Software Complexity: How Do We Bring Order to Chaos?
A physician, a civil engineer, and a computer scientist were arguing about what was the oldest profession in the world. The physician remarked, "Well, in the Bible, it says that God created Eve from a rib taken out of Adam. This clearly required surgery, and so I can rightly claim that mine is the oldest profession in the world." The civil engineer interrupted, and said, "But even earlier in the book of Genesis, it states that God created the order of the heavens and the earth from out of the chaos. This was the first and certainly the most spectacular application of civil engineering. Therefore, fair doctor, you are wrong: mine is the oldest profession in the world." The computer scientist leaned back in her chair, smiled, and then said confidently, "Ah, but who do you think created the chaos?"
"The more complex the system, the more open it is to total breakdown" . Rarely would a builder think about adding a new sub-basement to an existing 100-story building. Doing that would be very costly and would undoubtedly invite failure. Amazingly, users of software systems rarely think twice about asking for equivalent changes. Besides, they argue, it is only a simple matter of programming.
Our failure to master the complexity of software results in projects that are late, over budget, and deficient in their stated requirements. We often call this condition the software crisis, but frankly, a malady that has carried on this long must be called normal. Sadly, this crisis translates into the squandering of human resources—a most precious commodity—as well as a considerable loss of opportunities. There are simply not enough good developers around to create all the new software that users need. Furthermore, a significant number of the development personnel in any given organization must often be dedicated to the maintenance or preservation of geriatric software. Given the indirect as well as the direct contribution of software to the economic base of most industrialized countries, and considering the ways in which software can amplify the powers of the individual, it is unacceptable to allow this situation to continue.
1.1 The Structure of Complex Systems
How can we change this dismal picture? Since the underlying problem springs from the inherent complexity of software, our suggestion is to first study how complex systems in other disciplines are organized. Indeed, if we open our eyes to the world about us, we will observe successful systems of significant complexity. Some of these systems are the works of humanity, such as the Space Shuttle, the England/France tunnel, and large business organizations. Many even more complex systems appear in nature, such as the human circulatory system and the structure of a habanero pepper plant.
The Structure of a Personal Computer
A personal computer is a device of moderate complexity. Most are composed of the same major elements: a central processing unit (CPU), a monitor, a keyboard, and some sort of secondary storage device, usually either a CD or DVD drive and hard disk drive. We may take any one of these parts and further decompose it. For example, a CPU typically encompasses primary memory, an arithmetic/logic unit (ALU), and a bus to which peripheral devices are attached. Each of these parts may in turn be further decomposed: An ALU may be divided into registers and random control logic, which themselves are constructed from even more primitive elements, such as NAND gates, inverters, and so on.
Here we see the hierarchic nature of a complex system. A personal computer functions properly only because of the collaborative activity of each of its major parts. Together, these separate parts logically form a whole. Indeed, we can reason about how a computer works only because we can decompose it into parts that we can study separately. Thus, we may study the operation of a monitor independently of the operation of the hard disk drive. Similarly, we may study the ALU without regard for the primary memory subsystem.
Not only are complex systems hierarchic, but the levels of this hierarchy represent different levels of abstraction, each built upon the other, and each understandable by itself. At each level of abstraction, we find a collection of devices that collaborate to provide services to higher layers. We choose a given level of abstraction to suit our particular needs. For instance, if we were trying to track down a timing problem in the primary memory, we might properly look at the gate-level architecture of the computer, but this level of abstraction would be inappropriate if we were trying to find the source of a problem in a spreadsheet application.
The Structure of Plants and Animals
In botany, scientists seek to understand the similarities and differences among plants through a study of their morphology, that is, their form and structure. Plants are complex multicellular organisms, and from the cooperative activity of various plant organ systems arise such complex behaviors as photosynthesis and transpiration.
Plants consist of three major structures (roots, stems, and leaves). Each of these has a different, specific structure. For example, roots encompass branch roots, root hairs, the root apex, and the root cap. Similarly, a cross-section of a leaf reveals its epidermis, mesophyll, and vascular tissue. Each of these structures is further composed of a collection of cells, and inside each cell we find yet another level of complexity, encompassing such elements as chloroplasts, a nucleus, and so on. As with the structure of a computer, the parts of a plant form a hierarchy, and each level of this hierarchy embodies its own complexity.
All parts at the same level of abstraction interact in well-defined ways. For example, at the highest level of abstraction, roots are responsible for absorbing water and minerals from the soil. Roots interact with stems, which transport these raw materials up to the leaves. The leaves in turn use the water and minerals provided by the stems to produce food through photosynthesis.
There are always clear boundaries between the outside and the inside of a given level. For example, we can state that the parts of a leaf work together to provide the functionality of the leaf as a whole and yet have little or no direct interaction with the elementary parts of the roots. In simpler terms, there is a clear separation of concerns among the parts at different levels of abstraction.
In a computer, we find NAND gates used in the design of the CPU as well as in the hard disk drive. Likewise, a considerable amount of commonality cuts across all parts of the structural hierarchy of a plant. This is God's way of achieving an economy of expression. For example, cells serve as the basic building blocks in all structures of a plant; ultimately, the roots, stems, and leaves of a plant are all composed of cells. Yet, although each of these primitive elements is indeed a cell, there are many different kinds of cells. For example, there are cells with and without chloroplasts, cells with walls that are impervious to water and cells with walls that are permeable, and even living cells and dead cells.
In studying the morphology of a plant, we do not find individual parts that are each responsible for only one small step in a single larger process, such as photosynthesis. In fact, there are no centralized parts that directly coordinate the activities of lower-level ones. Instead, we find separate parts that act as independent agents, each of which exhibits some fairly complex behavior, and each of which contributes to many higher-level functions. Only through the mutual cooperation of meaningful collections of these agents do we see the higher-level functionality of a plant. The science of complexity calls this emergent behavior: The behavior of the whole is greater than the sum of its parts .
Turning briefly to the field of zoology, we note that multicellular animals exhibit a hierarchical structure similar to that of plants: Collections of cells form tissues, tissues work together as organs, clusters of organs define systems (such as the digestive system), and so on. We cannot help but again notice God's awesome economy of expression: The fundamental building block of all animal matter is the cell, just as the cell is the elementary structure of all plant life. Granted, there are differences between these two. For example, plant cells are enclosed by rigid cellulose walls, but animal cells are not. Notwithstanding these differences, however, both of these structures are undeniably cells. This is an example of commonality that crosses domains.
A number of mechanisms above the cellular level are also shared by plant and animal life. For example, both use some sort of vascular system to transport nutrients within the organism, and both exhibit differentiation by sex among members of the same species.
The Structure of Matter
The study of fields as diverse as astronomy and nuclear physics provides us with many other examples of incredibly complex systems. Spanning these two disciplines, we find yet another structural hierarchy. Astronomers study galaxies that are arranged in clusters. Stars, planets, and debris are the constituents of galaxies. Likewise, nuclear physicists are concerned with a structural hierarchy, but one on an entirely different scale. Atoms are made up of electrons, protons, and neutrons; electrons appear to be elementary particles, but protons, neutrons, and other particles are formed from more basic components called quarks.
Again we find that a great commonality in the form of shared mechanisms unifies this vast hierarchy. Specifically, there appear to be only four distinct kinds of forces at work in the universe: gravity, electromagnetic interaction, the strong force, and the weak force. Many laws of physics involving these elementary forces, such as the laws of conservation of energy and of momentum, apply to galaxies as well as quarks.
The Structure of Social Institutions
As a final example of complex systems, we turn to the structure of social institutions. Groups of people join together to accomplish tasks that cannot be done by individuals. Some organizations are transitory, and some endure beyond many lifetimes. As organizations grow larger, we see a distinct hierarchy emerge. Multinational corporations contain companies, which in turn are made up of divisions, which in turn contain branches, which in turn encompass local offices, and so on. If the organization endures, the boundaries among these parts may change, and over time, a new, more stable hierarchy may emerge.
The relationships among the various parts of a large organization are just like those found among the components of a computer, or a plant, or even a galaxy. Specifically, the degree of interaction among employees within an individual office is greater than that between employees of different offices. A mail clerk usually does not interact with the chief executive officer of a company but does interact frequently with other people in the mail room. Here, too, these different levels are unified by common mechanisms. The clerk and the executive are both paid by the same financial organization, and both share common facilities, such as the company's telephone system, to accomplish their tasks.