Liberal Arts Blog — The Math of Sex, Money, and Power (Part I)

Liberal Arts Blog — Monday is the Joy of Math, Statistics, Shapes, and Numbers Day

Today’s topic — The Math of Sex, Money, and Power (Part One)

The most important math to teach in elementary school is the math of the odds of pregnancy using a condom in the real world. This math is not that hard. It is definitely not beyond the reach of the average 8th grader. But it is counter-intuitive and in my experience a remarkably high percentage of Harvard students don’t really get it. And I have not seen any polling data, but my guess is that the overwhelming majority of American adults don’t get it either. The first step is to know the difference between theoretical and actual effectiveness. Say a condom is 98% effective in theory. The reality is that practice is not perfect and the actual effectiveness is about 85% (according to Planned Parenthood, see first link below). That still sounds pretty good, but here comes the horrible math. As the number of times you have sex rises, the odds of pregnancy rises incredibly rapidly. Beyond 3X and the odds of pregnancy are greater than 50%! after 10X 83%. After 14X greater than 90%. How many times is a teenager who has just discovered the joy of sex (whether with love or without love) going to have sex with a compatible partner? This math should be a reasonable end point of an elementary school math curriculum but also absolutely central to the sex education program before any child reaches puberty. It should also be central to the civics (aka history, aka social studies aka values or humanities) curriculum because making decisions related to pregnancy are the most important ones in a human’s life. How those decisions have been made and how those decisions have changed over time is absolutely critical to an understanding of the most important history to teach in school because importance in history is measured by its relevance to the critical decisions of a person’s life.

This is the first on a series on the math of money, sex, and power. This is a complex topic and deserves sustained attention. It involves economics, psychology, history, ethics, and political science. Each level of analysis involves math. Experts — please chime in. Correct, elaborate, elucidate.


1. To calculate probability sometimes involves adding probabilities other times multiplying them. Any 5th grader can understand this if taught by a competent math teacher. In calculating the odds of pregnancy over time you multiple say 85% times itself to get the odds of pregnancy after X number of events.

2. So after two events: .85 X.85 = .72

3. So after 14 events: .85X.85 X .85 X .85 X .85 X .85 X .85 X .85 X .85 X .85 X .85 X .85. X ,85 X .85 = .09. This means that the odds of pregnancy after 14 events is 91%!!!!!!!!!! (That is, 1-.09).

NB: This is a variation on the theme of the “Birthday Problem” which is often the “hook” in the opening lecture of an introductory statistics course at the college level (eg. Harvard). How many students do you need in a classroom to have a birthday match? Most think 365. The reality is that the odds are greater than 50% after only 23 students! (See above chart.)


1. The greater the wealth, the lower the fertility.

2. More educated the women, the less fertile.

3. Why would that be? Aren’t babies the best thing ever? Short answer: as education and wealth rise, the opportunity cost of parenthood rises.

NB: To many this was a shocking surprise. Who would have predicted it? China once had a one child policy. What is the right policy? No policy? The spread in fertility Niger and South Korea is 6.9 to 1.0. Should South Korea be the model for the world? Is a fertility rate of 1.0 the key to the economic empowerment of women? Or has the the value of parenthood been underestimated in this calculation due to misguided premises of newly fashionable ideologies with horrible consequences for a generation of women who woke up too late to realize that their chances of motherhood (other than adoption) were gone? Again, complicated issue. To be continued.


1. Key points: a.) out of wedlock births are rising for all ethnic groups. For example, the white rate today is higher than the black rate was when the controversial Moynihan report came out ringing an alarm bell; b.) this is a worldwide trend (see last link below).

2. Causation: the most scholarly article on the subject by two universally respected economists (Janet Yellen, current Secretary of the Treasury under President Biden, and former chair of the Federal Reserve, and her husband, Nobel-prize winner George Ackerlof) argued that the cause was the technology shock of the pill leading to the end of the tradition of the shotgun marriage. Other factors given higher weights by other analysts include: welfare eligibility requirements and the rising number and value of welfare programs.

3. Consequences: the most respected quantitative analyst of social mobility in the world today is Raj Chetty. His data show that of all factors influencing mobility, family structure is the most important. This fact has not been given the attention it deserves. Why? That too is a fascinating, complicated story. To be continued. But let me point out a little basic math. From experience, raising one child with two parents is not easy. How about many children with one parent? How about many children from different fathers with one parent? All single parent households are not created equal. The real problem as defined by Harvard’s progressive ethnographer Kathy Edin is “complex and unstable families.”

NB: You can’t understand these trends without understanding why women are choosing to have children out of wedlock. Most of these births are not unwanted. See the Harvard Magazine article about Kathy Edin’s work — the seventh link below.

FINAL WORD — Let’s teach the most important math, the most important history at an age early enough to influence the most important decisions in a child’s life.

1. Math matters.

2. Sex matters.

3. Money matters.

NB: Power matters.

This series will be about the relationship between the math of money, sex, and power. To understand that math you must also understand human psychology, the laws of economics, and the laws of politics. This requires setting aside political bias and donning the thinking cap of a scientist, judge, or the ideal, objective, independent-minded citizen-juror. This means playing the role of Ulysses who tied himself to the mast to prevent himself from hurling himself overboard when he heard the sirens’ song. The siren song of our time is political bias.


I dedicate this post to my good friend Robert Gross who for the last few years has been nagging me (almost incessantly) about my utter failure to address the critically important issues of sex and psychology. Bob, this is just the beginning. To quote John Paul Jones, “I have not yet begun to fight.” And this will be a tough struggle. To paraphrase Stephen King, the most important things are the hardest to write about. The actual quote is, I think, “The most important things are the hardest to say because words diminish them.”

Income and fertility

What Blocks Social Mobility? Single Parents.

Family structure matters, but can we do anything about it?

When Having Babies Beats Marriage

New mothers, not married: Technology shock, the demise of shotgun marriage, and the increase in out-of-wedlock births

Janet Yellen’s Surprisingly Traditional Views About Family Breakdown

Last three years of posts organized thematically:

PDF with headlines — Google Drive


Please share the coolest thing you learned this week related to math, statistics, or numbers in general. Or, even better, the coolest or most important thing you learned in your life related to math.

This is your chance to make someone else’s day. And to consolidate in your memory something you might otherwise forget. Or to think more deeply than otherwise about something dear to your heart. Continuity is key to depth of thought.



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