According to the theoretical worldview of the bell-shaped curve, for example, we can apply this statistical or proportional dynamic to almost anything. 

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. 

Interestingly, the same thing would apply to IQs of heart surgeons.

... or to IQs of college professors.

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.