Zodiac and Roman Army Camp construction

[PhilusEstilius]

That is the 4,000 mile long Foucault Pendulum I believe, all to do with the Coriolis effect and inertia.

[Longovicium]

The book by Eco spoofs the 'Holy Grail' genre with a fantastic concotion of Templar nonsense which takes on a 'swing' of its own. If I remember correctly, there is a moment in the novel where one of the main characters draws his partner to a window to point out a postbox in the street. He asks him what would a future civilisation make of us if that postbox were the only material remains to survive - and whose dimensions by an odd coincidence mirror exactly when added up the distance to the moon if multiplied correctly - or something that like! Surely a civilisation of lunar worshippers . . .

[PhilusEstilius]

Having worked in two Roman Forts I always thought that a fort is just a Fort a place where soldiers hang out and old retired amourers like me.

[Caballo]

My personal favourite is this holiday site which manages to combine Cathars, Celts, Fung Shui, Knights Templar, the holy bloodline of the Merovingian Kings, and the Holy Grail. http://www.fengshuiseminars.com/tours/So...dline.html

inexplicably, ley lines and astrology are omitted. But I am getting off topic....

[antiochus]

WARNING: THIS IS LONG

Macedon wrote: And why are the Polybian turmae 32 and not 30 man strong?

My mistake. When I wrote “during this period” I was referring to Augustus. A squadron of 32 men when halved gives 16, (as in the formula) and when halved again produces 8, and when halved again produces 4, halved again to 2. Could the Roman military system be based on even times even?

Macedon wrote: I would suggest that it was the Greeks who liked to use powers of 2 (at least at an ideal level) and not the Romans.

The Roman cosmos is a mixture of Greek, Etruscan interconnected with the Egyptian religious calendar.

Macedon wrote: Where in their tactics do they use triangular numbers (apart from wedges and rhombuses obviously and then again not in all forms of arrangement)?

This is a separate issue from tactics. A good book starter is “Ancient Mathematics” by S. Coumo, Routledge (2001)

Macedon wrote: As for Proclus' comments, of course mathematics are used in tactics as well as in Roman camp building, I guess it is with astronomy/astrology that you want to make a connection?

My source is not Proclus. Also I am not trying to make a connection with astronomy. I found the cosmos system in the primary sources and saw too many mathematical coincidences. Any person worth his salt would investigate first before dismissing the data.

Macedon wrote: And one more question, does your theory try to explain or also predict tactical numbers and patterns used by the Romans?

This is the main focus of the book…defining the legion’s organisation from Servius to Vegetius. This involves a comprehensive study using every legion size found in the primary sources, plus cohort sizes. Campaigns are covered for many periods, plus detailed battle analysis and army break downs. Dionysius remark the senate deliberated about what forces to send in the field should be seen as a warning they have a repertoire to choose from. Within the primary sources are references to a legion having 60 centuries. However, has anyone considered the possibility the number 60 gets mentioned because a 60 century legion could be the maximum allowable size for a legion? In 350 BC, Livy’s comment the consul brought up four legions to full strength. What does Livy means by full strength? Arrian says something similar when he describes the fifteenth legion as being more numerous than the twelfth legion. There are more references in the primary sources to full strength legions. Has anyone considered the possibility there could be also be 40-century and 50 century legions? If this is possible what do we now do with Cicero’s comment a cohort numbered 400 men? And what about those references to 500 man cohorts or 600 men cohorts? And doesn’t Sextius Rufius tell us Caesar conquered Gaul with 10 legions each numbering 3000 men. Could they be 30 century legions?

If a legion numbered 4800 men, then why does Tacitus write that Marcus Trebellius subdued the Clitae tribe with 4000 legionaries? Why does Tacitus write that the sixth legion had been reinforced during the night with 3000 men from the third legion to give the appearance the sixth legion looked like a single legion with one eagle? So was the sixth legion only 1200 men and the 3000 men from the third legion bought the sixth legion up to 4800 men? Why does Tacitus write that a force of 3000 legionaries, supported by raw Belgian cohorts and camp followers attacked the Batavians?

There is no answer to the above questions from academia. Neither is there a comprehensive study of campaign distribution patterns. All this material in the primary sources is being wasted and the blame has to be laid at the feet of academia. They’re too busy proving “nothing can be proven.”

You ask if I explain patterns in my book. Yes I do and quite a lot of them. This is where the tribal system comes into play which details the number of men being levied. Some examples are given below:

In 505 BC, in response to an invasion of their territory by a large Sabine army the Romans marched “with all their forces, led by both consuls.” Of the two consular armies in the field, one consular army encamped on some heights near Rome as a precaution to prevent a sudden attack on the city, while the other consular army took up a position on the bank of the river Anio.

This is the first distribution pattern of the Roman army. It is following Roman military system, which the Romans claim came from divine inspiration. Yes there is such a quote and it is referenced in the book.

In 501 BC, the dictator separated those who were of military age from the older men and distributing the former into centuries, he formed four bodies of foot and horse. He kept one, the best, about his person while of the remaining three bodies, he ordered Cloelius, who had been his colleague in the consulship, to choose the one he wished. Spurius Cassius, the Master of the Horse, to take the third, and Spurius Larcius, his brother, the remaining one; this last body together with the older men was ordered to guard the city, remaining inside the walls.” For the battle of Lake Regillus in 499 BC, Postumius divided the army into four parts, one he commanded, the second he gave to Titus Verginius the third to Titus Aebutius, and the fourth to Aulus Sempronius (praefectus urbi), whom he appointed to guard the city. In 494 BC, Titus Veturius conducted operations against the Aequians, Aulus Verginius the Volscians, and Manius Valerius (dictator), the Sabines, while Titus Larcius (city prefect) with the seniores guarded the city. Both Dionysius’ and Livy report the Romans levied 10 legions.

This is the second distribution pattern of the Roman army. The division of the army is now based on the total of iuniores and seniores, not solely the iuniores.

In 487 BC, “the senate voted that the youth already enrolled should be divided into three bodies, and that Gaius Aquilius (consul) should march against the Hernicans. Titus Sicinius (consul), with the second army against the Volscians, and Spurius Larcius, (city prefect), with the remaining third part, defend the portion of the country that lay nearest to the city. Those who were above the military age but were still capable of bearing arms should be arrayed under their standards and guard the citadels of the city and the walls, to prevent any sudden attack by the enemy while all the youth were in the field.”

Distribution pattern number three is based on military necessity. It differs from distribution pattern one as it now includes a third army to defend the country near Rome.

In 478 BC, when fighting the Aequians, the Veientes and the Volscians, the Romans levied three armies each of two legions. The consul Lucius Aemilius campaigned against the Etruscans, Gaius Servilius against the Volscians, and Servius Furius, (proconsul), against the Aequians.

What do we have here? Fighting on three fronts. Maybe smaller armies are required to meet the threat?

In 477 BC, Dionysius has the consul Gaius Horatius marched against the Volscians with two legions, while the other consul Titus Menenius set out against the Etruscans with another force of equal size.

Distribution pattern one again. Consuls assigned two legions. Wow! Some academics disagree because such an event is supposed to happen later (366 BC I think). Does a return to distribution one mean each consul commanded larger armies?

In 459 BC, in response to an invasion by an Aequian and Volscian army, the consuls enrolled all who were of military age, and “left a third part of their own army to guard the city.” In 458 BC, the consuls Gaius Nautius and Lucius Minucius divided the Roman army into three bodies, with one body guarding the city, while the other two went on campaign. This is straight forward so you know which pattern it is.

In 450 BC, the Decemvirs levied 10 legions. Two legions remained in the city; five legions confronted the Aequians, while another three legions engaged the Sabines. What a coincidence. There are 10 decemvirs and 10 legions. Again we find 10 legions being levied as had occurred in 494 BC. Makes you wonder who the source is. As to why there are 10 legions, this can be explained in both campaigns.

For the campaign against the Aequians in 418 BC, Livy cites the levy differed from the norm, with the men levied from 10 tribes drawn by lot and not from the whole population. This is simply worth its weight in gold. Pity some academics reject it.

In 406 BC, of the four consular tribunes elected, one remained at Rome while three consular tribunes campaigned against the Volscians. On meeting no organised resistance, the three consular tribunes divided the army into three divisions. Cnaeus Fabius Ambustus set out to capture the hill town of Anxur and a surprise attack by four cohorts helped capture the town. Three consular tribunes! Three army divisions! And the mention of four cohorts…taken from one army division to act as a diversion. It’s obvious these are big legions.

In 403 BC, Livy claims a precedent is set by electing eight consular tribunes. He also mentions for the same year the building of the siege works around Veii. It is plain to see they need more men to build the siege works. So does having eight consular tribunes mean from the number of men levied, each consular tribune commanded a smaller army? In the same year because of the loss of the siege works, we find equites private volunteering for Veii. Livy mentions foot-soldiers as well. Could it be the mobilisation of the seniores.

In 401 BC, of the six consular tribunes elected, four campaigns were simultaneously undertaken. So the number of consul tribunes has increased from four to six. What would make them do this? Did it on a whim perhaps? I wonder how the Romans guaranteed the two new consular tribunes commanded the same number of men as the other four consular tribunes? We can’t have some consular tribunes commanding less than the others, that would be an insult to their rank. Doesn’t Livy state that a law was passed one consular tribune must remain at Rome? Perhaps they increased the size of the army or divided the army by six (five field armies and one home guard) thereby making smaller divisions. Could it have something to do with the cosmos?

In 395 BC and 391 BC, of the six consular tribunes, four consular tribunes conducted simultaneous military campaigns. So we have four from six commanders in the field. Could this mean they commanded larger sized armies or legions? In 389 BC, Camillus (dictator) divided the iuniores and seniores into three divisions. One division marched against the Veientes the second division encamped in front of Rome, while the third division campaigned against the Volscians. Well, we still have a division encamped before Rome, but back in 501 BC and 499 BC, the army under a dictator was divided into four divisions, now it’s three. What has happened to make it change from four to three? Big legions perhaps.

For the battle of the Allia, Plutarch has the Roman army numbered at about 40,000 men. My tribal system shows for this period the tribes number about 40,000 men. Has Plutarch confused the tribal system for the Roman army? Maybe it’s just nothing more than mathematical coincidence between Plutarch and my tribal system.

In 386 BC, Marcus Camillus, dictator and Publius Valerius campaigned against the Antiates, while Quintus Servilius Fidenas, maintained a second army to be encamped before the city. A third army under the command of Titus Quinctius Cincinnatus mobilised the seniores and those invalided out of the army to defend the city. Here we have two field armies and a third body consisting of seniores. Hmm, could it be that the second army encamped before Rome represents only one legion?

In 381 BC, two consular tribunes campaigned against the Volscians. The size of the army numbered four legions each of 4000 men. That is interesting. An army of 16,000 men. This is totally in opposition to the theory the Roman only had an army of 6000 men in 366 BC. However, if Plutarch has the Roman army at the Allia at about 40,000 men, then an army of 16,000 men is quite feasible.

In 378 BC four consular tribunes campaigned against the Volscians. The Volscians, fearing an army might come from Rome and attack them, “confined their ravages to the extreme frontier.” In 377 BC, three Roman armies are enrolled, one garrisoned the city, another acted as an emergency reserve, while the third, and the strongest under the command of two consular tribunes was sent to Satricum. Because the third army is reported as being the strongest, could this mean the third army had larger sized legions, or just more legions? Is the emergency reserve the same army coming from Rome the Volscians were worried about in the 378 BC?

In 357 BC, while on campaign, Livy reports the consul put forward the proposal to levy a tax on manumitted slaves. After the soldiers voted in their tribes, the proposal was approved and made law. Some academics dismiss the legion voting in tribes. The men are levied from tribes so why is there a problem with the men voting in tribes? My research shows that each tribe contributes an equal number of men to a legion so that a legion consists of men in equal numbers from all the tribes. Doesn’t Polybius state four men are selected from a tribe and each of the four military tribunes selects one man from that tribe.

In 388 BC, six consular tribunes are elected. To deal with uprising from the Aequians and the Etruscans, two Roman armies are despatched; one to deal with the Aequians, the other army to capture the Etruscans town of Contenbra. To capture Contenbra, Livy states that the Roman army was divided into six divisions, and each division attacked the town for six hours before being relieved by another division. This reference establishes the organisation of the Roman legion for this period is correct. The six divisions are tribune cohorts and from this the size of the army is easily calculated.

In 349 BC, Livy proclaims the Romans raised 10 legions each of 4200 men and 300 cavalry. Eutropius also mentions 10 legions enrolled in 349 BC totalling 60,000 men. Could it be that Eutropius figure of 60,000 men is based on 10 legions at 60 centuries? Maybe Livy based his on 40 century legions. Is Livy’s sourcing Polybius?

For the battle of Asculum, Frontinus gives the opposing armies at 40,000 men. Dionysius numbers the Roman army at over 70,000 infantry, of whom 20,000 infantry and over 8000 cavalry were Romans, the rest made up of allies. Academia is divided into two schools. Those who believe 70,000 infantry were present (the Dionysius camp) and those who side with the 40,000 infantry (the Frontinus camp). Asculum is the easiest order of battle to decipher of all the battles in the primary sources. I still cannot understand how it is so grossly misunderstood.

For the battle of Ecnomus in 256 BC, according to Polybius the Roman fleet of 330 vessels numbered 140,000 men, with each vessel manned by 300 rowers and 120 legionaries, termed by Polybius as marines. When not rounded, this amounts to 99,000 rowers, and 39,600 men. However, Polybius omits the number of men on the two consul flagships. With the inclusion of the 240 men (which are cavalrymen) this brings the total to 39,840 men distributed among 332 vessels. This total includes both infantry and cavalry. With the inclusion of the 240 men, there is no rounding. Polybius’ numbers are perfect. Polybius mentions that the men were a picked force, so 39,840 men were not present at Ecnomus. After reconciling the army numbers given by Appian, Orosius (30,000 to 32,000 men) in Africa, and Polybius for the battle of Bagradas (15,000 men and 500 cavalry), then comparing the size of a legion based on the zodiac, which has not changed for centuries, Polybius’ fleet of 330 vessels (332 with the consul flagships), represents the fleet in Sicily without horse transports before embarking for Africa. The fleet at Ecnomus with horse transports numbers 330 vessels. What I have found is Polybius has combined the pre-Ecnomus fleet organisation with the Ecnomus fleet organisation (the fleet divided into four legions or squadrons, then in three divisions with the triarii during the battle).

Following this there is levy of 225 BC as reported by Polybius. I have the tribal system for 228 BC and when compared to Polybius levy, the difference in the numbers for the Romans is due to Polybius slightly rounding his numbers. The section on the Roman army numbers for the Second Punic war is 80 pages in length. Of all those ancient historians who give the army numbers for Cannae, I found Plutarch’s 88,000 men are closer to the mark. Plutarch does state those in battle array numbered 88,000 men, so Plutarch’s 88,000 men (rounded down) includes the officers and those supernumeraries required on the battlefield. The other supernumeraries are left in the camp. I start the Cannae campaign first by using the tribal system to levy eight Roman legions. What I get with the addition of the allied legions is Plutarch’s total without rounding. After the Second Punic war the book continues to the late Roman army, of which I now have a grasp of its organisation as the Romans are following their traditional patterns established since the centuriate legion.

I’ve been told there are some sharp swords on RAT. So they should have no problem in detailing the size of the armies from those examples, especially as the primary sources contain all the answers. So Macedon, all the above examples plus many more (Magnesia Pynda blah blah blah) are covered in the book. And all the examples interlock with the tribal system and yes the cosmos. Here’s the fun bit, I didn’t invent the cosmos to fit the army organisation. I found the complete information about the cosmos in the primary sources and saw how it fits with the military. However, without having the tribal system, the cosmos would have represented a bunch of meaningless numbers. To get a link between the cosmos and the military, I had to apply the correct mathematical practice employed by the Romans. Oh it’s really complex…you have to know when to divided or multiply by 10. The tribal system, the military systems, plus the cosmos (orbits of the planets interconnected with the zodiac) all fit like a custom made glove. No fudging required.

And here’s the best part. The Romans change part of the cosmos due to some new science as explained in the primary sources. I became aware of it after reading a secondary source. If you don’t change the numbers to the new cosmos at the same time as the new cosmos is introduced, you cannot reconcile the military numbers in the primary sources. But if you employ the new cosmos numbers, the system again interlocks with the military and continues doing so to Vegetius.

Mr Campbell wrote: You are putting words in Polybius' mouth! At Hist. 6.26.10, he actually refers to a theôrêma ("theory / scheme / plan") not specifically a formula, like your puzzling 162 - 142.

I copied the Penguin version which uses the word formula. See page 324 “No matter where this is done, one simple formula for a camp is employed.” So I can’t be held responsible for putting words in Polybius’ mouth! If you have an issue, take it up with Penguin. The 162 - 142 formula maybe puzzling to you, but not to me, and not to others studying disciplines not relating to the Roman military. The formula is related to the square zodiac, as opposed to the round zodiac. The zodiac I am referring to is not to be confused with the lunar zodiac.

Robert wrote: As for the zodiac, well...

I’d like to hear you views on the zodiac. So far no one has challenged the formula regarding the size of the 480 man cohort x 700 stadia divided by 35 tribes, and then split the result into 50/50 iuniores to seniores to get 4800 iuniores which is the agreed size of a legion at 80 centuries a legion. If you feel restricted by the rules of RAT and you want to be more candid, my email address is [email protected]

Jurjen Draaisma wrote: Well, when you take this holy formula and multiply the answer (60) by yet another mythical number (5)* you get the number of warriors (300) that King Leonidas took to fight the Persians at Thermopylae in 480 B.C.

If you don’t like the subject matter, don’t read the post. That is the mature approach. Yet again the topic has generated into mockery by some members so there is no point in going on with this discussion.

[nikgaukroger]

This is the main focus of the book…

Which is due out when?

[Macedon]

In my opinion, religious symbolism often permeates aspects of the life and society of the ancients among which the military. Yet, you are taking it to a whole new level, which understandably and I am sure you expected it, will be confronted with very much and sincere scholarly and rational doubt.

My mistake. When I wrote “during this period” I was referring to Augustus. A squadron of 32 men when halved gives 16, (as in the formula) and when halved again produces 8, and when halved again produces 4, halved again to 2. Could the Roman military system be based on even times even?

But your whole post seemed to have to do with the Polybian Romans. Anyways, I guess that you should take pains to be clear to what period you are referring when dealing with such a broad issue that has to do with Roman tactical division spanning 500 or 1,000 years. To me it is strange to view the Roman military divisional system as a single entity. Even if the powers of 2 play a role at certain times, they obviously do not at others, as for example in the Polybian armies where indeed 3 seems to be the basis of the system. The powers of 2 (2-4-8-16-32-64-128-256-512-1,024...) are universally used by all Greek tacticians when describing the ideal Greek armies, while of course exceptions do arise in the writings of historians (like depths of 10/25/50).

The Roman cosmos is a mixture of Greek, Etruscan interconnected with the Egyptian religious calendar.

I cannot say myself, never actually having been seriously occupied with the issue myself, although I think you are very probably right. Yet it is you who wrote that :

"The Romans are associated with the use of square numbers as opposed to the Greeks use of triangular numbers."

Now, this sounds as though you directly contrast the two systems. My question to you, though, had nothing to do with raw mathematics. It had to do with the issue at hand. I asked : "Where in their tactics do they use triangular numbers (apart from wedges and rhombuses obviously and then again not in all forms of arrangement)?". In your directing me to “Ancient Mathematics” by S. Coumo, Routledge (2001) it seems your comment had little to do with tactics but wasn't it the whole point to discuss the use of mathematical patterns in tactics? I remind you that the above comment was made in regard with the outline of the Roman camp.

My source is not Proclus. Also I am not trying to make a connection with astronomy. I found the cosmos system in the primary sources and saw too many mathematical coincidences. Any person worth his salt would investigate first before dismissing the data.

You wrote that :

"Some years back I found this interesting quote:

“they do not think it right to call tactics one of the parts of mathematics, as others do. Rather, they hold that it uses sometimes logistics, as in the tallying of companies, and sometimes geodesy, as in the division and measurements of camps.”"

Now this is from :

In primum Euclidis elementorum librum commentarii
G. Friedlein, Procli Diadochi in primum Euclidis elementorum librum commentarii. Leipzig: Teubner, 1873, page 38

ὥσπερ καὶ Γεμῖνος, καὶ ποιοῦσι τὴν μὲν περὶ τὰ νοητὰ μόνον, τὴν δὲ περὶ τὰ αἰσθητὰ [ἐνεργοῦσαν?] καὶ τούτων ἐφαπτομένην, νοητὰ δήπου καλοῦντες, ὅσα καθ’ ἑαυτὴν ἡ ψυχὴ θεάματα ἀνακινεῖ, χωρίζουσα τῶν ἐνύλων ἑαυτὴν εἰδῶν. καὶ τῆς μὲν περὶ τὰ νοητὰ πραγματευομένης δύο τὰ πρώτιστα καὶ κυριώτατα μέρη τίθενται ἀριθμητικὴν καὶ γεωμετρίαν, τῆς δὲ περὶ τὰ αἰσθητὰ τὴν ἐνέργειαν ἐχούσης ἕξ, μηχανικήν, ἀστρολογίαν, ὀπτικήν, γεωδεσίαν, κανονικήν, λογιστικήν. τὸ δ’ αὖ τακτικὸν οὐκ ἀξιοῦσιν ἕν τι τῶν μερῶν τῆς μαθηματικῆς λέγειν, ὥσπερ ἕτεροι, ἀλλὰ προσχρῆσθαι τότε μὲν λογιστικῇ, καθάπερ ἐν ταῖς ἐξαριθμήσεσι τῶν λόγων, τότε δὲ γεωδεσίᾳ, καθάπερ ἐν ταῖς διαιρέσεσι τῶν χωρίων καὶ ταῖς ἀναμετρήσεσιν, ὥσπερ δὴ πολλῷ πλέον οὔτε τὸ ἱστορικὸν οὔτε τὸ ἰατρικὸν μέρος εἶναι μαθηματικῆς, εἰ καὶ προσχρῶνται πολλάκις οἵ τε τὰς ἱστορίας γράφοντες τοῖς μαθηματικοῖς θεωρήμασιν, ἢ θέσεις κλιμάτων φράζοντες ἢ μεγέθη πόλεων καὶ διαμέτρους ἢ περιβόλους καὶ διαμέτρους ἢ περιμέτρους συλλογιζόμενοι, καὶ οἱ ἰατροὶ πολλὰ τῶν οἰκείων διὰ τῶν τοιούτων ἐφόδων σαφηνίζοντες.

This was written by Proclus in the 5th century AD. What did you mean?

Do you mean that the Roman "Cosmos" system was rigid enough to not be dependent on astronomy/astrology? Else why wouldn't you want to show that the Romans made a connection with astronomy regarding their military system? As for investigating the Roman cosmos, the thing is I still am struggling to understand what exactly you mean by it. Do you mean the Romans' understanding of the world and universe in mathematical patterns? As in what the shape and measurements of the earth and the universe were, the mathematical patterns behind the visible (and invisible) celestial bodies? And if so, what do their tribes and their numbers have to do with that? Anyways, whatever you might mean, it can shed little light on this discussion as long as we cannot read a presentation with specifics. You should not expect us to make the connection, since it obviously has demanded a great deal of synthesis from you.

This is the main focus of the book…defining the legion’s organisation from Servius to Vegetius. This involves a comprehensive study using every legion size found in the primary sources, plus cohort sizes. Campaigns are covered for many periods, plus detailed battle analysis and army break downs.

So, does it predict or explain?

I can have an army of 10,000 men and then another of 14,000 and explain them as the former being the number of angels in heaven and the other double the number of the holly cows of temple X (no irony here, just examples). Or I could claim that the men on campaign should be of a number relative to the heavenly army of God Y and thus relative to number Z. In the first case, I take existent numbers and try to explain them through symbolism as I see fit. In the second case I have to show that all armies of that nation are of a number relative to Z. And if I want to take it even further and really make predictions, I have to determine these relations and say that for example "the relation of the number of men in the army to Z changed according to the number of eclipses in each century" and so, when these eclipses were 50, the army was double than when they were 25..." Now this is the difficult part, for I have to find something in my cosmos theory that is not constant and so base the obvious changes on it and test them with the sources. Else, by justifying changes with change of symbolisms like "In the 4th century, the number of generals was equal to the number of solar eclipses while in the 5th it was half the number of the High Priests of Y", I cannot show that it was the military system that obeyed the Cosmos instead of the latter only serving as a religious symbol to sanctify rational military thinking.

So Macedon, all the above examples plus many more (Magnesia Pynda blah blah blah) are covered in the book. And all the examples interlock with the tribal system and yes the cosmos. Here’s the fun bit, I didn’t invent the cosmos to fit the army organisation. I found the complete information about the cosmos in the primary sources and saw how it fits with the military. However, without having the tribal system, the cosmos would have represented a bunch of meaningless numbers. To get a link between the cosmos and the military, I had to apply the correct mathematical practice employed by the Romans. Oh it’s really complex…you have to know when to divided or multiply by 10. The tribal system, the military systems, plus the cosmos (orbits of the planets interconnected with the zodiac) all fit like a custom made glove. No fudging required.

And here’s the best part. The Romans change part of the cosmos due to some new science as explained in the primary sources. I became aware of it after reading a secondary source. If you don’t change the numbers to the new cosmos at the same time as the new cosmos is introduced, you cannot reconcile the military numbers in the primary sources. But if you employ the new cosmos numbers, the system again interlocks with the military and continues doing so to Vegetius.

I guess that this could serve as an answer to my question above (I let the question be so that my point be better understood). I will not press you for more explanations since you obviously want to reveal your theory in your book and not here. The many paradigms you mentioned touch many aspects of military tactics and look irrelevant and incoherent without stating their relation to your theory and to each other. They read like a preview ad instead of arguments. What I can only say is that it is impossible for any of us here to make any real criticism since without knowledge of your system's mathematical details no checking and juxtaposition with these or other examples can be made.

I’d like to hear you views on the zodiac. So far no one has challenged the formula regarding the size of the 480 man cohort x 700 stadia divided by 35 tribes, and then split the result into 50/50 iuniores to seniores to get 4800 iuniores which is the agreed size of a legion at 80 centuries a legion.

What are the 700 stadia (about 118 km)? And what period are you with this referring to?

I would also like you to answer the rest of the questions I had in my previous post if possible :

1. What question exactly does the formula 162 - 142 answer? I kind of fail to see any crucial connection of the number 60 with Polybius' description of the Roman camp...

2. As for the cohorts of the Polybian Romans, aren't they normally 160 (dividable by 16 and not by 60) and 100 (not dividable by 60 or 16) man strong, when necessary reinforced to 200 and 110 respectively (both numbers not dividable by either 16 or 60)?

3. And since when is the Polybian camp a square itself divided in four equal squares or the consul quartered in its middle? I admit I have never sat down to draw one myself but the drawings I have seen and the reading I have done do not seem to shape such a pattern.

[Robert Vermaat]

Hi Steven,

Robert wrote: As for the zodiac, well...

I’d like to hear you views on the zodiac. So far no one has challenged the formula regarding the size of the 480 man cohort x 700 stadia divided by 35 tribes, and then split the result into 50/50 iuniores to seniores to get 4800 iuniores which is the agreed size of a legion at 80 centuries a legion. If you feel restricted by the rules of RAT and you want to be more candid, my email address is [email protected]

No need, I will do so in this thread, which has already derailed anyway.

I’m no expert in early Roman armies, nor am I an expert in the ancient Roman tribes, nor in the zodiac. So. I’ve said it, and you can regard everything below in the light of that statement.
I think I can call myself knowledgeable in the Late Roman army however, and the way you treated that discussion about unit strength did not make me happy.
However, what made me sad and a bit angry was how you dismissed researchers ‘en masse’ in your latest post. I thought that especially unfair, and almost always incorrect. Hence, some of my comments may be a bit sharp. Apologies for that.

However, has anyone considered the possibility the number 60 gets mentioned because a 60 century legion could be the maximum allowable size for a legion? In 350 BC, Livy’s comment the consul brought up four legions to full strength. What does Livy means by full strength? Arrian says something similar when he describes the fifteenth legion as being more numerous than the twelfth legion. There are more references in the primary sources to full strength legions. Has anyone considered the possibility there could be also be 40-century and 50 century legions? If this is possible what do we now do with Cicero’s comment a cohort numbered 400 men? And what about those references to 500 man cohorts or 600 men cohorts? And doesn’t Sextius Rufius tell us Caesar conquered Gaul with 10 legions each numbering 3000 men. Could they be 30 century legions?

Steven, to me this sums up why discussing this topic is so difficult. For myself, I see a lot of sources, discussing a changing subject like the Roman army over a number of centuries, in which the organization changes due to a number of influences. However, despite a large number of changing numbers, you keep coming back to the same influence. No matter if a cohort number 400, 500 or even 600, it’s always the zodiac or the tribal system underlying all this. Why not simple practical reasons? Such as available numbers?

If a legion numbered 4800 men, then why does Tacitus write that Marcus Trebellius subdued the Clitae tribe with 4000 legionaries?

perhaps because that legion was a) understrength or b) a vexillation was needed elsewhere?

Why does Tacitus write that the sixth legion had been reinforced during the night with 3000 men from the third legion to give the appearance the sixth legion looked like a single legion with one eagle? So was the sixth legion only 1200 men and the 3000 men from the third legion bought the sixth legion up to 4800 men?

Because that was the case? No religious or similar reasons behind it, simply because the generals thought this was the best tactic?

Why does Tacitus write that a force of 3000 legionaries, supported by raw Belgian cohorts and camp followers attacked the Batavians?

Because they did? If there had been 4000, he would have written that?

There is no answer to the above questions from academia.

That, Steven, is an outright misrepresentation of the facts. Maybe you don’t like the answers because they do not fit your theory, but there have been plenty of discussions of such battles, and mostly the academics accept these numbers as *reality*, not as the result of some religions drive that caused the Roman military command to ALWAYS take into account the zodiac, the ancient tribal system or some other formula to determine the actual number of combatants. Like my fellow-academics, I do not look for a continuous system determining these numbers throughout Roman military history. But that does not mean that there have been “no answers” from academics about troops strengths.

Neither is there a comprehensive study of campaign distribution patterns. All this material in the primary sources is being wasted and the blame has to be laid at the feet of academia. They’re too busy proving “nothing can be proven.”

is it better to accept that insufficient data exist, then to invent your own proof? Is misusing the primary sources the answer, to ignore common reason?

In your following summary of early Roman armies, you keep bashing researchers, while at the same time describing a constantly changing Roman reaction to a number of varying threats: differing armies, differing numbers of consuls, differing numbers of legions, legions of smaller sizes due to vexillations.. Is it me or are you describing, in reality, a Roman strategy which is adapting to the real-life threats by responding in variable ways, instead of responding in a fixed manner dictated by ancient tribal laws. I won’t discuss each quote, but my conclusions are similar along the line:

So the number of consul tribunes has increased from four to six. What would make them do this? Did it on a whim perhaps?

Or perhaps it was a measured response dictated by the threat at hand?

I wonder how the Romans guaranteed the two new consular tribunes commanded the same number of men as the other four consular tribunes? We can’t have some consular tribunes commanding less than the others, that would be an insult to their rank.

Do you know if they had to? Was it an insult? Is there some source which states that they had to? You are bashing researchers here, but what’s your replay to a question like this? You give your own answer, without providing any proof whatsoever. That’s not research.

Could it have something to do with the cosmos?

Perhaps it once did, or perhaps not. But without proper proof, I see no way of telling yes or no.

Asculum is the easiest order of battle to decipher of all the battles in the primary sources. I still cannot understand how it is so grossly misunderstood.

Then tell us, is your understanding of this battle based on sources who tell us the exact order of battle plus the numbers of the units (I’m no expert, so I don’t know), or is it based on what you assume must be the numbers based on your theory? If the latter, I don’t see the problem: two sources tell us different things. You can blame the researchers for being stupid and bash them for it, or you can accept that we have two sources telling us different things. One of them is obviously wrong (or both, we weren’t there), but it’s not done to blame researchers for not being able to determine who.

After the Second Punic war the book continues to the late Roman army, of which I now have a grasp of its organisation as the Romans are following their traditional patterns established since the centuriate legion.

First of all, I really think that this last statement is not based on any facts at all. It flies in the face of all the evidence, as I think was clearly shown by the discussion here on RAT. I think you have been cherry-picking from Vegetius and other sources, ignoring evidence to the contrary.

Secondly, a question: from the Punic wars to late Roman times? Why jumping all over the Principate? There must be a lot of primary sources to discuss?

Here’s the fun bit, I didn’t invent the cosmos to fit the army organisation.

Nobody says that you did, but I’m not so sure about the other way around.

[D B Campbell]

Well the first part of the formula numbers 16. ... The number 16 when doubled makes 32 which is the size of a cavalry squadron for this time period.

Sometimes Polybius assigns 300 cavalry to each legion, sometimes 200. He says that the cavalry should be divided into ten squadrons, and "from each they select three officers" (6.25.1). That doesn't sound like a squadron of 32 men to me.

My mistake. When I wrote “during this period” I was referring to Augustus. A squadron of 32 men when halved gives 16, (as in the formula) and when halved again produces 8, and when halved again produces 4, halved again to 2. Could the Roman military system be based on even times even?

You clearly believe that Augustus had cavalry squadrons of 32 men. Would you care to cite your source, please?

Some years back I found this interesting quote: “they do not think it right to call tactics one of the parts of mathematics, as others do. Rather, they hold that it uses sometimes logistics, as in the tallying of companies, and sometimes geodesy, as in the division and measurements of camps.”

It's helpful to cite references for this kind of thing. Luckily, as Macedon/George realised (thanks, George!), this is Proclus, a 5th century AD philosopher (with no military experience, unless you know differently?)

My source is not Proclus. Also I am not trying to make a connection with astronomy. ... Any person worth his salt would investigate first before dismissing the data.

That's odd. You have managed to reproduce a passage of Proclus in translation. Who did you think you were quoting?

When describing the Roman camp, Polybius states “one simple formula for a camp is employed which is adopted at all times and in all places.”

You are putting words in Polybius' mouth! At Hist. 6.26.10, he actually refers to a theôrêma ("theory / scheme / plan") not specifically a formula, like your puzzling 16[sup]2[/sup] - 14[sup]2[/sup].

I copied the Penguin version which uses the word formula. See page 324 ... So I can’t be held responsible for putting words in Polybius’ mouth! If you have an issue, take it up with Penguin.

It is standard practice, when quoting an ancient source, to check what (the standard text of) that ancient source actually wrote. Still ... now you know that Polybius refers to a "theory", not a "formula" ... You're welcome.

I was hoping that you might have responded to my other queries. In particular, I am keen to know where I (allegedly) "dabbled" with your arcane numbers. Just if you have time to respond.

[Macedon]

In defense of Steven in that "theorema" question, I would add that a "theorema" could be a mathematical theorem and thus roughly translated as a mathematical formula. I do not think that this is the biggest issue, Duncan, although I also would like to see more references to the original texts. I only can guess that Steven wants to keep things intentionally misty so as not to reveal the content of his book.

[D B Campbell]

It seems that we three were all typing simultaneously (above)!

In defense of Steven in that "theorema" question, I would add that a "theorema" could be a mathematical theorem and thus roughly translated as a mathematical formula.

Except that Polybius never uses the word in that sense. It only ever means "a theory leading to some practical end" or "a scheme for doing some practical activity" or "the principles governing a particular subject".

Consider his use of the word at 1.2.1. Polybius is trying to convey a sense of the enormity of his historical "scheme" (the practical task of organizing a History). Steven's Penguin translation (p. 42) has "grand spectacle". No question of a mathematical formula. At 9.14.5, the word is used (in the plural) to convey the sense of "the practicalities" of astronomy and geometry when applied to generalship. Steven's Penguin (p. 396) has "scientific principles". At 10.47.12 (not in the Penguin), where Polybius is attempting to encompass all practical learning, it has a similar sense (Schweighäuser's Lexicon Polybianum offers artes et disciplinae, "arts and sciences"). Nowhere does he use the word to indicate the kind of mathematical formula that Steven has in mind (namely, the still-puzzling 16[sup]2[/sup] -14[sup]2[/sup]).

[Macedon]

I wouldn't say he has to in order to make that translation. The word is only used by Polybius a handful of times anyways and with meanings that would not exclude this one. In this specific case, he is talking about a schematic based on mathematical and geometric calculations which he proceeds to present, my point being that even with such a translation, the "formula" given, for Polybius DOES analyze the issue, seems to not justify the 162-142 riddle.

[nikgaukroger]

The number 28 is intertwined with other practices and explains why Augustus set the number of legions and 28 ...

Did he? Are you sure?

This question intrigued me as 28 is the commonly quoted number. However, I do seem to recall once reading some old paper which suggested that in fact initially Augustus set the army at 26 or 27 legiones and then later increased the number to 28 when additional territory was added. Is this what you were hinting at Mr C?

Of course, he then lost 3 in Germany and did not replace them (despite large scale emergency levies IIRC), leaving the legion strength at 25 - which may well cast doubt on how special the number 28 actually was.

Does the numbers theory predict or explain the varying number of legiones after the reign of Augustus, or the change in size such as the larger 1st cohort later in the C1st?

[D B Campbell]

I do seem to recall once reading some old paper which suggested that in fact initially Augustus set the army at 26 or 27 legiones and then later increased the number to 28 when additional territory was added. Is this what you were hinting at Mr C?

Actually, I suspect that he may have started out with 29. But that's another story. The main point is that we don't know for certain. So it is rather unwise of Steven to build such a radical theory (the supposed Roman veneration of the number 28) on another theory.

[nikgaukroger]

I do seem to recall once reading some old paper which suggested that in fact initially Augustus set the army at 26 or 27 legiones and then later increased the number to 28 when additional territory was added. Is this what you were hinting at Mr C?

Actually, I suspect that he may have started out with 29. But that's another story. The main point is that we don't know for certain. So it is rather unwise of Steven to build such a radical theory (the supposed Roman veneration of the number 28) on another theory.

I'm just re-reading Coello's "Unit Sizes in the Late Roman Army" (which includes an introductory section on the Principate army) which is reminding me just how uncertain the evidence for a lot of the numbers regularly quoted actually is. Strikes me that any theory based on such numbers is going to be on very shaky ground at best, and a book about it would need a huge (but potentially interesting) section on that evidence and the reasons for choosing certain interpretations of the evidence.