In *Timaeus*, Plato describes the movement of the celestial bodies and the return of the planets to their original positions. There are two great circles: the outer one, called the circle of the Same, which represents the fixed stars, and the inner one, the circle of the Different, which is broken into seven parts, corresponding to the movements of the seven known planets (Mercury, Venus, Mars, Jupiter and Saturn, plus the sun and moon). The circle of the Different is the movement of the stars, which we could equate with the Zodiac or the ecliptic. As the earth's axis is slightly tilted, it creates a wobble, so that over about 25 920 years, a full cycle is completed, known as axial precession, or the precession of the equinoxes. Together, these eight circles represent the celestial order. The outermost circle is the motion of the fixed stars (the Same). The inner circles represent the motions of the seven planets, including the Sun and Moon (the Different). In total, there are eight circles of motion: the fixed stars plus the seven planets known to antiquity. Plato's description in the *Timaeus* gives a detailed account of the ordered cosmos, with the stars and planets following their harmonious revolutions, reflecting the structure and motion of the universe:

"The perfect number of Time fulfils the complete year when all the eight revolutions, having their relative velocities, are accomplished together and attain their completion at the same time, measured by the revolution of the Same and uniform; and this is true of the fixed and visible stars. But with regard to the planets which revolve in their own orbits and have a forward motion, time as a whole is fulfilled when their several periods of orbit have completed one cycle."(1)

In this passage, Plato refers to the idea that a cycle of time is fulfilled or completed when all the celestial bodies (including the planets) return to the same relative positions, a cycle known as the "Great Year." Plato doesn't give the number associated with this cycle, in which these heavenly bodies not only revolve around their own orbits but also move around the sun, and return to the same starting point for all. At the end of this "perfect number of Time", all the planets realign, bringing renewal.

Plato discusses the origins of the universe and cosmic order in his *Timaeus*, which is one of his key texts on cosmology. In this dialogue, he presents a mythical account of the creation of the universe, often referred to as a cosmological allegory, through the character Timaeus. Plato introduces the idea that the universe was created by a creator, called the Demiurge. This being does not create out of nothing, but rather organises pre-existing chaotic matter into an ordered cosmos. The Demiurge, driven by goodness and intelligence, aims to create the most perfect and harmonious universe possible.

"He was good, and in the good no jealousy can ever arise; and being free from jealousy, He desired that all things should be as like Himself as they could be." (Timaeus, 29e) (5)

The Demiurge uses reason and mathematics to impose order on the chaotic material, and the cosmos is constructed as a living being, endowed with soul and intelligence. Plato emphasises that the cosmos is governed by order, proportion, and harmony, reflecting the rational structure imposed by the Demiurge. The cosmic order is deeply rooted in mathematical ratios and geometric forms. In *Timaeus*, Plato describes how the Demiurge crafts the universe using ideal mathematical forms like the Platonic solids, which are associated with the elements (earth, air, fire, water, and ether).

In *Timaeus*, and *Republic*, Plato refers to eight celestial motions, reflecting a concept of an ordered universe governed by precise mathematical proportions and geometrical harmony.

The staff turned as a whole in a circle with the same movement, but within the whole as it revolved the seven inner circles revolved gently in the opposite direction to the whole, and of these seven the eighth moved most swiftly,(...). (Republic 617b) (6)

He then cut this entire compound along its length into two and situated the middles of each together like the letter χ, 36C bent each into a circle and attached each to itself and to the other one at the point opposite to where they overlap, included them in that kind of motion which turns around uniformly in the same place, and made one of the circles inner and the other outer. The outer movement he designated as the movement of Same, the inner as the movement of Other. He set the movement of Same revolving sideways and to the right, and that of Other diagonally and to the left, and he granted supremacy to the movement of Same 36D and similar, for he left it single and undivided. However he divided the inner circle six times producing seven circles based on the double and triple intervals, there being three of each[9]. He commanded the circles to go in opposite directions to one another, three at similar speeds; four at speeds dissimilar to one another and to the other three, but their movements were proportional.(Timaeus36b–37c) (7)

As Cornford remarked, Plato gives a very detailed account of the motions of the heavens for a discussion on creation.

The conclusion is that the Laws (certainly) and the Epinomis (quite possibly and, I should say, probably) are perfectly consistent with the theory of the Timaeus , which ascribes a compound motion to the seven planets. The conception is fundamental in the system of Eudoxus, who was working at the Academy before the Timaeus was written and who died before Plato. It is equally fundamental in Aristotle's adaptation of Eudoxus’ system of spheres. The system must have been known to Plato, and the probability is that he incorporated in the Timaeus as much of it as he could accept, consistently with his belief that the proper motion of each planet keeps to a circular track. It should not be forgotten that the Timaeus is a myth of creation, not a treatise on astronomy. The surprising thing is that Plato should have found room for so many details in his broad picture of rational design in the cosmos, not that he should have simplified by omitting subtleties which would contribute nothing to his main purpose and which might be superseded at any time, as indeed they were very soon afterwards. (2)

An important aspect of the universe is the order that has been imposed on it by the Demiurge, and an important aspect of this order is number, and geometry. So it would be very nice to know exactly what this perfect number of time was, but Plato doesn't say.

### What is the perfect number of time?

In Plato's *Laws* (7.809c), a discussion on numbers and religious practices highlights the significance of numerical harmony in both civic and religious life. The passage refers to "οἱ ἀριθμοί τελεώτατοι" (hoi arithmoi teleiotatoi), meaning "the most complete numbers" or "the perfect numbers," which suggests that certain numbers were considered especially sacred or perfect in ancient Greek thought. This concept is intertwined with the rites of the *hecatomb* (ἑκατόμβη), a grand sacrificial ceremony involving 100 oxen, traditionally offered to the gods during major festivals. The connection between these "most perfect numbers" and religious rites underscores the ancient belief that numbers were not just abstract concepts but had real, tangible importance in maintaining cosmic and social order. The hecatomb, with its emphasis on the number 100, demonstrates the reverence for numerical harmony, which extended into rituals that were believed to influence the divine.

In *Timaeus* (39d), Plato introduces the idea of the "perfect number of time" as "τέλειος ἀριθμός τοῦ χρόνου" (teleios arithmos tou chronou), meaning "the perfect number governing time." This phrase points to the belief that time itself is governed by numerical order and cycles. The choice of the word "τέλειος" (teleios), meaning "complete" or "perfect," emphasizes the philosophical idea that time follows a perfect, preordained structure, a reflection of the divine harmony of the cosmos. This reflection on numbers, particularly "οἱ ἀριθμοί τελεώτατοι" in *Laws* and "τέλειος ἀριθμός τοῦ χρόνου" in *Timaeus*, reveals Plato’s conviction that the universe and time itself are governed by mathematical precision.

If we multiply the time it takes for planets (Mercury, Venus, Mars, Jupiter and Saturn) to orbit the sun, as well as the orbit of the moon round the earth, and the precession of the equinoxes, perhaps we can have a go at guessing Plato's perfect number of time. These are the orbital periods defined in terms of earth years:

Mercury: 0.24 years

Venus: 0.615 years

Earth: 1 year

Mars: 1.88 years

Jupiter: 11.86 years

Saturn: 29.46 years

Moon: 0.0748 years (adjusted to the Earth year cycle)

Precession of the Equinoxes: 25 920 years

The value of 0.0748 years for the Moon is derived by considering the synodic month, the time it takes for the Moon to return to the same position relative to the Sun as seen from Earth, and based on a sidereal year of 365.256 days. The result of all these numbers multiplied together is 187 974.1949 years. Or if we omit the moon's orbit, the result is 2 513 023.9957 years, close to 800 000 π years.

There is no obvious connection to the numbers associated with the Indian great cycles of time, the yugas, such as 108, 1296, 4320 or 864. However, if the planetary orbits are multiplied together, as well as precession, and divided by the orbit of the moon, as 0.0748 earth years, and by 6² x 12³ x 10 000 000, the result is 0.998823, close to 1. This means that if half a precessional cycle of 25 920 years is multiplied by the 0.0748 year moon figure, and divided by all the other cycles, Mercury, Venus, Mars, Jupiter, Saturn, with Earth being 1, the result is 99.98733. So we can say the cycles of precession, Mercury, Venus, Mars, Jupiter, Saturn multiplied by each other and divided by a moon cycle as 0.0748, give a result close to 28 x 1 200 000, or 1296 x 25920.

25 920 x 0.24 x 0.615 x 1.88 x 11.86 x 29.46 / 0.0748 = 33 596 577.4823

33 596 577.4833 = 1 296 x 25 923.285 ≈ 1 296 x 25 920

= 28 x 1 199 877.7672 ≈ 28 x 1 200 000

= 20 / 9 x 108 x 108 x 1296.16425 ≈ 20 / 9 x 108 x 108 x 1 296

= 4 320 x 108 x 72.007775 ≈ 4 320 x 108 x 72

Using the ratio 365.256 / 27.321661 instead of the decimal number 0.0748:

25 920 x 0.24 x 0.615 x 1.88 x 11.86 x 29.46 x 365.256 / 27.321661 = 1 296 x 25 922.7991

≈ 1 296 x 25 920

It's possible that the role of the moon was to bring the other cycles together to create a number which was more or less divisible by the all important numbers 6 and 9. Then we get a number of years close to 1 296 x 25 920.

Alternatively, we can divide 1 earth year by the other cycles: 1 / (0.24 x 0.615 x 1.88 x 11.86 x 29.46 x 0.0748 x 25 920), and this is close to the fraction 158 / 29 700 000 = 0.000005319 8653198.

While we can't ever know what Plato considered the “perfect number of time,” we can have a go at thinking about these numbers, in keeping with the general spirit of cosmic cycles, perhaps with multiples of 6, 9 and 12, or with a view to a geometric interpretation, 2 513 024 years being close to 800 000 π. Multiplying the orbital periods of the planets (and dividing by the moon’s period) gives an interesting result: after 33 596 577.4823 years, the planets (along with the sun and moon) would theoretically return to their starting positions in relation to each other.

The *Àryabhatiya of Àryabhata* (c. 499) says that a solar year is a year of men, and twelve thousand of these years give a yuga of the planets.

Thirty of these make a year of the Fathers. Twelve years of the Fathers make a year of the gods. Twelve thousand years of the gods make a yuga of all the planets.(3)

But how does this work? I tried to fit the revolutions of the planets, the moon and precession into 4 320 000 years, but couldn't get it to work.

## Beyond Ancient Greece

As with Plato, in both Indian and Chinese cosmology, celestial bodies and their movements were tied to earthly events, morality, and cycles of time. Plato’s concept of eight revolutions governing the cosmos has a parallel in Indian and Chinese systems, though expressed differently: nine celestial bodies in Indian thought and five planets plus the Sun and Moon in Chinese thought. These traditions share a belief in cyclical time and a cosmic order that governs both the heavens and human life, influencing moral and political structures, and it is likely that other parts of the world held similar beliefs. The movements of celestial bodies were seen as fundamental to understanding the world and humanity's place within it, connecting Plato’s perfect cosmic harmony to the Indian Rita and the Chinese Dao.

There is another possible link to the geometry and size of the Giza plateau. Petrie gives the north-south length of the rectangle formed by the northernmost side of the Great Pyramid and the southernmost side of the third pyramid as 35 713.2 inches.

If we start with the number 12, and divide it by all the orbital periods listed above, and precession, and then multiply it by 10¹¹, the result is 35 717.9240, just a few inches more than the length as given by Petrie, 35 713.2 inches. Or another way of understanding this is to read the length in English feet. With Petrie's value, this is 2 976.1 feet. And the orbit of the earth as 1 year, divided by all the other orbits listed, and precession, is 2 976.4937. And the orbit of the earth as 1 year, divided by all the other orbits listed, and precession, is 2 976.4937.

### A connection to 28?

The length in inches is already remarkably close to 1 000 000 / 28 = 35 714.2857 inches. And 1 000 000 / (2976.4937 x 12) = 27.9971, almost 28.

The height of the Great Pyramid can be interpreted as 280 Egyptian royal cubits. The length of the rectangle just mentioned is 1 000 000 / 28 inches. The number 28 is associated with the lunar month, in that the sidereal month is just over 27 days long so rounds up to 28. As a number of days, 28 is of course easy to divide up into 4 weeks of 7 days. Also, some divisions of the zodiac historically were divided in 28 parts, or lunar mansions (and some into 27). The Zodiac and cubit rod's divisions into 28 parts also allude to this equivalence.

Bailly shows in his *History of Astronomy* that dividing by 27 or 28 was a reference to the sidereal month, and this number was used to create 27 or 28 divisions of the zodiac in many ancient cultures.

The number 28 is also a perfect number, as is 6, so it's interesting to see the fraction 1 000 000 / (6 x 28 x 2) approximately define the ratio of the earth to all the other orbits combines (planets, moon and precession).

The Great Pyramid is 5,776 inches high, which can be interpreted as 280 cubits, or 20.62857 inches / 0.5239657 m. The number 28 clearly displayed in inches is found in the length of the Giza rectangle, or at least 1,000,000 / 28, expressed in inches. The measurement of 35,713.2 inches is close to 1,000,000 / 28 = 35,714.285714 inches, and since it fits so well with the dimension given by Petrie, it must be considered as a possible interpretation.

Just as the path of the sun along the zodiac was divided into 28 parts, here the north-south span of the site, from the north side of the Great Pyramid to the south side of the third pyramid, seems to represent a division by 28 also, in this case, of a million inches by 28. An Egyptian royal cubit is also divided into 28 parts, or 7 x 4.

Why not simply make the rectangle 28 000 inches long? Possibly because the Giza design is based on a dynamic system, in which various elements are meant to be added, subtracted, divided or multiplied by each other, or by key numbers. Also, there fraction 1/28, has interesting connections to astronomical cycles, when these cycles are seen as numbers of days, and in conjunction with irrational numbers.

The number 28 is a curious one because 1 / 28 is 0.357142857, which as we have seen is connected to the length of the Giza rectangle in inches. But it is also very close to 2 π x 29.53059 / (3000 x √3), with 29.53059 being the number of days in a lunation.

When I remembered the equivalences in the table below, I tried again to connect the cycles of the planets with the yuga of 4 320 000 years.

If we take a yuga of 4 320 000 years, and multiply it by 3 x √3 / (200 π), we get a good approximation of the length of the Giza rectangle in inches, 35 726.1124 (Petrie gives 35 713.2 inches), and we know this is also close to 1 000 000 / 28 = 35 714.2857.

The fractions 3000 x √3 / (2 π x 29.53059), 223 x 29.53059 / 235, and 354.36708 x 10 000 / (365 x 345.6201) are all quite close in value, and to 28. These values are all derived from various cycles, see the table above.

The number 43 200 is close to π² x 4 000 x 29.53059 / 27 = 43 178.5542.

Also, if we divide a yuga of 4 320 000 years by not only all the planet orbits, and precession and the moon's sidereal month, all expressed in earth years, but also divide this further by the Metonic cycle of 19 years, we get very close to 1/28, or 2 π x 29.53059 / (3 √3).

4 320 000 / (0.24 x 0.615 x 1.88 x 11.86 x 29.46 x 0.0748 x 25920 x 19) ≈ 2 π x 29.53059 / (3 √3)

So that if we divide 100 000 000 earth years by all these cycles: the planetary orbits, the sidereal month, precession, and the Metonic cycle, all expressed in earth years, we get very nearly 28 exactly.

1 000 000 / (0.24 x 0.615 x 1.88 x 11.86 x 29.46 x 0.0748 x 25 920 x 19) = 27.999364

The Metonic cycle is a period of 19 years after which the lunar phases (synodic months) align closely with the solar year. It reconciles 235 lunar months with 19 solar years, a near-perfect synchronisation used by many ancient calendars to harmonise lunar and solar timekeeping.

So could 28, which is a perfect number anyway, be Plato's perfect number of time? It does make sense to include the Metonic cycle, even though Plato doesn't mention it, because this cycle of 19 years reconciles the earth's year to the sidereal month and to the lunation, or synodic month. 19 years are approximately 6 939.6018 days, which is close to 235 lunations, or 6 939.6887 days, and close also to 254 sidereal months, or 6 939.7016 days.

This might give further support to the reason why dividing a cubit ruler, or the zodiac, into 28 parts, may have been so important, and by extension, dividing by 7 more generally, as 28 is 4 x 7.

Although Plato does not explicitly mention the number 28 in his works, it would have been well-known to him, especially through his connection to Pythagorean philosophy. The Pythagoreans regarded 28 as a "perfect number" because it is the sum of its divisors (1, 2, 4, 7, 14) and had a symbolic connection to harmony and cosmic order. Moreover, 28 was widely recognised in the ancient world as representing the approximate length of the lunar month, a critical timekeeping unit for calendars and religious practices. Given Plato's deep interest in numbers, mathematics, and their role in the structure of the universe, it is curious that he never specifically refers to 28 (as far as I know). However, it is likely that he would have viewed it as important, especially in the context of cosmic cycles, lunar periodicity, and the harmony of time. His omission of 28 may reflect a broader philosophical focus on different mathematical concepts, but the number’s resonance with Pythagorean and celestial thinking would certainly not have been lost on him.

It's interesting in the context of the Giza rectangle measuring 1 000 000 / 28 inches in length that 1 000 000 / 28 is very close to all the cycles in earth years multiplied together: Mercury, Venus, Mars, Jupiter, Saturn, Moon, precession, and Metonic, expressed in earth years. The use of the inch to express time at Giza is researched in this article in particular: __https://www.mercurialpathways.com/post/71-hidden-time-cycles-at-giza__ , and the width of the same rectangle closely matches 80 years expressed in days and in inches.

The Great Giza Rectangle holds remarkable connections to various astronomical cycles and dimensions of the pyramids at Giza, reflecting a profound understanding of planetary orbits, lunar cycles, and geometric proportions. The width of the rectangle, measuring 29,227.2 inches, corresponds closely to ten *octaeteris* cycles, each cycle representing a period of eight solar years, during which the phases of the moon return to the same day of the year. These ten cycles also align with ten Venusian cycles, as Venus completes its orbit around the sun in eight Earth years. In terms of days, 80 solar years (or ten *octaeteris* cycles) account for 29,220 days, a value almost identical to the width of the rectangle in inches. This suggests a symbolic or numerical link between the width of the rectangle and these lunar and Venusian cycles.

The length of the rectangle, approximately 35,713.2 inches, encodes a more complex relationship to planetary orbits, precession, and lunar cycles. When we multiply the orbital periods of Mercury (0.24 years), Venus (0.615 years), Earth (1 year), Mars (1.88 years), Jupiter (11.86 years), Saturn (29.46 years), the moon (0.0748 years), the precession of the equinoxes (25,920 years), and the Metonic cycle (19 years), then divide the result by 100, we arrive at a value of 35,715.0970, a value which is very close to the measured length of the rectangle in inches. This demonstrates that the rectangle’s length appears to have been designed to reflect these astronomical cycles in Earth years, reinforcing the notion that ancient builders possessed significant knowledge of the cosmos.

The measurements of the pyramids also align with mathematical relationships derived from the rectangle. For example, dividing the sum of the rectangle’s length and width by 700π results in 29.53024, a close approximation to the duration of a lunation (29.53059 days). Similarly, the third pyramid’s side length (4,153.3 inches) is nearly identical to the result of multiplying the rectangle’s length by π and dividing by 27 (4,155.4195). These correspondences between the rectangle’s dimensions and the pyramids’ architecture underscore a deliberate integration of cosmic cycles into the design of the Giza complex.

The height of the Great Pyramid (5,775 inches) and the side lengths of the second and third pyramids also exhibit correlations with the rectangle's dimensions when adjusted by ratios involving the lunar cycle, the number 254, and other constants. Even the distances between the centres of the pyramids, such as the east-west and north-south measurements between the Great Pyramid and the third pyramid, demonstrate proportional relationships to the rectangle’s length when calculated using astronomical factors such as the Metonic cycle and the precession of the equinoxes. These precise measurements suggest a deep understanding of mathematical and astronomical principles that guided the construction of the Giza complex, linking the architecture of the pyramids to the natural cycles of the heavens.

Meanwhile, what about those 4 320 000 years of a yuga? Using the equivalences in the last table:

43 200 000 x 29.53059 x 354.36708 / (0.24 x 0.615 x 1.88 x 11.86 x 29.46 x 0.0748 x 25 920 x 19 x 365 x 345.6201) = 1.00338 ≈ 1

So we can obtain the 4 320 000 years this way, but it's not ideal as we are mixing up values in years and in days. Or alternatively:

4320 / (0.24 x 0.615 x 1.88 x 11.86 x 29.46 x 0.0748 x 25 920 x 19) x 223 / 235 x 29.53059² = 1.0009518 ≈ 1

or even:

0.24 x 0.615 x 1.88 x 11.86 x 29.46 x 0.0748 x 25 920 x 19 / 100 x 254 x 2 x 27.321661 / (365.25636 x π) = 432 008.0340 ≈ 432 000

(27.321661 days in a sidereal month and 365.25636 days in a sidereal year)

But here again there is a mix of months, days, and years, so while the numbers work, the units of time don't necessarily. So a unit of 4 320 000 years is still a mystery, unless taken as purely symbolic.

## Conclusion

Possible values for Plato's perfect number of time are:

All the orbital values and precession in earth years multiplied together: 187 974.1949 years.

All the orbital values and precession multiplied together except for the moon's: 2 513 023.9957 years, close to 800 000 π years.

Divide 1 earth year by the other cycles: 1 / (0.24 x 0.615 x 1.88 x 11.86 x 29.46 x 0.0748 x 25 920), and this is close to the fraction 158 / 29 700 000 = 0.000005319 8653198.

1 000 000 / (28 x 12) = 2 976.1905

1 000 000 / (0.24 x 0.615 x 1.88 x 11.86 x 29.46 x 0.0748 x 25 920 x 19) = 27.999364 ≈ 28

The search for Plato’s "perfect number of time" reveals interesting patterns in ancient cosmological thought, where the cycles of celestial bodies reflect a deeper order and harmony in the universe. By multiplying planetary orbits, precession, and the moon’s cycle, we arrive at values that suggest a connection between cosmic periods and mathematical precision. Whether we consider the resulting figures—187,974 years or approximately 2,513,024 years—both are symbolic of vast cycles governing the motions of the heavens, hinting at a cosmic alignment that is larger than human comprehension.

The exploration of 28 as a key number in both astronomical and geometrical contexts provides compelling evidence for its importance in ancient cosmological systems. The close numerical connection between the length of the Giza rectangle, the lunation cycle, and cosmic proportions supports the idea that the number 28 could indeed represent Plato's perfect number of time. Not only is 28 a perfect number in its own right, but it also unifies the celestial cycles through its relationship with lunar and planetary orbits, particularly when factoring in the Metonic cycle. This integration of planetary and lunar cycles suggests a harmony that may have influenced Plato's thinking, even if indirectly. By applying the relationships between planetary revolutions, precession, and lunar cycles to the concept of a Yuga or a Great Year, we see a striking convergence of ancient time-keeping systems across cultures.

In this sense, Plato's perfect number of time could symbolise not just a mathematical culmination but also a deeper understanding of cosmic unity—where numbers, geometry, and time cycles all reflect the same underlying order. The inclusion of the Metonic cycle, which reconciles the solar year with the lunar months, provides further weight to the argument that these ancient systems sought to capture the entirety of celestial motion in symbolic, yet mathematically profound terms. This connection may serve as a bridge between the cycles of the heavens, the divisions of space, and the lived experience of time, highlighting a shared cosmological vision across ancient civilisations.

If we translate the passage from *Timaeus* as follows, we can interpret it as a multiple of 100 or 1000 divided by a perfect number, which could correspond to the number 28:

And now, having come into being within time, the nature of the universe, possessing an eternal form, has completed the thousand-year cycle, the hundred-year cycle, and the entire cycle of time into a perfect number.

Plato's idea of a "perfect number of time" may remain elusive, but the pursuit of it allows us to glimpse how deeply mathematics and geometry were woven into ancient understanding of the universe. The relationship between numbers like 28, 12, and 1,296, and their potential connections to celestial mechanics, reflects Plato's broader philosophical vision: that the cosmos is governed by reason, proportion, and harmony.

This need for cosmic order finds parallels in other ancient cultures, such as the Indian Yugas or the Chinese Dao, suggesting that humanity’s fascination with the movements of the stars and planets is a universal theme. Just as the Great Pyramid may encode certain astronomical or geometrical principles, so too does Plato’s cosmology strive to encode a perfect, eternal cycle.

The ancient astronomical knowledge embedded in texts like the Indian yugas and Plato's writings should not be dismissed as mere symbolism or myth. These numbers reflect a highly sophisticated understanding of celestial cycles, one that took centuries, if not millennia, to develop through careful observation. The Metonic cycle, the octaeteris, the 60 and 600-year cycles, and others reveal the depth of ancient societies’ grasp of planetary and lunar movements. Far from being arbitrary, these cycles demonstrate a precision in calculating astronomical phenomena, such as the alignment of the solar and lunar years, or the complex patterns of planetary orbits. The astronomical insights that gave rise to such cycles represent a collective achievement, possibly lost or fragmented by Plato's time, but were originally based on sound empirical evidence. We should think about giving proper credit to this achievement, acknowledging that their advanced knowledge of astronomy was derived from generations of detailed observations. To dismiss these numbers as symbolic without appreciating the underlying astronomical reality risks underestimating the achievements of the ancient world. Of course, these values also came to be highly symbolic too, and that is an important aspect of Plato's legacy.

Ultimately, while the precise value of Plato’s perfect number of time remains open to interpretation, the enduring lesson is that the universe’s mathematical structure mirrors its intrinsic order, a harmonious design that invites contemplation and wonder.

## Notes

Plato, Timaeus

Cornford, Francis Macdonald, 1937,

*Platos Cosmology,*pp92-93__https://archive.org/details/in.ernet.dli.2015.221748/page/n111/mode/2up__*The Aryabhatiya of Aryabhata, An Ancient Indian Work on Mathematics and Astronomy*, translated with notes by Walter Eugene Clark, Professor of Sanskrit in Harvard University, The University of Chicago Press, Illinois, 1929. p.8

Plato, Timaeus, 29e

Plato, Republic, Plato in Twelve Volumes, Vols. 5 & 6 translated by Paul Shorey. Cambridge, MA, Harvard University Press; London, William Heinemann Ltd. 1969.

__https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0168%3Abook%3D10%3Apage%3D617__Plato,

*Timaeus*, Translation by David Horan,__https://www.platonicfoundation.org/translation/platos-timaeus/__This is ChatGPT's translation

## Appendix

Some pages from Bailly's *Histoire de l'Astronomie Ancienne* on the subject of planets.

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