April 14, 2011

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Tom Cassidy, associate professor of mathematicsLEWISBURG, Pa. — Tom Cassidy, associate professor of mathematics, studies the "birth, death and mathematics" connection. We asked him to explain. || Faculty Snap Talk video

Q: You've had the opportunity to study abstract mathematical structure and theory, but you've also had the chance to work in a relatively new field - demographics.  What does math tell us about this subject?

A: Demography is the study of populations, but it's more than just birth, death and mathematics, because a lot of interesting things happen between birth and death — our lives for example. Demographers are interested in what happens during the human lifetime. Issues like education, employment, when we get married and how many kids we have, whether money is transferred between generations — all these topics are interesting to demographers.

To do any sort of analysis like that for populations in aggregate you need mathematical reasoning. My background is in abstract algebra, not in population studies. But it is in mathematics, and mathematical reasoning is still applicable.

Q: Demography relies on many different disciplines, right?

A: Yes. Demography is a relatively young science that involves ideas from history and sociology, biology and economics, animal behavior and psychology — all sorts of disciplines merge together when you want to talk about populations as a whole and how they behave and what happens to them.  Certainly statisticians are involved, but so are mathematicians.

When I worked a year at the Max Planck Institute for Demographic Research in Germany, I saw people from all those different areas talking to each other, consulting each other, sharing ideas. It's a science that merges a lot of different fields in an interesting way. That's part of why I'm at a liberal arts college — because I'm interested in more than one thing. It also gives you a perspective on different disciplines that you wouldn't necessarily get if you stayed only within your own discipline.

Q: What are some of the interesting things you've learned along the way?

A:  In Western countries women have been postponing when they have children. That decision to have children later in life has consequences for the population. But it's hard to predict if we look at the fertility rates in a given year. It's hard to know whether a drop in fertility rates means that the women decided not to have children or whether they've decided to postpone childbirth. Knowing which of those events has happened is important if you want to make predictions. And policy-makers use the results of demographic studies that predict long-term population trends.

We were interested in distinguishing a choice to postpone birth from a choice not to have children. Other people have studied this as well — by looking at the population as a whole and the mean age at which women have birth. In the past, it was in the early 20s. Now, it's moved into the late 20s. That's a sign that while women are putting childbirth off, they are still choosing to have children. We came up with a mathematical model that would allow us to look at a current fertility rate and create a hypothetical rate that would have occurred had there been no postponement.

Q: What are some of the implications for women having children later in life?

A:  For over a decade now there's been concern in Europe that the fertility rates had fallen below what is called the replacement rate. The idea was that these countries were going to shrink and they were going to lose population. If you look at a given year's fertility rate, you might say the rate this year is so low, this country is going to vanish. But that rate may have been low simply because of postponement, and women cannot postpone birth forever. There are biological limitations here. So in recent years there's been a turnaround. A number of studies have indicated that fertility in Western Europe seems to be picking up — maybe just a little bit, but enough to rise above the replacement rate.

Q: What about the United States?

A: The U.S. has a higher fertility rate than Western Europe and we have more immigrants. Both of those things keep our population relatively young. People will talk about the graying of America because we are aging, but not quite the way Western Europeans are, or, in a more extreme case, Japan, which has become the oldest country in the world. The U.S. will stay relatively young for the foreseeable future.

Q: What are mortality rates telling you?

A:  Mortality rates around the world have been dropping for more than a century — everybody knows that. What's interesting is not just that mortality rates have gone down, but why and exploring what mechanism is driving this. Originally, mortality rates started dropping because of a reduction in infant mortality. The reduction in infant mortality meant people started having a longer life expectancy. But, for developed nations, infant mortality is now quite low. Future reductions in mortality have to come elsewhere in life — at the other end, basically. There's some evidence that this is starting. If that does happen, we will want to think about what life expectancy will be and the appropriate societal response.

If people start living to be 90 on average, does it still make sense to have people retire at 65? Is it even sustainable to have a country where a third of the population is retired and not working? Probably not. If we believe that people are going to live longer, we have to change the way we lead our lives. People have to think about working longer, but also possibly getting more education and staying in school longer. It's not clear how societies are going to respond. But it's clear, if the average age in your population is 25 or 55, those are very different populations. It has big implications for public policies.

Q: Like increasing the age for Social Security benefits, for example?

A: Absolutely. There is a big concern that, as the baby boom has now started to enter retirement age, we don't have the resources to support them. That may just be the beginning of it. Some people have very optimistic predictions about life expectancy in the U.S.; 100 could become the new norm.

We also need to think about the nature of work. If we need people to continue working, say, into their 70s, do we want them to keep doing the same job, or do we need jobs that are more appropriate for people in their 70s? We have a model in the country now in which you rise through the ranks and when you get to the top you just quit and go away. But we could have an economy where there are more part-time jobs for older people. A lot of changes might be necessary as the population ages.

Q: And demography — and math — can help point the way?

A: The role of demographers here is to make forecasts and try to understand not only how big the population might be in 10 or 20 years, but also understand details about that population's behavior. With that information in mind, policy-makers can think about what needs to be done to preserve the planet, for example.  

There are many, many disciplines in which knowing some mathematics is helpful — whether you are interested in sociology or biology, economics or psychology. When I talk about demography, what's lying under it is mathematics. You don't need to be a Ph.D. in mathematics to do demography, but you need some proficiency with numbers and the ability to handle data. If you have that, there are all kinds of interesting things you can study.

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