Margaret Hamilton's Apollo feats used so little storage memory
Margaret Hamilton, of Cambridge, Mass., mathematic and computer programmer at the MIT Instrumentation Laboratory, sits in a mock-up of the Apollo command module on display at the Cambridge school, Nov. 25, 1969, where she headed group that programmed Intrepid's pinpoint landing in the Sea of Storms on the moon. Credit: AP
The recent death of Margaret Hamilton merited a pause. Hamilton was the head of the programming team that developed software for the onboard computers for the Apollo missions. One was in the module that transported the astronauts from Earth, the other in the lunar module that landed on the moon.
Hamilton was a young mathematician at the Massachusetts Institute of Technology when she joined the Apollo team, the first female programmer on the NASA project. She later was given credit for popularizing the term "software engineering" to describe their work, a nomenclature massage that had the effect of putting software coding on a par with hardware design in the world of computing.
There was ample reason, in other words, to pay one's respects to Hamilton. But further grounds were found in a nugget deep in the reporting of her passing. Each of those two 70-pound computers on the Apollo spacecraft that contained Hamilton's mission-critical programming had all of 72 kilobytes of storage memory. An iPhone 18 has 2 terabytes at the top end — nearly 28 million times as much memory as was available to Hamilton.
As a mathematician, Hamilton probably appreciated that perspective. Numbers, after all, are not static, not as concrete as we might like to think. They do not exist in a vacuum. Numbers, like most anything, require context to fully understand. They rarely make sense without knowing from whence they came — as we see perhaps most clearly in sports where one player's statistics are meaningless without knowing those of other players.
The difference in scale for storage memory in Hamilton's heyday versus now is also a lesson in how numbers change over time. When my generation was growing up, 1 million was a huge number, a real divider between the haves and have-nots. A million dollars was an enormous sum, $1 billion was nearly incomprehensible, and $1 trillion was science fiction. Now, not so much. Not when a Long Islander with a mortgage-free house and a decent 401(k) easily has more than $1 million in assets, while not feeling the same sense of richness they would have in 1960 when that translated to more than $11 million nowadays. Not when government budgets and debts and some company valuations reach 13 digits. Not when astronomers study stars and planets hundreds of trillions of miles away.
Numbers, in other words, still can be difficult to get your head around and context still is helpful.
Consider this past week. Scientists announced they had sequenced the genome of the world's oldest known land animal. Jonathan, a giant tortoise who lives on the remote South Atlantic Ocean island of St. Helena, is around 194 years old. It's an impressive enough number that becomes even cooler when you realize he was born during the presidency of Andrew Jackson.
Soccer legend Lionel Messi played his final game for Argentina's national team. It was an incredible run of 21 years, but even more incredible when you realize that around 1.3 billion soccer fans were not yet born when Messi made his debut.
Artificial intelligence company OpenAI announced that its models had solved 377 of the most difficult open problems in math in fields like number theory, mathematical logic and topology. Each result took an average of three hours, remarkable on its own but even more so when you realize that hundreds if not thousands of mathematicians had been working an untold accumulation of years on the solutions.
Margaret Hamilton's team also labored long on those moon missions. On the 50th anniversary of Apollo 11, Google programmed its solar farm in the Mojave Desert to reflect the moon's light and create a beautiful nighttime portrait of Hamilton. It was composed of more than 100,000 mirrors — a stunning tribute to Hamilton and to the numbers she loved.
Columnist Michael Dobie is a retired member of the Newsday editorial board.
Michael Dobie is a retired member of the Newsday editorial board.
