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.”
“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.”
From Science News, August 10, 2017: “More than 300 years ago, the philosopher René Descartes asked a disturbing question: If our senses can’t always be trusted, how can we separate illusion from reality? We’re able to do so, a new study suggests, because our brain keeps tabs on reality by constantly questioning its own past expectations and beliefs. Hallucinations occur when this internal fact-checking fails, a finding that could point toward better treatments for schizophrenia and other psychiatric disorders.”
How do natural languages distinguish between fact and fiction? They don’t really. But they provide many tools for reality checking. I probed into this topic in my 2015 contribution to the Rome Science Festival. Here is the abstract for the talk: “Languages do not care all that much about the difference between fact and fiction. Stories tend to be told as if they were reports of known fact. You may have read somewhere that Mr. Palomar was standing on the shore, looking at a wave. Was it in a newspaper? Well, no, it’s from a story by Calvino. [Il signor Palomar è in piedi sulla riva e guarda un’onda.] Calvino’s story doesn’t tell you that it is a piece of fiction. There are no grammatical categories to indicate the merely fictional. There are no fictional declensions or conjugations in natural languages. Every sentence in every language describes a wide range of possibilities. When Calvino writes that Mr. Palomar was standing on the shore, he evokes a set of possibilities. When Wikipedia tells me that Calvino was born in Cuba, it, too, evokes a set of possibilities. But it does more. It also implies that the world we live in is one of them. When it comes to how to approach reality, languages do care. They have countless ways to modulate, fine-tune, and calibrate claims about reality. In a quarter of all the world’s languages, you can’t say that a man was standing on the shore without mentioning your evidence. Was it just hearsay? Did you see it with your own eyes? Did you infer the man’s presence from the footprints in the sand? In those languages, grammar forces speakers to be upfront about their evidence, just as Italian or English forces us to use tenses to locate events in time. Once the evidence is on the table, we may want to say something about the strength of the conclusions we can draw from it. Might there be an iguana in the reptile house? Is it certain? Or is there only a slim chance? Is there a better chance for there to be an iguana than a python? What means do languages have to indicate the strength of a conclusion from a piece of evidence? How do they compare possibilities? How do they talk about degrees of possibilities? Most importantly, how does grammar dip into this jungle of concepts and map them onto hierarchically structured sequences of words that we can use to reason about uncertainty in science and in daily life?”
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.”
“While working in a famously esoteric field, MIT philosopher Robert Stalnaker has focused his career on thinking about real-world concerns — including the fundamental nature of speech, thought, and decision-making. In so doing, he has catalyzed and provided the underpinnings for new research in many other areas, such as game theory, linguistics, decision theory, and economics. In all these research areas, Stalnaker’s influence has been widespread and profound, but his impact on modern linguistics — a field that was just coming into its own in the 1970s — has been especially significant, providing the first clear understanding of what is going on in conditional sentences that are counterfactual.”
“When you think about physics, you usually describe things in terms of initial conditions and laws of motion; so what you say is, for example, where a comet goes given that it started in a certain place and time. In constructor theory, what you say is what transformations are possible, what are impossible, and why. The idea is that you can formulate the whole of fundamental physics this way; so, not only do you say where the comet goes, you say where it can go. This incorporates a lot more than what it is possible to incorporate now in fundamental physics.”
Where can the comet go, given what? What is the range of possibilities that we consider live options? We are not considering all LOGICAL possibilities! This is where work on natural language semantics becomes important: we rack our brains about how humans project possibilities from the facts they encounter and how language helps us keep track, categorize, and compare those possibilities.
“What if the mind is not a storehouse of knowledge, but an engine of prediction? What if we are not Homo sapiens, but Homo Prospectus?” Martin E. P. Seligman
The University of Pennsylvania Positive Psychology Center has established a new branch of Cognitive Psychology: Prospective Psychology. Prospective Psychology investigates the mental representation and evaluation of possible futures. Through the Templeton Science of Prospection Awards, 22 two-year projects will explore the field of prospection.
Subash Khot is this year’s winner of the Nevanlinna Prize. If his “Unique Games Conjecture is correct, then for many of the problems people would most like to solve, it’s hard not only to find an exact solution—finding even a good approximation of the solution is beyond the reach of a computer. This conjecture may seem, on the face of it, like a pretty parochial statement (though possibly hard to prove, or even false). Over the past decade, however, computer scientists have found to their surprise that if the conjecture is true, then a host of problems—some of them seeming to bear little resemblance to the original Unique Games problem—are also hard to approximate.” Simons Foundation.
Source: Quanta Magazine
“For the problem of coloring the nodes of a network that has a collection of constraints about which color combinations are allowed (top left), it is sometimes possible to find a coloring that satisfies all the constraints (top right). But for some networks and constraints (bottom left), it is impossible to satisfy all the constraints simultaneously. The Unique Games Conjecture concerns the problem of finding a coloring that satisfies as many constraints as possible, such as the bottom right coloring, which satisfies all the constraints except the one for the thick edge.” Quanta Magazine.
From Kurzweil Accelerating Intelligence on Patrick Tucker’s The Naked Future: “Computer scientist Stephen Wolfram, and futurist Ray Kurzweil have famously painstakingly recorded every minute detail of their lives, from their diets to the keystrokes, in order to quantify and better their lives. Now, technology has made self-quantification easier than ever, allowing the “everyman” to record and study their habits just as Wolfram and Kurzweil have done, but with less hassle… So what happens in a future that anticipates your every move? The machines may have a better handle on us than ever, but we’ll live better as a result. The naked future is upon us, and the implications for how we live and work are staggering.”
Source: The Modern Word. Borges.
“In all fictional works, each time a man is confronted with several alternatives, he chooses one and eliminates the others; in the fiction of Ts’ui Pên, he chooses— simultaneously—all of them. He creates, in this way, diverse futures, diverse times which themselves also proliferate and fork.” The Garden of Forking Paths by Jorge Luis Borges.
From the Stanford Encyclopedia: Branching time semantics: “As an explicit (or formalised) idea, branching time was first suggested to Prior in a letter from Saul Kripke in September 1958. This letter contains an initial version of the idea and a system of branching time, although it was not worked out in details. “
More on branching time semantics: Around the tree. Semantic and Metaphysical issues concerning branching and the open future.
Counterfactuals “are often claimed to open up the past by demonstrating the myriad possibilities, thus freeing history from the straitjacket of determinism and restoring agency to the people. But in fact they imprison the past in an even tighter web: one tiny change in the timeline – Archduke Franz Ferdinand escapes assassination in Sarajevo, the British cabinet decides not to enter the war – leads inevitably to a whole series of much larger changes, sometimes stretching over decades almost up to the present day. Yet this ignores, of course, an infinite number of chances that might have deflected the predicted course of events along the way – Franz Ferdinand might have fallen victim to another assassin’s bullet, or died in a hunting accident; Britain might have entered the war later on; the US might have come into the conflict on the side of the French; Austria-Hungary might have collapsed in the face of nationalist revolts; and so on.”
“Much of my philosophical research has concerned the extremely improbable: events that we typically disregard because their probabilities are so low. And yet many such events should be important to philosophers, some of them should be important to scientists, and some of them should be important to all of us.”
“Extremely improbable events, like being struck by lightning, are typically disregarded or not taken seriously, because their probabilities are so low. However, one could argue that probability is not about odds, but about the belief in an existence of an alternative outcome. The chance of winning the lottery for example is extremely improbable. Nevertheless, people still buy tickets with the notion that it is a relatively small price to pay for considering the amount you can win. Does this logic work or are we fooling ourselves?” (Groningen Lecture)