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Honoring Pandrosion of Alexandria for Ada Lovelace Day

TL;DR: Women have made significant contributions to STEM since earliest times, but are often overlooked or discounted. With the big problems we need to solve we ignore the skills and abilities of 50% of the population at our peril.

This year the 13th of October is Ada Lovelace day. [Lovelace]() was a contemporary of hardware designer Charles Babbage and is generally acknowledged to have been the first person to understand the potential applications of the stored-program computer, not just as a tabulating machine, but as a general-purpose information processing device.

She is also credited with being the author and maintainer of the world’s first computer programs. As a programmer, I feel there is a connection between us at PaperCut Software and the pioneering work of Lovelace. We owe her and many other women a debt that is too often not acknowledged.

“Ada Lovelace Day (ALD) is an international celebration of the achievements of women in science, technology, engineering and maths (STEM). It aims to increase the profile of women in STEM and, in doing so, create new role models who will encourage more girls into STEM careers and support women already working in STEM.”

- []()

In honor of Ada Lovelace and her work in STEM, I thought I’d take the opportunity to write about another underrated woman of STEM, Pandrosion of Alexandria.

Please note that I am not a scholar, just a part time programmer (my job here at PaperCut Software means I do a lot of different things during the day), who wants more recognition for underrepresented people who helped develop the modern technology on which we all depend. The following is my personal interpretation from the results of a few online searches, and of course I’m making my interpretation through a lens of contemporary values.

I have recently been watching a documentary by Marcus du Sautoy on the [history of mathematics](). Of course he mentioned the Ancient Greeks, including the well known female mathematician [Hypatia](). However it appears that there was an even earlier female contributor to Greek mathematics, [Pandrosion of Alexandria](), who lived in the first half of the fourth century CE.

As far as we know Pandrosion developed a technique to calculate approximate, but numerically accurate, cube roots using a three dimensional geometric technique.

Simply put, the problem is to find the dimensions of a cube with a volume of two, i.e. ∛2.

She can also be credited with a method for calculating the geometric mean. As such she is the earliest known female mathematician. Of course she may have also developed other techniques which we don’t know about.

What I found curious is that

  1. She appeared to have been mis-gendered by 19th century western scholars and was until recently assumed to be male
  2. Her contemporary, Pappus, felt the need to criticise her work. In fact his explanation of why she was such a poor mathematician is how we know about her work.

At at least one writer has remarked:

One wonders whether his criticism would have been quite so terse if Pandrosion had not been a woman

[Winifred Frost, University of Newcastle, 1992]()

A case of [Plus ça change, plus c’est la même chose]().

However, things could have been worse. Hypatia, a Pagan, was killed by a group of fanatical Christian monks. I think that is taking the academic review process a little too far.

It’s also ironic that, if Pappus had not spent so much effort criticizing Pandrosion, she would be unknown to us, as none of her own work has survived (not uncommon given the antiquity). As no likeness has lasted either I could not add a portrait.

With [Ada Lovelace Day]() coming up, and as Lovelace is credited with being the first computer programmer, I thought it would be fun to implement Pandrosion’s algorithm on a modern computer as it connects two significant and important women from the world of STEM.

However I couldn’t find a suitable description of her method and so I had to make do with [Halley’s method]() instead.

Maybe one day I will be able to find out more about Pandrosion’s algorithm and do a proper job. So far the best information I have is from [Bronwyn Rideout]() and [Gabrielle Birchak-Birkman]() but I didn’t have time to decipher the maths.

You can find my toy code [here.]()

By the way, if you do need to calculate cube roots use the standard language features. For example in Python `round( x**( 1.0/3), 3)` may be good enough for many applications, or use specialist libraries for more exoteric numerical needs. Avoid writing your own numerical libraries; unless you are a skilled practitioner there are many traps for the unwary in floating point arithmetic. For example, `1.0/3` cannot be presented correctly in a modern computer.

Pandrosion of Alexander is another example of how far back in history women have been pioneering in STEM. Although my code is not great and was not created for real use, I found it a suitable way to celebrate Ada Lovelace day. Hopefully it helps us at PaperCut Software continue to reflect on why diversity, equity,  inclusion, and celebrating women in STEM is so important in the modern workplace.

Feature image: Portrait of Ada Lovelace (1815-1852) by Margaret Sarah Carpenter (1793-1872) from [Wikimedia Commons]().


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