Why did the ancient Romans use groups of eight?

What was the reason behind this consistent eight-fold division ?

• Using only the four fingers of both hands for “counting”1, to the exclusion of the thumbs ?

• Computational ease or convenience, based on repeated division by two ?

• Or perhaps something else2 entirely ?

1 I am not referring here to some systematic octal counting system, but rather only to an intuitive psychological
inclination of creating small groups of four, five, eight, or ten items, based on the natural arrangement of fingers
on each hand.

2 Including the distinct possibility that it might all be just a simple coincidence.

• Is this some kind of pareidolia in numerology? These examples are a small sample. Please provide some evidence for the "dominance of eight". Nundinae calls already nine days in inclusive counting; 625 feet to the stadium, eight stadia to the mile, and three miles to the league; Ten contubernia were grouped into a centuria, later lead by a decanus (number increased to 10 and later to 16). Looks to me your assumption is not based on a real pattern. – LаngLаngС Jun 12 '18 at 16:07
• As @LangLangC says, there doesn't seem to be any real evidence of the "consistent eight-fold division" you mention. Looks more like cherry-picking of examples. – KillingTime Jun 12 '18 at 16:33
• @LangLangC: Miles consisting of five thousand feet, and military units consisting of ten sub-units, are easily explained by the fact that, for rather obvious reasons, most humans count in base ten. Also, numbers greater than five, which do not divide by it, might arise naturally, within specific contexts (such as eight year cycles, for instance). However, the repeated division (which you suspect to be coincidental) into the same number of parts, which is neither small (halves, thirds, quarters), nor round, nor naturally-arising, seems puzzling. – Lucian Jun 12 '18 at 16:35

This is most likely not a real pattern. "The Romans" did not all subscribe to Pythagorean math-magic or numerology.

The pattern that was observed in the question is not a real pattern:

Calenderial coincidences

Nundinae is counting eight days, if we count like we do today. But the Romans counted days inclusively and that is the reason why the etymology is not based on oct- for eight but on non- for nine.
Then we get a calendar reform and the Romans adopt our now familiar seven days week.

Roman measurements of length

Roman measurements of length are also not showing much affinity to the number 8:

625 feet to the stadium, eight stadia to the mile, and three miles to the league
Wikipedia: Furlong

Ancient Roman units of length:

Roman unit   English name   Equal to      Metric equivalent
digitus      finger ​        1⁄16 pes      18.5 mm
uncia        inch
pollex       thumb          ​1⁄12 pes      24.6 mm
palmus       palm   ​        1⁄4 pes       74   mm
palmus major palm length    ​3⁄4 pes       22   mm
pes (Roman)  foot           1 pes        296   mm
palmipes     foot & a palm  ​1 1⁄4 pedes  370   mm
cubitus      cubit  ​        1 1⁄2 pedes  444   mm
pes
sestertius   step   ​     2 1⁄2 pedes       0.74 m
passus       pace            5 pedes       1.48 m
decempeda
pertica      perch          10 pedes       2.96 m
actus (length)             120 pedes      35.5  m   116.496 ft  60 passus or 12 decempeda
stadium      stade         625 pedes      185   m   607.14 ft   600 Greek ft or 125 passus
​1⁄8 mille
mille passus
mille passuum(Roman) mile 5000 pedes      1.48 km  4854 ft 0.919 mi 1000 passus or 8 stadia
leuga     (Gallic) league 7500 pedes      2.22 km  7281 ft 1.379 mi


Numbers in the Roman military:

The contubernium was the smallest organized unit of soldiers in the Roman Army and was composed of eight legionaries, the equivalent of a modern squad. The men within the contubernium were known as contubernales. […] The contubernium was led by a Decanus, the equivalent of a junior non-commissioned officer. […]
While a unit of eight "contubernales" does not adhere to the organizational system in multiples of 10 men (“decanus”, “centuria”), when two auxiliaries are counted as an implicit part of the unit, a contubernium does match the nomenclature. Wikipedia: Contubernium

Designating a small unit in the military was by no means fixed across all of the history of the Roman time. Under Hadrian the contubernium was enlarged to be composed of ten men, in Byzantine time this squad unit would count at 16 men.
Looks to me that the assumption is not based on a real pattern.

This flexibility for a small group of soldiers in an army is even observed today:
US: team (fireteam: 4 or fewer members) < squad (8–14 members)
German Army: Trupp (2–8 members) < Gruppe (8–12 members)
Wehrmacht: An infantry Gruppe consisted of ten men.

That the number eight pops up is just a coincidence as small groups have to have any small number and eight was one of the possibilities the Roman army had the option to choose from and did, for a limited time. Just like any army, they try a few things and stick to that what they think works best. And change that if they get any wiser over time.

Ancient Roman attitudes to numbers

“Ten is the very nature of number. All Greeks and all barbarians alike count up to ten, and having reached ten revert again to the unity. And again, Pythagoras maintains, the power of the number 10 lies in the number 4, the tetrad. This is the reason: If one starts at the unit (1) and adds the successive number up to 4, one will make up the number 10 (1 + 2 + 3 + 4 = 10). And if one exceeds the tetrad, one will exceed 10 too…. So that the number by the unit resides in the number 10, but potentially in the number 4.” (Aetius 1.3.8)

Conclusion

Early philosophers found harmony in numbers. The symbolism and beauty behind each number can be further extended to the essence of all following numbers. The mysteriousness behind the theories founded by Pythagoras and his followers is certainly deeply inspiring and symbolic.
Kate Hobgood: Pythagoras and the Mystery of Numbers

While there might be some features attributable to the number eight,

It has been argued that, as the cardinal number 7 is the highest number of item that can universally be cognitively processed as a single set, the etymology of the numeral eight might be the first to be considered composite, either as "twice four" or as "two short of ten", or similar.
Wikipedia: 8

Like a real connection to Etruscan world ages, the eight rays star of Ishtar/Venus and so on. But any mathematical connection is very likely more conicidence than anything else. Although there is flimsy scientific speculation that

It has been suggested that the reconstructed Proto-Indo-European word for "nine" might be related to the PIE word for "new". Based on this, some have speculated that proto-Indo-Europeans used an octal number system, though the evidence supporting this is slim.
Wikipedia: Octal

Pattern recognition as an explanation

The most likely explanation for assigning a special significance to the "mythical/religious" number eight (or "8") appearing in Roman clusters is the clustering illusion, a phenomenon closely related to pareidolia and apophenia. (Under no circumstances is that to be read as an insult or or an accusation of illness. It's just a human psychological phenomenon that we all share to varying degrees).

The Roman numeral system is based on or influenced by mainly natural phenomena, mesopotamian sexagesimal system and the good old base10 decimal system. A hopefully convincing argument might be made in comparing the actual Roman numeral VIII and the Latin way of constructing numbers with 8 (18: duo-de-viginti… that is a pattern for Roman use: absence of oct- but constructed as "X minus 2") against some so-called Properties of the number 8.

Theoretical counter example adapted to today: "The alphabetical list of the English spellings for the integers 0 throught 1,000 begins eight, eight hundred, eight hundred eight, eight hundred eighteen, eight hundred eighty and so on. The last entry, of course, is zero. How many of your readers can name the 100th, or next to last, number on the list?" –– Does this make the number eight any more significant for English speakers? –– From Martin Gardner: "The Magic Numbers of Dr Matrix", Prometheus Books: New York, 1985.
Further insight might be gained by reading: Dudley Underwood: "Mathematical Cranks. The Amazing Mathematical Solution for Everything", Mathematical Association of America, 1992, p29f.

• I was already aware of most of the information contained in this answer, and did not exclude the possibility that it might all be purely coincidental, nor have I ever mentioned either Pythagoras or numerology. My objections are twofold: on one hand, all the numbers contained in Roman lengths make sense, be it biological or decimal (all, except for the eight-fold division of the mile); on the other hand, one could argue that adding two auxiliaries to the original eight men unit was an attempt at decimalization, and that the sixteen men unit is simply a doubling of the traditional one. – Lucian Jun 12 '18 at 17:19
• Upvote for pareidolia alone. New word!! – Mark C. Wallace Jun 12 '18 at 17:19
• @Lucian You obviously weren't aware, or you wouldn't've included reckoning the nones in a discussion about eights. It was nine, to their method of reckoning, and has nothing whatever to do with 8 in the first place. Similarly, the stadion was a Greek measure used by Roman citizens while writing in Greek based on Greek sources; the furlong was German measure adopted for its use in medieval agriculture; and neither has anything whatever to do with Roman culture... – lly Jul 18 '18 at 7:24
• ...Pythagoreanism was a legitimate thing under the Romans and they credit some of the oddities of their calendar to the old kings having been subscribers; that said, you shouldn't pretend you understood LangLangC's points since they undermine every one of your supposed examples of the 'pattern'. – lly Jul 18 '18 at 7:24
• @lly Nevertheless, I'd really like to read a counter answer that runs with the question and challenges or even contradicts my answer. Or at least tries to. – LаngLаngС Jul 19 '18 at 11:56

What I have learned in Latin is that it was a special number like 3, 7, 13 for us. its also a lucky number in China. Pythagoreans called it the "little holy number" I don't think Romans counted to 8, they count in 5 steps.

I, II, III, IV, V VI, VII, VIII, IX, X XI, XII, XIII, XIV, XV and so on

• I didn't exactly mean to imply that Romans employed octal. – Lucian Jun 12 '18 at 12:30
• @Lucian using only 8 fingers would make you start over after the 8th which would make it octal – Maritn Ge Jun 12 '18 at 12:31
• I'm not saying they used their four or eight fingers to systematically count beyond eight. – Lucian Jun 12 '18 at 12:34
• @Lucian to answer your question, it were cultural/religious and not practical reasons – Maritn Ge Jun 12 '18 at 12:37
• Yes, I understood your main argument. Could you perhaps offer some documentation (online or offline) supporting it ? – Lucian Jun 12 '18 at 12:52