“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 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.

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 observed facts in science.
They are events that have happened. Deciding what should be the legal consequence
of those facts can be like using a scientific theory to predict what will
happen. 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.