Explore. The ladder of lengths
Figure 1 sets one rung for each power of ten, from the Planck length to the edge of the observable universe, about sixty-one in all. A designer chooses the rung where a world’s physics stops, and that floor fixes what the world can hold.
Each rung is a place where a world’s physics could stop, and wherever the designer stops it, everything above has to be built from what lies there.
The floor of a world
10to the power −35 mthe Planck length
All 61 rungs above it have to be built from what lies there.
It marks the scale at which gravity and quantum theory can no longer both be trusted, which is a fact about the theories.
A deep world lets life arise from chemistry and makes every body as costly as the matter it is made of.
A world shallow beneath life makes minds cheap, and it may never produce them.
A world too shallow to hold anyone fails at the one thing that matters, however cheaply it runs.
Put it at
The rungs the chapter names
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The edge of the observable universeabout 4 × 10 to the power 26 meters
The choice can be pictured on a ladder of lengths, shown in Figure 1, which runs from the Planck length, about 10 to the power −35 meters, where present theories are expected to fail, to the edge of the observable universe, some 4 × 10 to the power 26 meters away.
Chapter 2, The Depth of a World, ¶ 10
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A machine a light-second acrossabout 3 × 10 to the power 8 meters
A machine a light-second across needs at least a second for any part to hear from the part opposite it.
Chapter 2, Many Machines, Two Clocks, ¶ 65
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The lake, a cubic kilometer of waterabout a kilometer each way
A lake of modest size, holding a cubic kilometer of water, contains something like 3 × 10 to the power 37 molecules, so no machine built of classical parts could ever hold its full quantum state.
Chapter 2, The Depth of a World, ¶ 7
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The boyabout 1.7 meters
The boy stands about thirty-five rungs up and some twenty-six below the top, nearer by this measure to the edge of everything than to the bottom of his own matter.
Chapter 2, The Depth of a World, ¶ 10
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Cells and neurons, near the level of lifearound a hundredth of a millimeter
…a world that is shallow beneath the level of life, whose bodies are built from coarse units arranged to do what neurons do, with nothing finer underneath.
Chapter 2, The Depth of a World, ¶ 13
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A switch the size of a small proteina few billionths of a meter
Working on every molecule at once, with a switch about the size of a small protein for each operation, it would weigh as much as seventeen Earths, a forecast of molecular engineering far beyond anything yet built.
Chapter 2, Ceilings and Costs, ¶ 25
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An atom, and just above it a molecule of waterabout 10 to the power −10 meters, and about 3 × 10 to the power −10
The nucleus of an atom sits some twenty rungs above the bottom, the atom five rungs above the nucleus, and a molecule of water just above the atom.
Chapter 2, The Depth of a World, ¶ 10
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The nucleus of an atomabout 10 to the power −15 meters
The nucleus of an atom sits some twenty rungs above the bottom, the atom five rungs above the nucleus, and a molecule of water just above the atom.
Chapter 2, The Depth of a World, ¶ 10
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The Planck lengthabout 10 to the power −35 meters
The Planck length, about 10 to the power −35 meters, is often described as the pixel size of the universe, and the description goes beyond what is known.