![Bell-shaped Curve Bell-shaped Curve](/files/images/bell-shaped_curve1.jpg)
According to the
theoretical worldview of the bell-shaped curve, for example, we can apply this
statistical or proportional dynamic to almost anything.
![Normal Distribution Normal Distribution](/files/images/bell-shaped_curve1-1.jpg)
Let’s try the IQ of
garbage collectors, for example. According to the statistical worldview of the
bell-shaped curve, most garbage men have a similar IQ, and that is the average
IQ for a garbage man. However, all the way on the right of the bell-shaped
curve are a very few garbage men who have genius IQs. Also, on the far left,
are a few garbage collectors that really are so mentally challenged that they
should really not be allowed to be garbage men because they can barely do the
job.
![Garbage Men IQ Garbage Men IQ](/files/images/bell-shaped_curve2.jpg)
Interestingly, the same thing would apply to IQs of heart surgeons.
![Garbage Men IQs Garbage Men IQs](/files/images/bell-shaped_curve3.jpg)
... or to IQs of college professors.
![College Professors IQ College Professors IQ](/files/images/bell-shaped_curve4.jpg)
At the same time, though it may apply to rolling the dice, it is not entirely
clear when it will and when it will not apply. For example, the bell-shaped
curve will not apply in a meaningful way to the number of times it rains in a year in Maricopa
County, or the number of people who will get married in a year in the USA. These phenomena do not vary enough to be interesting or even meaningful statistically.
When it comes to
political polls, we like to think the bell-shaped curve applies, and that if we
sample the proper number of people, then we will have an approximation of the
average voter who is Democrat or Republican.
Yet, the truth is that
the whole idea of what it means for a person to be in a political party versus when that person will
decide who to vote for, along with considering that there are probably more
people in the USA who are not affiliated with either the Democrat or the Republican
Party, than are affiliated with either party, then the prospect of tapping into
a solid representative sample of the average Democrat or the average Republican
becomes more and more ambiguous.
For instance, when it is
difficult for millions and millions of people to self-identify with either
political party, and when there are fluctuations of opinion and ambiguous
feelings for millions of people in a presidential election, then the prospect
of every poll tapping into THE average voter itself becomes a disparagingly
ambiguous concept.
Ironically, the Los Angeles Times tried something different
last election and maintained a panel of the same voters who simply continued giving
their opinions on a regular basis throughout the campaign. For some reason,
this was deemed by many people as less than an optimal randomized poll – even though
it was better than most of the polls.
The point of this discussion is not to
indicate the best way or the proper way to look at this – the point is to show
how nebulous and volatile these concepts are and how experts still continually
disagree about the best way to conduct political polls.
So, what is the theory
behind political polling?
It basically amounts to having faith that if one
samples enough people, then one will get a good idea of how most people will be
voting. However, that seems more like common sense than a theory of political
polling.
Going another step with
these ideas, allow me to give an example of how there is really no theoretical
foundation for statistics. Imagine I want to study self-esteem by giving a
self-esteem scale to a group of people. Let’s say I decide to study self-esteem
among college professors. No problem.
I administer the scale, crunch the
numbers and analyze the statistical output. I can perform all kinds of analyses
and no one will question the theory underlying my choice of the scale instrument or the
quantitative analysis of the data. There is no use even discussing the
theoretical foundations for the statistics underling my study. It has been
shown to work nicely in numerous studies for decades.
Now, let’s assume I want
to study the self-esteem of mid-functioning people with autism. These people
have such weak social skills that they are often constrained to rigid regimens
in institutional settings. Such people are so deficient in their ability to do
normal social interaction that they could not even fill out the self-esteem
scale I used with the college professors.
This time, if I really want to do my
best, and cannot use the scale, then I will have to undertake a qualitative
study. I might try to volunteer where such people go to school and see if I can
find ways to detect what self-esteem is like for these people who have very low
thresholds and skill sets for social interaction. In fact, historically many people have said that ASD is a lack of social self-awareness.
Therefore, many would argue that people with strong
autistic perception do not have a sense of self, and I should not even try to
do a statistical, quantitative study. The fact they cannot even fill out the
scale means they cannot be studied statistically.
On the other hand, being
a ravenous contrarian, I would say that there is a reason to study their self-esteem. I
happen to know that in such constrained school settings where there may be
people with different levels of autistic perception, as well as caregivers and
teachers with normative perception, something interesting will happen. I heard
of such a situation, in which, left to their own devices, the two lowest-functioning people with
the strongest autistic perception would sit next to each other in a classroom and
away from everyone else. Think about that for a while …
Here is the point about
statistics. When statistics works, as in the study of self-esteem among college
professors, then it works and there is no discussion or need to discuss theory.
But, when statistics will not work, as in the study of self-esteem among people
with autism, and one has to do another type of study, maybe a qualitative
study, then all the statistical probability theory in the world will not make
it work, or mean a darn thing.
Not only is statistics limited,
but just because we have achieved statistical power is not an indication of
success. To say that statistics works when it can address inferences from data
representing consistent phenomena does not exactly count as a win for
statistical probability theory. We could say that, in terms of statistical
probability theory, a broken clock has a 100% probability of being right twice
a day. So what?
Furthermore, to say that
statistical probability theory provides the foundation for a scientific study
is like saying that finite mathematics provides the foundation allowing us to
predict where the hands of the clock will be at any given time. So what?
Bottom line: statistics
as an inference of probable accuracy drawn from numerical data only works when
it works, and it only works when the data are consistent enough to be analyzed
statistically, so the theory of why it works is tautologous at best.
A tautology is something
that is true, but we are not much better off for knowing it. Statistical
probability only provides a foundation for statistical inferences when they
seem reasonable, and when they do not seem reasonable then statistical
probability theory provides no foundation for anything.
Furthermore, if the data
are too much alike, then heteroscedasticity becomes a problem, and if the data
are not similar enough, then there is not enough basis for statistical power.
So, statistics only works in a certain range of fairly consistent, fairly
related phenomenon. The more ambiguous, paradoxical, volatile, or subjective
things become, the less theoretical probability you have that statistics will
work at all.
Finally, no one consults
or discusses the theory of statistics or methodology when they discuss statistics
or methodology. They either use it because it works reasonably well or they do
not use it because it won’t work. If it doesn’t work then you can try a
qualitative methodology.
In any case, you are
left doing your best to study what you want to study. If you study something that
is amenable to statistics and you are good at statistics, then everyone will
think you are a genius. If you study something that is not amenable to
statistical analysis and you do not care about statistics, then people will
think you are not as smart. But all the statistics in the world can only
estimate probabilities of events - it can never explain why they happen.
As I have mentioned elsewhere,
by the time you contemplate the political pollster who is weighting the weekly
poll for a network news station so that it will reflect the results they think
they would have obtained if they had done the poll correctly in the first place,
then political polling seems much more like rolling the dice in a casino and
hoping for the best, and much less like an example of how to apply a strong
statistical methodology that minimizes researcher and measurement bias.
In the Principia Mathematica, Russell and Whitehead labored to
explicate the theoretical premises for mathematics, but that was an exercise in
formal theory construction, using symbolic logic to lay the foundations for
finite mathematics. It was somewhat like using math with ideas to create the
premises for math with numbers. It was a similar project to Euclid laying out
assumptions with words, that led to the deduction of theorems creating
mathematical geometry.
Yet, the theory of
probability and statistics works based on assumptions of the distribution of
the phenomena being studied. There is no theory of statistics as much as there
is a set of guidelines for how and when to use statistics because statistics
cannot be applied to anything at all – only certain things that are reasonably
consistent and predictable in their activity. Statistics just addresses
inferences from particular distributions of data and it is not so much that the
theory of statistics actually informs the processes of science as much as it
constrains them.
Statistical theory does
not tell you anything about your data, it tells you how to use the math of
statistics in a limited and constrained way to study fairly cyclical or fairly
consistently associated phenomena. Statistical theory is absolutely not an
inherent theory of causality. There is a weltanschauung of statistics that
believes the principles of probability grab, or may be applied to, most of
reality, most of the time, or something like that. And when statistics does not
work, then we just go around it, and proceed on our merry way. Oh well ...
Yet, for some reason, in
a world of science based on theory and methods, to say that there is
practically no mention of the theory of statistical methodology occurred to me as
a startling thought. Everything is theory and methods, but there is no
discussion of the theory behind the methods because there really is none. There
are just rules and guidelines for which stats to use in which situations
because statistical inferences are in fact so constrained. That is why it is so
easy for political pollsters to stretch the rules and still appear scientific.
For some strange reason, this reminded
me of Buddha and the paradox of the three gunas.
In Hinduism, the Vedas
said that all life is made of the three gunas: sattva, or creation; rajas, or
maintenance; and tamas, or dissolution. Part of the lore of Buddha is comprised
in his arguments against Hindu scripture. For this reason, Buddhism has always
had a special place for logic in its heart. Buddha argued thusly: if everything
in the universe is made of sattva, rajas, and tamas, then each of the gunas
must also be made of sattva, rajas, and tamas, but in that case nothing could
exist. His revelation of paradox was the chink in the Vedic armor, and the
beginning of his claim to legitimacy.
That is one of the all-time,
great, seminal arguments in world philosophy ...
GONG …
I am sure Campbell
understands that the “theoretical” basis for political polling is the weltanschauung
of statistics and the bell-shaped curve. But, why did I have to put the word
theoretical in quotation marks? Because there is no theoretical basis for statistics,
per se, there is only the assumption of the mathematics behind it, and the
benefit of empirical applications that worked when they worked.
There is only the belief
that statistics will work as long as it works, and when it does not work, then
we will make do as best we can. However, that is no insurance against the abuse
of it either, and that is really the fundamental question.
No one needs to debate
whether science exists, it is just hard to say exactly at which point does great
science part ways with science that has become abused. We may not think all science
is balderdash, but we would like to know which part is which.
Every stats prof
I ever had told us the old joke: there are lies, there are damn lies, and there
is statistics. No one and nothing is perfect, and the fact is that there is no
single step in theory or methods anywhere in any scientific project that is not
completely and totally based on someone’s subjective judgment call regarding which
step to take next.
A great example of this
is Tommaso Dorigo’s (2016). Anomaly! Collider Physics and the Quest
for New Phenomena at Fermilab.
It is a new book in which details are given about the discussions, arguments,
and decision-making processes behind the engineering of world class particle
physics. It is really a book about the sociology of physics. The point is that
science is an aspiration to systematicity, but it is only the result of
discourse, that is, talk with words. People interact and they talk and they do
science, and one cannot be separated from the other. No science occurs in a
vacuum of pristine logic or method. Some things are amenable to scientific
investigation and some are not.
Physics aside for the moment, science itself is not necessarily
definable as an all-encompassing mission to construct a theory of everything.
In fact, to anyone who really understands
the nature of theory, the idea of a theory of everything is almost an oxymoron.
The Holy Grail of theory construction is parsimony - to epitomize the value of
simple elegance is referred to as theoretical parsimony. That means that a
fundamental statement about the nature of an object or subject of study will
not have dozens of fundamental components and be strung together in a way that
no one can understand. Fundamental means elementary and foundational. The idea
is to hone in on a topic of inquiry until its essence is distilled in a cogent,
logical statement or proposition. Less is more, it’s Occam’s Razor and no one
in their right mind would ever set out to conceive of a theory of everything.
We find where science
works and focus on that much. Then we figure out another way to work somewhere
else and move on to that point. There is no inexorable progress forward making one
inevitable step at a time.
There is no yellow brick road built of formal logic
that will take us all the way we want to go. Ultimately, no matter what
standards and technology we have for science, the use of it all comes down to subjective
judgments.
We just like to have the
guidance of scientific theory and methods in making these judgments. We would
like to hide behind the word science as if it were a shield that made us impregnable.
But, science is only as good as the scientists doing it, and that is why the
secret of science is its democracy of inquiry and replication. If science exists,
then it is product of rationalism, pragmatically applied, pushed to the
extreme, then tested and re-tested.
Therefore, people will
have to agree there are certain things that are scientific achievements, and
people will have to agree there are certain things that are scientific
delusions. The question is how do we know where we are on this continuum at any
given point in time regarding any given issue?
The answer is that we
continue arguing, but we also try to utilize the democracy of scientific
inquiry to establish some kind of growing consensus about what is going on.
That is the best we can ever do.
In other words, if people do not like
something that seems promising in the world of science because it is possibly
flawed, the best we can do is to continue pursuing science to improve upon the
situation. By testing, and abducing innovations, we can build track records of
scientific inquiry that will allow intelligent people to come to a consensus
about almost anything – theoretically.
You cannot just chuck
science in favor of prehistoric naturism. In some imaginary experiment, if you
have a group of people who have science at their disposal, and a group of
people who do not, then you would expect that the scientific group would at
least have the potential to solve more of their problems. That might not be
true, but the argument would be that science trumps common sense over the
long-run.
No person’s hunch will
ever outdo the continual application of science. That does not mean science can
be applied to everything, but whether or not science works is itself something
that is best determined by engaging a scientific and social process of discovery,
together, over time.
So, for example, if we have a crisis in the world of
science, then we establish as many independent tests of the phenomenon under
study, tracking individual data as carefully as possible, until we get a handle
on what is going on. In that sense, all we have is our ingenuity and the proof
of the pudding we make, and it is the pragmatic effects of our endeavors that
will tell the tale.
You can call it the spirit
of science or you can call it the spirit of capitalism – I think they are one
and the same thing ultimately. It is about the individual’s relentless pursuit of
rationalism, quality, and ingenuity, in collaboration and competition with other individuals, to
figure out how to make things work better.
There
is Science and Then There is Science
Once, I once took an article
out of my dissertation research, which was a laboratory experiment. The article chronicled a part of the experiment in which I had performed a test on an early measure of video facial
recognition, which I had developed way back in the early nineties. My data showed the test
I tried was not a good measure of facial recognition. I wrote it up – and
dutifully submitted it for publication – over and over again, until I got tired
of receiving the rejection letters.
Then it finally hit me –
you never see a scientific publication about something that did not work. Sure,
as a post-doc I was thinking in terms of pure science because I was still fresh
with grad student true believerism running all through my veins.
A scientific result is a
scientific result – right?
Wrong.
Go directly to jail, do not pass go, do not
collect $200, go directly to jail.
Pure science is a dream, like something that
exists for one brief shining Camelot moment, but in the real world, scientific
journal or not – no one wants to hear the results of a scientific test that
showed something that did not work.
There is a deeper lesson
in this – I learned that science has a measure of P. T. Barnum hucksterism and
promotion-mongering in it. You just have to figure out how to put the right
spin on it. In other words, I learned academics is full of cliques with social
codes as operating systems, and when you learn to start publishing, what you
actually learn is how to break the social code of the cliques – whether the clique
is a journal or a department. Translation: if you do not learn to espouse the
proper social codes for producing winning science, then you will never experience
success.
Then, what is science? It
can’t all be an illusion like the postmodernists say it is – can it?
Of course not, but real
science must be an attempt to do something as well as you possibly can do it.
It has to be something that someone else can then imitate and use to achieve
the same results. It really has to work. That means when old man Otis made that
first elevator, he had to get in it himself and test it out for the public. We
really don’t care how smart you think you are – just show us something that
actually works – problem solved.
So, can two people see
the same mirage?
I am absolutely sure of
it. From the standpoint of an Independent standing between the Democrat and the
Republican parties in the presidential election, all of the Democrats are
seeing the same mirage at the same time. Of course, all the Republicans are
also all seeing the same mirage at the same time. They are all looking at the same
country, the same media and internet information, blah blah blah, and they see
it all in two completely different ways – at exactly the same time.
You better believe two
people can see the same mirage at the same time. But, that is only the start of
it. If you are a Republican, then you will think you see reality, and the Democrats
and the Independents are each all seeing the same mirage.
Apparently, two groups
of people can each have members who are each seeing the same mirage at the same
time, and each entire group can be seeing a different mirage from the other
group, even though they are all beholding precisely the same reality. In fact,
the price of membership for joining in either group is that you have to agree
to start seeing the same mirage as everyone else in the group. Indeed, you will
have to engineer your own epiphany in which you, too, can now see what is
right, true, and good, as if the scales have fallen from your eyes.
Not only are there widely
diverging records of polls predicting outcomes from local to national levels,
but I will bet anyone all the tea in China that Democrat pollsters will yield
hopeful polls for their party and Republican pollsters will yield the same for
their party. Thus, science attempts a measure of protection against common
sense and human nature, but science will never be immune from either.
In a sense, in order for
two people to enter into the bond of a relationship together, they both have to
start seeing the same mirage at the same time. That is what a relationship is.
The entire project of society comes down to social propaganda projects, which
are designed to recruit members who will join in seeing the same mirage as
everyone else in the group. It’s called socialization.
The problem arises when
people try to use science as a tool to persuade others to see their mirage the
way they see it. The answer to this problem is that we have to learn to think
for ourselves and become acquainted with our own ability to think logically.
Unfortunately,
by the time you have earned a PhD in research methods, you can never trust
another study until and unless you have seen all the details of the methodology.
At the same time though, you become glaringly aware of the fact that an entire
society is rapt every time the media utters the words a recent study shows …
When I have told people
I am unable to enjoy hearing about research from the media because I cannot believe
any of it automatically, the response has often been something like you can’t just not believe everything you
hear. What are you going to do? Walk around the rest of your life living in a
shell and not believing any scientific research ever again? You have to believe
in something.
My response is: I don’t
have to believe in anything. I’ll believe in what I want to believe in when I
have enough evidence or enough intuition to guide me into believing it - the
same way I always have. To me, that is at least part of what it means to be American.
Sharing MIrages
Make no mistake, it is
this part about seeing and believing in the same social mirage that is the real
fascination of social psychology. Yes, the individual is a member of a group,
but the real deal is that in order for individuals to become members of groups,
they have to be able to see the same mirage at the same time as everyone else
in the group. It is the way that each of us does this, and the way we persuade
others to do this, that has always been the real fascination of life for me as
a social psychologist.
Having reached the age
of 57 now - allow me to quickly tell you a short story about the day I became a
social psychologist - I was 10 years old, and I remember it as if it happened
yesterday.
One day, my dad pulled
me aside and said, “son, your mother has a mental illness, and because she has
this mental illness that is why she behaves the way she does and why we have
the problems we have. We are all going to have to learn that she has a mental
illness and make adjustments in order to keep the peace and get along as best
we can. Okay?”
I said okay, my dad
walked away, and I stood there thinking tell
me something I don’t already know.
About two hours later,
my mom pulled me aside and said, “son, your father has a mental illness, and
because he has this mental illness that is why he behaves the way he does and
why we have the problems we have. We are all going to have to learn that he has
a mental illness and make adjustments in order to keep the peace and get along
as best we can. Okay?”
I said okay, my mom
walked away, and in that moment I became a social psychologist.
I stood there feeling
something profound and barely speakable. It was a not a full-blown thought, but
a deep-level sentiment: now I know
something that neither of them knows – now I am on the outside looking in, and
I see that each of them sees what they see, and yet they do not see what they
do not see. Each wants me to see the same thing they see, and each thinks they
persuaded me to do so today, but they are both surely crazy. They cannot both see
the same thing the same way, so they will never stay married. And I will always
stand here, on the outside looking in, and wonder what I am seeing ...
Imagine a 10-year-old
boy wondering, if both of my parents are
nuts, then what does that make me? A social psychologist – that’s what it
made me.
They
each tried to make me share their mirage.
Science is supposed to
be our best effort to achieve a consensus that we are all seeing something that
is real and not a mirage. We have to believe in it or all hope is lost. We have
to keep trying to find ways to establish the democratic consensus of independent
investigations that grows consensus independent of mirage – or at least do our
level best to come as close as possible.
What is the alternative
– to believe in hunches, mediocrity, and dogma? Science is a gold standard for
the logic of rhetorical persuasion – and it’s the best we can do. We have to
believe that such a thing as science exists in an attempt to cut through the
illusion of maya, and bypass the mirage of social relationship bonding, to catch
a glimpse of something real, if only for one brief shining moment. That was the
whole point of starting science in the first place.
Maybe everything
is a theory of logic, and we all do the best we can. Yet, the trickster in the
ointment is that meaning, emotions, and logic are the same thing before and
after words. So, while we cling to our logical and scientific view, we also are
being persuaded emotionally to see the same mirage as members of some group see
it, and we are always involved in juggling our meaningful experience of logic
and emotions, trying to figure out what works best.
But, I am sure
two people can see the same mirage.
Umberto Eco
famously said that society started when the first person told a lie. I think
another way to look at it might be to say that society is a place where two or
more people wake up every morning, and see the same mirage together, every day,
all day long. That is exactly what a society is … wherever two or more are
gathered having the holy, very real, experience of sharing one and the same mirage.
References
Dorigo, T. (2016). Anomaly! Collider Physics and the Quest
for New Phenomena at Fermilab. World
Scientific.
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