What is Science?

Operational Definition

This definition frees us from many of the objections that arise when trying to define the "scientific method" and "objective reality". In fact, it dissociates science from how science is done. The method of science becomes an economic question, rather than a question of principle. As an economic problem, the method of science must try to optimize the use of scarce resources in order to achieve the most meaningful results. Obviously, this also brings values into the method of science, so the process can be rightly seen as a very human (ie. embedded in a social context) activity even though it has a transcendental quality about it (which accounts for its stunning success). The collection of experimental results can be seen as an "objective reality" because the validity of the results is not tied to a specific culture, world view or paradigm (you just knew that word was going to appear, didn't you).

The value of science resides in the fact that it provides knowledge which is unassailable. The results of experiments are communicated in such a manner that anyone can reproduce the experiment to see if the same results occur. Our confidence in experimental results is directly related to how often an experiment is verified by an independent worker (or how likely we feel it is that the experiment may be reproduced). For example, we do not have a great deal of confidence in many high energy particle collision experiments because very few people have the means to reproduce those results, and among those who do, funding constraints prevent them from doing work that is already established. This is simply a result of the economics of doing science and does not undermine the value of science at all. Those who do science, are necessarily forced to be skeptical as a result.

Much is often made about the dichotomy between theory and experiment in science, thus it is worth clarifying the issue under the present outlook. The principle value of theory (in science) is its ability to summarize the results of experiments. Humans can only hold a few ideas in their minds simultaneously, therefore it is difficult to consider a body of experimental results, except individually. With a simple theory, in which the results of many experiments are seen as logical outcomes of the theory, the task of simultaneous cognition can be accomplished. Theory is useless, and sometimes even destructive, if the person is unaware of what experiments have actually been done and how they were done. This can lead to a completely inappropriate use of the theory (eg. proclaiming its logical consequences as fact or truth). Since the most important aspect of theory is to summarize the results of experiments, it is crucial to know the range over which a theory performs this task accurately. For this reason, scientists try to find predictions of a theory which they think are most likely to be contradicted by experiment. Once found, the experiment is carried out and the theory either has its range of usefullness extended or cropped. When a theory is found to have a definite boundary to its predictive power, then scientists try to find a more general theory which covers all the known experimental evidence (in which the previous theory can be derived under some limiting conditions). Thus the trend is science is to try to find the most general theories possible (some would like to find a single "theory of everything"). It should be noted, that theories are only in competition with overlapping theories which have already been proposed; in the absence of any other theories, a particular theory that manages to summarize a limited number of experiments is to be considered a valuable theory even if it can be proven wrong in some other domain. Any theory which has no known contradictions with experimental evidence (after many, many such experiments have been tried) is called a physical law. This is strictly a nomenclature of convenience which represents our confidence, it is a capital mistake to take such a convention literally.

Characteristics of the Scientific Method

• Experiment
  There are several fundamental aspects of scientific experiments that are observed by all in the field. The methods and results must be reported exactly and honestly. If a single report is found to be fraudulent, then the evildoer becomes persona non grata with no court of appeal. Since experiments must be reproducible, frauds are easy to spot (not always so easy, but if their work is regarded as significant, then it is inevitable that they are discovered, because they can't change the way nature works). These reports must be communicated in such a fashion that they are available to anyone with an interest in obtaining them (I don't regard it as a coincidence that science became dominant following the development of the printing press).

  To ensure the transcendental nature of experimental results, scientists try to do controlled experiments. This means that the experimenter has performed more than one experiment so that the confidence that the effect that is observed is due to some variable that is manipulated rather than something not considered. Experiments are not invalidated when some later work shows that there were other causes of the effect that was observed, but are combined with the new information to provide more complete knowledge of the phenomenon.

  Since the business of actually doing experiments requires money (for equipment, publication, food and shelter of the experimenter, etc.) one of the drawbacks to doing science is that some energy must be expended on generating revenue. Indeed, it could be argued that the principle activity of many scientists is writing grants for their experiments. As an economic activity, perhaps this is appropriate since we can't afford to discover as much knowledge as we are able.

• Hypotheses
  An hypothesis is an assumption that is made in which a cause-and-effect relationship is conjectured to explain some phenomenon. In order to be a scientific hypothesis, this assumption (or logical consequences derived from it) must be testable. This means that there are experiments which can be performed for which a class of results will contradict the hypothesis (falsifiability). There are, of course, perfectly valid hypotheses which can be proved true (eg. there are trout in that lake), however, these can always be rewritten in falsifiable form which is not always the case for the opposite situation.

• Theory
  A scientific theory summarizes the results of scientific experiments. The value of a theory lies in the amount of information which can be encoded as logical consequences of the theory (and the efficiency with which this encoding occurs). It happens to be true that a theory which is compatible with a significant number of experiments will also be useful for generating new hypotheses (and thus leading to more experiments). A theory also allows causal connections to be inferred between phenomena gleaned from different experiments. This is the basis of the link between science and technology, for example, the relationship between heat and pressure and the relationship between pressure and work can be connected to devise the basis for a steam engine.

• Mathematics
  Mathematics is often called the lingua franca of nature, due to its phenomenal success in physical theory. This is a result of two factors: firstly, mathematics is constructed rigourously from formal axioms. There is no ambiguity of language, nor any room for interpretation. Causal relationships can be specified with exact meaning. The second factor is that mathematics allows any implied relationships to be discovered and explored. Because mathematics is based on one set of axioms, an equation can be subject to any mathematical operation with the logical meaning of such an operation defined explicitly. This makes it tremendously useful for extending theories into realms which were not considered when the theory was first developed.

• Understanding
  What does it mean when we claim to understand something? It is surely more than simply applying an algorithm to a set of data; somehow, we have to have a precise model which represents this algorithm before we have understanding. For example, let's say we have an algorithm for predicting the phases of the moon in which the input is simply the current phase. Now we may predict that the moon will be full in 10 days, but do we understand why this will be so? If, on the other hand, we imagine the sun, earth and moon as spheres revolving about each other (details omitted), then we can see that our algorithm is simply a way of determining how the moon's illumination (by the sun) appears from the earth. Understanding the phenomenon means to identify a causative agent. Phenomena which defy understanding (eg. the two slit experiment in quantum mechanics) resist attempts at finding causative agents. I believe that understanding non-physical ideas follows a similar course: we make mental models in which the ideas are given physical significance (eg. a "number" as a point on a line) and then follow cause-and-effect reasoning throughout the process under study. The language of cause-and-effect is logic, therefore understanding is generally brought about by following a logical process of reasoning.

  Thus we have a mechanism (corresponding to an algorithm) and some axioms (the prior assumptions which are accepted (at least temporarily) without question) as the essential components that are required for understanding. The axioms may represent our most fundamental understanding of some phenomenon (eg. in magnetic repulsion, the axiom might be a magnetic force field, or the exchange of photons ala QED, according to our knowledge of the subject) or they may be an idealized concept that is logically uncoupled from the underlying principles (eg. an op-amp as opposed to a complicated circuit of transistors). However, there must be a set of axioms which we accept for any instance of understanding; it cannot be bootstrapped without some prior knowledge. In physical theories, the principles that we refer to as physical laws are either axioms or tautological. For example, the law of inertia can be used to derive the principle of least action, or the principle of least action can be used to derive the law of inertia. Neither is more fundamental as the derivation is circular. The constancy of the speed of light for all observers was given axiomatic status in order to preserve Maxwell's equations, but now the speed of light is defined by this assumption. Thus to try to show that the speed of light is different from how it is defined is roughly equivalent to saying that the speed of light is not the speed of light: a tautology. This sort of reasoning is especially apparent in biology, where the phrase "survival of the fittest" (without any objective definition of "fitness", other than survival) transforms to "survival of the survivors". So although understanding requires a mental model of cause-and-effect connections, there is always a set of unquestioned assumptions which underly these models.

  One must ask, in this context, why we do science. Of course, we can see the connection between science and technology (and technology is something we crave, for better or worse) butthis was not present when science began. More fundamentally, we are curious beings, andcuriosity means that we long for understanding. We can't help but to create symbolic modelsof the "external reality" that we perceive through our senses. Once we create these models, then they had better operate smoothly, or else we'll fall into a state of confusion. This is an intolerable state and we seek resolution. Science provides the best way that we know to resolve such internal confusion. By building models of nature that are constructed using mathematics, logical relationships are established which are free of contradiction.

• Trial and Error
  It is often assumed that science proceeds by deductive reasoning. Theories based on prior experiments are used to work out exactly the results of an experiment and then the experiment is performed as a formality. This is not at all the way it is done, nor is it possible to make any progress by this route. In fact, the primary source of inspiration for experiments is the method of guessing. Prior information is always incomplete, and several theories are usually present to account for what information is known. Even if two theories are empirically equivalent (experiments can never contradict both theories) then the scientist who is familiar with both will have an advantage in deciding what experiments are important. This is due to the mental modelling that occurs in the confused scientist. By imagining several scenarios which can lead to certain effects, the scientist may have an epiphany in which some other scheme would explain the success of the current theories as well as provide an extension which is experimentally testable. These new schemes are not generally just minor improvements of existing theories, but rather are completely different, and only transform into the previous schemes under limiting assumptions. The process of guessing at such schemes requires both knowledge of experiments that have positive results (either support or contradict theory) as well as those that have negative results (an effect is not seen). The phrase "chance favors the prepared mind" describes this necessity well, as guessing is largely a matter of making inferences based on prior information.

• Predictions
  Neils Bohr felt that the business of science was to make predictions of the results of controlled experiments, neither more nor less. This is an extremely narrow view and one must wonder what motivation there could be to engage in science at all within such a framework. Predictions of the results of experiments are necessary, of course, but understanding phenomena--satisfying curiosity--is surely as much a part of doing science (if not more) as making predictions. Since we must have axioms for all our understanding, it is ridiculous to limit our axioms to those which lie within the limits of physical measurement. We must be careful, however, to realize the limitations of our predictions. Any predictions which are not testable, should not be used to judge the value of theories (although this is difficult to avoid, since we must somehow rationalize such predictions within our mental model in order to escape a state of confusion).