# Blum shares Turing legacy

Lenore Blum, a computer science professor at Carnegie Mellon, recently presented a School of Computer Science Special Talk Lecture. The lecture, which took place Tuesday in Rashid Auditorium, was titled “Alan Turing and the Other Theory of Computation.” Alan Turing is a famous figure in computer science, and is well known for inventing the Turing machine and for his work with the theory of computation.

The lecture was an encore performance of one Blum delivered earlier this year to celebrate Turing’s 100th birthday.

Turing is known for his role in the development of the theory of computation, but Blum’s lecture focused on his work in what she calls the “other theory of computation,” based on “numerical analysis and continuous mathematics” in scientific computing, rather than “logic and discrete mathematics in computer science.”

She noted the differences between the two areas. Computer science uses “0s and 1s,” discrete mathematics, and the Turing machine; it solves problems exactly and is a function of input word size. Meanwhile, scientific computing employs real and complex numbers and uses algebraic analysis and continuous mathematics; it “solves problems to a certain accuracy” and is a function of “intrinsic word size.”

“They really are two cultures,” Blum said.

First, Blum spoke about “where Turing meets Newton and bridges the two traditions” of computer science.

Blum described how, in 1936, Turing demonstrated his interaction with real numbers in his first paper. He “used real numbers as a motivation to define his machine.”

Additionally, in a paper written afterwards, Turing returned to computing with real numbers.

Blum said Turing’s experience was positive, as it was “fashionable to talk about computing as a lens on the sciences.”

First-year English major Andy Hutner had a positive opinion of the lecture. “Well, I’m actually familiar with Alan Turing, even though I’m not in the mathematical field, because his theories on discrete mathematics play a big part in the study of linguistics,” he said. “I think Blum did a great job of showing Turing’s contributions to mathematics in a different way than most people would think of.”

Blum has been on Carnegie Mellon’s faculty since 1999. She has dedicated a large portion of her career to the advancement of women in mathematics and science. Blum is a founder of Women@SCS, as well as the founding director of Project Olympus, which supports Carnegie Mellon-based tech start-ups.