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This is a cutaway model of one, in the proportions of ITER, under construction in France."},"hall":{"key":"energy","name":{"zh":"能源、航天与探测","en":"Energy, Flight & Sensing"}},"layer":{"key":"technology","name":{"zh":"技术","en":"Technology"}},"field":"energy","url":{"zh":"https://world.lapla.si/zh/tokamak/","en":"https://world.lapla.si/en/tokamak/"},"embed":{"zh":"https://world.lapla.si/embed/zh/tokamak/","en":"https://world.lapla.si/embed/en/tokamak/"},"markdown":{"zh":"https://world.lapla.si/zh/tokamak/index.html.md","en":"https://world.lapla.si/en/tokamak/index.html.md"},"card":"https://world.lapla.si/cards/tokamak.webp","chapters":[{"id":"cover","n":0,"title":{"zh":"托卡马克聚变装置","en":"Tokamak Fusion Reactor"}},{"id":"goal","n":1,"title":{"zh":"一亿五千万度","en":"150 Million Degrees"}},{"id":"dt","n":2,"title":{"zh":"17.6 兆电子伏","en":"17.6 MeV"}},{"id":"lawson","n":3,"title":{"zh":"密度、温度、时间","en":"Density, Temperature, Time"}},{"id":"gyrate","n":4,"title":{"zh":"绕着磁力线转","en":"Round the Field Lines"}},{"id":"drift","n":5,"title":{"zh":"弯成环，又会漂走","en":"Bent into a Ring, Still Drifting"}},{"id":"twist","n":6,"title":{"zh":"让磁力线拧起来","en":"Twisting the Field"}},{"id":"section","n":7,"title":{"zh":"剖开：一层套一层","en":"Cut Open: Layer within Layer"}},{"id":"magnets","n":8,"title":{"zh":"零下 269 度的线圈","en":"Coils at −269 °C"}},{"id":"glow","n":9,"title":{"zh":"看得见的边缘","en":"The Edge You Can See"}},{"id":"wall","n":10,"title":{"zh":"包层与偏滤器","en":"Blanket and Divertor"}},{"id":"heating","n":11,"title":{"zh":"加热","en":"Heating"}},{"id":"status","n":12,"title":{"zh":"现在到了哪里","en":"Where Things Stand"}},{"id":"apart","n":13,"title":{"zh":"拆开来看","en":"Taken Apart"}},{"id":"lab","n":14,"title":{"zh":"等离子体电流","en":"Plasma Current"}}],"params":[{"id":"labels","kind":"toggle","label":{"zh":"标注","en":"Labels"},"default":true}]},{"slug":"euler","plate":"M06","title":{"zh":"转半圈，是 e 的 iπ 次方","en":"Half a Turn Is e to the iπ"},"kicker":{"zh":"欧拉公式","en":"Euler’s formula"},"summary":{"zh":"eⁱᵗ 是一个沿单位圆匀速行走的点，速度永远是位置的 i 倍。走过时间 π，它到了 −1。","en":"eⁱᵗ is a point walking round the unit circle at a steady pace, its velocity always i times its position. After time π it is at −1."},"description":{"zh":"eⁱᵗ 描述的是一种运动：速度始终等于位置乘以 i，也就是和半径垂直、长度为 1。这样的点沿单位圆匀速行走，走过时间 t，弧长就是 t。半圈的弧长是 π，所以 e^(iπ) = −1。","en":"eⁱᵗ describes a motion: the velocity is always the position times i, which means at right angles to the radius and of length 1. Such a point walks round the unit circle at a steady pace, so after time t it has covered an arc t. Half the circle is an arc of π, so e^(iπ) = −1."},"hall":{"key":"math","name":{"zh":"数学","en":"Mathematics"}},"layer":{"key":"ideas","name":{"zh":"思想","en":"Ideas"}},"field":"analysis","url":{"zh":"https://world.lapla.si/zh/euler/","en":"https://world.lapla.si/en/euler/"},"embed":{"zh":"https://world.lapla.si/embed/zh/euler/","en":"https://world.lapla.si/embed/en/euler/"},"markdown":{"zh":"https://world.lapla.si/zh/euler/index.html.md","en":"https://world.lapla.si/en/euler/index.html.md"},"card":"https://world.lapla.si/cards/euler.webp","chapters":[{"id":"cover","n":0,"title":{"zh":"转半圈，是 e 的 iπ 次方","en":"Half a Turn Is e to the iπ"}},{"id":"turn","n":1,"title":{"zh":"乘以 i：转四分之一圈","en":"Times i: a Quarter Turn"}},{"id":"grow","n":2,"title":{"zh":"增长的速度等于自己","en":"Growth at the Rate of Itself"}},{"id":"walk","n":3,"title":{"zh":"速度与位置垂直","en":"Velocity at Right Angles"}},{"id":"steps","n":4,"title":{"zh":"一百个小步","en":"A Hundred Small Steps"}},{"id":"rotate","n":5,"title":{"zh":"转动是一种运动","en":"Rotation as a Motion"}},{"id":"lab","n":6,"title":{"zh":"实验台","en":"The Bench"}}],"params":[{"id":"play","kind":"toggle","label":{"zh":"播放","en":"Play"}},{"id":"choice","kind":"choice","label":{"zh":"步数 n","en":"Steps n"},"default":"8","options":[{"id":"1","label":{"zh":"1","en":"1"}},{"id":"2","label":{"zh":"2","en":"2"}},{"id":"4","label":{"zh":"4","en":"4"}},{"id":"8","label":{"zh":"8","en":"8"}},{"id":"16","label":{"zh":"16","en":"16"}},{"id":"32","label":{"zh":"32","en":"32"}},{"id":"100","label":{"zh":"100","en":"100"}}]},{"id":"t","kind":"slider","label":{"zh":"时间 t","en":"Time t"},"min":0,"max":6.2832,"step":0.01,"default":2.4},{"id":"rule","kind":"toggle","label":{"zh":"铜尺","en":"Rule"},"default":true},{"id":"riders","kind":"toggle","label":{"zh":"滑块","en":"Riders"},"default":true},{"id":"labels","kind":"toggle","label":{"zh":"标注","en":"Labels"},"default":true}]},{"slug":"press","plate":"C05","title":{"zh":"活字印刷机","en":"The Printing Press"},"kicker":{"zh":"经典机器","en":"Classic machines"},"summary":{"zh":"一个个金属字排成版，上墨，盖纸，拉一下压杆：一页印好了。约 1450 年，美因茨。","en":"Metal letters set into a page, inked, covered with paper, one pull of the bar: a printed page. Mainz, about 1450."},"description":{"zh":"约 1450 年，约翰内斯·古腾堡在美因茨把几样东西凑成了一套办法：能调宽度的手铸字模，铅锡合金铸的活字，油性墨，和一台螺旋压印机。字可以拆开重排，一页可以印几百遍。下面这台模型照后来留下的木制手扳印刷机做，旁边的台子上是铸字和排字的工具。","en":"Around 1450 in Mainz, Johannes Gutenberg put several things together into one method: a hand mould that could change its width, type cast from a lead–tin alloy, oil-based ink, and a screw press. The letters could be taken apart and set again, and a page could be printed hundreds of times. The model follows the wooden hand press as later pictures show it; the tools for casting and setting type are on the bench beside it."},"hall":{"key":"classic","name":{"zh":"经典机器","en":"Classic Machines"}},"layer":{"key":"technology","name":{"zh":"技术","en":"Technology"}},"field":"print","url":{"zh":"https://world.lapla.si/zh/press/","en":"https://world.lapla.si/en/press/"},"embed":{"zh":"https://world.lapla.si/embed/zh/press/","en":"https://world.lapla.si/embed/en/press/"},"markdown":{"zh":"https://world.lapla.si/zh/press/index.html.md","en":"https://world.lapla.si/en/press/index.html.md"},"card":"https://world.lapla.si/cards/press.webp","chapters":[{"id":"cover","n":0,"title":{"zh":"活字印刷机","en":"The Printing Press"}},{"id":"copy","n":1,"title":{"zh":"一本书怎么来","en":"How a Book Was Made"}},{"id":"system","n":2,"title":{"zh":"古腾堡的办法","en":"Gutenberg’s Method"}},{"id":"stick","n":3,"title":{"zh":"反着排","en":"Set Backwards"}},{"id":"forme","n":4,"title":{"zh":"锁版，上墨","en":"Locking Up and Inking"}},{"id":"pull","n":5,"title":{"zh":"一拉","en":"One Pull"}},{"id":"apart","n":6,"title":{"zh":"拆开来看","en":"Taken Apart"}},{"id":"section","n":7,"title":{"zh":"剖开：铸一个字","en":"Cut Open: Casting a Letter"}},{"id":"bible","n":8,"title":{"zh":"四十二行","en":"Forty-Two Lines"}},{"id":"changed","n":9,"title":{"zh":"它改变了什么","en":"What It Changed"}},{"id":"lab","n":10,"title":{"zh":"压杆在手","en":"At the Bar"}}],"params":[{"id":"labels","kind":"toggle","label":{"zh":"标注","en":"Labels"},"default":true}]},{"slug":"turbofan","plate":"F07","title":{"zh":"涡扇发动机","en":"Turbofan Engine"},"kicker":{"zh":"尖端设备","en":"Frontier machines"},"summary":{"zh":"一台宽体客机用的大涵道比涡扇发动机，四分之一剖开：风扇、十级高压压气机、环形燃烧室、高低压涡轮，起飞时每秒吸进约 1.2 吨空气。","en":"A high-bypass turbofan of the kind under a widebody’s wing, a quarter cut away: fan, ten-stage high-pressure compressor, annular combustor, two turbines. 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The typewriter cast each letter as a piece of type and printed it at the touch of a key, the same size and just as clear every time. The model is a frontstrike machine of the kind of the Underwood No. 5, made from 1900: a black enamelled cast frame, glass-topped keys, and forty-two nickelled typebars in a half circle, striking the front of a rubber platen. 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A 100 : 1 reduction in one stage, with almost no backlash."},"description":{"zh":"机器人手臂和人形机器人的关节里，电机转得快、力气小，关节要转得慢、力气大、位置准。谐波减速器靠一只被椭圆撑弯的薄钢杯，一级减速 100 倍，几乎没有齿隙。这是一个剖开的关节模组，旁边是放大 2.4 倍、拆成三件的减速器。","en":"In a robot arm or a humanoid’s joint, the motor spins fast with little torque, and the joint must turn slowly, strongly and precisely. A strain-wave gear does it with a thin steel cup flexed by an ellipse: 100 : 1 in a single stage, with next to no backlash. Here is a joint module cut open, beside the same gear 2.4 times larger and taken into its three parts."},"hall":{"key":"energy","name":{"zh":"能源、航天与探测","en":"Energy, Flight & Sensing"}},"layer":{"key":"technology","name":{"zh":"技术","en":"Technology"}},"field":"making","url":{"zh":"https://world.lapla.si/zh/harmonic/","en":"https://world.lapla.si/en/harmonic/"},"embed":{"zh":"https://world.lapla.si/embed/zh/harmonic/","en":"https://world.lapla.si/embed/en/harmonic/"},"markdown":{"zh":"https://world.lapla.si/zh/harmonic/index.html.md","en":"https://world.lapla.si/en/harmonic/index.html.md"},"card":"https://world.lapla.si/cards/harmonic.webp","chapters":[{"id":"cover","n":0,"title":{"zh":"谐波减速器","en":"The Harmonic Drive"}},{"id":"reach","n":1,"title":{"zh":"一级减速 100 倍","en":"100 : 1 in One Stage"}},{"id":"problem","n":2,"title":{"zh":"电机快，关节慢","en":"Fast Motors, Slow Joints"}},{"id":"parts","n":3,"title":{"zh":"三个零件","en":"Three Parts"}},{"id":"ellipse","n":4,"title":{"zh":"被撑成椭圆","en":"Flexed into an Ellipse"}},{"id":"walk","n":5,"title":{"zh":"转一圈，退两齿","en":"One Turn, Two Teeth Back"}},{"id":"mesh","n":6,"title":{"zh":"很多齿同时咬合","en":"Many Teeth at Once"}},{"id":"section","n":7,"title":{"zh":"剖开关节模组","en":"The Joint Module, Cut Open"}},{"id":"motor","n":8,"title":{"zh":"无框力矩电机","en":"Frameless Torque Motor"}},{"id":"sensors","n":9,"title":{"zh":"两个编码器，一个制动器","en":"Two Encoders and a Brake"}},{"id":"bearing","n":10,"title":{"zh":"交叉滚子轴承","en":"Cross-Roller Bearing"}},{"id":"uses","n":11,"title":{"zh":"用在哪里","en":"Where It Works"}},{"id":"numbers","n":12,"title":{"zh":"真实型号的数字","en":"Real Numbers"}},{"id":"apart","n":13,"title":{"zh":"拆开来看","en":"Taken Apart"}},{"id":"lab","n":14,"title":{"zh":"实验台","en":"Laboratory"}}],"params":[{"id":"mark","kind":"toggle","label":{"zh":"标记一个齿","en":"Mark one tooth"},"default":false},{"id":"xray","kind":"toggle","label":{"zh":"柔轮透明","en":"Clear flexspline"},"default":false},{"id":"apart","kind":"toggle","label":{"zh":"拆开关节","en":"Take the joint apart"},"default":false},{"id":"cut","kind":"toggle","label":{"zh":"剖开关节","en":"Cut the joint open"},"default":true},{"id":"labels","kind":"toggle","label":{"zh":"标注","en":"Labels"},"default":true}]},{"slug":"seashell","plate":"48","title":{"zh":"壳口一行行画出的花纹","en":"A Pattern Painted One Line at a Time"},"kicker":{"zh":"贝壳的花纹","en":"Seashell patterns"},"summary":{"zh":"芋螺壳上的三角形，是在壳口边缘一行一行画上去的。每一行由边缘上的细胞决定：一处变强，就压住旁边。","en":"The triangles on a cone shell are painted at the edge of its opening, one line at a time. Each line is set by the cells along that edge: where one grows strong, it holds its neighbours back."},"description":{"zh":"贝壳只在壳口生长。新长出的每一窄条壳，都记下那一刻壳口边缘上色素的样子。一圈圈长下去，壳面就成了一张时间的图。","en":"A shell grows only at its lip. Each new strip of shell keeps the pigment the lip carried at that moment. 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Its columns are where the two basis arrows land; its determinant is the factor by which areas grow."},"description":{"zh":"一个 2 × 2 矩阵把整个平面一起搬动：网格线仍然笔直、平行、等距，原点不动。矩阵的两列，就是两根基准箭头 î 和 ĵ 落到的位置。单位正方形变成平行四边形，面积放大的倍数就是行列式。","en":"A 2 × 2 matrix moves the whole plane at once: grid lines stay straight, parallel and evenly spaced, and the origin stays put. The matrix’s two columns are where the basis arrows î and ĵ land. 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One turn of the handwheel, one stitch."},"description":{"zh":"手缝一分钟只有几十针。缝纫机的针眼开在针尖上，上面一根线、下面一根线，在布的中间互相套住，一分钟能缝几百针。这里的模型是一台黑漆铸铁的家用缝纫机，金色贴花，手轮、镀镍针杆和压脚，布下面是旋梭和梭芯。","en":"By hand, a few dozen stitches a minute. A sewing machine has its needle’s eye at the point and two threads, one above the cloth and one below, that lock in the middle of it, hundreds of times a minute. The model is a black japanned household machine with gold decals; the hook and bobbin sit under the cloth."},"hall":{"key":"classic","name":{"zh":"经典机器","en":"Classic Machines"}},"layer":{"key":"technology","name":{"zh":"技术","en":"Technology"}},"field":"making","url":{"zh":"https://world.lapla.si/zh/sewing/","en":"https://world.lapla.si/en/sewing/"},"embed":{"zh":"https://world.lapla.si/embed/zh/sewing/","en":"https://world.lapla.si/embed/en/sewing/"},"markdown":{"zh":"https://world.lapla.si/zh/sewing/index.html.md","en":"https://world.lapla.si/en/sewing/index.html.md"},"card":"https://world.lapla.si/cards/sewing.webp","chapters":[{"id":"cover","n":0,"title":{"zh":"缝纫机与锁式线迹","en":"The Lockstitch Sewing Machine"}},{"id":"problem","n":1,"title":{"zh":"手缝有多慢","en":"How Slow Sewing by Hand Is"}},{"id":"needle","n":2,"title":{"zh":"针眼在针尖","en":"The Eye at the Point"}},{"id":"lockstitch","n":3,"title":{"zh":"一针是怎么锁住的","en":"How One Stitch Locks"}},{"id":"feed","n":4,"title":{"zh":"送布牙","en":"The Feed Dogs"}},{"id":"timing","n":5,"title":{"zh":"转一圈，缝一针","en":"One Turn, One Stitch"}},{"id":"apart","n":6,"title":{"zh":"拆开来看","en":"Taken Apart"}},{"id":"inside","n":7,"title":{"zh":"机身里面","en":"Inside the Machine"}},{"id":"changed","n":8,"title":{"zh":"它改变了什么","en":"What It Changed"}},{"id":"lab","n":9,"title":{"zh":"自己缝几针","en":"Sew a Few Stitches"}}],"params":[{"id":"xray","kind":"toggle","label":{"zh":"透视","en":"X-ray"},"default":false},{"id":"labels","kind":"toggle","label":{"zh":"标注","en":"Labels"},"default":true}]},{"slug":"lidar","plate":"F11","title":{"zh":"激光雷达","en":"Lidar"},"kicker":{"zh":"尖端设备","en":"Frontier machines"},"summary":{"zh":"车顶上的激光雷达给光计时：一个脉冲来回 6.67 纳秒就是 1 米。128 束激光转一圈，四周的街道变成几十万个带坐标的点。","en":"A lidar on a car’s roof times light: 6.67 nanoseconds there and back is one metre. 128 beams spin, and the street around turns into hundreds of thousands of points with coordinates."},"description":{"zh":"自动驾驶汽车和机器人用激光雷达看三维：激光脉冲射出去、弹回来，记下用了多久，就知道多远。一列激光转起来，每秒测出两百多万个点。这里是一条 1:100 的街道模型，地上和墙上的点都是按真实的光束角度算出来的；旁边是按原大剖开的传感器头。","en":"Self-driving cars and robots see in 3D with lidar: a laser pulse goes out, bounces back, and the time it took gives the distance. A column of lasers spins and measures over two million points a second. 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Inside it is the earliest geared calculator known. It was made around the second century BC, it holds astronomical cycles in its tooth counts, and a turn of its crank works out, for any day, where the Sun and Moon stand, the phase of the Moon, the month of the calendar and the eclipses that may come. The model follows the reconstruction published by the UCL research team in 2021: a wooden case, bronze plates and gears, the zodiac and the display of the Cosmos at the front and two spiral dials at the back."},"hall":{"key":"classic","name":{"zh":"经典机器","en":"Classic Machines"}},"layer":{"key":"technology","name":{"zh":"技术","en":"Technology"}},"field":"sky","url":{"zh":"https://world.lapla.si/zh/antikythera/","en":"https://world.lapla.si/en/antikythera/"},"embed":{"zh":"https://world.lapla.si/embed/zh/antikythera/","en":"https://world.lapla.si/embed/en/antikythera/"},"markdown":{"zh":"https://world.lapla.si/zh/antikythera/index.html.md","en":"https://world.lapla.si/en/antikythera/index.html.md"},"card":"https://world.lapla.si/cards/antikythera.webp","chapters":[{"id":"cover","n":0,"title":{"zh":"安提基西拉机械","en":"The Antikythera Mechanism"}},{"id":"wreck","n":1,"title":{"zh":"海底的一团铜","en":"A Lump of Bronze from the Sea"}},{"id":"sky","n":2,"title":{"zh":"对不齐的周期","en":"Cycles That Don’t Line Up"}},{"id":"crank","n":3,"title":{"zh":"转动的是时间","en":"Turning Time"}},{"id":"trains","n":4,"title":{"zh":"齿数就是周期","en":"Tooth Counts Are Periods"}},{"id":"pinslot","n":5,"title":{"zh":"月亮的快与慢","en":"The Moon Speeds Up and Slows Down"}},{"id":"phase","n":6,"title":{"zh":"月相球","en":"The Moon Ball"}},{"id":"back","n":7,"title":{"zh":"背面的两个螺旋","en":"Two Spirals on the Back"}},{"id":"planets","n":8,"title":{"zh":"行星：证据和复原","en":"The Planets: Evidence and Reconstruction"}},{"id":"apart","n":9,"title":{"zh":"拆开来看","en":"Taken Apart"}},{"id":"changed","n":10,"title":{"zh":"它改变了什么","en":"What It Changed"}},{"id":"lab","n":11,"title":{"zh":"自己转","en":"Turn It Yourself"}}],"params":[{"id":"year","kind":"slider","label":{"zh":"年份","en":"Year"},"min":-260,"max":-40,"step":1,"default":-204},{"id":"survive","kind":"toggle","label":{"zh":"只看留存","en":"Surviving only"},"default":false},{"id":"found","kind":"toggle","label":{"zh":"出水时的样子","en":"As found"},"default":false},{"id":"back","kind":"toggle","label":{"zh":"看背面","en":"Show the back"},"default":false},{"id":"labels","kind":"toggle","label":{"zh":"标注","en":"Labels"},"default":true}]},{"slug":"hat","plate":"M14","title":{"zh":"只用一种形状，永不重复","en":"One Shape, Never Repeating"},"kicker":{"zh":"非周期单砖：帽子","en":"The hat, an aperiodic monotile"},"summary":{"zh":"一块由 8 个风筝形拼成的十三边形，可以铺满整个平面，但无论怎样铺，图案都不会周期性地重复。","en":"A thirteen-sided shape made of eight kites covers the whole plane, yet however it is laid, the pattern never repeats periodically."},"description":{"zh":"只用一种形状铺满平面，而且图案永远不会周期性地重复：这样的形状叫非周期单砖。人们找了五十多年，2023 年找到了「帽子」，一块由 8 个风筝形拼成的十三边形。","en":"A single shape that covers the plane, but only in patterns that never repeat periodically, is called an aperiodic monotile. The search took more than fifty years. 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Every map projection gives something up: area, angles, distance or straight lines."},"description":{"zh":"把地球仪的皮剥下来铺平，一定会撕开或拉伸。球面有曲率，平面没有，所以每张世界地图都要选择保留什么。","en":"Peel the skin off a globe and press it flat, and it tears or stretches. 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