Technicality: a reader has asked how to increase the size of the fonts. Try to press ctrl/+ (ctrl/=) many times, and/or go to View/TextSize/Largest in your internet browser. I don't plan any major changes in the design right now.
Many recent controversies that involved science in one way or another have shared the following basic question:
- If there exist different opinions about a scientific question, should the public believe the insiders or the outsiders?
We could end up with this punch line but such an analysis would be far too short and incomplete. Even though no simple sociological rule that would produce 100% correct scientific answers can ever be found, there are still many approximate rules that can help anyone to have more reasonable opinions about many questions. And there are also many myths and wrong rules that help to spread wrong opinions.
Emperor's new clothes vs. independent and neutral arguments
The first fact that we should always be aware of is that only the arguments of those people who know what they're talking about and who look at the scientific questions sufficiently carefully matter.
If someone tries to intimidate you with millions of people who believe in creationism, be sure that there exists no rational reason to accept their opinion. If someone tries to convince you that there is, you're being cheated.
If someone else wants to impress you with thousands of people who have random science PhD degrees and who have voted in one way or another in a poll about the climate or particle physics or anything else, be sure that what you see may be just an exercise in discipline or groupthink.
If you have reasons to believe that the poll question is more or less the most difficult type of question whose wording the respondents can understand, it is not unlikely that most of them will give you a wrong answer. The reason behind this rule is the very same reason as the explanation why a theorist should never pay too much attention to the last point in a graph produced by the experimenters. If the point were reliable, the experimenters would add another point. The lesson is that you should only trust someone's answers to questions that are simpler than other questions that the person would still be willing and able to address.
Fine. So the opinions or larger groups of people only matter if their owners obtained them carefully, mostly by using their own intellectual tools, and if there are reasons to believe that they are actually able to analyze these questions as well as slightly more difficult ones. A single careful analysis of a problem is more valuable than a superficial opinion of thousands of people.
Large groups of people - and scientists - have been wrong many times in the past. But surely, you would say, there must exist a sense in which many experts are more likely to be right than a small number of outsiders. Doesn't your humble correspondent believe this thesis, you might ask?
Yes, I do, but one must be very careful about the details of such a sociological argument.
Imagine that you have a group of people, XY, and the question is whether their majority opinion about a particular question, PQ, is justified and likely to be correct. Independently of the number of elements in XY and their degrees and credentials, their majority opinion may fail. There always exist sufficiently subtle questions that even a very selected group of people may end up with a wrong majority opinion simply because the question is too difficult for most of them. In the second half of the article, I will try to quantify how large the groups of qualified people are in various contexts.
You should ignore the majority opinion of XY if any of the following conditions is satisfied:
- you have good reasons to think that the unscientific motivations of XY to have a certain opinion - e.g. political, religious, financial goals or fear - are stronger than the scientific ones
- you have good reasons to think that a majority of XY has copied their opinion from others without looking at the question carefully enough
Fine. I have said too many things about this side of the argument. But still, there are people who know what they're talking about and who should be trusted more than random outsiders, aren't there? There must certainly exist people whom we should trust if the society is supposed to work. Yes, there are.
Hierarchy of experts in the U.S.
Let me try to estimate the number of people in the U.S. who are actually capable to decide rationally what the correct answers to certain questions are. I will start with two disclaimers:
- The numbers below don't count the people who happen to reach the right answer just because they're lucky: the figures systematically subtract anyone whose opinion could be viewed as a result of good luck or bad luck.
- On the other hand, the numbers below will include many people whose opinion will turn out to be incorrect at the end - but the way how they have obtained this opinion can be classified as a result of independent rational thinking based on the best kind of evidence that looks necessary for such a reasoning. The rational thinking may involve a limited portion of sociological considerations - a reasonable belief that certain other authorities are not cheating us and/or they must have figured out the right answers. But once again, the sociological reasoning must always be subdominant.
This question is just an innocent example to get started. I think that 220 million Americans are able to find a qualified answer to the question whether it is safe to jump from a skyscraper. An overwhelming majority of the complementary set are small children. Their parents should be careful if they visit a skyscraper together. I have only included this question because all other questions will have much smaller ensembles of the qualified U.S. citizens.
Evolution vs. creation: 20 million people
You might think that the number should have been much higher. I don't think so. I am convinced that most of the general discussion about the origin of life is irrational, political, and religious in nature. Moreover, while I believe that the very basic ideas of evolutionary biology are not rocket science or string theory, they are difficult enough so that a reasonably intelligent person could easily end up with a wrong conclusion. My order-of-magnitude estimate is that 20 million Americans can rationally understand and evaluate all the necessary facts to conclude that evolutionary biology is more or less inevitable to explain the basic properties of the world we see around us. Of course, I am convinced that most of these people end up believing Darwin's framework.
Does the low number have any consequences? Yes, it does. The relatively low number means that it doesn't make much sense to try to increase the number of people who answer "Yes" to evolutionary biology in the opinion polls. If you increase this number, it just means that you have brainwashed a larger segment of the population. If you change their opinions, it was most likely not a rational change. The society doesn't benefit too much from much higher percentages of the "evolutionary believers". The opinion of more than 90% of the population about the origin of life is inconsequential for the life of the society, whatever their answer is. The fact that the U.S. is the second most anti-evolutionary country after Turkey doesn't prevent America from being a leader in biology.
The fact that the number of the trustworthy sources in the context of the very facts about evolution is much smaller than the population of the U.S. also means that no rational person should allow her opinions to be directly formed according to the public polls if these polls include the whole population. Most of the results reflects irrational noise and unscientific pressures.
Innate cognitive differences between groups: 20 million
My estimate of the number of people who are qualified to scientifically answer the question whether different groups of people can have significantly different pre-requisites to do special things such as math is 20 million, too. Again, if you ask everyone, what they will answer will be nothing else than noise. On the other hand, I think that the required evidence to answer the question rationally is sufficiently accessible, much like the more general insights about biology that can be used to deduce the answer by other methods, and a visible fraction of the population is thus able to figure out the correct answer.
While the qualified ensemble in the case of evolution was dominated by left-wingers, the qualified ensemble in this case will be dominated by the conservatives. Note that the question whether there exist differences between the groups influences our life more directly than the validity of the evolutionary biology which is still, essentially, an academic discussion about the billion-year past of our planet.
Validity of special relativity: 5 million
My rough estimate of the number of Americans who can understand what the statements of special relativity are and whether they are a correct piece of well-established science is 5 million. What does it mean? Again, it means that if you rely on much more than 2% of the people who are most educated (or otherwise gifted) in physics, you will end up with garbage.
On the other hand, the number 5 million is much higher than some of my estimates of the ensembles that are relevant for much less esoteric questions than special relativity, for example questions in climate science. It is because I think that tens of millions of people have been exposed to special relativity and the basic evidence supporting this theory at one moment or another. Consequently, most people who have the ability to make a rational conclusion about this question got the opportunity to do so.
I could find many questions where the estimate would be in between tens of thousands and millions of people. But let us make a bigger jump.
Paleoclimate evidence for global warming: 5,000
Is there evidence of a recent unprecedented anthropogenic global warming that is based on the historical and geological data? I don't want to answer this question in this article. Instead, I want to estimate the number of people who have actually looked at this question carefully enough and with a sufficient amount of education and intelligence.
My guess is 5,000 only. This certainly doesn't mean that this piece of climate science is one of the most intellectually demanding part of science. The main limitation is that most people simply didn't get the opportunity or didn't have the time to look at all the necessary data. The number of people who have the sufficient abilities to decide about these questions could be as high as hundreds of thousands but the required data are not easy to find and the question hasn't been considered important for too long.
Similar figures could be associated with many other particular questions about the climate such as the validity of the climate models. There could also exist about 5,000 people in the U.S. who have a qualified opinion about the validity of the climate models because they have spent a sufficient amount of time and rigorous efforts to study what the climate models are all about and whether the evidence supporting them is sufficient.
On the other hand, I think that the number 5,000 is primarily composed of people who are not paid as climate modellers. It is my belief that this number is dominated by statisticians who are interested in the climate science. Many of them may attend various blogs and other platforms where these questions are being discussed - but many of these people could be silent visitors of these websites. The subset of the qualified set that you had a chance to hear is much smaller.
Is there some general reason why I think that there is such a small overlap between the community of the competent people and the community of the people who are actually paid for this job? Sure, there is. I think that the climate modellers are not a sufficiently selective community. They are doing something that many other people can do equally well or better as amateurs. Moreover, I find it obvious that the community of the climate modellers is much more spoiled by various financial and political pressures than an average amateur.
Uniqueness of string theory: 1,000
I estimate the number of the people who are competent to offer their qualified guess whether string theory is the only existing proposal to describe gravity in a consistent quantum-mechanical language to be comparable to 1,000. Again, I don't want to say what is the correct answer to that question - you know what's my answer anyway. Unlike the case of the climate science, this ensemble of 1,000 qualified Americans will nearly coincide with the community of the string theorists, whatever its exact definition is.
There are two main reasons why I think that the overlap is so strong. First, the string theory community actually contains a large percentage of the people who are interested in these questions and who can solve the technical problems that are necessary for a qualified opinion about the "big questions". Second, even though there are clearly many smart people who could answer these questions outside the community, the required knowledge of physics at many levels and the required experience are also high - high enough so that the talented outsiders simply couldn't have found enough time to go through all these things.
If you ask more than a few thousand of the most qualified people whether they think that string theory is the only known consistent way to describe quantum gravity in 4 dimensions or more, you will again collect noise. Of course, there exist methods how you can collect bad noise and nonsense selectively: for example, read the "Not Even Wrong" blog that is based on those who have no qualification to address these questions whatsoever but who are sufficiently self-confident about their wrong answers and not-even-wrong answers. Well, there are cases in which it is better to ask chimpanzees in the zoo.
High-energy physics evidence of eternal inflation and the anthropic principle: 100
As you can see, we are getting to ever smaller numbers. Now we think about another scientific problem: do we have a sufficient body of evidence that the anthropic principle follows from our knowledge of quantum gravity or string theory and that this principle is inevitable for solving the cosmological constant puzzle in a way that is consistent with the rest of physics? I won't tell you what the answer is - even though everyone knows that my guess is that "the anthropic principle is not inevitable" anyway.
Because I can't provide you with a guaranteed and proved answer, you won't be able to learn who the 100 people actually are. The group of 100 people who are qualified to answer the question will most likely be composed of a small subgroup of the theoretical physics community but I can't tell you which subgroup it is. The time will probably tell.
What are the final equations that describe everything? 0 or 1
Can we write down the final principle of Nature that can be used to deduce the rest of physics (and science, for that matter)? I estimate the number of Americans who are qualified to do so in 2006 to be 0 or 1. The number 1 is correct if God is a U.S. citizen.
We could analyze many more questions like that. Different questions will have very different sizes of the groups of the true insiders who are qualified to answer them. Different questions will also have very different degrees of overlap between the qualified groups and the groups who are paid for finding and knowing the right answers. In many cases, similar arguments like those above can be found to determine the sizes and correlation coefficients. In other cases, there exist many other social mechanisms and predispositions that must be taken into account before one constructs a qualified expectation about the relevance of the opinion of various groups.
If we want to use sociology of science as a supplementary method to find the truth, our job may be difficult. Nevertheless, it is often impossible for an individual to answer all of the questions that are relevant for his thinking in a strictly scientific and independent fashion. This is why some degree of confidence in other people's result must often be included which is why it is also important to have a reasonable idea which kind of confidence is likely to be justified.
However, it is critical for the scientific method to be primarily based on the actual scientific, independently verified, repeatable results rather than sociological theories, beliefs, groupthink, and the mutual confidence between different scholars.