Chapter 1 · The limestone skyline
The wall of decades: why 28 people in Roman Dacia are recorded at 50 and none at 49
Every block in the stage beside you is a named or commemorated person from an inscription of the Roman province of Dacia (modern Transylvania, Banat and Oltenia in Romania), broadly dated to the Roman period (the province lasted from 106 to 271 CE; some stones are only roughly dated), whose age in years is recorded as a whole number in the Epigraphic Database Heidelberg (EDH). Out of 504 age records from the province, 380 have a whole-number age in years in the EDH table, with no gap marked. That does not guarantee every numeral is read securely: where the text has a restoration or a question mark, the person’s card says so.
In a population that tracks exact birth years, one-fifth (20.0%) of adult ages at death end in zero or five, and one-tenth (10.0%) end in zero. On the tombstones of Roman Dacia, across the standard adult demographic window of ages 23 to 62, 72.1% (147 of 204) end in 0 or 5, and nearly half — 49.0% (100 of 204) — are carved as an exact multiple of ten: XX, XXX, XL, L, LX. On the index proposed by the historian Richard Duncan-Jones (1977), where 0 means no rounding and 100 means every adult age falls on a multiple of 5, Dacia scores 65.4.
D(is) M(anibus) / M(arcus) Aur(elius) Scenobarbus / vix(it) ann(os) C / M(arcus) Aur(elius) Si[---] (HD046115, Alburnus Maior / Roșia Montană)
“To the Spirits of the Departed. Marcus Aurelius Scenobarbus lived 100 years (C).” — The only centenarian in EDH’s person table for Dacia, in the Apuseni gold district. The same table has no age of 91, 92, 93, 94, 96, 97, 98 or 99.
The chasm between the decade towers and their immediate neighbours shows how mourners spoke to the stonecutter: 17 people are recorded at age 20 (XX) against four at 19 and three at 21; 15 people are recorded at 25 (XXV) against one at 24 and three at 26; 26 people are recorded at 30 (XXX) against three at 29 and zero at 31; 23 people are recorded at 40 (XL / XXXX) against one at 41; 28 people are recorded at 50 (L) against zero at 49 and two at 51; and 23 people are recorded at 60 (LX) against one at 59 and two at 61.
Chapter 2 · The threshold at twenty & the months illusion
Childhood without the wall of decades, adulthood on round numbers — and what happens when a stone adds months and days
Age-rounding does not begin at birth. To the left of age 20 (ages 1–19, 106 intact ages in Dacia), the stones spread across every year with no towers: two children at age one, seven at two, 11 at three, 11 at four, five at five, eight at seven, nine at 18. 17.0% of Dacian epitaphs under age 20 end in 0 or 5, close to the 15.8% chance would give (between 1 and 19 only 5, 10 and 15 end that way: three ages in 19). The one small sign of rounding is at 10: 8 children, against 5 at 9 and 2 at 11. Childhood does not show the adult pile-up on 0 and 5. The moment the spectrum crosses age 20 (ages 20–100, 274 ages), multiples of 5 jump from 17.0% to 70.8% (and 71.6% from age 60 upward).
What happens when an inscription records months and days alongside years — vixit annis ... mensibus ... diebus ...? Intuitively, a stone that counts days down to the last fortnight must have an exact year count. Testing all 957 intact inscriptions in EDH that state months or days alongside years breaks that assumption in two.
For children and youths under 23 whose stones include months or days, ages gather on 0 and 5 no more than chance would make them (17.0% multiples of 5). Yet among adults aged 23–62 whose tombstones also carve exact months or days (284 inscriptions in EDH), 38.4% of the year counts still end in 0 or 5 (109 of 284, Whipple = 191.9 — nearly double the unrounded 20.0% baseline). Exact months and days do not guarantee an exact year. One possible explanation, which the stones alone cannot prove: relatives knew the day of the year someone was born and could count the months since, but guessed how many years had passed. Even so, rounding on these stones is far lower than on stones without months and days.
Chapter 3 · What cannot be said about Dacia
Legion, gold mine or colony: rounding is everywhere, and the differences between towns are too small to be sure of
The obvious guess is that the big garrisons, with their paperwork, knew ages better. Dacia’s stones do not bear it out. At Apulum (modern Alba Iulia, base of Legio XIII Gemina), 78.1% of adults have ages ending in 0 or 5 (25 of 32), and at Potaissa (modern Turda, Legio V Macedonica) 80.0% (16 of 20). Trajan’s civilian colony, Ulpia Traiana Sarmizegetusa, sits lower: 59.1% (13 of 22).
But the numbers behind each bar are small: the largest town in the chart has 32 adults aged 23–62, the smallest only 3. The thin lines on each bar are 95% confidence intervals, and they overlap almost everywhere. Sarmizegetusa against the rest of Dacia (73.6%, 134 of 182) gives p = 0.21 on Fisher’s exact test; against all adults in the two legionary towns together (78.8%), p = 0.09. Neither clears the usual 0.05 line. The 90% bars at Alburnus Maior and Tibiscum rest on ten or eleven people each. What can be said is simpler: across the province as a whole, nearly three adults in four have a round age on their stone, and the data show no town that clearly departs from that.
D(is) M(anibus) / Antoniae Bonosae vix(it) ann[is] XXXVII / Aurel(io) Constantio eq(uiti) R(omano) dec(urioni) col(oniae) Vimin(acii) vixit annis VL / P(ublio) Antonio Viatori mil(iti) leg(ionis) VI victricis frum(entario) vix(it) ann(is) XVIIII (HD008368, Sarmizegetusa)
A family stone at Sarmizegetusa, set up by Publius Antonius Super, tribune of the Third Cohort of Dalmatians, who is himself listed on it at 84 in the editors’ restoration ([L?]XXXIIII, the L supplied in brackets with a question mark): Antonia Bonosa at 37 (XXXVII), the soldier Publius Antonius Viator at 19 (XVIIII), and the knight Aurelius Constantius at 45, carved in the rare form “VL” (five taken from fifty).
The same holds for women and men. On Dacia’s stones, 69.6% of adult women (39 of 56) and 73.7% of adult men (101 of 137) have ages ending in 0 or 5: p = 0.60, no difference that can be told apart from chance. With Duncan-Jones’s decade-by-decade formula the two indices come out practically equal: 66.9 for women and 66.8 for men. The difference lies elsewhere: the ages recorded for women are lower (median 29, against 37.5 for men).
Chapter 4 · The imperial fault line, Roman Britain & the Greek numeral test
From Rome (248.7) and Britannia (307.9) to the Danube — and why Greek epitaphs still heap on 5 without the Roman numeral “V”
Placing Dacia within the 59,814 intact funerary ages extracted across the entire Roman Empire (LIST v1.2, 525,870 Latin inscriptions) shows a clear geographic fault line, one that Richard Duncan-Jones had already measured in 1977 on thousands of epitaphs. In central Italy and the old Mediterranean towns, age-rounding is roughly half that of the Danube: Samnium (Regio IV) stands at a Whipple index of 213.4 (42.7% ending in 0 or 5), Umbria at 216.7, Latium and Campania at 247.4 (49.5%), the city of Rome (15,467 ages) at 248.7 (49.7%), and Africa Proconsularis (10,884 ages) at 272.3.
How does Roman Britain (Britannia) compare with Roman Dacia? Both were heavily garrisoned outer-frontier provinces added in the first and early second centuries CE. Across the 244 intact funerary ages from Roman Britain in EDH (151 adults aged 23–62, led by the legionary fortresses at Chester / Deva with 44 people, Caerleon / Isca Silurum with 25, and York / Eburacum with 19, alongside London / Londinium, Lincoln / Lindum, Bath / Aquae Sulis, and Cirencester / Corinium Dobunnorum), 61.6% of adult ages end in 0 or 5 (Whipple = 307.9, Duncan-Jones index 54.4). Britannia rounds substantially more than Rome (248.7), but 52.4 Whipple points less than Dacia (360.3) and the Danubian-Alpine arc — where Pannonia Inferior (367.8), Moesia Inferior (373.2), Moesia Superior (385.3), Pannonia Superior (404.7), and Noricum (437.5) form the highest age-rounding zone of the Roman world.
A(ulus) Alfid(ius) Pomp(tina) / Olussa ex tes/tamento her(es) / pos(uit) annor(um) LXX / na(tus) Atheni(s) / h(ic) s(itus) est (HD001389, Londinium / London)A. Alfid. Pomp. Olussa na. Atheni. — man with no title on the stone, at Londinium (modern London): age 70 years (LXX in the EDH text).
Could the spikes at 25, 35, 45, and 55 simply be a visual artifact of Roman numerals, which use a dedicated five-symbol (V)? Testing that hypothesis against an independent body of inscriptions — 1,121 Greek funerary ages (555 aged 23–62) extracted from Greek Inscriptions of the Roman Empire (GIRE v0.3) Greek-language inscriptions from across the Empire, from Rome to Egypt and Asia Minor — refutes the script explanation. Greek epigraphic numerals are purely decimal-alphabetic (Κ = 20, Λ = 30, Μ = 40, Ν = 50, Ε = 5), with no base-5 symbol: 25 is written ΚΕ (two letters, no shorter than 23 = ΚΓ or 24 = ΚΔ). Yet in Greek epitaphs, 51.9% of adult ages still end in 0 or 5 (25.9% in 0 and 25.9% in 5; Whipple = 259.5). So rounding to 5 does not need the Roman V: it appears where 25 is no shorter to write than 23 or 24. That does not rule out every influence of how numbers were written.
What was already known, and what is new here. Duncan-Jones (Chiron 7, 1977, Table 8) gave Dacia an age-rounding index of 61.2 for men (134 ages) and 65.0 for women (87), against 47.0 and 50.2 in Rome and 82.1 for men in Noricum; he himself warned that samples under a thousand ages are hazardous. With his formula applied to the 380 ages in EDH, Dacia comes out at 65.4: by sex, 66.8 for men and 66.9 for women, against his 61.2 and 65.0. His pattern holds, with slightly higher figures, on a modern database that largely covers the same stones. What is new: the test on Greek inscriptions, childhood without the wall, the split by town with its uncertainty, and the three reading traps below. Why the frontier rounded more (literacy, birth registers, who lived there) stays an open question that these data cannot settle.
Chapter 5 · Where the picture misleads & how well the reader reads
Three epigraphic traps that fabricate fake decades under naive text mining
Extracting numbers automatically from ancient inscriptions risks inventing fake age-heaping where a stone is merely broken or carved in non-standard orthography. Ages read automatically from the Latin text (LIST v1.2) were compared with the person table compiled by Heidelberg’s epigraphers in EDH. These are the same inscriptions, because LIST takes over EDH’s texts: the comparison tests the automatic reader, and rounding is still measured only once. It exposed three systematic traps:
1. The right-edge fracture bias (XX[---], L[---]): Roman numerals write tens (X, XX, XXX, XL, L, LX) on the left and units (I, II, III, IV, VI, VII, VIII) on the right. When the right side of a tombstone breaks off after the tens digit, only the round decade survives. Across EDH’s 661 broken/lacunary age records, 47.2% are multiples of 10, compared with 37.4% on intact stones — a difference of 9.8 percentage points between the two groups; that is why broken ages must not be mixed with intact ones, as happens when transcriptions silently strip [---].
2. The -IIX (duodeviginti) parser bug: Roman stonecutters carved 18, 28, 38, 48, 58, and 68 as XIIX, XXIIX, XXXIIX, XLIIX, LIIX, LXIIX (“two-from-twenty”, “two-from-thirty” — 54 cases in EDH). A standard textbook Roman-numeral algorithm reads the first I as +1 and the following IX as +9, summing to +10 and turning every age ending in 8 into a fake decade ending in 0 (turning XXXIIX = 38 into 40 on HD063739).
3. Line-break splits (XXXXV/III, L/I): Masons frequently split long numerals across lines of stone: XXXXV/III (age 48 on HD049343 in Dacia) or L/I (age 51 on HD049338). Replacing line-division slashes / with spaces truncates those numerals into 45 and 50. With all three traps corrected, the epigraphic parser achieves 98.04% exact agreement across 5,879 Empire-wide EDH person ages and 97.64% in Roman Dacia (297 ages, with a Whipple index error of just -0.8 points: 356.3 vs 357.1). Among the remaining differences are four places where EDH’s text and the same database’s person table disagree; which of the two matches the stone can only be settled from photographs or printed editions (HD020990 at Apulum, for a soldier of the Tibiscum Palmyrene unit, where the text has XXXVIIII = 39 and the table 38; HD011457, where the text has LV = 55 and the table 45; HD046365, where the text has XXXII = 32 and the table 43; and HD001804, where the text has LXXXVIII = 88 and the table 89).