Why Seven Hills

The paper next door measures Sheffield’s hills and finds exactly seven, at a bar chosen so that it does. The obvious complaint is that this is circular. The better question, which took longer to reach, is why the tradition settled on seven — and whether anybody, anywhere, ever got that number by counting.

The answer appears to be no. Not in Sheffield, not in Norfolk, and not in Rome.

1. What four thousand books say

Gazetteers, county histories, topographical dictionaries and English travel guides on the Internet Archive published before Orwell wrote — 4,180 of them, 4,479 MB of transcribed text — counted for the phrase “N hills”. If the number tracked terrain, small counts should dominate and fall away smoothly: most places have two or three hills worth mentioning, few have nine.

For two, three, four and five, that is exactly what happens.

“Seven hills” is nearly as common as “three hills” — 291 against 321 — where the curve that fits two, three, four and five says seven should barely occur at all. Counted by book, which no one talkative volume can inflate, the jump is the same shape: “six hills” appears in 25 texts and “eight hills” in 23, with “seven hills” in 150 between them.

Two numbers stand out in raw count, and only two: seven, and ten — the indivisible one and the round one. Eleven occurs three times in the whole 4,479 MB. Numbers people count are two to five, and they decay. Numbers people choose are seven and ten.

2. It is hills, not seven

The obvious objection is that English simply likes the number seven and hills inherit the preference. That is testable: run the identical count over the identical books for eleven other countable things, fit each one against itself, and measure how far its seven departs from its own curve. A noun that is merely common cannot inflate its own score that way.

A straight-line fit runs low for everybody, so the rows are only meaningful against each other. Churches is the best-measured control — 25,080 mentions of “two churches” alone — and its own seven sits 1.8× above its trend, which is what a noun people genuinely count looks like. Gates, arches and fields sit at or below theirs. Hills runs a hundred times over.

Hills lead. Second place belongs to windmills and should be ignored: 3 occurrences divided by a prediction near zero will always make a large number, and a ratio on that little is arithmetic rather than evidence. The row under it gives the game away. Oaks is Sevenoaks — a town in every gazetteer of England — and its column is bent by place-names throughout, Three Oaks and Four Oaks included. It outnumbers hills on the raw count, 440 to 291, which makes it a poor control and good evidence: the two nouns that depart furthest from their own trend, once the thin row is set aside, are both naming, not counting. And the effect is graded: several nouns below them sit a few times above their own trend. Hills sits a hundred times above its own.

The same scepticism is owed to the top row, so for the top row alone the sweep keeps the sentence each hit sits in. 91 of the 291 turn out to be back-of-book index entries — page references, not claims about ground. Of the 200 that are prose: 72 are Rome, 34 are cities outside England claiming the same thing, 29 are English burial mounds, 20 are an English town’s civic claim, 6 carry Seven Hills as a bare place-name, and 1 is Laodicea, out of a scripture gazetteer. The remaining 38 match none of those patterns and were read one by one: mostly gazetteer entries too broken by OCR to place, and not one of them describes anybody counting.

It is the 34 abroad that are worth the reading, because of where they go. The phrase does not stay in England, and it does not stay with Rome: it is attached in these books to Lisbon, to Prague, to Constantinople, to the hill forts of the Bombay Deccan, and to Providence, Rhode Island. A New England tourist handbook gives Providence seven hills in the same sentence-shape an English gazetteer gives them to Durham. That is what a portable formula looks like — and it is the same ten mentions of Providence arriving from ten separate scans of one handbook, which is also what the corpus looks like when you stop counting mentions and start counting books.

3. Rome never counted to seven either

The assumption under every imitation is that Rome at least has a real seven. It does not, and never did. The oldest layer is the Septimontium, a festival whose name means seven mounts and which Varro presents, in Platner and Ashby’s summary, as the name the place carried before it was called Rome. Four ancient lists survive and the independent ones disagree: seventeen distinct names between them, of which only the Palatine is on all four. The Capitoline, the most famous hill in Rome, is on one under its own name — Lydus’s “Tarpeian” would make it two.

And Festus’s version has eight names. Platner and Ashby’s response is the whole thesis in a sentence: “one of these eight names must obviously be omitted” — and they nominate Subura, on the grounds that it is “in no sense a mons”. An antiquarian striking a name to preserve a number. And their verdict on the ancient lists is that Roman antiquarians believed the festival marked the taking in of “seven hills or parts of hills, but … they differed as to which hills these were”: the number first, the hills recruited afterwards.

4. English soil says it out loud

Long before any English town compared itself to Rome, Seven Hills was a field-name for a group of burial mounds — and in every case the source recording the name also records that the name is wrong.

their sepulchres … are now called the Seven Hills, though there are many more

Fornham St Genevieve, Suffolk — Blomefield, 1739

Near Snarehill Lodge are twelve large barrows, called the Seven Hills

East Harling, Norfolk — The Scientific Tourist, 1818

The wording is Blomefield’s, and it travels: five books in this corpus carry the Fornham barrows with the correction attached, from 1781 to 1843 and one later still — the earliest of them Mostyn John Armstrong, copying Blomefield almost word for word forty years on. The prose around it drifts as gazetteers copy from each other — the Flemings are put to the sword in one and routed in another — but the name arrives with though there are many more every time, and not one of them proposes a better name. The sharpest instance is a single passage of Lewis’s Topographical Dictionary of 1831, describing two groups of mounds a few miles apart: “a range of eleven tumuli”, and “the most remarkable group of them being that called the Seven Hills”. Same author, same page, same kind of mound. Eleven when he is counting. Seven when he is naming.

Rome does it at scale. The Scripture Gazetteer of 1838 notes that the city was called Septicollis from the time of Servius Tullius, “but from the time of Aurelian it extended over ten hills” — and went on being the City of Seven Hills for fifteen centuries.

5. Sheffield is last in the queue

Sheffield’s entry is Orwell’s diary and is not from this corpus — because the corpus has no such entry. The sweep above is not silent on this, as this note used to say it was: it keeps the sentence behind every one of the 291 “seven hills”, and Sheffield is named in none of them. The towns making the claim are Bristol, Durham, Edinburgh, Norwich, Bath. That is a shelf of general gazetteers rather than a search of Sheffield’s own shelf, so a second sweep went over every digitised text catalogued to Sheffield, Hallamshire, Yorkshire or Derbyshire and published before Orwell wrote. It finds no attachment of the phrase to Sheffield either.

Sheffield is 147 years behind Bristol, and sixty behind a West Riding mill town of “upwards of 12,000 souls”. Its own civic guidebook, Pawson & Brailsford’s Illustrated Guide to Sheffield of 1879, had every commercial reason to reach for Rome and did not: in 160,432 words the phrase appears not once, and its 3 mentions of Rome are the Papacy, a marble statue and a masonic order. It says the town “is situated in an amphitheatre of hills”, and offers a different boast altogether — that there was no street in the town from which the country could not be seen. Then it checks that, and admits it is no longer true.

6. Why that number

Seven occupies a window nothing else does. It has to be indivisible, or it decomposes into something ordinary: six hills are two threes, eight are two fours, and a set that splits stops being a signature. It has to be too big to check at a glance — grasping a quantity without counting tops out at about four, unless the items form a familiar pattern, and five is exactly that exception: a hand, a die face, a tally gate. Hold up a hand against “five hills” and the claim is settled in a second. Seven cannot be tested without enumerating, and enumerating hills means first deciding what a hill is.

And it has to be inside the named range. Eleven is Old English endleofan, “one left over”; Latin undecim, “one-and-ten”. The word announces that somebody counted to ten and had one in hand. A signature must look chosen; eleven looks arrived at.

Which leaves the largest prime that fits in ten fingers. And that does not merely agree with the ancient argument, it derives it.

The Pythagorean tradition called seven Athena, because within the decad it is neither factor nor product: in the Theology of Arithmetic, a compilation drawing on a lost work of Nicomachus, the heptad is Athena “because it is a virgin and unwed … and is born neither of mother (i.e. of even number) nor of father (i.e. odd number), but from the head of the father of all”. The wording most often quoted in English is not that one but W. Wynn Westcott’s, who has it as Minerva, “unmarried and virginal, begotten neither by a mother, i.e. even number, nor from a father, i.e. odd number” — handsomer, and worth knowing that it comes at third hand from a Victorian occultist rather than from a classicist. But a prime p within the decad is a factor of something within the decad exactly when 2p ≤ 10. Two, three and five all have children; 2 × 7 overshoots. Seven is barren precisely because it is the biggest prime that fits in ten fingers.

On Miller. The modern thing people reach for here is 7 ± 2, and it does not support this — Miller said so himself. His paper is a warning that a number recurring across unrelated experiments is a coincidence: “and that is a fundamental mistake, as I shall be at some pains to demonstrate”. The memory span of seven has since been revised down to about four, and the part that survives is chunking, which nobody quotes. The ceiling carrying this argument is ten fingers, not seven slots.

Method, and what would overturn it

Seven subject and title queries against the Internet Archive, each capped at 1,600 results, which makes this a sample of the shelf, restricted to texts published 1700 to 1936; 4,180 returned usable OCR, 4,479 MB of it. Phrases matched as a number-word or digit followed by the noun, case-insensitively, with the long ſ folded to s before matching, and “feven” read as “seven” — eighteenth-century OCR renders the long s as an f far more often than as the character itself, and until it did, this sweep could not see Barrett’s 1789 Bristol. Line-break hyphens are closed up too: a printer breaking a word leaves “se- pulchres”, or “se- ven hills”, and both were being missed. Trend fitted as a log-linear regression on N = 2–5 for each noun independently. The sweep is docs/beaky/sevens.py; its output is src/_data/sevens.json, which is where every count, ratio and date on this page is read from. The attestation table is the one thing the sweep cannot supply: it keeps concordances for “seven hills” and for no other row, and a concordance is not a publication date, so the earliest claim for each town was found by hand and each row is a book you can open. Barrett’s Bristol is the one that moved, and it moved because of the long ſ.

The counts are not independent observations, either: Fornham’s sentence is copied forward through five gazetteers and each copy is counted, so the sevens cluster by borrowed wording — which is the thesis, but means 291 books do not say this 291 times. It is books, not newspapers — the British Newspaper Archive does not open to a script, and a civic boast lives in a local paper as readily as in a county history. The two-to-five baseline includes ordinary description, which is what makes it a fair null but not a baseline of claims. A good share of the sevens are Rome itself, which is the source rather than a confound. And it is OCR: the absolute counts are soft, the shape is not. How soft is now measurable, because the queries are capped and ranked by relevance and the Archive does not return the same subset twice — consecutive runs of this sweep moved individual nouns by around a tenth, churches by rather more. Every figure on this page is read from the last run’s output, and that run’s identifier list is written into it, so the numbers can at least be checked against the books that produced them.

It would be overturned by a pre-1789 English civic claim, by another countable landscape feature that beats hills on the same test, or by any seven-hills list anywhere that turns out to have been arrived at by counting.