EUREKA - Roman army troops

[nickw]

My research time and again kept showing that the Romans increased the tribes after 241 BC by 84000 men (2400 men per tribe).

What are the references for this?

Every time the zodiac covered this distance, the tribes increase, but it takes centuries to happen.

How does this actually occur?

One modern astronomer predicated the ancients were allowing 30 degrees of movement for the upper heaven every 2000 years. In regard to Roman mathematical ratios, information is also contained in Ptolemy’s works:

“The explanation of opposition is immediately obvious, because it causes the two signs to meet on one straight line. But if we take the two fractions and the two super-particulars 3/2 and 4/3 most important in music, and if the fractions one half and one third be applied to opposition, composed of two right angles, the half makes the quartile and the third the sextiles and trine (1/2 of 180 = 90 quarile and 1/3 of 180 = 60 sextile. Of the super-particulars, if the sesquialter and the sesquitertian be applied to the quartiels interval of one right angle, which lies between them, the sesquialter makes the ratio of the quartile to the sextiles and the sesquitertian that of the trine to quartile (3/2 = 90/60 and 4/3 = 120/90.”

Ptolemy’s 120/90 ratio is found in the two systems relating to the Earth being divided into three parts of 120 degrees, and the second system of dividing the Earth into four parts of 90 degrees. A century of 100 men is broken into two parts 60 men plus 40 men, which produces the ratio 3/2. What we basically have is two mathematical systems in play.

This doesn't make a lot of sense to me.

Now according to the ancient astronomers, the zodiac is made up of 12 signs each of 30 degrees, therefore, giving a zodiac circle of 360 degrees. My research shows a cohort of 480 men simply represents 480 degrees and when divided by 30 degrees per zodiac sign = 16 zodiac signs. This means 480 degrees represents one and a third zodiac cycles (4 parts Earth =360 degrees, one part diameter = 120 degrees). When the 480 man cohort is introduced is given by Virgil (Eclogue 4: The Golden Age) as occurring during the consulship of Pollio in 40 BC. My research positions 480 degrees as relating to the position of Saturn, which is exactly what Virgil claims, the return of Saturn during the reign of Augustus./quote]What is the source for this position of Saturn at that time? How does it work before this time? How does it work when Saturn moves in the future?

During this time, Virgil makes mention of Lucina which is the goddess of birth. I’ve learnt that when Lucina is mentioned in the primary sources it is symbolic of a reform being undertaken, and Virgil is right on the money.

When else is it mentioned?

Other interesting aspects of the zodiac is each 30 degree sector is subdivided into 10 degree sectors called decani, and each decanus is considered master of his own 10 degree sector. Each 10 degree sector was in turn subdivided into smaller sectors ruled by subdecani. A system of smaller subdivisions covering fractions of a degree was called myriogenesis, which can number up to 216,000.

And what does any of this mean?

How is this so? Can you elaborate? The Roman system is not based on observation on a weekly or monthly basis; it is permanently modelled on the cosmos system. Although the ancients calculate the upper heavens as moving, it is a theoretical system, and does not correspond to the observation of the planets or fixed stars from Earth. The mathematical system informs the Romans which part of the upper heavens rules them and for how long, similar in concept to Cassius Dio’s description of the gods governing the day. After a number of solar years that correspond with the circumference and diameter of the Earth, coupled divisible by the 60 parts of the Meridian circle, the Romans know which god now rules over them, and because the maths related to a new god greater in degrees than the last one, they increase the tribes in accordance. In this manner, a Roman priest knows what the size of the tribes will be centuries in advance. The system is not concerned with the lunar calendar, with differing days for each month, but the system is aligned with the solar calendar. However, regardless of whether they get the solar year wrong and allow 390 days, 255 days, or 365 days a year, it is the number of years the Roman believe it to be that tells them what position within the universe they are at. What I am saying is I am not randomly picking out degrees in the cosmos system to make the system work, far from it, and it remains faithful to Geminos, Cleomedes, Hipparchos, Pliny and many many others.

Why is there not even a hint of this in the major texts such as Polybius, Livy, Appian, Tacitus, etc?

There’s a reference in the Suida, given in Greek, of which I don’t have the correct font, that the Athenians organised the tribes of Solon on the months, four seasons and year. Plato recommends mathematical astronomy for his ideal state. Plato even allocates numbers to the planets (1, 2, 3, 4, 8, 9 and 27).

Organising tribes is a little different to organising armies. And the Athenians later were able to add more tribes to honour major powers and allies.

And how do you shrug off Boethius? In his De Institutione Arithmetica, Boethius, compares the arithmetical proportion to the state, which is ruled by a few (oligarchy) because “the greater ratio is with the smaller numbers.” Boethius writes that “a state of the very best is a musical proportion.” Boethius lists five classes of inequality; the first class is called “multiple;” the second class the superparticular ratio, consisting of either the “sesquialter” or the “sesquitertian” ratio. The third class contains two parts the “superbipartient” and the “supertripartient” ratio. The fourth class contains the “duple-sesquialter” or “duple-sesquitertian” ratio, the fifth class is termed the “multiple superpartient” and contains the “duple-superbipartient” and the “triple-superbipartient” ratios.

Coincidently, the Servian constitution has five classes, and Boethius’ reference to a state being ruled by a few because the greater ratio is with the smaller number, somehow coincidently relates to the explanation given by Dionysius and Livy that in the voting system on the century assembly, the greater ratio of Class I, being smaller in number dominate the others, being greater in number (but not in the voting ratio). Maybe this is again, just mathematical coincidence. How do we know? Has anyone explored the possibility?

Seems rather coincidental, especially given Boethius was writing a millenium later.

First, I did not say the orbit of Venus restricted the number of centuries to 60. I stated the five known planets visible to the naked eye multiplied by the 12 signs of the zodiac produce the number 60. This is common knowledge in astronomic circles. Also it is common knowledge the Romans, like the Babylonians, used the sexagesimal place value system, (based on five planets and the zodiac), not the decimal; that is the numbers are based on sixes, not tens.

Didn't they only use this for astronomy not everyday calculations?

The figure of 60 is ten parts of 6, not six parts of ten. The modern system of counting hours, minutes and seconds is derived from it. Everything is broken into 60 parts, so one part is one sixtieth, and five parts, five sixtieth. Polybius’ legion of 4200 men is made up of 70 parts (70 sixtieths), and Livy’s 5400 man legion at Magnesia is made up of 90 parts. If you go up the next level, to one part being 600 men, Polybius’ legion is 7 parts and Livy’s legion, 9 parts.

Why? How do you explain Polybius' legion of 5,000 in "especial danger"?

Ancient astronomers like Geminos, Eratosthenes, Pliny and others give the circumference of the Earth at 252,000 stades.

Eratosthenes actually measured it to be 250,000.

Therefore, as Geminos is using the sexagesimal system, he writes the Earth contains 60 parts each of 4200 stades. The Romans allocate 600 stades to a degree, so 4200 stades = 7 degrees, and Livy’s legion of 5400 men equates to 9 degrees, and 6000 stades to 10 degrees. The Earth (252,000 stades = 420 degrees), so Polybius legion of 7 degrees represents one sixtieth (420 divided by 7 degrees). This is the system behind the legion and it is driven by their cosmos system.

Again, I don't understand. Also, doesn't Ptolemy say 500 stades to a degree? I've also seen a number of other amounts. In fact, per an article by S. Pothecary in Phoenix, "The length of the stade, the longest unit of Greek linear measurement, is one of the vexed issues of classical metrology, with stades of various lengths being attributed to geographical writers such as Eratosthenes, Polybios, Artemidoros, Poseidonios and Strabo respectively."

But have modern writers’ explored ancient mathematics, which is intertwined with geometry and astronomy? To answer this question, simply look up the bibliographies of every book you have on the Roman legion. If the author hasn’t, then this is akin to buying a 1000 piece jigsaw puzzle, and throwing out two thirds of the pieces. This methodology will always result in never seeing the complete picture, therefore no consensus of opinion, and this has been going on for hundreds of years.

I've still not seen anything that suggests a tight link between the army and cosmology.

Question: if the Roman system does not reflect their cosmos system, then why do the Romans then assigned gods to hours of the day as described by Cassius Dio (History of Rome, XXXVII, 19.1-3):

This appears to be a non sequitur question. :?:

There's a lot of various maths and astronomy, which unsurprisingly tie up, but not a lot to suggest from what you've posted that it's the foundation of the Roman army. I look forward to reading the full book if it is ever published.