outer concepts in that section and now look at the identity-maintaining and developing concepts here.
There seem to be two possible paths for an individual truth body to come into existence, given the structures presented in Unification Thought. First, it may appear as the multiplied body in a developing four-position base. Second, it may appear when two (or more) existing beings, that were separate, develop a give-and-receive relationship and unite into one combined body that contains both of the original beings.
In the first path the multiplied body is actually formed from a part of the subject and a part of the object, and the resulting union is of the same, or lesser, order of complexity and size as the subject and object it is multiplied from. In the second path the new existence is formed from the whole of the subject and object and it has an additional layer of structure and complexity than either the subject or the object. It is tempting to ascribe this to an identity maintaining four-position base. Indeed Dr. Lee seems to do so in a discussion of the formation of a family in the section on the structure of the Original Image.27 However, strictly speaking the identity maintaining four-position base refers to how an individual truth body maintains its existence, not to how that individual truth body comes into existence. This second path thus does not easily fit the identity-maintaining/developing structures presented by Dr. Lee. Moreover, even though this second path is not explicitly discussed in Unification Thought, I believe it is a key to connecting the upward process of creation to the ontological structures presented in Unification Thought.
Modern physics has a well-developed scenario for the earliest stages of development of the physical universe. I think that the beginnings of another component of a possible evolutionary theory, or connection to the ontological structures of Unification Thought, can be discerned from a consideration of that scenario.
The universe began in an explosion – not an ordinary explosion, but a tremendous burst of energy filling all space… During this initial phase [first 10-4sec.] of the universe, the temperature was so high that ordinary matter, such as molecules, atoms, and even nucleons, could not exist. Instead, shortly after the big bang, the universe was a soup of photons (radiation), leptons, antileptons, quarks, and antiquarks, though not necessarily in equal numbers… but as the soup cooled, it began to “condense” into elementary particles, including protons and neutrons. As the temperature dropped further, these nucleons condensed into nuclei. Further condensation gave rise to molecules and matter in bulk.28
The early universe thus passed through a series of what we can call phase changes. A number of phase boundaries are defined by the time, temperature and pressure of the existing universe where the change occurs. Before the first phase boundary only certain possible individual truth bodies can exist, i.e. only certain identity maintaining four-position bases can exist. No further combination is possible. After the boundary the identity maintaining structure of the universe is different. It is more than just a "building up" from what already exists, even though it appears that way after the boundary has been passed. The whole universe has changed in a substantial way. It has evolved, or rather, a whole new set of individual truth bodies and layer of complexity has been created by God in the upward process of creation. This succession of phase boundaries is a second key to understanding the observed layered structure and evolution of existing beings.
Thus, the identity maintaining structure of the universe at a particular time is like a snapshot of that time. It is probably fairly constant between phase boundaries, but will change as a boundary is passed and something new has a possibility of existence, or rather is created. Thus it gives the appearance of evolution when viewed from an external point of view such as that taken by science.
A third key should be a consideration of God’s connection to this process and its ongoing unfolding, which in turn leads us to a consideration of Universal Prime Force. Such an undertaking is not addressed here, but will be the topic of another paper.
In sum, Unification Thought does a good job of explaining existence as it is now, the interconnectedness of structures and the relational nature of existence. The ontological structures presented in the English texts do not, however, clearly explain how things come into existence. Some tighter definitions of terminology (such as identity maintaining and developing four-position bases) and additional explanations are probably required. More problematic for the ontology of Unification Thought, and difficult to address within the given structure, is describing the apparent evolution of the universe. I believe the starting points for such a theory lie within Unification Thought, the modern understanding of how the physical universe has developed, and a consideration of the universe as an individual truth body in its own right. Outlining such a theory will be substantial task.
Unification Thought’s ontology is not as comprehensive and complete as it appears at first sight. The theories developed in the extant works are important and give insight into existence. However, the lack of systemization and gaps in content will probably hinder its acceptance by a wider public. What is presented above is not an exhaustive list of issues, but shows some areas where development is needed. I believe that any effort for further development or expression of Unification Thought will need to address these issues. In particular, any further systemization will need to address stricter definitions of terms, the logic implicit in the arguments, and the ramifications of such things as the spirit world for the structure of ontology.
Finally, most traditional ontologies were developed before the advent of modern science. Since the early 1920’s science has completely revolutionized our understanding of the physical universe and our place in it. Therefore arguments developed prior to this time, including evolutionary arguments, need to be reevaluated in the light of modern discoveries. Thus it is important for any new ontology, such as that presented in Unification Thought, to take into consideration, and account for, modern scientific understandings.
- See Etienne Gilson, The Christian Philosophy of Saint Augustine (New York: Vintage Books, 1967), p. 245.
- What is meant by an evolutionary theory in the context of this paper is discussed in section four. It is somewhat different from the Darwinian notion that usually springs to mind. Darwin’s theory has been addressed in a tract published by the Unification Thought Institute entitled From Evolution Theory to a New Creation Theory – Errors in Darwinism and a Proposal from Unification Thought, but is not discussed here.. There it is stated that Unification Thought presents a true theory of creation rather than a theistic theory of evolution. I do, however, believe it is still appropriate to use the term evolution within the context of Unification Thought, and have done so in this paper, as long as it is understood apart from the trappings of Darwinian theory.
- “Ever since the creation of the world His invisible nature, namely, His eternal power and deity, has been clearly perceived in the things that have been made. So they are without excuse.” (Rom. 1:20)
- Divine Principle (New York: HSA-UWC, 1977), p. 20. There are no substantial differences in the 1991 translation.
- Sang Hun Lee, Essentials of Unification Thought (Tokyo: Unification Thought Institute, 1992), p. 41.
- Ibid., pp. 51-52. This topic is discussed further in section 3.
- Lee, Essentials, p. 9.
- Divine Principle, pp. 57 - 58.
- Divine Principle, pp. 58 - 59.
- Divine Principle, p. 62.
- Divine Principle, pp. 60 – 61.
- Lee, Essentials, p. 93.
- Pierre Teilhard de Chardin, Activation of Energy, trans. Rene Hague (New York: Harcourt Brace Jovanovich, 1971), p. 101. Teilhard does not postulate spiritual matter, though suggesting the presence of spirit in physical matter.
- Lee, Essentials, pp. 30-31.
- Ibid., p. 68.
- Ibid., p. 52.
- Ibid., p. 71.
- Here I would include the four physical forces known to science and the force of love. There may also be other forces in the creation that we are not currently aware of, especially in the spirit world.
- In traditional thought, although the universe was originally created by God, since then it has been essentially unchanging.
- Sang Hun Lee, Explaining Unification Thought (New York: Unification Thought Institute, 1981), p. 35.
- Ibid., p. 69.
- Lee, Essentials, p. 23.
- Ibid., pp. 32-33.
- Ibid., pp. 31-32.
- Ibid., p. 33.
- Edwin Jones and Richard Childers, Contemporary College Physics, 3rd ed. (New York: McGraw Hill, 2001), p. 1021.