Today in Nautilus:
“Impossible!” Feynman finally said. I nodded in agreement and smiled, because I knew that to be one of his greatest compliments.He looked back up at the wall, shaking his head. “Absolutely impossible! That is one of the most amazing things I have ever seen.”
From The Second Kind of Impossible: The Extraordinary Quest for a New Form of Matter by Paul Steinhardt. Copyright © 2017 by Paul J. Steinhardt. This is a fascinating book. Paul Steinhardt was a fellow fellow when I was at the Radcliffe Institute. I heard his story then. Here is a summary of his book from the publisher’s website.
“When leading Princeton physicist Paul Steinhardt began working in the 1980s, scientists thought they knew all the conceivable forms of matter. The Second Kind of Impossible is the story of Steinhardt’s thirty-five-year-long quest to challenge conventional wisdom. It begins with a curious geometric pattern that inspires two theoretical physicists to propose a radically new type of matter—one that raises the possibility of new materials with never before seen properties, but that violates laws set in stone for centuries. Steinhardt dubs this new form of matter “quasicrystal.” The rest of the scientific community calls it simply impossible.
The Second Kind of Impossible captures Steinhardt’s scientific odyssey as it unfolds over decades, first to prove viability, and then to pursue his wildest conjecture—that nature made quasicrystals long before humans discovered them. Along the way, his team encounters clandestine collectors, corrupt scientists, secret diaries, international smugglers, and KGB agents. Their quest culminates in a daring expedition to a distant corner of the Earth, in pursuit of tiny fragments of a meteorite forged at the birth of the solar system.”
This year marks the 25th anniversary of Natural Language Semantics. Irene Heim and I have been the editors since then. We still meet – at a table, not on a screen – to discuss the papers that have been submitted. Natural Language Semantics was the brain child of Martin Scrivener, the Linguistics editor of what was then Kluwer Academic Publishers. Martin thought that the time had come for a journal to bring together syntactic work in the generative tradition and formal semantics work in the tradition of David Lewis and Richard Montague. From the very start, the journal attracted work on cross-linguistic semantics and the syntax-semantics interface. Early highlights include Mats Rooth’s and Roger Schwarzschild’s papers on focus interpretation and givenness, Veneeta Dayal’s paper on scope marking, Sigrid Beck’s paper on what is now called the “Beck Effect”, Lisa Matthewson’s seminal papers on wide-scope indefinites and on cross-linguistic variation in the expression of quantification, Polly Jacobson’s paper on paycheck pronouns, Lisa Green’s paper on aspectual “be” in African American English, Gennaro Chierchia’s and Sandra Chung’s papers on reference to kinds across languages, Dorit Abusch’s paper on the de re interpretation of the present tense, Mona Singh’s paper on non-culminating accomplishments, and Jo-Wang Lin’s paper on distributivity in Chinese, among many others. All papers are free for anyone to read, share, and annotate.
Ever since Quine’s “On What There Is”, discussions of the types of variables in natural languages have occupied a special place in semantics. According to Quine, “to be assumed as an entity is, purely and simply, to be reckoned as the value of a variable.” After eleven years in the archives, Meredith Landman’s landmark 2006 dissertation on Variables in Natural Language has now been made publicly available on ScholarWorks. Landman’s dissertation argues for severe type restrictions for object language variables in natural languages, targeting pro-forms of various kinds, elided constituents, and traces of movement.
In his 1984 UMass dissertation Gennaro Chierchia had already proposed the ‘No Functor Anaphora Constraint’, which says that ‘functors’ (e.g. determiners, connectives, prepositions) do not enter anaphoric relationships. Landman’s dissertation goes further in arguing for a constraint that affects all object language variables and also rules out properties as possible values for them. Her ‘No Higher Types Variable Constraint’ (NHTV) restricts object language variables to the semantic type e of individuals.
Landman explores the consequences of the NHTV for the values of overt pro-forms like such or do so, as well as for gaps of A’-movement and for NP and VP ellipsis. Since the NHTV bars higher type variables in all of those cases, languages might have to use strategies like overt pro-forms or partial or total syntactic reconstruction of the antecedent to interpret certain types of movement gaps and elided constituents. The NHTV thus validates previous work arguing for syntactic reconstruction and against the use of higher-type variables (e.g. Romero 1998 and Fox 1999, 2000), as well as work arguing for treating ellipsis as involving deletion of syntactic structure.
The topic of the type of traces has most recently been taken up again in Ethan Poole’s 2017 UMass dissertation, which contributes important new evidence confirming that the type of traces should indeed be restricted to type e.
(This post was crafted in collaboration with Meredith Landman, who also provided the pictures).
Maryam Mirzakhani has died today. She was 40 years old. From Stanford News: “A self-professed “slow” mathematician, Mirzakhani’s colleagues describe her as ambitious, resolute and fearless in the face of problems others would not, or could not, tackle. She denied herself the easy path, choosing instead to tackle thornier issues. Her preferred method of working on a problem was to doodle on large sheets of white paper, scribbling formulas on the periphery of her drawings. Her young daughter described her mother at work as “painting.” “You have to spend some energy and effort to see the beauty of math,” she told one reporter. In another interview, she said of her process: “I don’t have any particular recipe [for developing new proofs] … It is like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out.”
In her honor, I am reposting a 2014 post from this blog. Sources: Wikepedia. Article on Maryam Mirzakhani in the Guardian. Article and video in Quanta Magazine.
Jordan Ellenberg‘s popular explanation of what earned Mirzakhani the Fields Medal in 2014: “… [Her] work expertly blends dynamics with geometry. Among other things, she studies billiards. But now, in a move very characteristic of modern mathematics, it gets kind of meta: She considers not just one billiard table, but the universe of all possible billiard tables. And the kind of dynamics she studies doesn’t directly concern the motion of the billiards on the table, but instead a transformation of the billiard table itself, which is changing its shape in a rule-governed way; if you like, the table itself moves like a strange planet around the universe of all possible tables … This isn’t the kind of thing you do to win at pool, but it’s the kind of thing you do to win a Fields Medal. And it’s what you need to do in order to expose the dynamics at the heart of geometry; for there’s no question that they’re there.”
One of 10 people who mattered this year in science: Nature, volume 516, issue 7531, 17 December 2014. 2017 obituary in the New Yorker.
Andrew McKenzie (University of Kansas) has been awarded a 3-year NSF (National Science Foundation) grant for “Investigations in the Semantics of Kiowa, a Native American Language of Oklahoma.” The grant description explains how research in semantics can have a big impact on Native American communities. Andrew McKenzie is a linguist specializing in formal semantics and linguistic fieldwork, with a focus on Native American languages, especially Kiowa.
Photo: Marianne McKenzie
From the grant description published by the NSF: “Led by a linguist who is also a tribal member, this project will conduct an in-depth investigation into Kiowa semantics. Semantics forms a crucial component of language, but linguists have not thoroughly documented any language’s semantics with depth and precision, because the theoretical framework to do so was only recently developed. This project will apply this framework of language documentation, in order to uncover the semantics of phenomena crucial to the Kiowa language. The investigators will elicit language judgments from native speakers of the language, which can tease apart subtle aspects of meaning that are often impossible for speakers to define with words. The project will also record and examine new texts that document naturalistic language use, especially in cultural domains under-represented by currently available Kiowa texts. Kiowa grammar includes multiple areas of interest to formal semantics, such as evidentiality, modality, incorporation, quantification, and degree, all of which are also important areas for learners to acquire. This project will result in a reference grammar and teaching materials that will greatly aid these programs by covering the areas in semantics that remain poorly understood by teachers and researchers. This reference grammar will also serve as a manual for researchers of other Native American languages, especially those who are not trained in this research framework. This study will offer new insight for researchers on dozens of phenomena that occur in many languages besides Kiowa. In doing so, it will re-emphasize the longstanding contribution of Native American languages to linguistics, a scientific understanding of what is possible in human language, and thus a deeper understanding of what is possible in the human mind.”