Part 1 — The Turing Machine

The Paper

On Computable Numbers (1936)

Alan Turing's paper defined computation itself: any algorithm can be run by a machine with a tape, a head, and a table of rules.

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The Big Idea

Universality

One machine can simulate any other by reading its description from the tape: the idea behind software.

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1939–1945

From Theory to Bletchley

In WWII Turing built the electromechanical Bombe to break Enigma — engineering, not a Turing machine, but the same mind.

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Why It Still Matters

The Legacy

Tape ≈ memory, head ≈ memory bus, rule table ≈ program, state ≈ CPU registers. Every dashboard after this one is an elaboration of these four parts.

Section A

A Turing machine that adds one

Program: binary increment. Tape starts at 1011 (11) and must end at 1100 (12).

state register

tape = 1011

decimal 11

⟶

target 1100 · 12

Infinite tape — both ends run on forever Head position 0 Symbol under head 1 Alphabet 0 · 1 · ␣

Step 0 / 0

running

State register

Current state

Read symbol

Write symbol

—

Move

—

Next state

—

q0Scan right to the end of the number.

q1Add 1, propagating the carry leftward.

q2Rewind left to the first digit.

HALTNo rule applies — the machine stops.

Transition table — the “program”

State	Read		Write	Move	Next

Nine rules, three states, three symbols. That is the entire “software” of this machine — and by Turing's universality argument, a table like this could itself be written onto the tape and interpreted by another machine.

Step log

What maps to what Tape → RAM Head → memory bus Rule table → program State → CPU registers Swap “one cell at a time” for “a 64-byte cache line at a time” and you have Part 2.

Section B

The Imitation Game (2014)

Where the film gets it right — and what the machine on screen actually was.

Benedict Cumberbatch as Alan Turing, Bletchley Park

Hut 8 · Government Code & Cypher School · 1939–1945

The film follows Turing through wartime Bletchley Park, where a team of cryptanalysts attacked the German Enigma cipher. The great clattering machine Turing builds on screen — the one he names “Christopher” after a boyhood friend — is the Bombe.

The Bombe was an electromechanical device: banks of rotating drums, each drum emulating one Enigma rotor, wired into chains of logical implication. Given a crib (a guessed fragment of plaintext), it spun through candidate rotor settings and stopped whenever it found one that did not contradict itself. Humans then checked the stops by hand.

Honest clarification The Bombe is not a Turing machine. Turing's 1936 machine is pure mathematics — an imaginary device invented to define what “computable” means and to prove some things are not. The Bombe is applied engineering — a special-purpose searcher, not programmable, with no tape and no stored program. The film compresses both into one story: the theorist of 1936 and the engineer of 1940 were the same man, but they were not building the same thing.

17,576

rotor positions per run (26³)

~20 min

wall-clock time per run

≈15 / s

positions tested per second

Bombe drum banks — each drum emulates one Enigma rotor

Section C

Mechanical rotation vs electronic clock

The same computation, seven orders of magnitude apart.

moving parts

Hard disk platter

7,200 rpm = 120 revolutions/second
One revolution takes 8.3 ms. Mass, inertia and air drag set the ceiling.

no moving parts

Modern CPU

4 GHz = 4,000,000,000 ticks/second
Electrons in silicon; the only real limits are heat and the speed of light.

simulated ticks since you opened this page

In the time the disk platter completes ONE revolution (8.3 ms), a 4 GHz CPU has ticked 33 MILLION times.

And the Bombe? It tested about 15 rotor positions per second — 17,576 positions took roughly twenty minutes of drums grinding round. A modern CPU could brute-force all 17,576 positions in a few microseconds: less time than it takes the disk platter to turn one degree.

Operations per second — log scale (base 10)

10⁰10²10⁴10⁶10⁸10¹⁰

Bomberotor positions tested

10^1.2

15 /s

Hard disk platterrevolutions at 7,200 rpm

10^2.1

120 /s

1980s CPUIntel 8086-class, ~5 MHz

10^6.7

5e6 /s

Modern CPUone core at 4 GHz

10^9.6

4e9 /s

Log scale is honest but merciless: the Bombe's bar looks only ~8× shorter than the modern CPU's, yet the real gap is 10⁹⋅⁴ ÷ 10¹⋅² ≈ 270,000,000×. Each 10% of bar width is one full power of ten. That compression is exactly why intuition about computer speed fails — and why the rest of this series measures things in nanoseconds.