f57v a little more on mathematics and geodesy

One of the less comfortable things about those figures at the centre of  f57v is that they are drawn dreadfully, and dreadfully in precisely the same way that Kircher’s are in that picture containing ‘Machauter’. While I might speculate on the reasons for that correspondence, I can’t doubt the C-14 dating and can only suppose Kircher had access to (and copied) some image derived from the figure of Matsya (illustrated below).   Originally a Creator deity, then a figure who “forewarns Manu about an impending catastrophic flood and orders him to collect all the grains of the world in a boat”, and finally an avatar of Vishnu in the Hindu pantheon, Matsya is not a deity widely known or honoured, and this fact may well prove relevant one of these days.

Of the few sites remaining today dedicated to Matsya, the two most important are at  Bet Dwarka in Gujarat ( 22.23°N 68.97°E) on India’s north-west coast, and on the eastern (Coromandel) coast.   Vedanarayana Temple stands in what is now a small village named Nagalapuram (13.4000°N 79.7833°E).

Both those  sites are near river-mouths and near to the most important of the ancient ports;  Barygaza in the west and Arikamedu on the eastern, Coromandal, coast.   Higher north on the eastern coast  is a site named St.Thomas’ Mount, where tradition held that the saint had been martyred. Revered for more than a millennium by the indigenous Christians, it was to become  a centre of Latin Christianity, richly endowed and the centre of a large foreign enclave.  (A different Nagalapuram exists in the Ramanathapuram District).

Kircher's Mer-godf.57v centre roundel detail blogFishtail vishnu Matsya_Avatar






 Muziris, which is so well known to western authors lay to the south-west. Pliny said Barygaza was preferable, to avoid pirates, but in Muziris had stood a temple of Augustus, pictured in the Tabula Peutingeriana. And Muziris too  was associated with Thomas, and another mount whose name was popularly derived from Thomas’ “peacock” emblem. 

Hence – just  by the way –  my posited identification for the  group of plants forming the subject of  f.32v: Eastern ‘peacock trees’ – but more on that later).

What has this to do with mathematics and the ‘folded world’ – indeed.

Late in the 5thC AD, an Indian mathematical genius named Aryabhata wrote works in sutra style: a highly condensed style aimed less at prose record than compacting information to enable easier committal to memory and easier recall of details.

It condensed not as an enciphered text would be, but from formal custom just as (in a different way) maths notation is. And he didn’t use numerals but signs, similar to the dual use of alpha-numerics.

Aryabhata, by the way, described the irrational nature of about thirteen centuries before it was explained to western Europe.

His works were preserved in India by repeated copying (he is still best known in the southern, Tamil regions) and also by translations made into Arabic, and in that way later into medieval Latin.

We may have the idea of the ‘folded world’ because of a mistranslation of his ‘shorthand’ term for the sine.

Aryabhata discussed the concept of sine in his work by the name of ardha-jya, which literally means “half-chord”. For simplicity, people started calling it jya. When Arabic writers translated his works from Sanskrit into Arabic, they referred [to] it as jiba. However, in Arabic writings, vowels are omitted, and it was abbreviated as jb. Later writers substituted it with jaib, meaning “pocket” or “fold (in a garment)”.

(In Arabic, jiba is a meaningless word.) Later in the 12th century, when Gherardo of Cremona translated these writings from Arabic into Latin, he replaced the Arabic jaib with its Latin counterpart, sinus, which means “cove” or “bay”; thence comes the English sine.

Hence – “I like the cut of your jib?” 🙂

Al-Biruni and  al-Khwarizmi are among writers in Arabic who evidently knew the  Aryabhatiya, which covers arithmetic, algebra, plane trigonometry, and spherical trigonometry. It also contains continued fractions, quadratic equations, sums-of-power series, and a table of sines.

If you imagine these added to the calculations by Eratosthenes, there was not much more that a chartmaker would need in his repertoire save a chart of latitudes and longitudes.

So in this way, again, those regions referenced by the imagery show a pattern consistent with the historical record.

As noted earlier, the style in which additions to f.86v appear to me to have been made accords with the time that the Genoese had contact with Persia, the time when the crossbow reappears in western Europe (chiefly associated with the Genoese), and while in the north, in Trebizond, a Byzantine scholar was melding such sources as Claudius Ptolemy’s tables and the work of al-Khwarizmi.

So I think the ratios given the four radii at the centre of f.57v are most likely meant as ratios for the cartographers’ world.

But whose ratios is the problem, isn’t it?

I’ll come back to this – and to paranatellonta – at some stage.




7 Replies to “f57v a little more on mathematics and geodesy”

  1. I confess that I have inferred use of al-Khwarizmi’s works at Trebizond in addition to the certain use of al-Tusi’s.
    Note too, that some descriptions of mathematics and astronomy in Islam downplay the degree to which the Muslim scholars simply translated and used entire older works of Indian scholarship, as they did the Greeks’. This is not to deny advances made by individuals in the borders of Islam, but to correct impressions of the kind too often seen online ~ as for example this wiki article.


  2. Think/See/Fly, just )-)100 years before your time – line here.

    about 1100 AD (+/-)

    *Yes I know the carbon-dating (when was the LAST written?) 1400’s*

    1st !!! is: ES> “IT IS OLDER THAN YOU THINK”

    -=se=- steve (THE TIME IS NOW) ekwall 🙂 Date: Tue, 19 Mar 2013 01:13:17 +0000


  3. Oh? – ow/how/woh Did I get back to HERE? ~strange~. 3/21/2013: 1:16mst.

    Diane: your ~center point~ is correct, remember though a spun/spinning of clay/mud
    can make saucers, plates, cups etc of ALL sizes (the original THIS BIG SIZE) kings foot
    or elbow etc..small little bigger biggerYET & Biggest of all (AfTeR FiRiNg). Inking around is a piece of cake/pizza pie? (perfect) ’round’ – ~See the older/ original source~ of/for circle.

    fun: change focus on Shapes: relax:
    1 snip see (5 pointed star) http://www.ushistory.org/betsy/flagstar.html

    steve (&i don’t do origami) ekwall 😎


  4. Oh, I remember sorry about using your bandwidth…
    wifEy says it’s ADDos (attention deficit disorder * oh shiney!)

    your lines above (center of f57vms) make a cross – rotate them to 11:2:4:8: to make an “X”
    and you’ll be at the START positing to decode it.

    3/21/2013 1:29mst


  5. Steve, you may think it odd, but I have very little interest in the written text. Apart from having no particular gift for languages, and programming skills so rusty they’d fall apart if I tried them out, and a zero interest in ciphers, I fully expect that if or when the text is deciphered it will either be nothing we haven’t already from other sources, or something hardly intelligible to a modern reader (like the ‘Gnosis on the Silk road’ texts), or totally yawn-worthy because what people thought way-hay technological secrets in the fifteenth-seventeenth centuries – like mustard essence medicine, you can look up on the internet these days. So all the interest and puzzlement, for me, is in the imagery itself. It doesn’t even appear to have been any kind of secret-secret. Mysterious, surely, but only seemingly as other peoples’ customs can seem until you live there a while.

    (since writing the above I have found, with some amusement, a similar view expressed years ago by an earlier Voynich researcher, who also said that he expects the text may prove disappointing).


  6. Steve – I don’t know how you know what you know, but thought I’d tell you that I’ve recently come to think that almost all the additions were complete by the 1400s. As you said earlier..

    “… Yes I know the carbon-dating (when was the LAST written?) 1400’s* “


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