# mixedmath

Explorations in math and programming
David Lowry-Duda

In the early 1930s, Hillel Shapiro and Harry Zwarenstein, two South African researchers, discovered that injecting a pregnant woman's urine into an African clawed frog (Xenopus laevis) caused the frog to ovulate within the next 18 hours. This became a common (and apparently reliable) pregnancy test until more modern pregnancy tests started to become available in the 1960s.

Behold the marvels of science! (Unless you're a frog).

When I first heard this, I was both astounded and... astounded. How would you discover this? How many things were injected into how many animals before someone realized this would happen?

### Sources

• https://en.wikipedia.org/wiki/African_clawed_frog

• Hillel Harry, Shapiro Zwarenstein (March 1935). "A test for the early diagnosis of pregnancy". South African Medical Journal. 9: 202.

• Shapiro, H. A.; Zwarenstein, H. (1934-05-19). "A Rapid Test for Pregnancy on Xenopus lævis". Nature. 133 (3368): 762

## Before frogs, there were mice

In 1928, early-endocrinologist Bernhard Zondek and biologist Selmar Aschheim were studying hormones and human biology. As far as I can tell, they hypothesized that hormones associated to pregnancy might still be present in pregnant women's urine. They decided to see if other animals would react to the presence of this hormone, so they then went and collected the urine of pregnant women in order to... test their hypothesis.1 1This is one of the cases where I really wish negative results were published. Do you think that they tried first with the blood of pregnant women? Really, what fluids did they apply to what animals? Science! It turns out that they were right. The hormone human chrionic gonadotropin (hCG) is produced by the placenta shortly after a woman becomes pregnant. And this hormone is present in the urine of pregnant women. But as far as I can tell, hCG itself wasn't identified until the 50s — so there was still some guesswork going on. Nonetheless, identifying hCG is common in many home-pregnancy tests today. Zondek and Aschheim developed a test (creatively referred to as the Aschheim-Zondek test2 2in a rare deviation from Stigler's Law of Eponymy ) that worked like this:

1. Take a young female mouse between 3 and 5 weeks old. Actually, take about 5 mice, as one should expect that a few of the mice won't survive long enough for the test to be complete.
2. Inject urine into the bloodstream of each mouse three times a day for three days.
3. Two days after the final injection, kill any surviving mouse and disect them.3 3Science?
4. If the ovaries are enlarged (i.e. 2-3 times normal size) and show red dots, then the urine comes from a pregnant woman. If the ovaries are merely enlarged, but there are no red dots, then the woman isn't pregnant.4 4In fact, the ovaries apparently always become enlarged. This is due to different hormones present in the urine.
In a trial, this test was performed on 2000 different women and had a 98.9 percent successful identification rate. From this perspective, it's not as surprising that young biologists and doctors sought to inject pregnant women's urine into various animals and to see what happens. In many ways, frogs were superior to mice, as one doesn't need to kill the frog to determine if the woman is pregnant.

### Sources

• Ettinger, G. H., G. L. M. Smith, and E. W. McHenry. “The Diagnosis of Pregnancy with the Aschheim-Zondek Test.” Canadian Medical Association Journal 24 (1931): 491–2.
• Evans, Herbert, and Miriam Simpson. “Aschheim-Zondek Test for Pregnancy–Its Present Status.” California and Western Medicine 32 (1930): 145.

## And rabbits too

Maurice Friedman, at the University of Pennsylvania, discovered that one could use rabbits instead of mice. (Aside from the animal, it's essentially the same test). Apparently this became a very common pregnancy test in the United States. A common misconception arose, where it was thought that the rabbits death indicated pregnancy. People might say that "the rabbit died" to mean that they were pregnant. But in fact, just like mice, all rabbits used for these pregnancy tests died, as they were dissected.5 5For the gods of science too demand animal sacrifice. Maybe.

### Sources

• Friedman, M. H. (1939). The assay of gonadotropic extracts in the post-partum rabbit. Endocrinology, 24(5), 617-625.

bold, italics, and plain text are allowed in comments. A reasonable subset of markdown is supported, including lists, links, and fenced code blocks. In addition, math can be formatted using $(inline math)$ or $$(your display equation)$$.