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Below, Tom Griffiths shares five key insights from his new book, The Laws of Thought: The Quest for a Mathematical Theory of the Mind. Griffiths is a professor of psychology and computer science at Princeton University and director of the Princeton Laboratory for Artificial Intelligence. Whats the big idea? How can we study something we cant see or touch? Mathematics allows us to develop rigorous theories about how minds work. It also lets us use those theories to build artificial intelligence systems. Just as physicists seek to identify Laws of Nature, cognitive scientists hope to discover the Laws of Thought. Listen to the audio version of this Book Biteread by Griffiths himselfin the Next Big Idea app. 1. The story of AI goes back hundreds of years. For many people, AI seems to have come out of nowhere. In late 2022, it suddenly became possible for anyone to have a conversation with chatbots that could draw on more knowledge than any human. Dig a little deeper and you might discover that the approach behind those chatbotsbuilding bigger and bigger artificial neural networkshad its first dramatic demonstration in 2012, when it was used to significantly improve how well computers identify images. But the story goes back much further than that. When Enlightenment thinkers, like René Descartes or Gottfried Wilhelm Leibniz, first began using mathematics to effectively describe the physical world around us, they also suggested that the same kind of approach might be used to describe the mental world inside us. Those early efforts led to the development of mathematical logic and digital computers, which in turn led to the creation of cognitive science by psychologists who used mathematical ideas to come up with new theories about the mind. Modern AI springs from that tradition: Key advances in the development of artificial neural networks came from psychologists seeking to understand how the human mind works. 2. No single piece of mathematics describes the mind. Cognitive scientists started using mathematical logic to describe thought, but after a couple of decades realized that wasnt going to work. Concepts have fuzzy edges that logic just cant capture. Artificial neural networks were developed in parallel and became much more powerful after a group of psychologists showed how they could be used to learn more complex relationships than anyone had thought possible. Continuing to scale up those neural networks takes us to modern AI. But understanding how neural networks learnand how to create systems that learn more like peoplerequires a different approach, one that uses ideas from probability theory. These three mathematical traditions intertwine to give us a more complete picture of how the mind works. 3. Crucial discoveries come from pursuing unpopular ideas. The first neural networks that could learn were built by a computer scientist who abandoned the project after deciding that, in order for them to learn anything interesting, they would have to be much larger than he considered practical. But a psychologist worked out how to make them learn better, which caused a lot of excitement about the potential of that approach. However, that same computer scientist then showed that even those neural networks had fundamental limitations, and they decreased in popularity. A decade later, some psychologists became interested in neural networks as tools for understanding human cognition, cracked the problem of how to get them to learn more complex relationships, and neural networks became popular again. Then, machine learning researchers became interested in the statistical foundations of learning, and neural networks decreased in popularity. Soon, more powerful computers and larger datasets made it possible to use neural networks to solve even more challenging problems, bringing us to the present day. This back-and-forth between disciplineswhere an unpopular idea in one discipline is picked up and improved upon by researchers in another disciplineis a nice illustration of how an interdisciplinary field like cognitive science can have a huge impact. 4. We are closer than ever to understanding the human mind. I used to tell my students that cognitive scientists have made a lot of progress in figuring out how to ask questions about the mind, but were still a long way from having answers. But now, the progress in AI over the last decade is beginning to suggest answers to some of our deepest questions about human intelligence. Mathematical frameworks like logic and probability theory are fundamental to describing the nature of thought and learning, but the abstract rules and inferences they identify need to be implemented in real human brains. Artificial neural networks give us important hints about how that might work. Putting these pieces together gets us remarkably close to fulfilling the vision that Descartes and Leibniz had centuries ago of having a mathematical framework for describing thought. 5. There are still big differences between human minds and AI. Despite all that progress, modern AI still has some important gaps. One of the biggest regards learning. If you read aloud all of the text that is used to train todays chatbots, it would take tens of thousands of years. By contrast, a human child learns to be a fluent speaker of their native language in less than 10 years. That means that theres something in human brains that is different from what is inside our AI algorithms. Figuring out what that might be is a problem that we study in my lab, and a preoccupation of many cognitive scientists. There are also interesting questions about what exactly it is that artificial neural networks are learning, and whether they represent the world in the same way as us. In some cases, they may be, but in others, we can show that they are quite different. Figuring out what AI systems know and when they are likely to succeed or fail at a task is a great opportunity to use the methods that cognitive scientists have honed by studying humans. For a long time, we have only had one species that demonstrated this kind of intelligent behavior, so having another one to study opens the door to not just understanding more about AI but understanding more about ourselves. Enjoy our full library of Book Bitesread by the authors!in the Next Big Idea app. This article originally appeared in Next Big Idea Club magazine and is reprinted with permission.
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Your colleagues decide in less than a minute whether your email is worth replying to. Microsofts 2025 Work Trend Index Report shows that the average employee receives 117 emails a day, and most are skimmed in under 60 seconds. In other words, if your email takes someone more than a minute to understand, theres a strong chance you wont be getting a timely response. Well-written emails dont just make you sound smarter; studies show that they also reduce misunderstandings and speed up responses. Here are five simple ways to get faster email responses, while also helping your recipient preserve mental energy and time. BREAK UP WITH THE EMAIL BRICK Long blocks of text are the enemy of attention. Research shows that visually uncluttered text (with white space and intentional spacing) is easier for busy readers to scan and digest quickly. Simply formatting your email with bullet points, bold text for important questions or updates, and short paragraphs will significantly increase your chances of getting a prompt response. Structure is just as important as length. If the email is longer than this article, consider your reader overwhelmed. DONT LEAD WITH SMALL TALK One of the biggest mistakes professionals make is burying the lead. Instead of opening with a short anecdote or unrelated small talk (Hope your week is going well), start with the purpose of your email, and ideally, the action you need. In military and executive communication, this is known as BLUF (Bottom Line Up Front). BLUF requires you to put key information, like the request or decision needed, in the first sentence or two. After you have led with the key information, you can share further details that the recipient can read if they need background context. And yes, you can still ask your coworker if they have plans for the weekend or how their dog is doing. But for the sake of everyones sanity, leave this to the end. DONT PLAY EMAIL TENNIS The back-and-forth dance of unanswered questions (When works for you?, Morning works, What time?) costs time and demands cognitive switching. One survey of modern workplace behavior found that knowledge workers spend roughly 28% of their workweek managing email, with a large portion of that time simply waiting on or chasing down replies. To reduce this, try to include all relevant details on the first send. One way to address this is, if youre proposing a meeting, include your availability windows, the purpose of the call, and how long you expect it to take in a single message. If you want a call back, include your direct phone number rather than waiting for the other person to ask. Write a clear subject line In a crowded inbox, the subject line acts as a decision filter: Is this relevant? Is this urgent? Can this wait? Studies show that email subject lines critically influence whether a recipient opens, defers, or ignores an email (before theyve read a single sentence of the message).Do your best to craft a subject lines that are specific, concise, and action-oriented. For example, Budget Review Needed by 3 PM is more effective than a generic phrase like Quick Question. BUILD EMAIL TRUST If you teach people over time that your emails are concise and to the point, you are building email trust. This means that recipients are more likely to respond positively and quickly when they see your name. Researchers in written communication emphasize that consistency in formatting and clarity doesnt just improve readability, it builds an implicit reputation for professionalism. Getting faster email replies isnt about sounding smarter. Its about making decisions easier for the person on the other side of the screen. When your emails are clear, scannable, and consistent, you reduce mental load, build trust, and teach people to respond to you faster.
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What do you envision when you think of meekness? You probably see a mousy doormat, someone sheepishly acquiescing to the will of the stronger. When Jesus says, Blessed are the meek, for they shall inherit the earth, you might think that those wimps will hand it over without a whimper or word of objection to stronger, more ambitious people. The philosopher Friedrich Nietzsche called meekness craven baseness. Indeed, one of the Oxford English Dictionarys definitions is inclined to submit tamely to oppression or injury, easily imposed upon or cowed, timid. Meekness, then, is a weakness. Why would you ever want to be meek? The same goes for docility, often characterized as a near neighbor of meekness. We can get a feel for its usage these days from the Corpus of Contemporary American English, where one finds that a docile person is slow, controllable, obedient, submissive, compliant, passive, and under control. Or consider condescension. You likely envision someone self-important looking down her nose at a service worker, or some insufferable prig unwilling to come off his high horse to mingle with the peasants. Being condescending, far from being a virtue, is universally acknowledged as a vice. Meekness, docility, and condescension: three traits with no cultural capital today. And yet, our ancestors typically understood these traits to be virtues. How in the world could that be? As any philosopher will tell you, in a case of seeming disagreement, you need to settle the definitions of the words in play. How many arguments have been abruptly dissolved by someone saying, Oh, thats what you mean? When we check the meaning of these three terms, I think we come to see that theres been a switcheroo. As Ive found in my philosophical research and teaching, some of the virtues that were most celebrated in yesteryear but now go undersung are traits that can help us lead good lives, even now. Forgotten virtues Consider meeknessbut allow me to start with a little vignette. In 2018, mixed-martial-arts champion Matt Serra was having a family meal in a restaurant when a belligerent drunken man entered, threatening servers and patrons. Serra could have knocked him out cold. But instead, he calmly pinned him, waiting for security to arrive. A similar trait is on display when exasperated parents react with control, harried teachers dont rise to students provocations, and police de-escalate situations. In each case, they kept control of their emotions, especially their anger. One common feature of these stories is that the person wasnt powerless; rather, it was precisely because they understood how much power they had that they used restraint. Such a traitexcellence with respect to ones angerused to be called meekness. We hear an echo of this original meaning even today in horse training, where to meek a horse means training it to subjugate its great power to its master, not letting its passions take control. Likewise, meekness once meant not becoming weak, but subjugating power to reasonnot letting anger take control. In the Gospels, when Jesus calls himself meek, it is the same Greek word used for a meek horse: praus. A horse is not weaker on account of being meeked; no Greek warrior wanted a wimpy steed. The horse retains its strength, now safeguarded by self-control. This is quite a different notion of meekness than we find in our contemporary lexicon. Yet in its traditional sense, the word names a trait almost everyone deeply values. No one wants her best friend, child, teacher, coach, or deputy to be unable to control her anger. Such control is an important character trait for living a good life, but we no longer have a concept for it. What term do people use today for being disposed to pick battles prudently, not letting anger cloud ones judgment, not being easily baited into action theyll come to regretwithout being easily biddable or callous to real injustices? Self-control, a broad category that covers facing temptations, enduring difficulties and myriad things in between, is too broad a notion to do the work. Nor do we have a word for someone excellent at receiving instruction and insightsbut at the same time whos unafraid to think for herself, to disregard the advice of a snake-oil salesman. That used to be called docility. Condescension, the most surprising of the three, now suggests someone deigning to speak down from their lofty height. Yet it once described excellence at respecting people, regardless of their social status: easily connecting with those on a lower rung so they feel seen and valued, but without causing embarrassment or awkwardness. What term do we have now for inculcating such an important trait? Why words matter To be clear, Im not here from the Language Reclamation League. Im not necessarily advocating for a return to older languageand certainly not just because it is older. But without replacements for ethical concepts weve lost, were faced with a moral void, unable even to conceptualize the goodness that we want to see in ourselves and those we love. Maybe you think that not much is lost. Bridges fall when engineers cant distinguish varieties of physical strength; whats lost if people cant distinguish varieties of character strength? To my mind, there are at least three reasons why it is important to have some term or other for these traits. First, theres good psychological evidence that goals of approachI want to get healthy, I want to get financially stableare a stronger motivation for us than avoidance goalsI want to stop being sick, I want not to be poor. Approach goals typically yield more effort, more satisfaction, and more well-being. But they require naming the moral virtue you want to cultivate. Second, the positive traits named by these old virtues are what you really want. You dont merely want your loved ones to stop acting out of wrath. You want them to be able to restrain their power in the face of their anger. You are ignorant of your real goal if you dont have a concept for it. Third, consider the detriment caused by not having shared language for an ethical concept. The philosopher Miranda Fricker has written of the time before the term sexual harassment was coined in 1975. She provides multiple instances of women being wronged in the workplace but being unable to articulate that wrong to those in power, owing to a lack of a shared label for it. And not only that, but the lack of an adequate concept preventd the victims from fully understanding the wrong themselves. Having positive concepts for the traits we want to enable in ourselves and others is essential, then, to the moral life. The fact that weve let several go the way of blatherskite and bumfuzzled is telling. We still have terms for a bloviating windbag or being bewildered, so we dont need those archaic, though admittedly fun, words to express important truths. But when it comes to undersung virtues, we do need some way to highlight character traits that help form us into our best selveseven if the words of yesteryear no longer fit the bill. Timothy J. Pawl is a professor of philosophy at the University of St. Thomas. This article is republished from The Conversation under a Creative Commons license. Read the original article.
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