“Chief Justice French’s background in science has been useful in expressing ideas. He has suggested that identifying elements of administrative justice is “a little like the identification of ‘fundamental’ particles in physics. When pressed, they can transform one into another or cascade into one or more of the traditional grounds of review developed at common law”. [Robert French “The Rule of Law as a Many Coloured Dream Coat” (Singapore Academy of Law 20th Annual Lecture, Singapore, 18 September 2013) at 18.] It has also come in handy when cases before the Court have dealt with scientific concerns, such as

*D’Arcy v Myriad Genetics Inc*, [[2015] HCA 35, (2015) 325 ALR 100] a case about the patentability of DNA. But I wonder whether the real insight to be obtained from what his scientific background has brought to the Chief Justice’s work is to be picked up from his reference to his gratitude that he was exposed to a “culture” of science. That may give some insight into a style of leadership that, to an outside view, seems more collaborative and cooperative, less competitive than is sometime encountered in appellate courts, perhaps because their members are often drawn from a section of the profession with a very different, more competitive culture.” (footnotes from original, inserted in square brackets)
Sian Elias, Address On The Occasion Of The Supreme And Federal Courts Judges’ Conference Retirement Function For The Hon Robert French, Chief Justice Of Australia, Perth, Western Australia, 23 January 2017, at [13].

Science is about finding out what happens, theorising about why it happens, and using that to predict what will happen. Observations usually involve measurement and consequently mathematics. From observations theories can be formulated, again they are usually mathematical. The mathematics should suggest what future observations will be. Predicting observations using mathematics is not always accurate, in which case refinements of the theory are needed. Refinements are prompted by unexpected observations.

For example, looking at magnets and wires, inconsistencies between the predictions of classical mechanics and Maxwell's equations about the forces impelling a current in a conductor, depending on whether the conductor or the magnet is moved, prompted Einstein - at least according to the way he wrote his paper - to develop what later came to be known as the special theory of relativity. The paper announcing this was called (in English translation), On the Electrodynamics of Moving Bodies. Measurements of an event made from different frames of reference (here, in the special case of reference frames moving in straight lines at constant velocities) depend on the point of view, and this in turn has implications for measurements within a single frame of reference. Using observations on the constancy of the speed of light in a vacuum, and theorising that the laws of physics are the same everywhere, Einstein borrowed mathematical techniques developed by Lorentz and showed that some refinements - albeit extremely small ones for the events we normally observe - must be made to Newton’s laws of motion. In a later addendum he showed that the same mathematics he had used also predicted how the energy in matter is proportionate to its mass.

While that sort of mathematics has proved to have great predictive value where observations are made at the macroscopic level, it is not so useful at the sub-atomic level. It seems that the smaller something is, the greater the need for a mathematics incorporating probability. At the sub-atomic level, mathematics is a less accurate predictive tool than it is for events at a larger scale. To compensate for the reduced usefulness of basic mathematics at the sub-atomic level, new forms of mathematics are devised, starting with quantum mechanics. Specialists develop new forms of mathematics to meet the needs of inquiry; Descartes combined algebra and geometry, Newton and Leibniz independently developed calculus, and today there are many forms of specialised mathematics, taking their topics far beyond a lay-person’s understanding.

Unless a mathematical refinement has predictive value for those who must use it, it is worthless to science. The same need for predictive value applies to theories that are not mathematical. But having predictive value is not the same as identifying what is real. The correct interpretation of reality using quantum mechanics has yet to be achieved. A theory may predict observations while not necessarily saying what is real.

Law is like science in that in considering a legal problem a lawyer will try to predict what a court would decide the answer should be. The facts of the legal problem are like measurements in science. But they also claim to speak of reality. Deciding what should be the legal consequence of the forensically decided reality can be like using a scientific theory to predict the result of an experiment. Where a judge has a discretion, or where judgment must be exercised by a court, there is room for a predictive theory to be developed. Those areas of law, where there are discretions to be exercised and evaluations to be made, are different from other areas where the answer to a legal problem can simply be looked up. Discretion and judicial evaluation invite analysis and development of predictive theory.

Two areas of judicial decision-making that have particularly interested me both involve evaluative judgments: deciding whether improperly obtained evidence should be ruled inadmissible, and deciding whether the evidence in a case is sufficient proof of guilt.

My study of the decision whether a court should rule improperly obtained evidence inadmissible is available at https://www.tinyurl.com/dbmadmissibility . There is a method behind my theory which has mathematical analogues: the Cartesian plane, a diagrammatic representation of results of cases, a boundary curve reflecting the rationality of the decision process. It provides a pictorial representation of results, and a method for identifying wrong decisions. Wrong decisions are like inaccurate scientific observations; they do not require rejection of an inconsistent theory unless they build up in number and have consistency among themselves to the point where it is no longer useful to call them wrong.

The sufficiency of evidence as proof of guilt is an inherently probabilistic question. Reasoning with conditional probabilities is something we all do instinctively, but mathematical analysis can reveal fallacies in intuitive thinking. Analogies from mathematical theory can indicate the probative value of items of evidence and the effect of those on the probability that a defendant is guilty. Law does not require mathematical precision, but mathematical method can be a useful tool. I illustrate this in my draft paper (draft because I like to have the opportunity to keep these papers up to date) available at https://tinyurl.com/dbmpropensity .

Those are illustrations of some of the ways in which a background in science can be of assistance to a lawyer.