Thursday, November 25, 2010

Knowledge, Science and Technique: Looking at Economics as a Science

Edward Dougherty in his many papers (On the Epistemological Crisis in Genomics) has addressed this issue in considerable detail, namely he looks at what he calls the epistemological crisis in genomics. Dougherty has written a brilliant set of papers which set the path for those in genomics but it should also be a warning for economists.

Let us look at Dougherty from the aspect of the genomist. Keep in the back of our minds the same issues for the economist.

Dougherty begins his paper by stating:

There is an epistemological crisis in genomics. At issue is what constitutes scientific knowledge in genomic science, or systems biology in general. Does this crisis require a new perspective on knowledge heretofore absent from science or is it merely a matter of interpreting new scientific developments in an existing epistemological framework? This paper discusses the manner in which the experimental method, as developed and understood over recent centuries, leads naturally to a scientific epistemology grounded in an experimental-mathematical duality.

He continues:

The change brought about by the “new science” of the Sixteenth and Seventeenth Centuries is based on the integration of two principles: (1) design of experiments under constrained circumstances to extract specifically desired information; and (2) mathematical formulation of knowledge. The two principles arise from the two sides of the scientific problem, the source of knowledge and the representation of knowledge in the knower. Perhaps the greater revolution in knowledge is the design of experiments. One need only think of Archimedes’ mathematical analyses of fluidics and mechanics to see that the ancients recognized the central role of mathematics, even if they did not understand that role in the modern sense. But the modern concept of experiment is a different matter altogether.

Dougherty then proceeds to emphasize the need and usefulness of the mathematical model, namely the ability to predict. He specifically states:

A mathematical model alone does not constitute a scientific theory. The model must be predictive. Mathematics is intrinsic because science is grounded in measurements; however, a model’s formal structure must lead to experimental predictions in the sense that there are relations between model variables and observable phenomena such that experimental observations are in accord with the predicted values of corresponding variables.

These predictive relations characterize model validity and are necessary for the existence of scientific knowledge.

The predictive ability of a model is essential. Frankly the ability to go from experiments to prediction, albeit with uncertain but projective results, is at the heart of a scientific approach and it is essential to the engineering approach that we aim for herein. Just having the experimental data is necessary but not sufficient. One must be able to link the data in some mathematical models which in turn is in itself predictive of alternative and future results. Dougherty continues:

The fundamental requirement of a scientific validation procedure is that it must be predictive. A scientific theory is not complete without the specification of achievable measurements that can be compared to predictions derived from the conceptual theory. Moreover, it depends on the choice of validity criteria and the mathematical properties of those criteria as applied in different circumstances.

Again in genomics we have collections of data, and as we shall demonstrate herein for prostate cancer, that data is enlightening and descriptive but is not predictive and the mathematical models of what is transpiring is missing. It is not that we cannot construct a model, and indeed such a construct would itself be subject to continuing change as we learn more, but the intent must be there to construct such a model, and a framework, a paradigm, must be ever present.

Dougherty makes another interesting observation as follows:

Consider the following statement of Steven Jay Gould: “Science tries to document the factual character of the natural world, and to develop theories that coordinate and explain these facts”. Perhaps this statement would have been accurate during medieval times, but not today. While it is true that theories coordinate measurements (facts), it is not the documented measurements that are crucial, but rather the yet to be obtained measurements. Gould’s statement is prima fascia off the mark because it does not mention prediction.

The point that Dougherty is making is that science, the science of systems particularly, which we will discuss herein, focuses on not the facts, but the process, and the predictability of the models we develop from facts, connected and ordered facts, facts which are quantified. In Gould’s world view, that of a botanist or zoologist of the early 20th century, he is a collector and organizer of facts. He is not the builder of models which can be used to predict forward based on prior data. True systems approaches are valid if and only if they have the predictability capability.

As Dougherty states after this, the true nature of systems science and engineering is not the fitting of data, it is not the clustering of data points in some microarray. As Dougherty quotes Norbert Wiener from Wiener’s classic, Cybernetics, the true nature of systems is a combination of models, predictability and uncertainty.

Finally Dougherty comments on the use and abuse of logistic analysis. Simply put he demonstrates via the arguments of others, especially William Feller, that frankly one can get a logistic fit to anything. It does not demonstrate any physical causality. In physics we have the relationship between mass and momentum, through the variable velocity.

We have rate equations for reactions demonstrable by experiment and validatable by predictive use. We understand forces and torques so that we can analyze and design a bridge, and we understand the multi body problem so that we can predict what trajectory a rocket may take as it traverses the galaxy. For genomic analysis and especially for cancer can we develop such a methodology.

Now the epistemology of Dougherty for genomics applies in spades for economics. The ability to predict anything with unanimity of agreement is lacking. That should be the aim, the goal. Until then perhaps they should remain quiet!