Predicting the Universe: An Astronomical Calculation
It was a dark, cool night. He stepped outside away from the warm glow of the fireplace into the gentle breeze. He loved admiring the stars, so tonight he again looked up to the heavens and admired their beauty. Countless stars shimmered in the dark black sky, unobscured by any electric light. Suddenly something flashed across the sky. It was bright and by its light the other stars seemed to dim. It was beautiful…it was majestic, but he didn’t recognize it.
Edmond Halley was a man of science and he knew he could figure out what that brilliant streak was.
Halley took to his books to find 24 similar occurrences seen between 1337 and his in 1682 (Kinoshita, “1P/Halley.”). All were comets, but three were of particular interest. Edmond Halley was a scientist and, most importantly, a mathematician. He used his skills to determine that the orbits and trajectories of three comets, one seen in 1531, another in 1607, and then the one seen by his own eyes in 1682, were all the same object (Garfinkel and Grunspan 34).
Halley had been a close friend of Sir Isaac Newton who developed the theory of gravity. It was with this knowledge that Halley was able to track the path of the comet. Halley determined its orbit was affected by the gravitational nature of the planets it passed by, specifically Jupiter and Saturn (Garfinkel and Grunspan 34). He predicted that the strange comet would return in 1758 (Kinoshita, “1P/Halley.”). Unfortunately, Edmond Halley died in 1742 and never knew if his prediction was correct (Kinoshita, “1P/Halley.”).
I’m sure you’ve guessed that Edmond’s comet, seen in 1682, is now known as Halley’s Comet, one of the most famous comets in our night sky.
The comet was named after Edmond Halley when it streaked again through the sky on December 25, 1758 (Kinoshita, “1P/Halley.”). Halley had predicted the return of the comet, and his math was correct. Yet he was unable to develop an exact set of equations to determine the path of Halley’s Comet (Garfinkel and Grunspan 34).
By the 1750s, scientists and mathematicians were using math to describe nearly everything around them. They discovered mathematical relationships in nature, among humans, and nearly everywhere one could look. One such example is the golden ratio, or pi described as 3.14 (Mann, “Phi: The Golden…”). It’s found in seashells, flowers, and even in microscopic organisms. Humans have used it in art and even construction. Therefore, equations are really the language of our world.
In 1758, French mathematician, Alexis-Claude Clairat found Halley’s prediction and he determined to find a set of equations that would describe the trajectory of the comet (Garfinkel and Grunspan 34). His solution was a bit crude, yet he developed “a clever solution to the problem…his method solved the problem numerically — that is with a series of arithmetic calculations” (Garfinkel and Grunspan 34). However, these problems involved hours of calculation and mathematical problem solving.
For the task, Clairat worked with friends Joseph Jerome Lalande and Nicole-Reine Lepaute. They became human calculators, or computers, in the summer of 1758 (Garfinkel and Grunspan 34).
If you’ll remember, a piece I wrote a few weeks ago spoke of humans as the first computers. Before the 1940s, the word computer was used to refer to humans that completed mathematical calculations. In fact, during the space programs of the 1960s, NASA employed a number of human calculators until they were later replaced by digital computer machines. Until relatively, recently the word computer referred to humans.
Those three computers did determine a solution to their problem.
They developed a set of equations that calculated the path of Halley’s Comet as accurate to within 31 days (Garfinekl and Grunspan 34). Halley’s Comet has been tracked through the years with Clairaut’s equations. The comet was last seen in 1985 and is predicted to return in 2061 (Breitman and Byrd, “Edmond Halley’s…”).
Calculating the path of the comet was thrilling and it was also important for scientific research and understanding, however, the importance of equations to describe the world around us is far more vast. After developing their predictions, Clairaut’s friends, Lalande and Lepaute, were hired by the French Academy of Sciences. It was here that they developed computations for the French almanac, Connaissance des Temps (Garfinkel and Grunspan 34). Five years later, the British government hired six of its own computers for its almanac (Garfinkel and Grunspan 34).
These almanacs were much more than a farmer’s guide, they predicted the positions and paths of stars and planets in the heavenly bodies above.
These calculations formed the base of celestial navigation, that is, navigation by way of the stars and planets in the nighttime sky (Garfinkel and Grunspan 34). This new form of navigation allowed greater reach for the European colonies around the world and it represented not only the power of mathematical equations, but the use and real-life application of this knowledge.
Late in the 18th century, one man started the largest human computer calculation project ever to be attempted, at least at the time. Gaspard Clair Francois Maire Riche de Prony hired ninety-six human calculators to produce a 19-volume set containing a collection of trigonometric and logarithmic tables over the course of six years. His project was commissioned and developed by the French government (Garfinkel and Grunspan 34).
In the 17th and 18th centuries, digital computer machines were still hundreds of years away, but that didn’t stop many from understanding the importance of math in our world and in our culture. I understand mathematics isn’t everyone’s cup of tea, it certainly isn’t mine.
But math forms the basis for our world and, as binary arithmetic illustrated last week, forms the basis for our computers as well.
To understand the importance and history of computers we must first understand and appreciate the importance of math to everything we do.
Math can also teach us much about our Creator. We see these mathematical equations all around us, I mentioned the golden ratio above as an example. We were created by a brilliant God who seeks order and longs for us to continue to explore and learn more about Him. As we create computers and devices based on the principles and laws He created, we also learn much more about our own creation after His Image.
The equations produced by those three computers in the summer of 1758 form the tenth major milestone in the history of computing.
More on the Importance of Math:
More on the History of Computers:
Works Cited
Andrews, Evan. “A Brief History of Halley’s Comet.” History.com, A&E Television Networks, 8 Nov. 2016, www.history.com/news/a-brief-history-of-halleys-comet-sightings.
Breitman, Daniela, and Deborah Byrd. “Edmond Halley’s Magnificent Prediction.” EarthSky, 8 Nov. 2019, earthsky.org/space/today-in-science-edmond-halley-nov-8–1656.
“Comet Halley.” University of Rochester, www.pas.rochester.edu/~blackman/ast104/halley.html.
Eggen, Olin Jeuck. “Edmond Halley.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., 10 Jan. 2020, www.britannica.com/biography/Edmond-Halley.
Garfinkel, Simson, and Rachel H. Grunspan. The Computer Book: from the Abacus to Artificial Intelligence, 250 Milestones in the History of Computer Science. Sterling, 2018.
“Halley’s Comet.” Georgia State University, hyperphysics.phy-astr.gsu.edu/hbase/Solar/Halley.html.
Kinoshita, Kazuo. “1P/Halley.” Cometography, cometography.com/pcomets/001p.html.
Mann, Adam. “Phi: The Golden Ratio.” LiveScience, Purch, 25 Nov. 2019, www.livescience.com/37704-phi-golden-ratio.html.
