Indexing the archive…
Your Universe of Digital Possibilities
Dennard, 1974: shrink a transistor by k and it switches k times faster on k² less energy, so a chip’s power density stays put — the rule that ran computing for thirty years. Then the voltage hit Boltzmann’s limit of about 60 mV per decade, stopped falling near 2005, and the power wall arrived: clocks stalled near 4 GHz and the extra transistors had to stay dark. Shrink the node from 100 µm to less than an atom and watch the die.
Shrink every length and the voltage by 1/k: each transistor switches k times faster on k² less power, and k² more of them fit — so the power per area holds still. It held until the voltage could fall no further.
Every switch charges a capacitance C to V and dumps it: energy CV², f times a second. With V pinned and f stalled, shrinking L by k raises the power density by k² — the power wall.
Below threshold a transistor’s current is a Boltzmann tail: it can rise no faster than tenfold per S of gate voltage. Turning it off by five decades costs ≈ 0.3 V of swing — a floor the voltage cannot pass.
Not a law of nature but a schedule: components per chip doubling every year (1965), then every two (1975). Each doubling is a shrink of about √2 in feature size.
Rolf Landauer’s 1961 result: erasing one bit of information in a thermal environment costs at least kBT ln 2 joules — irreversibly dissipated as heat. This is the bridge between information theory and thermodynamics: information is not just abstract, it is physical.
The Lemuel grammar: a quantity as a power of body size. On log–log axes every allometric law is a straight line whose slope is the exponent b — fitted, on every instrument of the edition, from the sizes you visit.
The ninth size is the smallest the edition builds by hand. Moore counted the transistors (1965); Dennard showed why shrinking them was free (1974); Boltzmann’s kT, through the subthreshold swing, ended the free part around 2005; and the same kT, through Landauer, sets the floor no switch can go below. The Demon pays that floor for every bit it forgets; The Circuit wires the switches; the last size, The Mountain, asks what sets the size of the atoms the transistor runs out of.