# A Mathematical Model for Human Intelligence

People have been trying to figure out what intelligence is, and how it differs from person to person, for centuries. Much has been written on the subject, and some of this work has helped people. Unfortunately, much harm has been done as well. Consider, for example, the harm that has been done by those who have had such work tainted by racism, sexism, or some other form of “us and them” thinking. This model is an attempt to eliminate such extraneous factors, and focus on the essence of intelligence. It is necessary to start, therefore, with a clean slate (to the extent possible), and then try to figure out how intelligence works, which must begin with an analysis of what it is.

If two people have the same age — five years old, say — and a battery of tests have been thrown at them to see how much they know (the amount of knowledge at that age), on a wide variety of subjects, person A (represented by the blue curve) may be found to know more, at that age, than person B (represented by the red curve). At that age, one could argue that person A is smarter than person B. Young ages are found on the left side of the graph above, and the two people get older, over their lifespans, as the curves move toward the right side of the graph.

What causes person A to know more than person B, at that age? There can be numerous factors in play, but few will be determined by any conscious choices these two people made over their first five years of life. Person B, for example, might have been affected by toxic substances in utero, while person A had no such disadvantage. On the other hand, person A might simply have been encouraged by his or her parents to learn things, while person B suffered from parental neglect. At age five, schools are not yet likely to have had as much of an impact as other factors.

An important part of this model is the recognition that people change over time. Our circumstances change. Illnesses may come and go. Families move. Wars happen. Suppose that, during the next year, person B is lucky enough to get to enroll in a high-quality school, some distance from the area where these two people live. Person B, simply because he or she is human, does possess curiosity, and curiosity is the key to this model. Despite person B‘s slow start with learning, being in an environment where learning is encouraged works. This person begins to acquire knowledge at a faster rate. On the graph, this is represented by the red curve’s slope increasing. This person is now gaining knowledge at a much faster rate than before.

In the meantime, what is happening with person A? There could be many reasons why the slope of the blue curve decreases, and this decrease simply indicates that knowledge, for this person, is now being gained at a slower rate than before. It is tempting to leap to the assumption that person A is now going to a “bad” school, with teachers who, at best, encourage rote memorization, rather than actual understanding of anything. Could this explain the change in slope? Yes, it could, but so could many other factors. It is undeniable that teachers have an influence on learning, but teacher quality (however it is determined, which is no easy task) is only one factor among many. Encouraging the “blame the teacher” game is not the goal of this model; there are already plenty of others doing that.

Perhaps person A became ill, suffered a high fever, and sustained brain damage as a result. Perhaps he or she is suddenly orphaned, therefore losing a previous, positive influence. There are many other possible factors which could explain this child’s sudden decrease of slope of the blue “learning curve” shown above; our species has shown a talent for inventing horrible things to do to, well, our species. Among the worst of the nightmare scenarios is that, while person B is learning things, at a distant school, the area where person A still lives is plunged into civil war, and/or a genocide-attempt is launched against the ethnic group which person A belongs to, as the result of nothing more than an accident of birth, and the bigotry of others. Later in life, on the graph above, the two curves intersect; beyond that point, person B knows more than person A, despite person B‘s slow start.  To give credit, or blame, to either of these people for this reversal would clearly be, at best, a severely incomplete approach.

At some point, of course, some people take the initiative to begin learning things on their own, becoming autodidacts, with high-slope learning curves. In other words, some people assume personal responsibility for their own learning. Most people do not. Few would be willing to pass such judgment on a child who is five or six years old, but what about a college student? What about a high school senior? What about children who have just turned thirteen years old? For that matter, what about someone my age, which is, as of this writing, 48? It seems that, the older a person is, the more likely we are to apply this “personal responsibility for learning” idea. Especially with adults, the human tendency to apply this idea to individuals may have beneficial results. That does not, however, guarantee that this idea is actually correct.

I must stop analyzing the graph above for now, because the best person for me to examine, at this point, in detail, is not on the graph above. He is, however the person I know better than anyone else: myself. I’ve been me now for over 48 years, and have been “doing math problems for fun” (as my blog’s header-cartoon puts it) for as long as I can remember. This is unusual, but, if I’m honest, I have to admit that there are inescapable and severe limits on the degree to which I can make a valid claim that I deserve credit for any of this. I did not select my parents, nor did I ask either of them to give me stacks of books about mathematics, as well as the mathematical sciences. They simply noticed that, when still young, I was curious about certain things, and provided me with resources I could use to start learning, early, at a rapid rate . . . and then I made this a habit, for, to me, learning is fun, if (and only if) the learning is in a field I find interesting. I had absolutely nothing to do with creating this situation. My parents had the money to buy those math books; not all children are as fortunate in this respect. Later still, I had the opportunity to attend an excellent high school, with an award-winning teacher of both chemistry and physics. To put it bluntly, I lucked out. As Sam Harris, the neuroscientist, has written, “You cannot make your own luck.”

At no point in my life have I managed to learn how to create my own luck, although I have certainly tried, so I have now reached the point where I must admit that, in this respect, Sam Harris is correct. For example, I am in college, again, working on a second master’s degree, but this would not be the case without many key factors simply falling into place. I didn’t create the Internet, and my coursework is being done on-line. I did not choose to be born in a nation with federal student loan programs, and such student loans are paying my tuition. I did not create the university I am attending, nor did I place professors there whose knowledge exceeds my own, regarding many things, thus creating a situation where I can learn from them. I did not choose to have Asperger’s Syndrome, especially not in a form which has given me many advantages, given that my “special interests” lie in mathematics and the mathematical sciences, which are the primary subjects I have taught, throughout my career as a high school teacher. The fact that I wish to be honest compels me to admit that I cannot take credit for any of this — not even the fact that I wish to be honest. I simply observed that lies create bad situations, especially when they are discovered, and so I began to try to avoid the negative consequences of lying, by breaking myself of that unhelpful habit.

The best we can do, in my opinion, is try to figure out what is really going on in various situations, and discern which factors help people learn at a faster rate, then try to increase the number of people influenced by these helpful factors, rather than harmful ones. To return to the graph above, we will improve the quality of life, for everyone, if we can figure out ways to increase the slope of people’s learning-curves. That slope could be called the learning coefficient, and it is simply the degree to which a person’s knowledge is changing over time, at any given point along that person’s learning-curve. This learning coefficient can change for anyone, at any age, for numerous reasons, a few of which were already described above. Learning coefficients therefore vary from person to person, and also within each person, at different times in an individual’s lifetime. This frequently-heard term “lifelong learning” translates, on such graphs, to keeping learning coefficients high throughout our lives. The blue and red curves on the graph above change slope only early in life, but such changes can, of course, occur at other ages, as well.

It is helpful to understand what factors can affect learning coefficients. Such factors include people’s families, health, schools and teachers, curiosity, opportunities (or lack thereof), wealth and income, government laws and policies, war and/or peace, and, of course, luck, often in the form of accidents of birth. Genetic factors, also, will be placed on this list by many people. I am not comfortable with such DNA-based arguments, and am not including them on this list, for that reason, but I am also willing to admit that this may be an error on my part. This is, of course, a partial list; anyone reading this is welcome to suggest other possible factors, as comments on this post.

# Explaining China, Part II: What Do I Know, About China, and How Did I Learn It?

In the map above, the People’s Republic of China (PRC) is shown in red, while the Republic of China (ROC) is shown in yellow. “Barbarian” nations (from the point of view of the Han, or the ethnic group we call “Chinese” in English) are shown in orange, and both oceans and large lakes are shown in blue. The third (and only other) majority-Han nation, the island city-state called Singapore, is not shown on this map, as it is too far to the South to be seen here. From the point of view of the Han, “barbarians” have been, historically, those humans who were not Han, while “the Han” can be translated as “the people.”

This historical xenophobia I just described among the Han is hardly unique; it is, in my opinion, simply human nature. The British rock band Pink Floyd explained this, quite well, in the following song, “Us and Them,” from 1973’s classic Dark Side of the Moon. This album, in the form of a cassette tape which had to be purchased by my parents (for I would not let go of it in the store we were in), happens to be the first musical album I actually owned, back when it was newly-released (I was born in 1968). If you choose to listen to this song, please consider this idea of xenophobia, as simply being a human characteristic, while it plays.

Ancient Greeks had the same “us and them” attitude about those who did not speak Greek, and the English word “barbarian” is derived from Greek, with a meaning which parallels what I have described in China. Eurocentrism, in general, in the study of “world history,” is well-known. Moving to another continent, the people where I live, the USA, are famous for learning geography one nation at a time . . . as we go to war with them, of course. Only a tiny percentage of Americans knew where either Korea was located until we went to war there, and we (as a people) did not know where Vietnam was until we went to war there. More recently, Americans learned — twice! — where Iraq is, though many of us still, inexplicably, confuse it with Iran. This list of xenophobic nations is far from complete, but these examples are sufficient to make the point.

When, in 1939, British Prime Minister Winston Churchill uttered the famous phrase, “It is a riddle, wrapped in a mystery, inside an enigma,” he was referring to the Soviet Union (or USSR), although the proper noun he actually used was “Russia.” However, this quotation applies equally well to the PRC, which has one indisputable advantage over the USSR: the People’s Republic of China still exists, while the Soviet Union does not. In the last post here, I began an ambitious series, with the goal of explaining China. I promised, then, that my next post in the series would explain my qualifications to write on the subject of the PRC, the ROC, Greater China, and the Han — so that’s what I need to do now.

I am currently working on my second master’s degree, in an unrelated field (gifted, talented, and creative education). However, my first master’s degree was obtained in 1996, when Deng Xiaoping, while no longer the PRC’s “paramount leader,” was still seen as its most prominent retired elder statesman. It was Deng Xiaoping, primarily, who made (and defended) the decision to send the tanks in, and crush the pro-democracy demonstrators in Tiananmen Square, in Beijing, in June of 1989, which I watched as they happened, on live TV. I was horrified by those events, and this has not changed.

During the early 1990s, I began studying the economic reforms which made the era of Deng Xiaoping so different from Chairman Mao’s China, trying to figure out the solution to a big puzzle: how so much economic growth could be coming from an area dominated by a huge, totalitarian, country which, at that time and now, was one of the few remaining nations on Earth which still claimed to be Communist. This study was done during the time of the “New Asia” investment bubble, as it was called after it “popped” (as all investment bubbles do, sooner or later). New Asia’s economic growth was led by the “Four Tigers” of Hong Kong (still a British colony, at that time), Singapore, Taiwan, and South Korea. South Korea is, of course, Korean, but the other three “tigers,” all had, and still have, majority-Han populations. What money I had, I invested in the Four Tigers, and I made significant profits doing so, which, in turn, led to a general interest in East Asia.

Motivated by simple human avarice, I studied the Four Tigers intensely, leading me to focus (to the extent made possible by the course offerings) on 20th Century East Asian history, during the coursework for my first master’s degree. There was a problem with this, though, and I was unaware of it at the time. My university (a different one than the one I attend now) had only one East Asian history professor, and he was very much a Sinophile. Sinophiles love China uncritically, or with the minimal amount of criticism they can get away with. When we studied the rise to power of Mao Zedong, and the PRC under the thumb of Chairman Mao, I heard it explained by a man who viewed China, and Chairman Mao, through rose-colored glasses, even while teaching about others who made the same error, to an even greater degree. I had already read one book about the Cultural Revolution, earlier in the 1980s, so I was skeptical, but he was also my only professor. The result was confusion. This was the book I had already read, along with a link to a page on Amazon where you can purchase it, and easily find and purchase the Pink Floyd music posted earlier, if you wish to do so. This is Son of the Revolution, by Liang Heng and Judith Shapiro, and you can buy it at https://www.amazon.com/Son-Revolution-Liang-Heng/dp/0394722744/ref=sr_1_1?ie=UTF8&qid=1468869380&sr=8-1&keywords=son+of+the+revolution.

This book was read for an undergraduate sociology course, at my first college, during the Reagan years. The important thing to know about Liang Heng, the book’s primary author, is that he was, himself, of the Han, as well as being from the PRC itself. The professor for this course wanted us to see the horror of a mass movement gone horribly wrong, and she chose this insider’s view of the Cultural Revolution, during which I was born, to do that. What I heard from my East Asian history professor did not mesh well with what I was taught by my East Asian history professor, and so I left that degree program confused. This professor’s argument, in a nutshell, was Chairman Mao was a figure of tremendous importance (true) who had good intentions (false), and tried to do amazing things (half-true, and half-false by omission, for these were amazing and horribly evil things), but had them turn out wrong (true), with many millions of his own people dying as a result, over and over (definitely true; Mao’s total death total exceeds that of Hitler or Stalin, either one). The “good intentions” part was what confused me, of course, for Mao was a monster, yet, from my later professor, I was hearing him described as a Great and Important Man.

I would have remained in this confused state, has I not also read this book, also written, primarily, by a person of the Han: the amazing Jung Chang, who has her own page on Amazon, at http://www.amazon.com/Jung-Chang/e/B00N3U50ZO/ref=sr_tc_2_0?qid=1468870698&sr=8-2-ent. (On that page, I notice she has a newer book out, which I have not read, and she is such a fantastic author that I am buying it now.) This, by contrast, was her first well-known book, and the one I read as an undergraduate:

Wild Swans tells the story of three generations of Han women: Jung Chang’s maternal grandmother (who had bound feet, and could barely walk, for that reason), then the author’s mother, and then finally Jung Chang herself, who found herself a Red Guard during the Cultural Revolution at the age of 14. This book tells their story, and is riveting. It has nothing nice to say about Chairman Mao, and contains much criticism of “The Great Helmsman,” as his cult of personality enthusiastically called him, yet he is not the focus of Wild Swans. The author’s family, over three generations, is.

I did my master’s degree work from the Sinophile professor described earlier, and then, later on still, I encountered Sinophobes. The opposite of Sinophiles, people who have Sinophobia have nothing nice to say about China, nor the Han. They hate and fear things Chinese because they fear the unknown — in other words, Sinophobia is a more specific form of xenophobia.

So, first, I read Liang Heng, and then, later, I started reading Jung Chang. Next, I heard the Maoist viewpoint explained quite thoroughly by my Sinophile professor, while my reading of Liang Heng and Jung Chang had exposed me to an anti-Mao, but non-Sinophobic, point of view, which is a direct consequence of the fact that both authors were actually of the Han, and had direct exposure to Maoism. Later came the Sinophobes, and their written and spoken, anti-Chinese, case for . . . whatever. (Actually, the Sinophobes never make a case for anything, unless one counts hating and fearing China and the Han as being “for” something. I do not.) Later still, one of my close friends studied ancient Chinese history and philosophy extensively, and we had (and still have) many talks about both ancient and modern China, including Chairman Mao, and the silliness of the Sinophobes, but this friend is more interested in talking about, say, Confucianism, rather than Maoism, or Mao himself. I was primed to learn the truth about Mao, but had to wait for the right opportunity.

Think about this, please. How many books have been written that accurately describe Stalin as a monster? How many exist about Hitler? I should not have had to wait so long to find out something about Mao I felt I could believe, and that described him as the monster he was, but wait I did, for no such book existed . . . until Jung Chang came to my rescue, with her next book, after 1991’s Wild Swans. All 800+ pages of it.

It took her many years to write this tome, and it was published in 2005. She grew up under Mao, having been born in 1952, not long after the revolution of 1949, which established the People’s Republic of China. Chairman Mao finally died in 1976. Two years after that, Jung Chang was sent to Great Britain as a college student, on a government scholarship. Being highly intelligent, and not wanting to return to China, she went on to become the first of the Han to receive a Ph.D. at any British university. This book, focused on Mao’s formative years, rise to power, and tyrannical rule, all the way to his death, is, as its subtitle states, “The Unknown Story” of this historical period. Jung Chang was uniquely qualified to write this story, having lived through so much of the events described in her book. She knew how expendable people were to Mao, having witnessed it, and survived. To the extent possible (and she was quite resourceful on this point) she used primary sources. This is why I give her much credibility.

These are the ways I have learned about China: from three books by two of the Han, long talks with a personal friend, and two college professors with different points of view on China, and Mao in particular. I have rejected the points of view of both the Sinophiles and the Sinophobes, and now I try to learn what I can from other sources, especially sources who are, themselves, of the Han — although I am weakened in this respect by the fact that I am only bilingual, with my two languages being mathematics and English, in that order. If you think this approach makes sense, I hope you will read my other posts, past and future, about China and the Han.