In spite of Plato’s scepticism, most Western philosophers have been satisfied with the definition of knowledge as belief that is both true and justified. Plato recognized that the meaning of the word knowledge is inextricably entwined with what constitutes sufficient justification for belief. All knowledge, however, derives ultimately from a set of assumptions or beliefs for which there is no formal proof - a difficulty that lies at the heart of philosophy, and which Descartes, (often referred to as the “Founder of Modern Philosophy”) attempted to address via his famous principle cogito ergo sum. Epistemologists (philosophers who study the nature of knowledge) must also address the range (or field) of meaning of the word itself. Knowledge of what is (descriptive, or propositional knowledge), for example, is not the same as knowledge of how to (procedural knowledge) although either, without the other, is of limited, if any value. Unprovable, but justifiably true beliefs (such as Euclid’s five axioms or postulates that apply to plane or Euclidean geometry) provide a point of departure for the construction of the entire edifice of scientific knowledge - through measurements of natural phenomena or made in the course of experiments and interpretation of their meaning. Such measurements, which require procedural knowledge, constitute, in effect, quantified experience. It is, however, precisely because scientific knowledge is based on evidence (scientific justification) that it is subject to a degree of uncertainty. This arises in part from the quality, quantity and completeness of the evidence, and in part from the psychology or “world view” of those who draw conclusions from it. Opinion, unsubstantiated statements, incomplete information or tradition do not provide sufficient justification for belief, an issue that Plato addressed two and a half thousand years ago. His concept of Forms - the universal truths that underlie the material world - demonstrates that perfect knowledge implies the possession of absolute truth which, in practice, can never be achieved. All “knowledge” is subject to caution and caveat; new or more accurate evidence, or reinterpretation of existing evidence, may demonstrate even long held beliefs to be partially or wholly false. Euclidean geometry and Newtonian physics, for example, provide approximations to physical reality which continue to serve us well in many contexts, but which are inadequate formulations in the realms of the very large or the very small - where relativity and quantum physics reign supreme. In contrast, the longstanding belief that the sun revolves around the Earth was shown by Copernicus to be entirely unfounded. The constant remodeling of what is considered to be known is familiar to mathematicians and scientists, who recognize the external and internal determinants of the quality of what might be called “practical” knowledge (propositions in which belief is more or less proportional to the evidence of their validity) and therefore the seemingly paradoxical uncertainty that is inherent in justified belief - perhaps because it is, after all, merely a product of the human mind.

From Axiom to Algorithm

In 1900, David Hilbert, a brilliant German mathematician set the course of mathematics for much of the next century by listing 23 major mathematical problems that remained unsolved. His own goal, or program, as it became known, was no less than an attempt to demonstrate that all of mathematics could be shown to follow from a finite set of well-chosen axioms (Hilbert provided 20 such axioms in place of Euclid’s), stated and manipulated according to a set of formal rules and comprising a complete, self-consistent system. Such a system would contain no mathematical contradictions and would allow the formulation of algorithms from within its own formal structure that could determine whether any mathematical statement were true or false. Demonstrating the completeness and, in essence, infallibility of mathematics, seemed to be a natural corollary to its blossoming, in the minds of a serious of outstanding European mathematicians (starting with Descartes himself), to the point where quantitative description had become possible, in algebraic or geometrical notation, of phenomena in fields as diverse as fundamental physics, biology and economics. It seemed logical to assume that using an axiomatic approach (the term axiom now being expanded to include a range of formal logical statements from which other statements can be derived), contradictions in any field of knowledge would be impossible, and the need for intuition (the basis, for example, of Euclid’s axioms) would be eliminated. In 1931, however, Gödel, a 25 year old Viennese mathematical logician, published his undecidability or incompleteness theorems, which provided mathematical proof that Hilbert’s conjectures were false, and that for any formal axiomatic system involving the natural numbers (and therefore, for the whole of mathematics) there exist true statements that cannot be proven to be either true or false using the axioms inherent to the formal system. In effect, Gödel showed that to prove that mathematics is consistent, one had first to assume that it is! This seemingly arcane conclusion is a demonstration of the existence of mathematical versions of propositions of the kind: “this statement is false.” To prove it correct is to prove it false and vice versa. It is also, perhaps, ironic, if also tragic, that Gödel, one of the greatest logicians of of the 20th century, a man who was for many years a close friend of Albert Einstein, suffered from paranoid delusions. He believed that strangers were trying to kill him by poisoning his food and for much of his life would only accept meals prepared by his wife. Eventually, in a final attempt to avoid being poisoned, he starved himself to death.

Although Gödel's theorems appeared to rock the very foundations of mathematics, it eventually became clear that a good deal of Hilbert’s program could, after modification, be salvaged, while a restatement of the incompleteness theorems in 1936 by Alan Turing, an English mathematician, led to the concept of the Turing Machine (a thought experiment rather than an actual machine) and Turing’s proof that such machines could perform any mathematical manipulation as long as the latter could be expressed in the form of an algorithm. Turing had developed, in essence, stored computer programs, and recognized, via his concept of a Universal Turing Machine, i.e., one able to perform the functions (execute the programs) of any other Turing machine, that a single machine, suitably programmed, was all that was needed to carry out or control almost any conceivable task. Turing, who had played a major role in deciphering the German military codes used in World War II, and whose work had provided the logical foundation of computer science, was arrested in 1952 after admitting to a homosexual relationship. He died two years later after eating an apple laced with cyanide.

The Chinese character for "Listen" contains several of the elements relevant to both knowledge acquisition and management. The contained characters for heart, eye and ear imply both a deeper understanding and shared learning.

Knowledge Acquisition

Computers, as their name suggests, are ultimately dependent upon computations - i.e., the manipulation of data according to precisely defined rules. Philosophers have discussed, since the time of Plato, whether the world consists of mathematical objects waiting to be discovered, or whether mathematics is a purely human invention imposed upon the world. Whichever is correct, every aspect of the world we live in can be quantified. Even sentences can be expressed mathematically, particularly when in the form of a proposition, i.e., a statement or assertion that can be determined to be either true or false. Thus, the language of mathematics permits more precise - sometimes exquisitely precise - description and provides a connecting matrix for the seemingly separate entities around us and the changes that occur in them. The simplest of entities are the elementary units of knowledge. Language, including mathematics, allows representation of these elementary units and exploration of the relationships among them, leading to the construction, fact by fact, of a more or less complete picture, or theory, of one or more aspects of reality. Knowledge, in the computer age, can be seen to be well-substantiated answers to a series of questions, which must be correctly structured if the ultimate goal - truth - is to be achieved. In Einstein’s words: “The formulation of a problem is often more essential than its solution.”

Data, which is a plural word derived from the Latin for “a given,” are the propositions that represent reality, i.e., measurements or observations of a variable (something that can be quantified). Data can be in the form of numbers, words or images, all of which can be expressed in binary code and thus “digitalized” for analysis by computer. The quality of data depends upon many factors. An essential prerequisite is a precise definition for each data element (e.g., age, complete response). Such definitions are often compiled in a data dictionary and must be identical in different data sets if the latter are to be accurately compared. This resembles the need to use standard definitions of words used in specific contexts in order to understand and to be understood. It is also essential that data are collected with great care, and that for any meaningful interpretation of data derived from a controlled experiment, such as a clinical trial, the experimental protocol must be closely adhered to. Meaning emerges when data are analyzed and expressed symbolically as text, graphics or sound. Processed data (as opposed to the original or raw data) are usually referred to as information, which, when used to determine the truth of a proposition or hypothesis, is referred to as evidence. Such propositions must be formulated so as to be falsifiable, i.e., they can be shown to be either “true” or “false.” The degree of confidence in the truth of the hypothesis, if necessary, is assessed by statistical analysis, which varies with respect to its power to confirm or refute the hypothesis according to the amount of available data. And ultimately, sufficient evidence leads to justifiable belief in the proposition - i.e., knowledge.

But knowledge, in spite of the claims of some mathematicians and scientists, is not the final goal; knowledge without consequence, in the words of the Chinese epithet, is “thunder without rain.” And regardless of the motives of the creators of knowledge, sooner or later it will have practical value to the community. Moreover, just as propositional and procedural knowledge are complements of each other, so action is essential to the creation of knowledge. The greater the knowledge, the more effective can be the action, and the greater the action, the more knowledge can be accumulated. Sufficient information (comprised of a web of individual facts, or validated propositions) leads eventually to understanding. This implies an ability to recognize the linkages between the known elements of a system, to derive its informational content and to be able to reproduce and use such information (Figure 1). Knowledge, it can be seen, lies somewhere between - and overlaps - information and understanding. And understanding, of necessity, includes a liberal seasoning of knowledge with intuition. For imagination is required to perceive the linkages among seemingly disparate units of knowledge - a process that is both dependent upon and complements the formal systems which provide the logical structure essential to the strength and endurance of the whole. And while intuition will often prove to be incorrect, identifying what is not the case is as important to understanding as recognizing what is. Intuitive assumptions provide the foundation on which all knowledge is built. They play a critical role in formulating the right questions to ask and in the process of inductive reasoning (such as generalization). Eventually, they lead to the slow dawning of understanding and the consequent validation of entire mental constructs. Paradoxically, it required Gödel’s logical genius to prove that this is so.

Figure 1. A knowledge mandala: reality is understood via actions that create knowledge through a process of data gathering, analysis and assessing the evidence for or against a proposition or hypothesis. Once there is knowledge and/or understanding, interventions (action) can be undertaken to modify reality.

Cancer Research

In the health sciences, the purpose of collecting data is to create evidence that can serve as the basis for action designed to improve the health of individuals or populations. It should be recognized that sound evidence and effective action are not dependent upon understanding. Empirical observation, in which there may be limited mechanistic understanding, provides perfectly legitimate evidence - for example, of the effect of treatment on a tumor or the observation of a decrease in the incidence of a cancer when exposure to an associated environmental agent is reduced. But understanding can lead to novel interventions, which are much more specific and likely to be much less toxic. In the last several decades great progress has been made in unraveling the molecular pathways that lead to cancer, and we are now beginning to reap the benefits of the new understanding that has derived from the simultaneous advance of propositional and procedural knowledge; a large fraction of new drugs under development (including antibodies) are targeted to the molecular lesions which cause cancer and which, for the most part, are specific to cancer, or to molecules highly expressed in particular cancers. The broad sweep of progress in molecular biology has also allowed the development of new vaccines that prevent infection by microorganisms which cause diseases associated with the development of cancer.

While everyone uses knowledge as a part of everyday life, the acquisition of specialized knowledge, - whether at the level of data collection or interpretation -, itself requires expertise. This means that the majority are dependent upon evidence collected by the minority - i.e., knowledge transfer is essential. In the case of health care professionals, most have limited or no research training and have neither the necessary skills nor incentive to participate in high-quality research. One of the consequences of this is that in most high-income countries only a small percentage of patients participate in clinical trials. This is a serious problem, for it leads to a marked reduction in the speed with which knowledge can be acquired. An obvious, but often overlooked source of knowledge is the developing countries, where more than 50% of all cancer occurs, along with novel opportunities to understand more about cancer (sometimes via simple, inexpensive research) and to utilize this knowledge to the benefit of all. Unfortunately, the limited infrastructure means that the amount of research conducted is markedly less than in high-income countries and the abundant sources of knowledge in developing countries remain, to a large extent, untapped. The lack of the procedural knowledge required for research leads not only to a dearth of propositional knowledge relevant to the local situation, but also to a less than scientific approach to patient care and a negative impact on professional education. As a consequence, the numerically large populations of developing countries are unable to realize their potential and medical care and cancer control are significantly less efficient than need be, even within the constraints imposed by socioeconomic circumstances. This situation is compounded by the continuous leak of human resources to higher income countries (most often the best educated members of the population), where economic and professional rewards are greater.

The limited evidence base derived from research in the developing countries themselves means that the bulk of the evidence used for cancer control comes from high-income countries, not all of which is pertinent to the developing countries - or even meaningful in the specific circumstances they face. Major differences in populations and environments lead to different patterns of cancer and a broad set of problems that negatively influence access to care. Incidentally, these differences in the cancer patterns - an essential foundation for cancer control planning - are poorly documented because of the paucity of cancer registries (which also have an important role in the assessment of the impact of interventions). It is clear, however, that cancer is much more advanced at the time of presentation in developing countries, due to poverty, ignorance and limitations in cancer services; consequently, early diagnosis and palliative care should be assigned correspondingly higher priorities. Finally, the techniques used to detect and treat cancer in high income countries may be too expensive, not feasible because of the limited resources, or less suited to developing countries for cultural or other reasons. In order to begin to remedy these problems, to the extent possible within the existing socioeconomic constraints, it will be important to establish the size and quality of the existing evidence base pertaining to all aspects of cancer control in developing countries, to make it more accessible and to identify effective methods of expanding it. Only by improving the acquisition and management of propositional knowledge, which will require the transfer of the necessary procedural knowledge, will resource-poor countries be able to develop and sustain cancer control programs that are more specifically targeted to their needs. This topic is dealt with in a subsequent article in this issue of Network.

Knowledge Management

Knowledge management is a term most often used in the context of business, where the most effective use of knowledge is likely to lead to maximum profit. Knowledge can also be bought and sold as a commodity. Hence, businesses have a strong incentive to accrue, store, classify and exchange knowledge, and to ensure that staff members are kept well informed, at least with respect to the knowledge areas in which they work. And while knowledge of products or services must be widely disseminated, the withholding of knowledge, even if not in the interests of the community at large, can lead to considerable economic benefit or political advantage. Indeed, patents, which permit short-term monopolies, were introduced centuries ago to provide incentive to inventors while not indefinitely withholding valuable information or products from the community. In non-profit situations the incentives may be different but the need for knowledge is equally great. Frequently, civil society is the only source or purveyor of information that is critically important to the public good. But no matter what their origin, whether or not messages directed to various sectors of the community are received and acted upon is often critically dependent upon the way in which knowledge is presented; optimal presentation requires understanding of the psychological factors that influence its reception. These differ widely in different populations and age groups as well as in men versus women.

Figure 2. Components of the community concerned with cancer control - each has its own knowledge base and methods of knowledge management. The effectiveness of cancer control would be greatly enhanced if the intervening divides could be bridged.

A major problem with respect to knowledge management in cancer control is its compartmentalization. A broad range of experts is required to train and educate the workforce, develop the products and equipment required to undertake the range of necessary interventions and to collect, review and make available the knowledge derived from research. It is not possible to encompass in one organization, even less in a single individual, knowledge of each of these areas, but there is a need for the divides that separate the various components, some of which are shown in Figure 2, to be bridged if maximal benefit is to be gained from available knowledge. Such bridges would lead to increased understanding of the way in which the various components of the cancer control web fit together and to the possibility of “tuning” the system such that greater harmony is achieved among its parts.

Knowledge Diffusion and Transfer

Even technically advanced countries derive information from other countries, but developing countries obtain a disproportionate amount of information in this way. In order to select the appropriate knowledge to transfer, it will be necessary to establish a dialogue between those who have knowledge and those who would like to use it, and to identify the most effective approaches to transfer it. Knowledge diffusion implies a non-targeted process, whereby information is made available through books, journals, the Internet and a variety of meetings. While this approach may be reasonably effective in societies where the majority of health professionals have access to such sources, particularly when requirements for continuing education are in place, the implementation of research findings in health care has, in the past, taken as long as two decades even in the most developed countries. This results from poor knowledge management coupled to the lack of a research ethos, which doubtless has its roots in medical education and the structure of health services. In developing countries the situation is far worse. Knowledge transferred from more developed countries may fall upon “deaf ears” because of differences in the knowledge base or in the perspectives of the messenger and recipient. Sufficient knowledge of the subject matter is required if a message is to be understood, and appropriate resources and opportunity if knowledge is to be translated into action. Insufficient attention is paid to these issues.

Clinical Trials     Clinical Practice Guidelines     Designed for a specific population in the context of available resources     Based on available evidence, which may be out of context     Requires disciplined adherence to the planned protocol on the part of all participating investigators     May be modified at the discretion of each individual user     Usually entails collaboration and mutual learning     Rarely entails collaboration or learning that leads to understanding     Associated with quality assurance and ethical review     Not routinely associated with quality assurance; no ethical review     Identifies deficiencies in care and data management via audit and monitoring     Generally unsupervised, such that problems go undetected     Encourages measures to improve follow-up     No incentives to improve follow-up     Associated with outcome measures     No outcome measures     Generates new information     No new information generated   Table 1. Comparison of Clinical Trials and Clinical Practice Guidelines.

The consequence of the knowledge deficit in developing countries is that, with the exception of occasional centers of excellence, the majority of patients are likely to be treated with outdated techniques or treatment regimens. The situation is compounded by frequent failure to complete therapy because of poverty and ignorance, while accurate measures of outcome are, for the most part, entirely lacking. Prevention and early detection are underplayed because all available resources are used to deal with the overwhelming number of patients with advanced cancer and because of the lack of knowledge, expertise or advocates. These problems will need to be addressed in a logical and stepwise fashion, and research will be an integral element in their resolution.

Clinical Trials as a Multivalent Solution

Clinical trials directed towards the early detection and primary management of cancer, while addressing important questions in the setting of the local resources, the patient population and the local cancer pattern, also represent an effective means of providing more efficient and effective patient services and an effective platform for the training and education of health professionals. This follows from the fact that clinical research demands accurate diagnosis, knowledgeable treatment design (using sound scientific and ethical principles), discipline with respect to the administration of treatment and meticulous documentation of results. In addition, appropriately designed trials must take into account the available resources (human, financial and material) and may have as an objective, the development of cost-effective or resource-sparing approaches to care. Since research is more difficult to undertake in developing countries, many advocate the use of clinical practice guidelines. While these provide a useful source of information, they are, of necessity, largely based on evidence collected in high-income countries. Moreover, they are unlikely to be as valuable, from the perspectives of patient care and education, as the conduct of carefully selected clinical trials (see Table 1). Finally, the conduct of relevant clinical research will gradually lead to the establishment of a culture of scientific, evidence-based medicine, i.e., one based on effective knowledge acquisition, management and dissemination in settings, including major cancer centers or university hospitals, where this is presently absent or very limited. Eventually, improved professional circumstances should help to staunch the loss of talent to high-income countries.

Plato’s concern as to what constitutes sufficient justification for belief is as pertinent today as it was two and a half thousand years ago. Incomplete information may lead to false belief, and false belief to inappropriate action. To avoid this, knowledge will need to be harvested from wherever it is to be found - including from the developing counties, which accounts for more than 80% of the worlds people - and managed efficiently and with equity. Information technology, set in motion by the recognition of the limits of logic, will play a vital role in the next stage of the voyage of discovery which comprises, surely, the destiny of the human race.