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Zeno of Elea created several paradoxes about motion more than two thousand years ago. The most famous versions all play with the same uncomfortable idea. Before you reach a destination, you must travel half the distance. Then you must travel half of what remains. Then half again. Read more
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Berry’s Paradox lives in the uncomfortable space between language and mathematics. A common form of the paradox asks us to consider: “The smallest positive integer that cannot be described in fewer than twenty words.” At first, this sounds like a valid description. Read more
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The Raspberry Pi went on sale on February 29, 2012, and demand immediately overwhelmed the distributors’ websites. The $35 Model B was a complete ARM-based Linux computer on a board roughly the size of a credit card. Read more
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Hilbert’s Hotel is one of my favorite ways to think about infinity. Imagine a hotel with infinitely many rooms. Room 1, room 2, room 3, and so on forever. Now imagine that every room is occupied. In an ordinary hotel, the answer is obvious: there is no space for another guest. Read more
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The Birthday Paradox is not a real contradiction. It is a contradiction between probability and intuition. Imagine a room with 23 people. What is the probability that at least two of them share the same birthday? Most people expect the probability to be small because there are 365 possible birthdays. Read more
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The Banach-Tarski Paradox sounds impossible the first time we hear it. In very informal language, it says that a solid mathematical ball can be divided into a small number of special pieces and then rearranged using only rotations and translations to create two balls, each the same size as the original. One ball becomes two. No stretching. No ordinary copying. Read more
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Consider the sentence: “This statement is false.” It is only four words, but it creates a problem that has troubled philosophers and logicians for centuries. Suppose the sentence is true. Read more
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The Barber Paradox is a simple story that carries the same logical problem as Russell’s Paradox. Imagine a village with one barber. The rule is this: The barber shaves all men in the village who do not shave themselves, and only those men. At first, the rule seems clear. Read more
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Raspberry Pi production began in early 2012 after the foundation finalized a board that could be sold at an unusually low price. Manufacturing a computer this cheaply required controlling not just component cost but board complexity, testing, packaging, and distributor margins. Read more
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Russell’s Paradox is one of those problems that looks harmless until one sentence turns mathematics against itself. Bertrand Russell discovered the paradox around 1901 while thinking about the foundations of set theory. The problem begins with a simple question. Can a set contain itself? Read more
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Mathematics began very close to the physical world. People counted objects, measured land, followed the movement of stars, and solved practical problems. Read more
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The name “imaginary number” sounds almost like a joke. How can a number be imaginary? The idea appears when we try to solve equations that have no answer among the real numbers. A simple example is Read more
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By 2011, HTML5 had become the direction of mainstream web development even though the specification was not yet a final W3C recommendation. Browser vendors were implementing new capabilities that reduced dependence on plug-ins such as Flash. Read more
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By late 2011, the Raspberry Pi team was moving from prototype boards toward mass production of a low-cost computer intended for programming education. Keeping the price around $25–$35 forced unusually strict hardware choices. Read more
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Apple introduced Siri as a built-in feature of the iPhone 4S in October 2011 after acquiring the original Siri company the previous year. Instead of requiring users to navigate menus, Siri accepted spoken requests such as setting reminders, sending messages, or checking the weather. Read more
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Some technologies disappear loudly. Read more
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There are technical problems that begin with a sentence so innocent that you already know the evening is lost. Read more
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Some places begin as stores and somehow become part of a city’s social life. Read more
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Microsoft gave developers a detailed preview of Windows 8 at the BUILD conference in September 2011. The most dramatic change was a new touch-first interface built around large tiles, while the traditional Windows desktop remained underneath. Read more
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Google announced an agreement to acquire Motorola Mobility for about $12.5 billion in August 2011. Motorola was an Android handset maker, but one of the most important assets in the deal was its large portfolio of mobile patents. Read more