Grace Lindsay - Models of the Mind: How Physics, Engineering and Mathematics Have Shaped Our Understanding of the Brain

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In memory of my father

Contents

As I write this I am pregnant with my first child. They say it takes a village to raise a kid. I believe that is eventually true, but so far it has been a relatively solitary experience. Writing a book, on the other hand, seems to take a village from the start.

First, I have to thank my husband, Josh. We met while both getting our PhDs at the Center for Theoretical Neuroscience at Columbia, which meant he had to serve both as moral support and as fact-checker throughout this process. He also did a good job of making sure I at least occasionally ate proper meals and saw some friends. Id also like to thank members of his family Sharon, Roger, Laurie for their support and excitement.

I owe a tremendous debt to the NeuWrite community. I first joined this group of scientists and writers when I was a graduate student in New York and quickly joined the London chapter once I moved to the UK. In addition to putting me in contact with the people at Sigma, the members of NeuWrite also provided advice and commiseration about book-writing in general. The opportunity to regularly workshop my chapters with this group helped quell my writing anxiety and, of course, made the book better. Special thanks to Liam Drew, Helen Scales, Roma Agrawal and Emma Bryce.

Ive relied on many friends both practising neuroscientists and not to provide input and feedback on the book. Theyve made these chapters clearer. Much thanks to Nancy Padilla, Yul Kang, Vishal Soni, Jessica Obeysekare, Victor Pope, Sarahjane Tierney, Jana Quinn, Jessica Graves, Alex Cayco-Gajic, Yann Sweeney and (my sister) Ann Lindsay.

I also relied on the diverse and amorphous community of researchers known as neuroscience twitter to sound ideas off and crowdsource resources. Many thanks to this engaged crowd of friends and strangers alike!

I reached out to some researchers with particular expertise to look over different chapters. Im very thankful for the time and knowledge of Athanasia Papoutsi, Richard Golden, Stefano Fusi, Henning Sprekeler, Corey Maley, Mark Humphries, Jan Drugowitsch and Blake Richards. Of course, any errors that remain in the text are my own fault.

The Bloomsbury Sigma team is the reason this book is a reality instead of merely an ill-formed wish in my mind. Thanks to Jim Martin, Angelique Neumann and Anna MacDiarmid for shepherding both me and the book through the process.

A general thanks is due to my family (particularly my sisters, Sara and Ann) and friends who have been patiently hearing about the book for some time. And finally, Id like to express my gratitude to the computational neuroscience community as a whole. Floating around this field for nearly 10 years and soaking in knowledge from many different researchers gave me the proper foundation for writing this book.

What mathematics has to offer

The web-weaving spider Cyclosa octotuberculata inhabits several locations in and around Japan. About the size of a fingernail and covered in camouflaging specks of black, white and brown, this arachnid is a crafty predator. Sitting at the hub of its expertly built web, it waits to feel vibrations in the webs threads that are caused by struggling prey. As soon as the spider senses this movement, it storms off in the direction of the signal, ready to devour its catch.

Sometimes prey is more commonly found in one location on the web than others. Smart predators know to keep track of these regularities and exploit them. Certain birds, for example, will recall where food has been abundant recently and return to those areas at a later time. Cyclosa octotuberculata does something similar but not identical. Rather than remembering the locations that have fared well that is, rather than storing these locations in its mind and letting them influence its future attention the spider literally weaves this information into its web. In particular, it uses its legs to tug on the specific silk threads from which prey has recently been detected, making them tighter. The tightened threads are more sensitive to vibrations, making future prey easier to detect on them.

Making these alterations to its web, Cyclosa octotuberculata offloads some of the burden of cognition to its environment. It expels its current knowledge and memory into a compact yet meaningful physical form, making a mark on the world that can guide its future actions. The interacting system of the spider and its web is smarter than the spider could hope to be on its own. This outsourcing of intellect to the environment is known as extended cognition.

Mathematics is a form of extended cognition.

When a scientist, mathematician or engineer writes down an equation, they are expanding their own mental capacity. They are offloading their knowledge of a complicated relationship on to symbols on a page. By writing these symbols down, they leave a trail of their thinking for others and for themselves in the future. Cognitive scientists hypothesise that spiders and other small animals rely on extended cognition because their brains are too limited to do all the complex mental tasks required to thrive in their environment. We are no different. Without tools like mathematics our ability to think and act effectively in the world is severely limited.

Mathematics makes us better in some of the same ways written language does. But mathematics goes beyond everyday language because it is a language that can do real work. The mechanics of mathematics the rules for rearranging, substituting and expanding its symbols are not arbitrary. They are a systematic way to export the process of thinking to paper or machines. Alfred Whitehead, a revered twentieth-century mathematician whose work we will encounter in goal of mathematics is to eliminate any need for intelligent thought.