Draft: this lesson was written with AI help and has not yet been read by a human editor.
1 What your class asks
This lesson asks you to collect and organise data to answer a question about a population, and to analyse data by asking questions, challenging first guesses and drawing conclusions. The museum offers one method of counting letters to read a hidden message, and its warning about small samples. 1
Curriculum expectations, with their official codes
- D1.2 collect qualitative data and discrete and continuous quantitative data to answer questions of interest about a population, and organize the sets of data as appropriate, including using intervals
- D1.6 analyse different sets of data presented in various ways, including in histograms and broken-line graphs and in misleading graphs, by asking and answering questions about the data, challenging preconceived notions, and drawing conclusions, then make convincing arguments and informed decisions
2 The lesson
When is a count enough to draw a conclusion?
Look at the expectation about challenging preconceived notions. Count the letters in a short text and in a longer one, and compare how steady the results are before you decide what they show.
Go deeper
The method starts from a language, not from a message. Al-Kindi's treatise asks for a sample in the same language as the concealed message, about a skin's worth, in which each kind of letter is counted and the kinds are ranked from the most frequent downward 2. Next the shapes of the concealed message are sorted and counted, and the commonest shape is matched with the top letter of the sample, the next with the second, and so on 2. Then the author slows the rush at short messages: they may not contain every letter, and a letter unusually common in one passage may be balanced by another only in a longer text 2.
Why they did it
In his introduction, as the record reports it, al-Kindi says that earlier philosophers and thinkers used unfamiliar signs to restrict access to their books, and that recovery can help readers understand them 3. The record says his introduction places the usefulness in recovering meanings hidden by unfamiliar signs 3. That is the statement of purpose the record gives.
Often misunderstood
A tally can look like a machine that solves everything, but al-Kindi does not make the numbers his final verdict: a short message may depart from ordinary usage, and a guess needs checking against letter combinations and context 4. If two letters are guessed, he asks whether they can combine in that language, and contradictions prevent fixing a letter's identity merely because its frequency rank seemed suitable 5. The record adds that the method's textual conditions include language, cipher type, enough material and cross-checks 6.
Think about it
Al-Kindi warns that a short message may not contain every letter. You counted the letters in a short paragraph and in a long one. Which of your two tables do you trust more to match the usual pattern of the language, and why? What would you need to see before you trusted the short one?
Into the museum
- Al-Kindi's letter-frequency cryptanalysis: the steps of counting and matching in order, and his warning about short messages.
- Al-Kindi: what the museum's record says about the author and his letter analysis.
Try this
Read the record on al-Kindi's letter-frequency method. Count the letters in a paragraph of your choice, organise the counts in a table, and say what a short sample could get wrong.
3 Check yourself
Nothing here is marked or sent anywhere. It is for you.
In your own words: what does Al-Kindi's letter-frequency cryptanalysis have to do with this lesson?
Compare with the card
Counting letters to read a hidden message. Letters in a concealed message may change their names while repetition remains a clue. Al-Kindi describes counting letters in a sample of a known language, ranking them by use and comparing that ranking with the message's symbols. Numbers are not his final verdict: a short message may depart from ordinary usage, and a guess needs checking against letter combinations and context. What would you count first, and how long a sample would you want?
I can now
Notes
- 1. Ontario Ministry of Education, The Ontario Curriculum: Mathematics
- 2. Al-Kindi's cryptanalysis treatise — Damascus edition in Ilm al-ta'miya, 1987, p. 216
- 3. Al-Kindi's cryptanalysis treatise — Damascus edition in Ilm al-ta'miya, 1987, pp. 213–214
- 4. Al-Kindi's cryptanalysis treatise — Damascus edition in Ilm al-ta'miya, 1987, pp. 216–218
- 5. Al-Kindi's cryptanalysis treatise — Damascus edition in Ilm al-ta'miya, 1987, p. 217
- 6. Al-Kindi's cryptanalysis treatise — Damascus edition in Ilm al-ta'miya, 1987, pp. 216–219, 225–226