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Indecision trained him in two fields
He had already ruled out chemistry, which seemed dull to him: too many isolated facts and too few general principles. He disliked facts he could not bring under a rule and abstract his way out of.
The dual degree was no grand design for a career. It was simply adolescent indecision, since he was not sure what he liked best. It paid off because a generation later the two curricula were merging into one. Those studies also gave him his first taste of communication engineering, which he found especially to his liking because it blended practice and theory, as he did for his entire life.
Someone content to build things might have been happy with a single engineering degree, and someone drawn to theory might have been satisfied with math alone. Shannon, mathematically and mechanically inclined, could not make up his mind. The result was training in two fields that proved essential to his later successes.
How did Boole's algebra reach circuits?
George Boole published The Laws of Thought in 1854, using the values 1 and 0 to stand for true and false. Shannon later recalled running across Boole's work in a philosophy course at Michigan. His 1937 master's thesis at MIT matched Boole's operations to relay switches. That match made it possible to design telephone switching systems and computers with algebra.
How did Hartley prepare the ground for Shannon?
Ralph Hartley, a Bell Labs engineer, published 'Transmission of Information' in 1928. He measured information as the logarithm of the number of possible message sequences, which made it a quantity that could be counted. Harry Nyquist had shown in 1924 how the speed of a telegraph line is limited by its bandwidth. Shannon cited both men in his 1948 paper.
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