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  "events": [ {
    "tStartMs": 1040,
    "dDurationMs": 3680,
    "segs": [ {
      "utf8": "Have you ever noticed that big windows on \nbuildings are bendy and wavy – it’s like  "
    } ]
  }, {
    "tStartMs": 4720,
    "dDurationMs": 3600,
    "segs": [ {
      "utf8": "the stereotypical look of modern architecture – \nand have you ever looked at those wavy windows  "
    } ]
  }, {
    "tStartMs": 8320,
    "dDurationMs": 3520,
    "segs": [ {
      "utf8": "and wondered… if the reflections are so \nwobbly and distorted from the outside,  "
    } ]
  }, {
    "tStartMs": 11840,
    "dDurationMs": 2800,
    "segs": [ {
      "utf8": "why can people see just fine \nlooking out from the inside? "
    } ]
  }, {
    "tStartMs": 14640,
    "dDurationMs": 3760,
    "segs": [ {
      "utf8": "\u2028In fact, when I gently touch this window \nfrom the outside, I can easily distort the  "
    } ]
  }, {
    "tStartMs": 18400,
    "dDurationMs": 3360,
    "segs": [ {
      "utf8": "image in the window, but nothing of the sort \nhappens when looking out from the inside."
    } ]
  }, {
    "tStartMs": 21760,
    "dDurationMs": 3040,
    "segs": [ {
      "utf8": "It turns out this wavy window \nparadox is explained by a key  "
    } ]
  }, {
    "tStartMs": 24800,
    "dDurationMs": 2640,
    "segs": [ {
      "utf8": "difference between the physics \nof looking out and looking in."
    } ]
  }, {
    "tStartMs": 27440,
    "dDurationMs": 4000,
    "segs": [ {
      "utf8": "The fact that windows work at all is a minor \nmiracle of physics: light behaves like a wave,  "
    } ]
  }, {
    "tStartMs": 31440,
    "dDurationMs": 3200,
    "segs": [ {
      "utf8": "so when it passes from a material where \nit’s traveling one speed (like air) to  "
    } ]
  }, {
    "tStartMs": 34640,
    "dDurationMs": 3680,
    "segs": [ {
      "utf8": "a material where it’s traveling another (like \nglass), it ends up bending towards the slower  "
    } ]
  }, {
    "tStartMs": 38320,
    "dDurationMs": 3200,
    "segs": [ {
      "utf8": "material. There’s a mathematical formula \ncalled Snell’s law for the amount light  "
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  }, {
    "tStartMs": 41520,
    "dDurationMs": 3520,
    "segs": [ {
      "utf8": "bends - it depends on the incoming angle and \nthe relative speed of light in the materials,  "
    } ]
  }, {
    "tStartMs": 45040,
    "dDurationMs": 2960,
    "segs": [ {
      "utf8": "and while the details are important if \nyou’re, say, designing a camera lens,  "
    } ]
  }, {
    "tStartMs": 48000,
    "dDurationMs": 2800,
    "segs": [ {
      "utf8": "they aren’t important at all for our \nwindow question - what matters to us is  "
    } ]
  }, {
    "tStartMs": 50800,
    "dDurationMs": 4640,
    "segs": [ {
      "utf8": "that the formula is completely symmetric - if the \nmaterials are reversed, then the angles reverse."
    } ]
  }, {
    "tStartMs": 55440,
    "dDurationMs": 2960,
    "segs": [ {
      "utf8": "Which means, for light passing through \na glass window, the light first passes  "
    } ]
  }, {
    "tStartMs": 58400,
    "dDurationMs": 3440,
    "segs": [ {
      "utf8": "from air to glass and is bent inwards, \nthen passes from the glass back to the  "
    } ]
  }, {
    "tStartMs": 61840,
    "dDurationMs": 3600,
    "segs": [ {
      "utf8": "air and is corrected back outwards the exact \nsame amount… light passing through a window  "
    } ]
  }, {
    "tStartMs": 65440,
    "dDurationMs": 3520,
    "segs": [ {
      "utf8": "ends up traveling the exact same direction \nthat it started, just offset a little bit."
    } ]
  }, {
    "tStartMs": 68960,
    "dDurationMs": 3040,
    "segs": [ {
      "utf8": "So as long as you have air sandwiching \nboth sides of a layer of glass,  "
    } ]
  }, {
    "tStartMs": 72000,
    "dDurationMs": 2960,
    "segs": [ {
      "utf8": "the glass can rotate or bend quite \na lot and not really affect your  "
    } ]
  }, {
    "tStartMs": 74960,
    "dDurationMs": 3680,
    "segs": [ {
      "utf8": "ability to see through it! In simple \nterms, you can see through a window. "
    } ]
  }, {
    "tStartMs": 78640,
    "dDurationMs": 2080,
    "segs": [ {
      "utf8": "If the glass surfaces aren’t perfectly parallel,  "
    } ]
  }, {
    "tStartMs": 80720,
    "dDurationMs": 4320,
    "segs": [ {
      "utf8": "then the relative angles do change a bit: if the \nsurfaces are, say, a degree off from one another,  "
    } ]
  }, {
    "tStartMs": 85040,
    "dDurationMs": 3520,
    "segs": [ {
      "utf8": "then the image you see will be displaced by \nabout half a degree, so if the window varies  "
    } ]
  }, {
    "tStartMs": 88560,
    "dDurationMs": 3920,
    "segs": [ {
      "utf8": "in thickness you will see some distortion, \nlike what you see looking out of old windows."
    } ]
  }, {
    "tStartMs": 92480,
    "dDurationMs": 2720,
    "segs": [ {
      "utf8": "However, when you’re looking at the \nwavy reflections of trees from the  "
    } ]
  }, {
    "tStartMs": 95200,
    "dDurationMs": 3120,
    "segs": [ {
      "utf8": "outside of a building, you’re of course \nnot looking at light passing through the  "
    } ]
  }, {
    "tStartMs": 98320,
    "dDurationMs": 3920,
    "segs": [ {
      "utf8": "glass - you’re looking at light bouncing off \nthe glass, and that makes all the difference. "
    } ]
  }, {
    "tStartMs": 102240,
    "dDurationMs": 3680,
    "segs": [ {
      "utf8": "Reflections only involve one surface, so they \ndon't have a chance to get “corrected” the way  "
    } ]
  }, {
    "tStartMs": 105920,
    "dDurationMs": 3760,
    "segs": [ {
      "utf8": "light does on its way out through the back of \na window. A beam of light coming in at an angle  "
    } ]
  }, {
    "tStartMs": 109680,
    "dDurationMs": 4080,
    "segs": [ {
      "utf8": "relative to the glass bounces off at the same \nangle, just flipped, so a 1 degree deflection  "
    } ]
  }, {
    "tStartMs": 113760,
    "dDurationMs": 3440,
    "segs": [ {
      "utf8": "of the glass results in a 2 degree change in \nthe apparent position of the light source. For  "
    } ]
  }, {
    "tStartMs": 117200,
    "dDurationMs": 4400,
    "segs": [ {
      "utf8": "example, if you’re 10 meters away from a window, \na 1 degree deflection of the glass will move the  "
    } ]
  }, {
    "tStartMs": 121600,
    "dDurationMs": 4240,
    "segs": [ {
      "utf8": "apparent position of the sun vertically upwards \n70cm! You can see the same effect by tilting a  "
    } ]
  }, {
    "tStartMs": 125840,
    "dDurationMs": 3680,
    "segs": [ {
      "utf8": "laptop screen towards you - the apparent \npositions of reflections move upwards. "
    } ]
  }, {
    "tStartMs": 129520,
    "dDurationMs": 3280,
    "segs": [ {
      "utf8": "So if window glass is a little bit wavy or \ncurved the light passing through it will  "
    } ]
  }, {
    "tStartMs": 132800,
    "dDurationMs": 3760,
    "segs": [ {
      "utf8": "be essentially fine, but the images reflecting \noff of it will be moved around inconsistently.  "
    } ]
  }, {
    "tStartMs": 136560,
    "dDurationMs": 2480,
    "segs": [ {
      "utf8": "It doesn’t take much to move the \nreflection - gently touching a  "
    } ]
  }, {
    "tStartMs": 139040,
    "dDurationMs": 3120,
    "segs": [ {
      "utf8": "window can result in surprisingly large \ndistortions of the reflections in it!  "
    } ]
  }, {
    "tStartMs": 142160,
    "dDurationMs": 3040,
    "segs": [ {
      "utf8": "You can try it - gently - the next time \nyou’re in front of a window or mirror!"
    } ]
  }, {
    "tStartMs": 145200,
    "dDurationMs": 2720,
    "segs": [ {
      "utf8": "So the solution to the wavy window \nparadox is that the path of light  "
    } ]
  }, {
    "tStartMs": 147920,
    "dDurationMs": 3600,
    "segs": [ {
      "utf8": "passing through a window is miraculously \nresilient to deviations of the surface,  "
    } ]
  }, {
    "tStartMs": 151520,
    "dDurationMs": 3840,
    "segs": [ {
      "utf8": "while reflections off of it are not resilient. \nAnd during the day when it’s bright outside,  "
    } ]
  }, {
    "tStartMs": 155360,
    "dDurationMs": 3280,
    "segs": [ {
      "utf8": "if we’re outside a window looking in, we’re \ntypically looking at reflections, while if  "
    } ]
  }, {
    "tStartMs": 158640,
    "dDurationMs": 4320,
    "segs": [ {
      "utf8": "we’re inside we’re looking out through the window. \nAt nighttime, the situation is reversed and we’re  "
    } ]
  }, {
    "tStartMs": 162960,
    "dDurationMs": 4080,
    "segs": [ {
      "utf8": "more often looking at easily distorted reflections \nwhen we’re inside, and we’re looking in through  "
    } ]
  }, {
    "tStartMs": 167040,
    "dDurationMs": 4560,
    "segs": [ {
      "utf8": "the window from the outside.\u2028\u2028And that’s it: the \nnext time you successfully look through a window,  "
    } ]
  }, {
    "tStartMs": 171600,
    "dDurationMs": 6560,
    "segs": [ {
      "utf8": "whether in or out, remember to say thank \nyou to the symmetry of Snell’s Law!"
    } ]
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}