You had that action and counteraction which, in
the natural and in the political world, from the reciprocal struggle of
discordant powers draws out the harmony of the universe. These opposed and
conflicting interests which you considered as so great a blemish in your old,
and in our present constitution interpose a salutary check to all precipitate
resolutions. They render deliberation a matter, not of choice, but of
necessity; they make all change a subject of compromise, which naturally begets
moderation; they produce temperaments preventing the sore evil of harsh, crude,
unqualified reformations, and rendering all the headlong exertions of arbitrary
power, in the few or in the many, forever impracticable.
– Edmund Burke (1729-1797), Reflections on the
Revolution in France
Socially and technologically,
the world is perhaps more impermanent and unsettled than it has ever been. The
20th century was best characterized by the decade. For the 21st
century that division may prove to be even smaller. Despite such uncertainty, innovation
and change continue to be popularly embraced as good in and of themselves. In a
strange reversal, the tried and true are more often viewed with feelings of
mistrust and quite often, outright hostility. To take an important contemporary
example, we are currently facing the very real possibility of losing the “first
past the post” electoral system. Leaving aside the claimed merits of the
current and proposed systems, in the surrounding debate how often is the fact
that this system has functioned satisfactorily for the past 800 years used as an
argument against its favour? I remember an email advertisement from the NPD
that made point explicitly, noting in particular and with disdain that the
“first past the post” system predates penicillin and the Internet (what that
has to do with anything, I do not know). MP Elizabeth May made a similar
argument in the House of Commons claiming, incorrectly I might add, that the
Medieval Britain believed that the Earth was flat. It is not this political
issue that I want to discuss, but rather what it means about our society that major
political parties and high-profile public figures can get away with such weak
reasoning on such a major question. What has happened to the modern world that
we are so deficient of caution that we happily trade nearly a millennium of continuity
for vague and untried abstractions? What is the source of this remarkable
confidence in innovation?
This question of innovation
and the confidence we place in it came to my mind last week. In one of my
classes, we were discussing the current practices used in schools to integrate
children with special needs more fully into the classroom. We were shown a
quote from a government document that immediately struck most of the class as
going against the current wisdom. A wave of comprehending “ahhs” swept through
the room when it was revealed that the document dated way back to 2006. I
wondered then what it means when an educational policy hardly 10 years old
would be so recognizably out of date. I suppose one could argue that it is all
part of that inexorable march forwards, but I am not so sure. If this or that
policy or curriculum has a shelf life of barely a decade, what confidence can
we reasonably place in the supposed merit of the current version? Will we
always wake up a few years later, recognize it’s indefensible shortcomings and
go back to the drawing board? Grounded to nothing, is education to be stuck in
an endless present, constantly in a state of overhaul and reinvention? Do
children really change that much? Does math?
I suspect that the penchant of
politicians to implement frequent changes in policy based on innovation and the
latest ideas, as well as the willingness of the public at large to accept them,
is that these ideas lay claim to a foundation in science and “the latest
research”. It is nothing new (nothing ever really is), but I seem to be
noticing more than ever that the public perceptions of science and ‘expertise’
appear to be more akin to a banner of authority than as a method of
investigation that welcomes scrutiny and debate. I believe that the practical
effect of treating science and expertise as an ipso facto authority, combined with a dismal and socially endemic level
of numeracy, is a general loss of useful skepticism. An interesting and
thorough investigation of this idea can be found in Dr. Thomas Sowell’s book Intellectuals and Society.
I believe that skepticism
coupled with logic is perhaps the most important regular use of arithmetic. Yet
I think it is one of the least inculcated. We are flooded with facts and
figures everyday, through the news, political advertisements, commercial
advertisements etc. Are we as a society equipped to properly decipher this
information, and to separate the solid from the untrustworthy? I would like now
to cover a few of the ways in which we can do this. Do we catch the notable
omissions, such as numerators without denominators? I saw a simple example of
this in a political ad from the last federal election. Then Liberal Party
candidate Justin Trudeau presented a graph comparing of the growth of the size
of the economy over the past few decades, compared to the seemingly small
growth in household income. I can’t exactly remember the message and I don’t
want to misrepresent it but I think it was along the lines of “the rich are
getting richer and poor are getting poorer” (paradoxically, people have been
saying that unceasingly for hundreds of years). The issue is that household
income is a numerator without a denominator. It is not a useful number without
corresponding trends in household size and the number of earners per household.
The graph then, though factually correct, did not present information from
which conclusions could be reliably drawn.
Do we ever track down the
original data or do we except shocking statistics at face value? Do we
naturally ask follow-up questions? I’ve heard that the best one to ask, after
“what is your evidence?” is “compared to what?”. To take an example from the
economist Thomas Sowell, there was a media scare in the United States about
20-30 years ago when statistics appeared painting a very dire picture about
hunger in the United States. Different news outlets everywhere started
reporting on the national crisis. Dr. Sowell found the numbers suspiciously
high and tracked down the original data. It turned out that the methodology
used in the original report was unreliable. In order to measure hunger, the
authors defined as “hungry” anyone who is eligible for food stamps but not receiving
food stamps. This meant that someone who worked a job that was low income but
included food and board was by definition hungry, which greatly inflated the
numbers. Incidentally, the ‘hungriest’ county in the United States turned out
to be a farming community where they grew and ate their own food. Is this to
say then that there wasn’t a hunger problem? Not at all! But a countrywide
crisis would require a very different response than localized malnutrition in,
for example, poor urban centres. The information as it was presented generated
an inappropriate response, and could have caused some damage. This kind of fact
checking is hard in practice, but a good sense of numbers should provide even a
non-expert with an instinct for reasonable statistics.
Are we in the habit or
checking whether bold claims clash with our own experience? Although people can
make abstract arguments against the rote teaching of arithmetic, I cannot bring
myself to reject the rote method (n.b. arithmetic, not mathematics). This is
not because I have no faith in science or reason, but because I believe that
the claim is too bold and the evidence I have seen too meager against my
personal experience, both as a student and as a tutor. I consider myself to
have a good sense of numbers, and I attribute it to the fact that my homework
when I was young often consisted of pages of arithmetic problems (without a
calculator), and that my mom and my grandmother would randomly ask me
arithmetic questions at home. I’ve never come across a student who had no
capacity or even slight affinity for abstract mathematics, but I have met many,
even in university, who were predestined to failure by a very poor sense of
numbers, rendering even the simplest equation rearrangement, or expression
simplification an ordeal.
The other danger of misplaced
confidence is that it can allow nonsense with the appearance of rigor to go unchallenged. A funny example of a
falsehood presented with an air of presumed authority and under the banner of
SCIENCE is found in Friedrich Engels' polemic Anti-Dühring. The Russian mathematician and colleague of Alexandr
Solzhenitsyn, Igor Shafarevich wrote a tract entitled The Socialist Phenomenon that explored the common themes of
Socialism throughout the world and throughout history. In the chapter on 19th
century socialism, he is particularly critical of the apparent regard the
writers had for the scientific method, which he says in practice amounted to
little more than lip service:
The
concept of the ‘scientific method’ was of extraordinary importance for the
development of 19th century socialism. Hence it was steadily and
persistently elaborated, first by Fourier [not the mathematician Fourier] and Saint-Simon and later in a much more
sophisticated manner by Marx and Engels. The scientific method provided the
socialist doctrines with a ‘sanction’ of the first order. Furthermore, the
theses of socialist doctrine thereby acquired the appearance of objectivity and
a certain inevitability, being presented as a consequence of immanent laws
independent of human will.
In other words, science was
used to provide the guise of objectivity, but was not actually used. One of
many examples he gives comes from Friedrich Engels and his use of mathematics
to justify a position on epistemology. In the forward to Anti-Dühring, Engels states “Awareness of the fact that I have not
sufficiently mastered mathematics has made me careful: no one will be able to
find me trespassing against the facts.” He then goes on to state several bold
claims about mathematics which are either completely false or represent a gross
misunderstanding of the subject. Shafarevich then slyly notes:
As
for political economy or history, Marx and Engels clearly did not believe that
they had ‘not sufficiently mastered’ these subjects; nothing prompted them to
be ‘careful’ as with mathematics. One may well imagine how resolutely they
operated in these areas.
What I hope to illustrate by
this little example is what I worry is a growing trend in the world of public
policy, namely the use of SCIENCE not to further a discussion, but to end it.
Setting aside Marx, Engels and my grim Cold War paranoia, how often in the news,
particularly in relation to the newest public policy do we hear words and
phrases like “evidence-based decision making”, “leave it to the experts”, “the
latest research”, and “the scientific consensus”? How often are those terms
used to placate or rebuke a perturbed public? Science, properly done, should
welcome skepticism and scrutiny. Whether it can withstand the scrutiny is what
marks it as good science. It should always be able to substantiate bold claims.
The difficulty in going
against fashionable ideas is that it can have the appearance of contrarianism
or audacity. No layman in his right mind would contradict Hawking in physics,
or Chomsky in linguistics. But there is something intrinsically different about
fields such as psychology and education. By their direct influence on public
policy, these fields are more immediately impactful on our lives than, for
example, the latest research in cosmology. Additionally, the nature of data is
much different. Setting controls in social science experiments can be vastly
complicated. Correlation and causation are not as easily distinguished. Reproducibility
is harder to verify. There is a very interesting phenomenon called the “Decline
Effect” in which the empirical evidence for a phenomenon gradually disappears
over time (but I’ll leave that for another day).
To distinguish true from false,
and plausible from implausible is a skill that nobody can possess perfectly,
but it is a skill that we all need to some degree. We can’t all be economists
or financiers (I’m certainly not), but a decent sense of numbers combined with
a prudent degree of caution is an invaluable tool. I do not believe skepticism
in science or statistics should be explicitly taught (and definitely not to
young children), because that may lead to mistrust and cynicism. But I do
believe that actively thinking about
the numbers we encounter everyday should be encouraged, both for the mental
exercise and the practical effect of encouraging a healthy position of caution.
The examples that I gave in this article focused more on economics but it
appears everywhere. Is this a good deal on a loan? Do the numbers advertised by
that organization asking for a donation make sense? Does my answer to a word
problem on my physics assignment sound
right? It is a practical, and dare I say, fun daily application of mathematics,
but because it is predicated on a certain degree of comfort with arithmetic, it
may not be a practical habit to encourage so long as the current state of
numeracy amongst students entering high school remains so discouraging.
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