With a few exceptions, most scholars from antiquity onward were either hostile to population growth or deeply ambivalent about its potential effects on human welfare. Of course, more people meant larger armies and more taxpayers, which is what mattered to the feudal lords of yesteryear, but population growth also meant greater pressure on available resources and other calamities.

That was not an irrational prism through which to view population growth. For thousands of years, the world was, in fact, stuck in what came to be known as a Malthusian trap. The world’s population fluctuated, growing during the times of good harvests and collapsing when food got scarce. According to the U.S. Census Bureau, the world’s population at the time of Jesus was somewhere between 170 million and 400 million. Fourteen centuries later, it was somewhere between 350 million and 374 million.

In the 18th century, the speed of scientific and technological progress enabled some scholars to look at population growth with growing optimism. They began to see human life as intrinsically valuable and problems concomitant with population growth as eminently solvable. The French economist Nicolas Baudeau, for example, argued that the “productiveness of nature and the industriousness of man are without known limits” because production “can increase indefinitely.” As such, “population numbers and well-being can go on advancing together.”

Other leading intellectuals of the day went as far as to argue that good government is one that leads to the maximization of the human population and its well-being. The Scottish philosopher David Hume, for example, noted that “wherever there are most happiness and virtue and the wisest institutions, there will also be most people.” The French philosopher Jean-Jacques Rousseau held that “the Government under which … the citizens increase and multiply the most is infallibly the best.”

These were, to put it mildly, revolutionary ideas, and the almost inevitable backlash against them soon arrived. The Rev. Thomas Robert Malthus was born in Westcott, England. He studied English, classics and mathematics at Cambridge University. Over time, Malthus became fascinated with geometric and arithmetic growth rates. A geometrically growing value increases in proportion to its current value, such as always doubling (for instance, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1,024). An arithmetic growth rate, in contrast, increases at a constant rate (1, 2, 3, 4 or 1, 3, 5, 7).

In 1798, Malthus published “An Essay on the Principle of Population.” He argued that “population, when unchecked, increases in a geometrical ratio. Subsistence (by contrast) increases only in an arithmetical ratio.” He then warned that if “the proportion of births to deaths for a few years indicate an increase of numbers much beyond the proportional increased or acquired produce (i.e., food) of the country, we may be perfectly certain that unless an emigration takes place, the deaths will shortly exceed the births. … Were there no other depopulating causes, every country would, without doubt, be subject to periodical pestilences or famine.”

Malthus believed that history validated his theory, which it did. He also insisted that what was true in the past would also be true for all eternity, and that was not to be. Malthus in fact lost his main argument even before his first book went to print. Between 1700 and 1798, the population of England increased 62.3 percent. Relative to income, however, the price of bread fell by 26.6 percent. In other words, it became more abundant. While Malthus was proven spectacularly wrong, his theory remained influential among many scholars, including the Stanford University biologist Paul Ehrlich.

In 1968, Ehrlich published a book called “The Population Bomb.” It sold 3 million copies, was translated into many languages, and brought Malthusian concerns into the mainstream. It started with a prediction: “The battle to feed all of humanity is over. In the 1970s, hundreds of millions of people will starve to death in spite of any crash programs embarked upon now.” In 1970, Ehrlich appeared on “The Tonight Show.” The show, wrote John Tierney in The New York Times, “got more than 5,000 letters about Ehrlich’s appearance, the first of many on the program. Ehrlich has been deluged ever since with requests for lectures, interviews, and opinions.”

Ehrlich’s message scared and scarred generations of Americans, inspiring such movies as the 1973 ecological dystopian thriller “Soylent Green.” (The more recent “Avengers: Infinity War” is based on the same premise.) On the other side of the country, the University of Maryland economist Julian Simon remained unconvinced. He looked at the numbers and noticed that prices of resources were falling, rather than rising. That implied that resources were becoming more abundant — even while the population grew.

In 1980, Simon bet Ehrlich $1,000 on $200 quantities of five metals: chrome, copper, nickel, tin and tungsten. The futures contract stipulated that Simon would sell these same quantities of metal to Ehrlich for the same price in 10 years’ time. Since price reflects scarcity, Simon would pay if population increases made these metals scarcer, but if they became more abundant and therefore cheaper, Ehrlich would pay. Over the next 10 years, all five metals became cheaper, and Ehrlich mailed Simon a check for $576.07, representing a 36 percent decrease in inflation-adjusted prices.

Since 1990, some scholars have argued that Simon got lucky. To test that hypothesis, we have analyzed the prices of hundreds of commodities, goods and services spanning two centuries. In our book, “Superabundance: The Story of Population Growth, Innovation, and Human Flourishing on an Infinitely Bountiful Planet,” Gale L. Pouley and I found that resources became more abundant as the population grew. That was especially true when they looked at “time prices.”

Most people are familiar with the so-called “current” prices, which the shopper sees on the supermarket shelf, and “real” prices, which take into account inflation. What’s missing from both prices is the amount of dollars in your wallet. How often have you heard your grandparents complain that a gallon of gas cost 50 cents and a loaf of bread 5 cents “back in the good old days”? “True, Grandma and Grandad,” ought to be your response, “but what happened to your incomes over your working lives?”

Typically, though not always, individual incomes increase at a higher rate than inflation. That’s because people tend to grow more productive (i.e., they use new knowledge or inventions to generate more value per input, such as an hour of work, an acre of land and amount of capital available) over their lifetimes and across time. Just think of the economic output or productivity of a worker with a shovel versus that of a driver of a giant excavator.

Whereas nominal and real prices are measured in dollars and cents, time prices are measured in hours and minutes. To calculate a time price, all you need to do is to divide the nominal price of a good or service by your nominal hourly income. That tells you how long you must work to afford something. So long as your nominal hourly income increases at a faster pace than nominal prices do, goods and services get more abundant.

Take, for example, an unskilled worker — say, a janitor — in the United States. Between 1850 and 2018, the time price of rice fell by 98.1 percent. So, the same amount of work that bought him one pound of rice in 1850, bought him 52.92 pounds in 2018. Instead of one pound of pork, he was able to buy 35.56. His personal “abundance” of cotton rose from one to 32.74; of wheat from one to 30.79; of corn from one to 26.04; of wool from one to 24.99; of lamb from one to 3.78; of beef from one to 3.23, etc. All the while, the population of the United States rose from 23 million to 327 million.

What happened to global time prices of resources? They fell by 84 percent between 1960 and 2018. The personal resource abundance of the average inhabitant of the globe rose from one to 6.27 or 527 percent. Put differently, for the same amount of work that he or she could buy one item in the basket of resources we looked at, he or she can now get more than six. Over that 58-year period, the world’s population increased from 3 billion to 7.6 billion. It will reach 8 billion around the time you read this article.

More importantly, we also found that personal resource abundance increased at a faster pace than the population grew — a relationship we call “superabundance.” On average, every additional human being created more value than he or she consumed. This relationship between population growth and abundance is deeply counterintuitive, yet it is true. But, how does all that progress happen?

Committees don’t have ideas. Algorithms don’t have ideas. Machines don’t have ideas — at least not yet. So far, ideas have always been a product of human intelligence. Those ideas lead to inventions, and in turn, inventions tested by the market lead to innovations that drive economic growth and rises in the standards of living. But large populations are not enough to sustain superabundance — just think of the poverty in China and India before their respective economic reforms. To innovate, people must be allowed to think, speak, publish, associate and disagree. They must be allowed to save, invest, trade and profit. In a word, they must be free.

Society provides the incentives that either encourage or discourage individuals to manifest their ideas in reality. Individuals, who lack equal legal rights and face onerous regulatory burdens, confiscatory taxation or insecure property rights, will be disincentivized from turning their ideas into inventions and innovations. Conversely, people who function under conditions of legal equality, sensible regulation, moderate taxation and secure property rights will apply their talents to their benefit and, ultimately, to that of society.

The possibilities for creating new value are thus immense. The world is a closed system in the way that a piano is a closed system. The instrument has only 88 keys, but those keys can be played in a nearly infinite variety of ways. The same applies to our planet. The Earth’s atoms may be fixed, but the possible combinations of those atoms are infinite. What matters, then, is not the physical limits of our planet, but human freedom to experiment and reimagine the use of resources that we have.