2 . Imagine living in an apartment in Manhattan. When Covid-19 hits, you have nowhere to escape. Instead, you go up to the rooftop, where, to your surprise, other renters have come, too. After some awkwardness, everyone starts meeting nightly, drinks in hand, to share stories about themselves. This is the background setting of Fourteen Days, a “collaborative novel” edited by Margaret Atwood and Douglas Preston. In addition to these two, 34 authors of varied backgrounds contributed to the book. It is one of a growing number of new works, which are written together in some way.

AI services, such as ChatGPT, have started to become co-authors, too. Such models are also conversational machines, which can suggest phrases, give feedback and answer questions. “Cyborg authorship” is what MrRettberg of University of Bergen calls this. He published a book with Cyborg authorship, in which ChatGPT is tasked with generating reviews of famous works in the style of well-known authors — think Jane Austen writing about William Burroughs’s Naked Lunch.

Writing with collaborators, be they human or artificial, will only become more common. But individual authors will still dominate creatively. That is because collectively written books rarely make for great literature. Many contributions to Fourteen Days are cleverly woven together. But the book does not work quite well. Then there is authorial ego (自我价值感). Getting all 36 authors of Fourteen Days to agree on the text was a challenge, with some writers taking issue with how their story ended up being framed and referred to by other contributors later. And AI is not yet fully accepted in literary circles. Recently KudanRie, the winner of Japan’s top prize for literature, admitted she used ChatGPT to write around 5% of her science-fiction novel Tokyo Sympathy Tower. Such honesty is rare because most would never admit using AI. A new sort of “ghost writing” may be having a moment, but many writers will never want to name ChatGPT as their co-author.

6 . Ariel Procaccia has thought a lot about how to cut a cake over the last 15 years. As the father of three children, he knows how hard it is to divide a birthday cake to everyone’s satisfaction. But it’s also because Procaccia’s work focuses on exploring the mathematical rules for dividing stuff up fairly. One way to do that is to think abstractly about dessert.

For decades, researchers have been asking the seemingly simple question of how to cut a cake fairly. The answer reaches far beyond birthday parties. A mathematical problem at its heart, cake cutting connects strict reasoning to real-world issues of fairness, and so attracts not only mathematicians, but also social scientists, economists and more. “It’s a very elegant model in which you can distill what fairness really is, and reason about it,” Procaccia says.

The simplest approach is called the “divider-chooser” method, where one person cuts the cake into two equal pieces in his view, and the other person picks first. Each receives a piece that they feel is as valuable as the other’s. But when personal preferences are taken into account, even the easiest rule becomes complicated. Suppose Alice and Bob are to divide a cake, and Alice knows Bob prefers chocolate, she may knowingly divide the cake unequally so the smaller piece contains more chocolate. Then Bob will choose according to his preference, and Alice will get the larger piece. Both of them are satisfied with what they get, but the meaning of fairness changes in this situation.

The cake is a symbol for any divisible good. When cake-cutting principles are employed to settle disagreements, they are potentially helping the world find solutions. Procaccia has used fair division algorithms (算法) to model food distribution. Social scientist Haris Aziz is exploring situations ranging from how to divide up daily tasks to how to best schedule doctors’ shifts in hospitals.

Even after decades of investigation, cake cutting isn’t like a simple jigsaw puzzle (拼图) with a well-defined solution. Instead, over time, it has evolved into a kind of mathematical sandbox, a constructive playground that brings together abstract proofs and easy applications. The more researchers explore it, the more there is to explore.