Marchetti’s constant

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Marchetti's constant is the idea that people across history budget, on average, about an hour a day for travelling. Originally observed by Yacov Zahavi, it came from the observation that even as our means of transport sped up, instead of travelling less each day, we would just travel further. As in the sketch, this leads to a conclusion that the size of our cities increases partly according to how efficiently we can travel in and out—they generally increase to a size that maintains about an hour round-trip journey.

Cesare Marchetti observed that Greek villages and ancient walking cities, for example, as marked by ancient city walls, tend to share a radius of about 2.5km. Walking at a typical 5km/hr makes a one-hour round-trip journey. He also pointed out that: “Even people in prison for a life sentence, having nothing to do and nowhere to go, walk around for one hour a day, in the open.”

Unfortunately, if you live in London, the average round-trip seems to be an exception of 1h30 .

This is also known as the constant travel time budget hypothesis.

Also see:

Isochrones. It might be interesting to look at these according to transport method
Our senses are built to take in information at human pace

Image adapted from: Marchetti, C., 1994: Anthropological Invariants in Travel Behavior, Technological Forecasting and Social Change , 47 :75–88, Internal Publication, International Institute for Applied Systems Analysis.

Published 25 Nov 2018

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Isometric projection

Thesis, antithesis, synthesis

Isometric projection is a simple way to draw 3D shapes. The meaning of isometric is "equal measure," from the Greek words iso- for equal and metric for measure. So, in an isometric drawing, all three axes, x, y, and z, are scaled equally, giving a clear, undistorted view of an object in three dimensions. Except that isometric drawings can look a little odd and oversimplified. This is because of the lack of perspective, a visual distortion of 3D shapes we experience in the real world. In a perspective drawing, parallel lines converge in the distance towards a vanishing point, but in an isometric drawing, parallel lines stay parallel, and sizes don't get smaller in the distance. The lack of perspective in an isometric view can make it look artificial, but it always looks clear. I learned isometric drawing when studying engineering. Armed with a stack of isometric paper with a printed isometric grid, we had to reel off exercises involving drawing isometric views of 3D objects. And isometric projection is really handy for this. It can take a long time to build the skills to sketch a realistic 3D-looking object, perspective and all, but with isometric paper, you can quite quickly produce something that communicates to you or others what's in your head or on the workbench. Isometric projection is handy for boxy shapes—I chose an approximation of the Bauhaus Dessau building by Walter Gropius to show it. If you need curves and angles, just like with perspective drawings, it can help to draw more boxes around these areas and use them to align your curves and meeting points for your lines. Isometric views and their variations have had somewhat of a resurgence of late in video and board games. It turns out they're pretty helpful in map-based or city-building games such as Zynga's Farmville, Civilisation, or Sim City as the isometric view allows all parts of a scene to be viewed equally—in the distance or up close—while still seeing every detail in, say, a building, wherever it is. If you want to try some isometric drawings, making your own isometric grid paper is easy. Just draw equally-spaced vertical stripes and then a criss-cross of lines in both directions at 30 degrees from the horizontal. This gives a host of equilateral triangles and an easy base to start drawing your 3D objects. Or just download some templates online. You'll find that building up more complex shapes out of cubes is dead simple if you keep to the lines on the isometric grid. Just as in the drawing here, sometimes shapes drawn in isometric view lend themselves to curious optical effects. The lack of perspective can make the difference between heights and depths ambiguous. So, you can't always tell if two surfaces are at very different heights or if one is in the distance. The brilliant puzzle game Monument Valley uses this quirk of isometric projection to create mind-bending puzzles that are well worth a try. For instance, rotating a high surface can suddenly make a platform that extends far into the distance 🤯. Isometric-like projection can also help make impossible shapes, such as the Impossible Staircase, or Penrose stairs. Another type of projection, anamorphosis, creates a drawing that only looks correct from a particular viewpoint. Anamorphosis leads to some remarkable street art. Also see: 2.5D objects, including an old video of me drawing a sketchplanation Orthographic projection One-point perspective Two-point perspective Three-point perspective Atmospheric perspective Anamorphosis The Impossible Staircase, or Penrose stairs When drawn nice and faint, the isometric grid is an example of a ghost grid Isometric projection is quite the opposite of "draw what you see, not what you think." Foreshortening can be hard to get the hang of. Life is 3D—give edges thickness…Isometric projection is a simple way to draw 3D shapes. The meaning of isometric is "equal measure," from the Greek words iso- for equal and metric for measure. So, in an isometric drawing, all three axes, x, y, and z, are scaled equally, giving a clear, undistorted view of an object in three dimensions. Except that isometric drawings can look a little odd and oversimplified. This is because of the lack of perspective, a visual distortion of 3D shapes we experience in the real world. In a perspective drawing, parallel lines converge in the distance towards a vanishing point, but in an isometric drawing, parallel lines stay parallel, and sizes don't get smaller in the distance. The lack of perspective in an isometric view can make it look artificial, but it always looks clear. I learned isometric drawing when studying engineering. Armed with a stack of isometric paper with a printed isometric grid, we had to reel off exercises involving drawing isometric views of 3D objects. And isometric projection is really handy for this. It can take a long time to build the skills to sketch a realistic 3D-looking object, perspective and all, but with isometric paper, you can quite quickly produce something that communicates to you or others what's in your head or on the workbench. Isometric projection is handy for boxy shapes—I chose an approximation of the Bauhaus Dessau building by Walter Gropius to show it. If you need curves and angles, just like with perspective drawings, it can help to draw more boxes around these areas and use them to align your curves and meeting points for your lines. Isometric views and their variations have had somewhat of a resurgence of late in video and board games. It turns out they're pretty helpful in map-based or city-building games such as Zynga's Farmville, Civilisation, or Sim City as the isometric view allows all parts of a scene to be viewed equally—in the distance or up close—while still seeing every detail in, say, a building, wherever it is. If you want to try some isometric drawings, making your own isometric grid paper is easy. Just draw equally-spaced vertical stripes and then a criss-cross of lines in both directions at 30 degrees from the horizontal. This gives a host of equilateral triangles and an easy base to start drawing your 3D objects. Or just download some templates online. You'll find that building up more complex shapes out of cubes is dead simple if you keep to the lines on the isometric grid. Just as in the drawing here, sometimes shapes drawn in isometric view lend themselves to curious optical effects. The lack of perspective can make the difference between heights and depths ambiguous. So, you can't always tell if two surfaces are at very different heights or if one is in the distance. The brilliant puzzle game Monument Valley uses this quirk of isometric projection to create mind-bending puzzles that are well worth a try. For instance, rotating a high surface can suddenly make a platform that extends far into the distance 🤯. Isometric-like projection can also help make impossible shapes, such as the Impossible Staircase, or Penrose stairs. Another type of projection, anamorphosis, creates a drawing that only looks correct from a particular viewpoint. Anamorphosis leads to some remarkable street art. Also see: 2.5D objects, including an old video of me drawing a sketchplanation Orthographic projection One-point perspective Two-point perspective Three-point perspective Atmospheric perspective Anamorphosis The Impossible Staircase, or Penrose stairs When drawn nice and faint, the isometric grid is an example of a ghost grid Isometric projection is quite the opposite of "draw what you see, not what you think." Foreshortening can be hard to get the hang of. Life is 3D—give edges thickness

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