The Elegant Philosophy of Ones and Zeros

A 1936 master’s thesis written by Claude Shannon changed the computing world overnight. Shannon’s insight seemed to come out of nowhere, but collections from the Bentley archive show how the genius idea grew from a revamped engineering campus and one elective class.

By Robert Havey

The modern world we live in would not be possible without the work of Claude Elwood Shannon (pictured above, 1932). Over his long and decorated career as a mathematician, electrical engineer, inventor, and cryptographer, Shannon’s theoretical insights led directly to the creation of digital circuits, advanced telephony networks, and the internet.

His work was so ahead of its time, it was a challenge to even categorize. In 1948, Shannon’s paper “A Mathematical Theory of Communication” established a whole new field of science: information theory. Before that, his 1936 master’s thesis at MIT, “A Symbolic Analysis of Relay and Switching Circuits,” became the language at the foundation of modern computing. 

Shannon wasn’t driven by wealth or ambition, but by his endless curiosity. He spent time tinkering, inventing things like a trumpet that shoots flames when played and a mechanical mouse that navigates a maze. He had to be reminded by his colleagues to actually publish his findings. “Many things I’ve done and never written up at all,” Shannon said in a 1987 interview with Omni magazine. “Just knowing is probably [my] main motivation.” 

Collections at the Bentley Historical Library reveal what a perfect environment the University of Michigan College of Engineering in the 1930s was to nurture his curious mind, including an elective class that would lead to one of his most incredible breakthroughs.

Dispatches from Nowhere

Gaylord Michigan was a city of fewer than 2,000 people when Shannon was born in 1916. Most of its inhabitants worked for the Michigan Central Railroad or for one of the businesses that relied on it.

Shannon spent much of his time taking things apart and, if he could, putting them back together. “As a young boy, I built many things, working with mechanical stuff. Erector sets and electrical equipment, built radios, things of that sort,” Shannon said in a 1997 interview. “I remember I had a radio-controlled boat.”

Communication was particularly interesting subject for the young Shannon. He constructed a telegraph system using the barbed-wire fences that surrounded the local farms. As a Boy Scout, Shannon won first place in a “wig-wag” contest, a competition where scouts would use flags to send and receive Morse code.

Shannon’s application to the University of Michigan, archived in his alumni file at the Bentley, reveals him to be a good but not perfect student. He received A’s and B’s at Gaylord Public School, particularly excelling in his math classes. For the question asking if the applicant “earned any money in your high-school course?” Shannon wrote: “Yes, peddling papers and delivering telegrams.”

In 1932, Shannon was accepted into the University of Michigan School of Engineering.

Engineering Transformation

Engineering education at U-M had radically changed since the first class in metallurgy was taught in 1854. In 1901, demand for engineers in the rapidly industrializing world led the U-M regents to approve construction of the West Engineering building, adding more than 150,000 square feet of floor space. The East Engineering building, completed in 1923, would add 163,000 more. 

Dean of Engineering Mortimer Cooley was a driving factor behind the rapid expansion. Under his leadership, engineering enrollments went from 18 in 1881 to more than 2,000 by 1929, surpassing enrollments from both U-M’s Law School and School of Medicine. When a colleague mentioned that engineering was second in size only to the College of LSA, Cooley replied, “By Jove, we’ll pass them yet.” 

The engineering curriculum was changing, too. More and more specialties were added, including electrical, chemical, and marine engineering. Classes in “wireless telegraphy” were beginning to be taught just a decade and a half before Shannon’s arrival. 

There was also more emphasis placed on the common foundation of all engineering: math. This suited Shannon just fine, as he wanted to pursue degrees in both electrical engineering and mathematics. 

Asked about his choice of dual degrees in an interview years later, Shannon said it was driven mostly by indecision rather than a plan for his future career. “I wasn’t really quite sure which I liked best,” said Shannon. “It was quite easy to do because so much of the curriculum was overlapping.” 

Shannon’s favorite engineering classes were in communication engineering, mostly because they were “the most mathematical, I would say, of the engineering sciences.” 

Although Shannon earned his degrees in a little over three years, the 1936 Michiganensian yearbook showed he still had time for extracurricular activities. He was in the Junior Math Club, Radio Club, and on the gymnastics team. (The gymnastics training stayed with him his whole life, as he was often seen in the halls of Bell Labs on a unicycle juggling bowling pins.) 

Elective Success

During his whirlwind undergraduate career, Shannon found time to take an elective class from the Department of Philosophy that would lead to his first groundbreaking paper. Philosophy 33: Introduction to Logic taught students “the general principles of both inductive and deductive logic,” according to the U-M General Register. 

Students would learn how to break down and diagram paragraphs like they were math problems. A simple example might be: 

All archivists have a college degree. Sue is an archivist. Therefore, Sue has a college degree. 

Given the first two sentences are true, the last one is also true. Compare that to: 

All archivists have a college degree. Bob has a college degree. Therefore, Bob is an archivist. 

The last statement is not necessarily true, since people other than archivists also have college degrees. 

An archived final exam for Philosophy 33 from the Department of Philosophy collection at the Bentley reveals how complicated these statements could get. One question asks students to “Symbolize the following arguments and show whether or not they are valid.” The first statement: 

“To say that a thing has the attributes of infinity, omniscience, and perfection implies a denial that it has potency. Now God, as pure act, has no potency. Therefore God is infinite, omniscient, and perfect.” 

Shannon’s answer to the exam question, unfortunately, is lost to history. 

Inspiration in Boole

It was in this class that Shannon was introduced to the work of philosopher George Boole. Boolean algebra is a system of logic in which statements are given values 1 and 0, with a true statement written as 1 and a false statement as 0. Statements can be considered together with conjunctions such as and, not, and or. 

Anyone who has done any sort of computer programming will immediately find this familiar. Today, all programing languages use Boolean logic as a foundation. But when Shannon first learned it, it was in his elective philosophy class, not in engineering. 

Shannon wouldn’t have to wait long to make use of his newfound Boolean knowledge. He graduated from U-M with his two degrees in 1936 and, after seeing a postcard advertisement pinned to a bulletin board in the West Engineering building, Shannon started his post-graduate studies at the Massachusetts Institute of Technology (MIT). 

Shannon spent most of his time at MIT operating and repairing the differential analyzer, a room-sized machine dedicated to solving advanced mathematical problems like the behavior of scattering electrons. The machine was an analog computer, an unwieldy amalgamation of gears, electrical switches, spinning discs, and graph paper. 

Three years working closely with the machine led Shannon to an aha moment that would connect Boole to the machine, as he recalled in a 1987 interview:

“The main machine was mechanical, with spinning discs and integrators, and there was a complicated control circuit with relays. I had to understand both and work on them. The relay part got me interested. I knew about symbolic logic and realized the Boolean algebra was just the thing to take care of relay and switching circuits.”

This insight would become his master’s thesis.

His paper, “A Symbolic Analysis of Relay and Switching Circuits,” proved that Boolean algebra could be used for circuit design. The binary ones and zeros that all modern computers are based on today are the “trues” and “falses” of Boole.

Shannon’s big idea wasn’t for circuit design, but instead for the process of how to use mathematics to describe and refine circuits before they are even built. Suddenly, you could look at a circuit diagram written out on paper and know for sure if it would work and if it could be made more efficient.

When later an interviewer asked him about how he made the connection between relay circuits and Boolean algebra, Shannon was characteristically humble: “Oh, it’s trivial! Once you make it!” The project was “a lot of fun, working that out. I had more fun doing that than anything else in my life.”

Despite the tremendous impact of Shannon’s work, it was his pursuit of fun and interesting problems that drove him. “I do what comes naturally, and usefulness is not my main goal. I like to solve new problems all the time. I keep asking myself, How would you do this? Is it possible to make a machine to do that? Can you prove this theorem? These are my kinds of problems. Not because I’m going to do something useful.”

Claude Shannon has been remembered in many ways at U-M. In 1961, he was awarded an honorary Ph.D. Though he died in 2001 at the age of 84, U-M hosted the Shannon Centennial Symposium in 2016, celebrating Shannon’s 100th birthday with lectures and events attended by hundreds of people from around the country. Today, a statue of Shannon deep in thought sits outside the west entrance of the Electrical Engineering and Computer Science Building on North Campus.

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Sources for this story:

A Mind at Play by Jimmy Soni and Rob Goodman (2017, Simon and Schuster). “Interview: Claude Shannon” by Anthony Liversidge, Omni magazine, 1987, p. 61–66.