Discovery is the seeing of what has never before been seen. There's no greater rush than the realization that we've turned up something that answers bigger questions about how the world really works that no one else has seen or appreciated. It drives us not just to dig deeper, but intrigues us to go on to build new foundations of understanding.

And it's all the more intriguing to us when it's unexpected.

Earlier this year, we constructed a mathematical model of the number of households in the United States since 1900. Using data from the U.S. Census Bureau, we found that there was a one-time upward shift in the overall trajectory in the number of U.S. households that occurred after 1947, which we attributed to the introduction of mass-production techniques to U.S. home construction at that time, which made houses more affordable to more people. The chart below updates the information we originally presented with data through 2013:

We later went on to consider the case of single person households. Our next chart likewise updates what we had originally presented to include data through 2013:

In this second chart, we can see that the relative share of single-person households in the United States has increased significantly over time. Since our mathematical models for both would appear to closely follow the actual data, we can use them to closely approximate how that relative share has evolved over time:

Here, we observe that the number of single person households has grown from being 5.5% of all U.S. households in 1900 to be approximately 26.8% in 2013. What's more, we see that the change over time has followed an S-shaped curve, where the relative share of single person households among all U.S. households was growing at an increasing pace up through 1967, but whose growth has slowed dramatically since.

The timing of that change is troubling. In terms of the demographics of the U.S. population, we would expect the number of single person households within the nation to begin rising dramatically after 1964, which is when the oldest members of the leading edge of the baby boom generation would turn 18 and begin establishing their own households.

We would also expect to see a dramatic increase coincide with the increase in divorce rates that occurred in the U.S. after 1967:

But after 1967 is when we see the growth rate of the share of single person households begin to decelerate, so we must discount the increase in the divorce rate as a driving factor behind the increase in the number and share of single person U.S. households.

Instead, the data indicates that the great increase in the relative share of single person households took place much earlier, with the greatest growth in the 1940s and 1950s, which also means that it couldn't possibly have been driven by the Baby Boomers.

Clearly, it had to be driven by people older than the Baby Boomers. Unfortunately, the U.S. Census Bureau's historical data for the age demographics of persons living alone is severely lacking before 1967, which is when they began paying closer attention to that particular aspect of the composition of American households.

It occurred to us though that most people, once they are well established in their living arrangements, don't change them very often. If we want to find out what compelled Americans to begin living alone in single person households in increasing numbers in the 1940s, we should consider the population of adult Americans who were living alone long afterward.

So we dug deeper into the U.S. Census Bureau's data, and extracted the number of Americans living alone Age 65 or older for the years for which that data is available. Our next chart shows that data along with that for the number of all single person households in the U.S.

Our next chart presents the share of Age 65+ single person households among all single person households in the U.S. from 1960 through 2013, for the years for which the U.S. Census Bureau provides data.

Even though we have only two points of data to go by in establishing what the pre-1967 trend before looked like, for 1960 and for 1965, it would appear that is enough to explain why 1967 is significant as the break point in the growth rate of the number of single person households in the United States. It would appear that 1967 marks the point in time when the number of Americans Age 65 or older living alone peaked as a share of the entire population of Americans living in single person households.

We next took things to the next level deeper, looking at the number of both Age 65+ Men and Women living alone for the years for which the U.S. Census Bureau provides that information.

What's unexpected in this chart is that we see that there is a clear break in the trend that takes place after 1992. After 1992, we find that the number of Age 65+ men living alone begins to increase at a faster rate at the same time that the increase in the number of Age 65+ women living alone begins to decelerate.

What makes this significant is because that simple change in trajectory provides the key to unlocking why the population of Americans living alone in single person households really took off in the 1940s.

Working backwards in time, a person who turned Age 65 in 1992 would have been born in 1927. Going forward in time again, that same person would have turned 18 years old in 1945, the last year of the Second World War.

As it happens, 18 is the minimum age that an American man would have been subjected to the draft lottery during World War 2, which in 1945, would mean a high likelihood of seeing combat in operations that saw some of the highest casualty rates during World War 2.

But a man born one year later, in 1928, would most likely miss seeing service in the war altogether unless they specifically enlisted if they were 17 years old in 1945. American men born in that year or later would therefore be much more likely to live to be Age 65 or older. Our chart below shows both the birth years for which a American man alive during World War 2 that correspond to their eligibility to enlist or be drafted into military service for the war, as well as the year for which they would turn Age 65 if they survived.

The vast majority of men who served in the U.S. armed forces during World War 2 were conscripted into service through the draft lottery, which placed American men between the ages of 18 and 37 in approximately equal numbers by age. The oldest men who were drafted, who would have been Age 37 in 1942, would have turned Age 65 in 1970. Meanwhile, the oldest men who voluntarily enlisted into service during the war, who would have been Age 45 in 1941, would have turned Age 65 in 1961.

During the war, over over 416,000 American men died in military service between 1941 and 1945, with most of these deaths concentrated in 1944 and 1945. If they had lived, the period from 1961 through 1992 would represent when they would have turned Age 65.

For those that died in the war however, the period from 1961 through 1992 would represent when their surviving spouses, or rather, their widows, who were presumably at or near the same age, reached Age 65.

So the data for the Age 65+ population who live alone does indeed tell us why so many Americans began living alone in such large numbers in the 1940s, just as it tells us why the population of American Age 65 or older who live alone has evolved as it has in much more recent years.

Since 1992, we see that both the number of American women living alone over Age 65 is growing at a decreasing rate, while the population of men living alone over Age 65 is growing at an increasing rate, as compared to the years before. Both changes may be attributed to the larger number of men, born in the years 1928 and afterward, who were too young to see combat during the Second World War.

And that's why the number of widows peaks in the years from 1990 through 1992, which we can see in the percentage share of all U.S. households represented by the number of Age 65+ women living alone:

Note that as a percentage of all U.S. households, the number of men Age 65 or older living alone was essentially flat in the years from 1970 through 1992, which corresponds to the ages when men selected for the draft in World War 2 would have turned that age.

The widows peak in the early 1990s is the unexpected discovery to which we alluded earlier in this post. In our next installment, we'll reveal how its existence answers a much bigger question when we consider the lasting impact of the men who died while serving their country.