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2022 January Mini-Course
20 Dec 2021
In the following January, Harvard GSAS kindly supports me to offer a mini-course on “What is Computation? From Turing Machines to Blackholes and Neurons”. In this blog post, I’m going to share the motivation for teaching this mini-course and give an overview on what you will learn if you are interested in participating!
Computation is not an exotic word for people living in the 21st century. In high school, kids have to learn and do all sorts of computations in arithmetics (and some even start to write computer programs!). For scientists, computational methods become more and more common and sometimes even completely change the paradigm of a field. There are computers of different forms hiding in our daily life ranging from your smartphones to the toy of your pets. Also, from time to time we see excitement on the news about the development of quantum computing and artificial intelligence. Computation has become central in human civilization, however, do we really understand what computation is?
Let me first convince you why asking and attempting to answer this question is important.
Traditionally, at least on Wikipedia, computation is defined as “any type of calculation that includes both arithmetical and non-arithmetical steps and which follows a well-defined model (e.g. an algorithm)”. Indeed, for computer scientists and mathematicians, computation is about solving computational problems via an abstract mathematical model known as Turing machine. In particular, the Church-Turing Thesis, which can be viewed as Newton’s laws in computer science, asserts that all effective computational methods in the world can be captured by Turing machines. That is to say, in the mathematical world, computation is something axiomatized and can be studied and understood parallel to the empirical world.
On the other hand, for the majority of people, computation is something more concrete and has a physical realization such as a digital computer. The rise of computer science in the past few decades is certainly owing to the great technological success of building up modern computers. The fascinating advances of technology seem to close the gap between theory and reality (similar to Newton’s laws!). Nevertheless, in the frontier of scientific research, the recent surging developments of quantum computing and artificial neural networks started to challenge our understanding in computation - the ways they compute are so different from the traditional Turing machines and we don’t really know why and how they work so well!
In my opinion, we need to revisit the notion of computation in order to attack these mysteries. Specifically, the approach should be interdisciplinary.
As computer scientists are used to think of computations as composing different resources and subroutines, the computations in physics and biology tend to be rather holistic and open-ended. When talking about computations, people from different fields often think a bit differently. Such distinctions across fields should not be barriers or problems, instead, it could potentially serve as seeds to enrich our understanding in the essence of computation.
This mini-course is an invitation to rethink about what computation is through different angles. We will focus on but not limit to three perspectives including mathematics, physics, and biology. Through theories, examples, and experiments, we are going to see the similarities and differences between these disciplines. Six guest speakers coming from a diverse background (from computer science and physics to neuroscience and modern art) will join us and provide lots of examples and stories from their home field. The aim of this mini-course is to remind people of the diverse nature of computation and envision the possibilities of future interdisciplinary research.
There will be three modules and each contains three 50-minute interactive lectures and 1-3 guest talk(s). The first module focuses on the mathematical foundation of computations in which the students will learn the concept of Turing machines, computability, reductions, and most importantly, the underlying philosophy. The second module is about the computations in the physical world where we will launch from classical mechanics, to statistical mechanics, quantum mechanics, and gravity. The third module looks into the computations in biology, ranging from genomes, evolution, to neuroscience. The mini-course will end with a panel discussion with all the guest speakers and students.
Please visit the course website for more information and hope to see you in January!