The key to fol.67r -ii is not that it includes a sequence of moons, but the twelvefold division in which they are set. This, together with the numerical factor of 8 provided by the central flower from a point in which a dotted line signals the point of beginning-and-end speak to the diagram’s function. The form given the central flower tells us still more about it.
It has been suggested (see following comments) that the diagram refers to computus, and it would not be surprising to find a computus diagram in a book of extracts made for a fifteenth-century scholar.
In this case, though, I believe that the diagram’s factors of 12 and 8, quite apart from its relative simplicity or the context in which it occurs, require a different (if tangentially related) reference~ i.e calculations of time and tide for navigation itself.
For a fuller discussion of computus, and examples of early charts in that context (including an early tidal chart) see
Folios considered from the manuscript’s botanical section have already pointed the reader towards the ‘great sea’ and the world east of the Bosphorus or Suez. So too will the bathy- section ~ and so also the inclusion of this diagram, which applies so naturally to the older maritime method for calculating time and tide in terms of the moon and compass ‘rose’. This interpretation of its function is one consistent with both the diagram’s form and with content in these other folios considered so far.
Cresques’ pictorial almanac ~ which I’ve had reason to mention before ~ included as early as 1375 a chart to enable calculation of tides along the coasts of the western Mediterranean.
Ibn Majid says, in the fifteenth century, that calculations of the date for the eastern sailings begin from the date (also in Spring) of the Persian new year, Nowruz.Precise calculation was essential in seas whose traverse had to be made under the seasonal monsoons, miscalculation of which would leave a ship becalmed, or delayed for as much as a year by contrary winds.
And since Easter’s date, though calculated by computus, was also fixed by reference to a particular full moon, the method used for its calculation was not so far removed from these others. [see also the Computus Runicus found in Gotland]
I apologise for the poor quality of this linked image to Cresques’ tidal chart. Its caption contains disputed information, too, but I can find no other readily available online – if you know of a better, please leave a comment and I’ll change the link).
Computus and the Voynich
After I’d first written about this diagram, I found a post in ciphermysteries discussing Steve Herbelin’s suggestion of connection to computus – methods for calculating Easter’s date.
Easter’s date was also a major religious feast for Christianity, and was calculated according to a method originally used for the pre-Christian calendars of the East, specifically one gained from older Christian Egypt. As a mathematical problem, this calculation was considered non-trivial and computus became a subject on which eminent masters of the quadrivium would write as a matter of course, and not only clerics. Easter was the first day of the year in medieval Europe.
I don’t think that the purpose of the digram on fol.67r-ii is to assist computus, but in any case Steve’s suggestion has been given its historical and technical background in that excellent post at ciphermysteries, so I see no reason to add more here, save to emphasise that the method for computus originated in Alexandria, and that if the mathematical issue intrigues you, Mosshammer’s monograph covers that earlier period.
Time and Tide: the Egyptian ‘lotus’ Rose
It is very generally the case that maritime customs of the Mediterranean world owe a great deal to earlier Egypt, and perhaps one of these days, I should outline that impact. In reference to the manuscript, it is noteworthy that the master Ibn Majid still dismisses all Mediterranean mariners of the fifteenth century (save perhaps Barbary men) as [mere] ‘Egyptians’ who know nothing of the star-compass of star-bindings (a technical term of navigation), or the custom of using the form of the ship to define that of the world.
From this, I should have been less startled perhaps than I was at seeing here in the centre of fol.67r-ii a form for the rose which was that used in dynastic Egypt.
One might say, rather, that Egypt had two such ‘roses’ forms: for the day hours, the blue Nymphaea caerulea stood for the world and the hours about its horizon; the white Nymphaea lotus served a comparable purpose in regard to the hours of the night, and it is N.lotus ~Egypt’s white lotus ~ which was normally drawn with its petals speckled. (Examples follow)
After that first shock of recognition, I came to find its presence in the manuscript more reassuring than otherwise.
It is so accurately drawn that it cannot be argued pure invention. The antiquity of the image and the natural link between the white ‘night’ lotus and the outer circuit showing lunar phases reinforced a sense that this diagram described a means to calculate the lunar periods by reference to the points of the compass.
We know how this was done, and altough our later descriptions use a twenty-four fold series to represent the hours or both night and day – whereas this uses only a twelvefold division for the compass, I think their common nature will be clear enough in the description which follows.
But first, a couple of illustrations to show the relationship between this version of the compass ‘rose’ and the form given the lotus/rose in older Egypt. How long a diagram of this type might have survived in use I shan’t try to guess, although within these lotus bowls below, those most like the design of fol.67r-ii are the oldest, and all pre-Hellenistic.
During the Ptolemaic dynasty, the older Nymphaea was replaced by the Asian Nelumbo. In this form it more closely resembles the form of the later medieval compass-diagrams. (see e.g. that on the Breton Tables shown below, and also the Nautical Alamanac, and Portolan chart of Guillaume Brouscon (Fr. 1543).
The relationship of those bowls to ones which Layard discovered in Mesopotamia, formed in the Phoenicians’ characteristically Egypto-Persian style is not a subject that has been studied in depth, I think ~ but some may carry similar import. Not to digress, but here’s one:
On both the older Egyptian bowls, a point is distinguished from the rest; on the New Kingdom bowl by leaving that point blank, and on the Abydos bowl (whose date I omit to avoid alarm), by providing one of the white lotus flowers with a thicker stem.
In fol.67r-ii the same is done, but in this case the marker is a line of dots extending from one point. The number of points with which the lotus could be pictured can differ, just as the number of points on our own compass ‘rose’.
Here, by the way is another version of the Egypt’s ‘rosamundi’, showing the four cardinal points, or four quarters, each with their distinct character.
Just as one could refer to the horizon/rose by eight points, or fewer, or as many as 32 or eventually even 64 points, so too the horizon ‘rose’ could be divided into 12 or 24 to represent direction, seasonal times, hours and combinations of those things.
In fol. 67r -ii, the central lotus has a principal division of eight, which is the basic number of points for the compass-rose diagram, although the inclusion of the underlying form as the Carian ‘rose’ or a pointed leaf of Nymphaea might suggest the possibly finer division, in the same way that each of the Egyptian bowls has its dual or doubled level.
Fol.67r-ii clearly emphasises a division into eight (by the rose) and by twelve (by the moons).
And those are the factors by which time-and-tide were being calculated by Mediterranean mariners ~ sometimes as a doubling, tripling or quadrupling of the ‘8’ ~ to as late as the sixteenth century.
The antiquity of the method was well known, as Frake points out when quoting from a work published about 1500:
[Although] There is a difference between the astronomers and the mariners concerning the course of the moon… and although the astronomers may be right in this matter and the mariners wrong, the difference of three minutes is so slight that it makes no difference … We will therefore follow the opinion of the mariners, since the tides are more easily calculated by the compass than in any other way, according to the ancient practice of mariners.
as quoted in Charles O. Frake, ‘Cognitive Maps of Time and Tide Among Medieval Seafarers’, Man, New Series, Vol. 20, No. 2 (Jun., 1985), pp. 254-270 [JSTOR] p.266
Frake also describes the method, although the terms he employs differ from the custom evident in our diagram, he referring to the period post-12thC when the Mediterranean now used a magnetised needle upon its compass rose diagram.
The change meant that people began referring to direction as distance towards a magnetically defined point, where in the older way it was defined by the point from which the wind came which would carry a ship in the opposite direction.
In addition, too, we have an increased number of temporal and geographic divisions , including a use of the twenty-four hour circuit, rather than the twelve of day and twelve of night, but nonetheless I think it will be clear enough how the combination of an eightfold rose and a twelve-fold ‘time-horizon’ ( or e.g. by two hours per division] had earlier achieved the same result. I have re-ordered Frake’s paragraphs for clarity:
Medieval sailing directions, and presumably the memories of sailors before written directions, specify the tidal regime of a given place by stating the lunar time, named as a compass bearing, of a given state of the tide, usually high. ‘All havens be full at WSW moon between the Start and the Lizard’ (Taylor1956: 132). This ‘establishment of the port’ means that, on this area of the Channel coast, it will always be high tide at the lunar time of ‘WSW moon’.
The compass rose was the clockface of the medieval sailor. The .. points of the compass divided the twenty-four [12 x 2] hours of the day…The advantages of this seemingly odd division of the day become apparent when we consider lunar time, the time of the tides.
When the moon reaches its highest point in the sky as it crosses the meridian, it, like the sun, always bears due south in the latitudes of northern Europe. This lunar time can be thought of as lunar noon and named ‘moon bears south’.
Of course the moon cannot always be seen at lunar noon, but lunar noon can always so be named. Similarly ‘moon bears east’ names the lunar time of moonrise whether or not the moon is visible at that time and whether or not the moon actually bears due east at that time (the rising and setting bearings of the moon vary through an even greater arc than those of the sun and, like the sun, are due east and west only when the moon is on the celestial equator).
‘Moon bears north’ names the time when the moon crosses the opposite meridian when it is never visible. At full moon, when the moon and sun are in opposition, ‘moon bears north’ names a lunar time that corresponds with solar noon, ‘sun bears south’.
Since WSW is six compass points past south [on a 32-point compass diagram], the lunar time of WSW moon occurs about four and a half hours after lunar noon (‘moon bears south’) when the moon crosses the meridian.
Like lunar time, solar time can also be represented by a compass bearing.
During the middle ages, scarcely one person in thousand could calculate a calendar or predict eclipses. And so even printed works, when they had to speak of practical applications for such knowledge, turned from the astronomer’s way to the longstanding, practical customs of the mariner.
Taylor’s explanation of the Breton tables, used for such calculations in the later medieval Mediterranean, is shown below. Once more, this is the later and more complex style. But what this implies for the diagram on fol 67r-ii is, again, that in both form and substance it represents an older source. It is also possible that the inscriptions refer to ports rather than to astronomical or temporal points.
*The lunar phase-diagram
The appearance of the moon at a given time will be different, of course, depending on a person’s position on the earth. This site will explain more efficiently than I can here why this is so. To adjust for your own location and time-zone, first go here.
*Egyptian tradition – dynastic
The Egyptians themselves made much the luminous petals of the white Nymphaea lotus, and the way these the two different Nymphaea species opened for the sun or for the night, alternately. Thus, describing the blue:
Nymphaea cerulea… “was said to rise and fall with the sun [though] is not, in fact so…. The flower buds … rise to the surface over a period of two to three days, [after which] the ..buds open at approximately 9-9:30am each day and close about 3pm. The flowers have pale bluish-white to sky-blue or mauve petals…”
The quoted passage is from the wiki article.
One can understand persistence in tradition concerning the blue, and the white, but the way the flower is drawn on 67r-ii seems more directly connected to the older iconographic habits.
* Egyptian tradition – Christian era
During the early Christian centuries, the Egyptian style of monastic life greatly impressed early commentators, who (directly and indirectly) link the customs of some to what were apparently much earlier maritime ones, including the custom of chanting the ‘stars’ of the night watches, the division of watches into 12 and so forth. In that regard, the Tabbenitic monks are especially noted, and William of Rubruck mentions that those at Canopus had maintained a fleet in service to Byzantium up until the abandonment of Egypt to the Arab tribes. Soon afterwards, the old port of Canopus was lost, sliding beneath the sea along with the pre-Hellenistic ‘Greek’ port of Heracleion. To one or another of those we may, ultimately, owe this diagram.
The monastic centres of Christian Egypt were also noted centres for the production of glass and pottery.
Like a number of other plants (e.g. Martynia annua), Nymphaea caerulea was transported into the east, to India and even as far as Thailand, at some very distant time. .. an important point in this context.
Although the tides of human fluids were believed, like those of the sea, to wax and wane in strength with the moon, the following is the sort of chart used for that type of calculation. (from the personal florilegium of an English physician: 12thC). Diagrams of lunar mansions and planets were normally circular, but I see no suggestion of the planets (or indeed of astrology) in fol.67r-ii.
A credit to Ellie Vellinska who today (15 March 2013) discovered another example Egerton 747 f. 111 and brought it to the notice of the Voynich mailing list.