He Drew a Person and Got a Machine

The listener is a child; the reader is a parent. This page is here so you can answer the questions your child asks after the story. The story script is available through the script button during playback.

What this is about

What Alan Turing drew in 1936 was not a machine but a person. He turned what a human being actually does with paper and pencil into an extremely simple picture. In the words of our source: "He intended it as a representation of human computation" (DOI: 10.1093/oso/9780198747826.003.0049).

And what he proved with that picture was not that something can be done, but that it cannot: the Hilbertian Entscheidungsproblem can have no solution — that is stated in the summary of Turing's own paper (DOI: 10.1093/oso/9780198250791.003.0005).

The irony that follows in the same source is where this episode lands: "By a nice irony it came to define what is achievable by non-human computers and has become deeply embedded in modern computer science."

What actually happened

• In 1936 Turing invented a mathematical model of computation, known today as the Turing machine. He had two intentions — to represent human computation, and to serve as a vehicle for refuting a central part of David Hilbert's programme to mechanize mathematics (DOI: 10.1093/oso/9780198747826.003.0049).
• Turing's own definition: "According to my definition, a number is computable if its decimal can be written down by a machine." He also showed that the computable numbers do not include all definable numbers, giving an example of a definable number that is not computable (DOI: 10.1093/oso/9780198250791.003.0005).
• The conclusion of that same summary: "it is shown (§11) that the Hilbertian Entscheidungsproblem can have no solution." Turing himself notes that Alonzo Church, using a differently defined notion of "effective calculability," reached similar conclusions about the same problem (same DOI).
• Emil Post had independently arrived at a substantially similar analysis by 1936. Post's "problem solver" worked in a "two way infinite sequence of spaces or boxes," where a box "admitted of but two possible conditions" — empty, or holding a single mark — and followed "a fixed unalterable set of directions" with five primitive acts: see whether the current box is marked, erase, mark, move right, move left (DOI: 10.1093/oso/9780198250791.003.0006).
• The paper contained mistakes. Turing corrected some of them in a short note published in the Proceedings of the London Mathematical Society a few months after the original. Post's critique followed in 1947 (same DOI).
• One example is enough to show what a Turing machine is. The one our source uses is a machine for deciding which whole numbers, written in binary, are multiples of 3 — 105 is 1101001, and following those digits from node to node gives the answer (DOI: 10.1093/oso/9780198747826.003.0049).
• On 21 June 1948 the drawing became hardware. The first electronic universal stored-program computer ran its first program; built in Manchester, it was the world's first universal Turing machine in hardware. It was called Baby (DOI: 10.1093/oso/9780198747826.003.0029).
• In October 1945 Turing was recruited by the National Physical Laboratory to lead computer development. His design, the ACE (Automatic Computing Engine), was idiosyncratic but highly effective; the Pilot ACE, completed in 1950, was the fastest medium-sized computer of its day (DOI: 10.1093/oso/9780198747826.003.0030).

Questions your child may ask

"So he didn't actually build it?" Not in 1936. It was a drawing on paper — a tool for thinking, not a product. The real machine came twelve years later.

"Why did he watch a person?" Because nobody had ever defined what "calculating mechanically" actually means. To make a definition, Turing looked at the one clear example: a human being. Look, erase, write, move along — realising that this is all of it is the discovery.

"He proved it can't be done? Is that good?" Yes. Knowing for certain that something is impossible is knowledge too. It stops people spending their lives chasing it. And the tool he built to prove it ended up defining the computer.

"Did Turing do it all alone?" No. Church reached the same conclusion by another route, and Post arrived at almost the same picture separately. Several people reaching the same place at the same time, without knowing about each other, is not rare in science. This episode puts that in the story on purpose.

"There were mistakes in the paper?" There were. And Turing published corrections himself. A good line for a child: "Fixing what you got wrong and publishing it again is part of the job too."

"Why was it called Baby?" Our source only gives the name ("Fittingly, it was called simply 'Baby'"). It was a small prototype, but we have no evidence for the reason, so the story just passes on the name.

Ideas inside the story

• Defining things — sometimes you must fix exactly what the question means before you can answer it.
• Proofs of impossibility — finding out that there is none is a result.
• A tool outgrowing its purpose — a model built to refute something became the foundation of a field.

What is established and what is not

Well established The 1936 model and its two intentions; that the Entscheidungsproblem has no solution; the existence of non-computable numbers; Church's independent conclusion and Post's independent model; the errors in the paper and Turing's own corrections; Baby in Manchester on 21 June 1948; the 1945 ACE design.

What this piece was careful about Turing's codebreaking at Bletchley Park is not included. It is famous, but it is a different thread from this episode's subject (what computation is), and it is not the centre of the sources we collected. It deserves its own episode.

Deliberately left out — a note for parents In 1952 Turing was arrested and tried for being gay. The court convicted him and sentenced him to chemical castration. Our source calls this "disgraceful treatment by the nation that he had done so much to save" (DOI: 10.1093/oso/9780198747826.003.0010). He died two years later.

This is not in the child's story — not to hide it, but because the context a young child would need (the law of the time, sexual orientation, state violence) cannot be handled honestly inside the story. When and how to tell it is your call. If your child hears about it somewhere and asks, a good place to start is: "The law itself was wrong then. The country has since apologised for it."

Sources and what followed

Source papers

• On Computable Numbers, with an Application to the Entscheidungsproblem. DOI: 10.1112/plms/s2-42.1.230 (1937)
• On Computable Numbers, with an Application to the Entscheidungsproblem (1936). DOI: 10.1093/oso/9780198250791.003.0005 (2004)
• On Computable Numbers: Corrections and Critiques. DOI: 10.1093/oso/9780198250791.003.0006 (2004)
• Decidability and the Entscheidungsproblem. DOI: 10.1093/oso/9780198747826.003.0049 (2017)
• Baby. DOI: 10.1093/oso/9780198747826.003.0029 (2017)
• ACE. DOI: 10.1093/oso/9780198747826.003.0030 (2017)
• Crime and punishment. DOI: 10.1093/oso/9780198747826.003.0010 (2017)

What followed

• The drawing became hardware. On 21 June 1948 Manchester's Baby ran its first program and became the world's first universal Turing machine in hardware. Every computer today stands in that line (DOI: 10.1093/oso/9780198747826.003.0029).
• Turing designed machines too. At the National Physical Laboratory from 1945 he designed the ACE; the 1950 Pilot ACE was the fastest of its size (DOI: 10.1093/oso/9780198747826.003.0030).
• Impossibility became a discipline. "What cannot be computed" became one axis of computability theory — and together with the Boolean algebra of this episode's companion piece on Shannon (1938), it forms one of the two pillars under the modern computer.

Things to try together

• Build a paper Turing machine. Draw a row of squares on graph paper and use coins or stickers as "marks." There are only five rules: look / erase / mark / move right / move left. You write a rule table, and your child follows it like a robot. The whole point is "don't think — just read the table."
• Play "can you write that as rules?" Take something your child does well — brushing teeth, putting on shoes — and have them write it in very small steps. It always takes far more steps than expected. That is exactly the problem Turing ran into.
• Finding out something is impossible is also finding out. When your child discovers something cannot be done, try saying "you found out it can't be done" instead of "it didn't work." That is this episode's whole point.