Does learning probability
and statistics improve critical thinking?
This is an interesting question. Naturally, much of the answer hinges on just
what is meant by “critical thinking’, as another Quora responder noted. It’s a vague term that can be interpreted in
many ways.
Literary or Cultural Critical
Thinking.
We all learn a bit of this in school and via our discussions
with others about cultural matters, including what we see or read in the media. But, I think most of us would generally agree
that a lot of it comes down to “taste”, which differs from person to person and
group to group.
So, does knowledge of statistics and probability help in
this regard? Perhaps a bit – for
example, we do note how successful various cultural products are in the
marketplace, via such statistical markers as sales, books sold, movie
attendance and so forth. That can be
somewhat helpful in separating the wheat from the chaff, but only up to a
point. We all know of many examples of high quality products that didn’t get
the attention that they deserved, and low quality products that were far more
successful than they had any right to be.
Statistics and probability also help us to judge the likely
truth value of cultural works – i.e. how well the story or song content lines
up with known facts, if they are available.
People with a good grounding in statistics and probability are more
likely to be skeptical of cultural products than those without such a
grounding, if the story seems highly improbable (though we might still enjoy it
from an escapist point of view). So, for
example, statistically minded people are less likely to take adventure movies
seriously, if the hero mows down 500 of the enemy without ever being hit by one
of them.
So, probability and statistics are helpful to critical
thinking here, but they are generally of secondary importance in this domain.
Political,
Religious and Social Critical Thinking.
We learn this from family, school, church, media and the
surrounding social world in general.
Most of this relates to “values”, or efforts to persuade us of various
ideas and modes of life that are considered to be appropriate by these
influencers.
Does knowledge of statistics and probability help in this
domain? I would say quite a bit. Of course the belief in the usefulness of
ideas like statistics and probability can be highly value weighted itself, but
I will leave that aside, and just assume that most people believe that testing
values and ideologies against evidence is a good idea, at least in principle
(religion is somewhat immune from this).
In these areas a proper knowledge of statistics and
probability can be extremely helpful for critical thinking, as they aid us in
evaluating the actual real-world results of various values and ideologies. For example, if underlying ideas that lead to
certain policies don’t seem to work, as judged by statistical evidence, we are
quite likely to abandon those ideas, or at least significantly revise them
(though that can take quite some time).
There will be a lot of conflicting claims and counter-claims
advanced to support or refute various ideas – a good grounding in statistics
and probability theory can help us to sort out which claims (and claimants)
that we ought to put our trust in, though it’s not infallible. Statistics can be used to mislead, but that
just reinforces the need for critical thinkers to really understand statistics
and probability, so that they won’t be thrown off, by a misleading graph or
correlation vs causation argument.
So, a good knowledge of probability and statistics can be
very helpful here, as many of these issues are capable of being subjected to
real-world tests. But, one must always be
careful, as not all social questions are amenable to statistical analysis, and
even when they are, it can be very difficult to determine which dataset and
which statistical arguments one ought to find most compelling.
Personal and
Relationship Critical Thinking.
I think we use probability and statistical thinking a lot in
these domains, though we often aren’t aware if it.
Sometimes it is unconscious.
For example, we often estimate how much we can trust a person or a
situation, based on prior experience and a sub-conscious probability
calculus. We often call this intuition
or gut feeling, but in my opinion those are generally terms used in place of
“sub-conscious probability calculus”.
Some people are better at this than others, and it seems to me that
knowing probability theory probably makes a difference in this regard, even at
this sub-conscious level.
At other times our use of statistical and probabilistic
reasoning is conscious but not necessarily rigorous. For example, we might consciously think that
our probability of succeeding at something is high or low, but not be able to
put a specific number on it. But it is
still useful to know such basic facts about probability, such as high
probability X low probability = low probability, so that we can more carefully evaluate
a course of action. Being able to
understand the difference between independent events and dependent events can also
help one to avoid costly errors. And the
understanding that correlation is not necessarily the same as causation can be
crucial in day to day critical thinking.
Finally, there are those occasions where a deep knowledge of
probability and statistics can affect a person’s life in a major way. For example, I once had a major flirtation
with gambling, particularly horseracing.
That led me to study probability and statistics at a young age and
eventually work in the field, which proved to be professionally and financially
advantageous.
I had a pretty good run at the track for a couple of years,
based on collecting and analysing Racing Form data systematically. While doing so, I was motivated to take a lot
of courses in mathematical statistics and multivariate analysis. I came to have a really deep appreciation for
such things as the pitfalls of post-hoc multiple comparisons, data snooping, and
atheoretical statistical analyses.
Eventually my system quit working, and I gave back the money that I had
won, after a lot of hard work. But,
though I ultimately didn’t make a gambling windfall, I learned a lot about
statistics and probability which turned out to be valuable throughout my life.
It was fun and educational, but I could never play a
negative expectation game (e.g. casino games), or a game with a high takeout
(e.g. the track) for long after that. That
probably saved me a lot of money and related grief.
So, in conclusion: hurrah for statistics and probability
theory, they really can help with critical thinking.
--------------------------------------------------------------------------------------------------
Now that you have reflected upon some real math and science, you should read some science fiction. Either of the Kati of Terra series or the
Witch’s Stones series would be excellent choices. Alternatively, you could try the short story
“The Magnetic Anomaly”, which features some references to Fourier analysis as used in geophysics, which is pretty mathy (though you don't need to know advanced math to enjoy the story).
Kati of Terra
How
about trying Kati of Terra, the 3-novel story of a feisty young Earth woman,
making her way in that big, bad, beautiful universe out there.
The Witches’ Stones
Or, you might
prefer, the trilogy of the Witches’ Stones (they’re psychic aliens, not actual
witches), which follows the interactions of a future Earth confederation, an
opposing galactic power, and the Witches of Kordea. It features Sarah Mackenzie, another feisty
young Earth woman (they’re the most interesting type – the novelist who wrote
the books is pretty feisty, too).
The Magnetic Anomaly: A Science Fiction Story
“A geophysical crew went into the Canadian
north. There were some regrettable accidents among a few ex-military who had
become geophysical contractors after their service in the forces. A young man
and young woman went temporarily mad from the stress of seeing that. They
imagined things, terrible things. But both are known to have vivid
imaginations; we have childhood records to verify that. It was all very sad.
That’s the official story.”
No comments:
Post a Comment