Today is publication day for Tom Griffiths new book, The Laws of Thought: The Quest for The Quest for a Mathematical Theory of the Mind.
Tom is the co-author of one of my favorite books, Algorithms to Live By. This new book is a must-read in this age of AI, exploring the history of the quest to describe the way we think in mathematical terms or laws, from its origins three hundred years ago to the ideas behind modern AI systems and the ways in which they still differ from human minds.
Tom is the Director of the Computational Cognitive Science Lab, a research group focused on understanding the mathematical foundations of human cognition, and the Princeton Laboratory for Artificial Intelligence, a new effort that supports innovative research efforts in AI and related fields. He works with graduate students in Psychology, Computer Science, and Neuroscience, as well as other units on campus.
Tom was kind enough to write the piece below. Enjoy!
For many people, AI seems to have come out of nowhere. All of a sudden a couple of years ago it became possible to chat with a computer in the same way we do with other human beings. Now computers help us answer math questions, write code and emails, and even make decisions.
If you know a little more about how AI chatbots work, you know that they are based on artificial neural networks, and that important breakthroughs in creating the bigger and bigger neural networks used in modern AI systems were made about a decade ago.
But the story of AI – and of how people have tried to use math to capture the nature of thought – goes back much further than that. It’s a story that twines back and forth between fields, from math to computer science to neuroscience to psychology and back. It’s also a story of creating a new kind of science that integrates insights from all of those fields, called cognitive science.
My new book The Laws of Thought tells that bigger story through the smaller stories of the people who had some of the important ideas that led up to this moment. It explores the origin of mathematical approaches to studying the mind in the 18th and 19th centuries — the puzzle that the great genius Gottfried Wilhelm Leibniz couldn’t solve but that was cracked by the young schoolteacher George Boole. It describes how psychologists and linguists began to test those ideas in the 20th century, creating a “cognitive revolution” in their field by using math to express precise hypotheses about the nature of thought and language. And it tells the tale of how artificial neural networks have risen and fallen and risen and fallen in popularity before rising again in our modern AI systems.
I love these stories – they capture the human insights behind intelligent machines. But they’re also a tool for introducing some of the mathematical ideas that are needed to understand not just how those machines got smarter, but what challenges they might face and where things could go from here. In writing this book, I wanted to give readers the broader context for having informed conversations about AI and its implications for understanding human minds. Just as Algorithms to Live By explained ideas from computer science using examples from everyday life, The Laws of Thought gives you the tools you need to make sense of AI through the stories of the people who have spent the last couple of centuries struggling with – and ultimately solving – some of its challenges.
By knowing how artificial neural networks work, you can know some of the things that AI chatbots might find difficult (they tend to be very sensitive to the data they are trained on, and will mix up things that should be kept distinct from one another). You can also know some of the alternative approaches to making intelligent machines, such as using logic or probability theory. These pieces of math help us understand why the large language models that underlie modern AI systems are able to solve the seemingly impossible problem of learning language just by reading text, and help to explain why they need so much text – thousands of times more input than a human child needs to perform the same feat. And how we might be able to make systems that can learn much more efficiently.
In school, we learn the Laws of Nature. But to a citizen of the 21st century, it’s perhaps even more important to learn the Laws of Thought.