A Lusospherical Triangle [Draft]

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A LUSOSPHERICAL TRIANGLE

Pradip Baksi

ABSTRACT: This paper is about a Lusospherical triangle, thevertices of which are, geographically speaking, located atLisboa/Lisbon, Kolkata/Calcutta and So Paulo and, conceptuallyspeaking in some responses to the mutually interrelatedgrammatical, aesthetic and mathematical domains of theNorthern and Western Mediterranean Basin Culture. Theseresponses came, respectively, from: Manoel da Assumpam/Manuel da Assumpo [c. 1700+; dates of birth and death stillunknown] of Portugal, Henry Louis Vivian Derozio [1809-1831] ofBengal, India and, Ubiratan DAmbrosio [1932-] of Brazil. Theassumption that the planet Earth is spherical is anoversimplification. The geographical contours of these three cities,consequently the latitudes and longitudes of their centers, theconceptual concerns and priorities of the domains of grammars,aesthetics and mathematics and, their interrelationships haveshifted in the past, are continuing to shift at present and, will

probably shift in future along many random, chaotic, complex,dynamic and nonlinear paths; hence, the title of the paper isprovisional and tentative. It is a first approximation of manycomplex and chaotic grids of conceptual networks. The title willprobably be changed into something else by the future


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investigators of the various conceptual networks of this andsimilar cultural spheres.

KEYWORDS: Lusosphere; Grammar; Aesthetics; Mathematics.

We are now living in a time which resembles the intellectual effervescence of theMiddle Ages. It is thus justifiable to speak of a new renaissance.

Ubiratan DAmbrosio, 2006: 19

1. DATA

LUSOSPHERE

Lusosphere is the cultural sphere, created by the people of Portuguese ancestryand/or, the Portuguese speaking people of the world, over the last severalcenturies. On this term see: Seminar, #630, February 2012 [see link in theReferences below (henceforth, see link)]. In this paper the geometrical terms havebeen used in their literal and metaphorical senses. The usage is literal, because onemay provisionally use a spherical triangle to join the central points of the threecities of Lisboa, Kolkata and So Paulo on the planet earth. This usage is

metaphorical, because here we are dealing with the circulation of some ideas over acultural triangle in the widest sense of the term. The centers of these three urbanlandscapes, the various aspects of human culture of these three cities, includingtheir relative positions within the Lusosphere, the trajectories of grammars,aesthetics and mathematics and, their mutual relationships in human culture havechanged, are changing and, will probably continue to change over time. That is whythere is some uncertainty about the possible title of the paper.

VERTEX ONE: GRAMMAR

Aquas do Gange, e a terra de Bengala

Fertil de sort que outra no lhe iguala.

Os Lusiadas, VII. 20

Manoel da Assumpam /Manuel da Assumpo, was born [date of birth not known]in Evora, Portugal, where he entered the Order of the Augustinians [Zwartjes, 2011:

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Later scholars have noted that Assumpam discussed only the morphology andsyntax ofBangla but, did not say anything about its phonetics [Kaium, 2012: 28]. Itmay be mentioned here, that even though writing in those days of dominance ofLatin grammar over the consciousness of Portuguese missionary grammarians,Assumpam made the sociolinguistic observation that Bengali has a colloquial and,

a more prestigious Brahminical style [Zwartjes, 2011: 59]; that it does not entirelycorrespond with Latin. He also compared Bengali with Hebrew and Aramaic(Chaldean) [ibidem: 60]. He was guided by the dominant ideological belief that themissionaries are duty bound to learn the local languages of the people of theirrespective areas of residence, in the interests of proselytization [ibidem: 61]. Inother words, even at that moment of imposition of the dominant grammaticalculture of the Northern and Western Mediterranean Basin over the linguisticcultures and styles of Bengal, Assumpams work reflected some elements oflinguistic truth, certain cultural cosmopolitanism and, a morality based on amissionary sense of commitment to the needs of proselytization.

Assumpams Breve Compendio da Grammatica Bengala is a small part [pp.1-40] ofhis large book. The rest of the book has 2 parts: Vocabolario: Bengala-Portuguez[41-306]; and, Vocabolario: Portuguez-Bengala [307-592].The last 20 pages of thisbook contain semantically arranged lists of words; such as, the names of the days ofthe lunar fortnights, numerals, planets and, most interestingly, the names of somebooks about the sects, laws and sciences of the gentiles [Zwartjes, 2011: 58]. Thestructures of these lists remind one of the Nighantu and Nirukta of Yaskacharyaand, of the Amarakosha [c. 400-600] of Amarsingha [see links]. Nothing is knownabout the level of Assumpams exposure to classical Greek, Latin, Portuguese,Persian and Sanskrit lexicography and grammar. However, Faridpur, where he

stayed and worked, was very famous for Sanskrit, Persian and Arabic learning, for aconsiderably long period of time; and, he or the other Portuguese missionaries whomay have helped Assumpam in this task, might have come in contact with some ofthe local scholars. Assumpam became the Rector of the Church of St. Nicolao of

Tolentino [St. Nicholas of Torentino], located at Naagari [see links], in the Reyno deBengala, in the year 1742. The place and date of his death remain unknown.

Assumpam began a process of standardizing codified literary Bengali language inthe image of Latin. This task was subsequently taken up by the English missionariesand some members of the Bengali Bhadralok [see link] literati of the nineteenthcentury, under the dual influences of Latinized English grammars and Sanskrit

grammars popular in Bengal of their time. This period in the history of Bengal iscalled the Bengal Renaissance [see link; Sen, 1946]. An important humancomponent of that process was a group of young men known as the Derozians or,the Young Bengal [see link], who were inspired by the rationalist spirit of theiryoung Luso-Anglo-Bengali teacher Henry Louis Vivian Derozio, poet, philosopherand free-thinker [Edwards, 1884: 1]. His interventions in aesthetics gave rise to oursecond vertex in early nineteenth century.

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VERTX TWO: AESTHETICS

In splendour London now eclipses Romeand in similar respects, Calcutta rivalsthe head of empire. But in no respect can she appear so eminently so, as in her

publicationsIf in Europe, the number of publications gives the ground toratiocinate the learning and refinement of particular cities, we may place Calcuttain rank above Vienna, Copenhagen, Petersburg, Madrid, Venice, Turin, Naples oreven Rome.

William Dune, in The World (Calcutta), October 1791; quoted in Schwarz, 2000:563

There were two places in India where the most recent works issued from the pressof Britain could be found. These were the shelves of the most enterprisingbooksellers and the library of Derozio, frequently the latter alone.

Edwards, 1884: 7-8

Henry Louis Vivian Derozio [18 April 1809-26 December 1831] was born, grew upand died in the city of Calcutta/Kolkata, Bengal, India. His mother Sophia Johnsonwas from Hampshire, England. She married his father Francis Derozio, ChiefAccountant of a mercantile firm, at Calcutta. Henrys grandfather MichaelDerozio/DeRozario [1742-1809] was a Portuguese Merchant and Agent in the city[Derozio, 2001: III]. Henrys mother died in 1815 and, he was admitted at theenlightened Scottish educator David Drummonds Durrumtollah Academy in thesame year. The curriculum in that school at that time included English, Latin, Greek,French, Bengali, Persian, Arithmetic, Book-Keeping, Geography, Astronomy,

Geometry, Trigonometry, Algebra and Drawing [Mukhopadhyay, 2004: 228-230].Henry received his instructions there up to the age of 14. For the remaining 8 yearsof his life, he continued to educate himself. He worked for a while as a clerk in themercantile firm where his father was employed and, in an indigo plantation atBhagalpur, Bihar. In the year 1826 he became a sub-editor of the India Gazette and,the fourth teacher of the Hindu College, both at Calcutta. His first collection ofpoems came out in 1827 and the second collection in 1828 [Derozio, 2001: VI and507]. He taught English Literature and History in the college and, was respectedand loved by his students as he encouraged them to examine every issue critically.For this very reason he was slandered by the conservative sections of the gentry of

Calcutta, dominant in the governing body of the college and in the local press. Hewas forced to resign from the post of teacher in the College on 25 April 1831. Heestablished a daily newspaper named the East Indian on the 1st of June and, died ofcholera on the 26th of December the same year.

During the period 1760-1840, the languages used in Calcutta and its environsincluded Arabic, Bengali, English, Hindustani, Persian, Portuguese and Sanskrit[Clark, 1956: 453]. Portuguese was one of the main lingua francas in the Indian

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Ocean worlds of trade and law during the founding first decades of Calcutta [Raj,2011: 61].Six years after Derozios death, that is in the year 1837, there were 3181Portuguese, 3138 English, 4746 Eurasians and, 165385 Bengalis in Calcutta [Finch,1850: 172]. Hence, it may be said that both ethnologically and linguisticallyspeaking Calcutta of Derozios time belonged to multiple linguistic and cultural

spheres and, Lusosphere was one among those.

Derozios ancestry is connected to the Lusosphere on one side and to theAnglosphere on the other. He was exposed to the aesthetics of the Northern andWestern Mediterranean Basin Culture mainly through the medium of Englishlanguage and literature, in India. He is one of the first Indian English poets andthinkers born and brought up in Bengal. He was among the few sparks that ignitedthe Bengal Renaissance; and, for that single reason alone he not only belongs to themodern Bengalosphere, through the attainments of his students and their followers,he is one of its principal architects.

Of his many contributions, those related to his critique of the then dominant canonsof European art, literature and aesthetics are the objects of our special attention inthis paper. In his article On the Influence of Poetry, published in the India Gazetteon Friday, the 22nd of January 1830, he wrote: we are not insensible to the truth ofmuch that has been written by Milton, Shakespeare, Dante, Burns, Byron, Shelly,Wordsworth and Campbell, but even in the writings of these great men, how manysentiments are to be found, which, in their general consequences, may beproductive of more evil than good? Granting, however, that none such may bediscovered in their works, can we not name a host, the greater portion of whosewritings have the most direct tendency to degrade human nature, to beautify time-sanctioned fallacies, to give greater currency to erroneous opinions, and, in short toretard the moral and intellectual advancement of human nature? Deroziocontinued: Let it not be understood from the general tenor of the precedingremarks, that we are opposed to the cultivation of poetry. Let us not be chargedwith a heresy which we loath. On the contrary we wished to see a radical reformeven among poets; and we hope that this age of investigation will direct itsattention to a subject concerning which more false notions prevail than any otherwith which we are acquainted. Poetry cannot be destroyed; for it is the productionof taste and imagination, and the expression of passion. It only indicates theexistence of these, and while they exist, they will operate; and the result of theiroperation will be poetry and the fine arts. The hope that aspires to eradicate them

from the human mind is impotent, and will fail; but that which endeavors to securefor them a proper direction needs only a persevere, and its object will be attained.

The stream of poetic thought has generally flowed through poisonous channels,corruption. Let it be the aim of the present age to open new springs; let the mindengage in voyages for the discovery of happiness; let the poet abandon war,misanthropy, romances and false feeling and let his enthusiasm be on that sidewhich espouses mans best interest; let it be his object to improve, while he

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delights, and to promote the advancement of society, while he scatters flowersalong its path: and he may rest assured that fame will not only await his steps butthat he will attain a high rank among the best benefactors of mankind [Derozio,2001: 321-322]. This text has been hailed as Henry Derozios Manifesto on theNew Indian Aesthetics [Williams, 2008a; for an acquaintance with Derozios poetic

creativity see Williams, 2007 and 2008b].

Our second vertex, located in Calcutta/Kolkata, is about a critique of Western andNorthern Mediterranean Basin style literary canons and aesthetics of earlynineteenth century. In a sense Derozio was a Tolstoy in art and literature, about onehundred years before Lev Nikolayevich Tolstoy [1828-1910].

Our third vertex is about a Tolstoy in mathematics about one hundred years afterTolstoy, involved in evolving a programme of reevaluation and reconstruction of theplural grammatical [structural] and aesthetic [creative] heritages of mathematics onour planet. It is now called the Ethnomathematics [see links] Programme. Many

Portuguese speaking persons as well as many people from outside the Lusosphereare associated with it. In the present paper we are drawing the attention of ourreaders to one of its central figures: he is Ubiratan DAmbrosio [see link] of SoPaulo, Brazil.

VERTEX THREE: MATHEMATICS

No sou nada.

Nunca serei nada.

No posso querer ser nada.

parte isso, tenho em mim todos os sonhos

Do mundo.

Tabacaria, lvaro de Campos, 1928; quoted in DAmbrosio, A. S. and B.S.DAmbrosio, 2007: 1

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Ubiratan DAmbrosio [born 8 December 1932- , in So Paulo] is an EmeritusProfessor of the State University of Campinas, So Paulo, Brazil. He is recipient ofthe Kenneth Ownsworth May Medal of History of Mathematics (2001) granted by the

International Commission of History of Mathematics and, of the Felix Klein Medal ofMathematics Education (2005) granted by the International Commission ofMathematics Instruction. He is an historian and educator of mathematics andscience, a transdisciplinarian and, activist of the movements devoted totransculturalism and peace in the world. He is one of the principal organizers andleading figures of the Ethnomathematics movement, oriented on studying manykinds of mathematics as components of various human mathematical cultures onplanet earth.

He was trained in, conducted investigations on and, taught various branches, topicsand aspects of the currently globally dominant Northern and Western

Mediterranean Basin style mathematics in Brazil, Italy, USA and Mali. He arrived athis early ideas of ethnomathematics in 1970. His ideas and the EthnomathematicsProgramme are still evolving [see DAmbrosio, Ubiratan and Beatriz SilvaDAmbrosio, 2013]. Competent people have written about the intellectualcontributions of Ubiratan DAmbrosio to ethnomathematics [Scott, 2011]. Ipersonally think that in view of his still evolving encyclopedic interests and multipleengagements as an activist, it is not possible to say anything final about his lastingcontributions right now. This much can be said, however, that irrespective of theglobal academic acceptance or rejection of the ethnomathematics programme innear or distant future, the days of world-wide uncritical acceptance of all thedogmas of mid-nineteenth-century Northern and Western Mediterranean Basinmathematical culture as The Mathematics are over. In the present and futurecontext of literacy, matheracy and technoracy [DAmbrosio, 1998], when heutagogy[Hase and Kenyon, 2001; 2007] and virtual open schooling are poised to replace theold preconceptions and infrastructures of instruction, then the schools anduniversities of the world may choose to ignore Ubiratan DAmbrosios sage adviceonly at their own peril.

2. DISCUSSION

Grammars represent the structures of codified literary languages. Literatures in

such languages reflect the hegemonic literary canons and aesthetics of a givenplace and time. All mathematics happens to be codified languages of various kinds,the strings of symbols/alphabets of which have their domain-specific formation rulesand transformation rules; that is to say, they have their grammars. Mathematicalliterature of a given place and time are expressions of human imagination andcreativity and, as creative literature they reflect the hegemonic mathematical-literary canons and aesthetics of that place and that time. It is in this sense thatgrammars, aesthetics and mathematics are connected to, and, enter into, each

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other, within the sphere of human culture and, within the many specific linguistic-cultural spheres that constitute the totality of it.

Any three points on the surface of a sphere describing a spherical triangle may bejoined by various deterministic curves like the great circles or, by non-deterministic

curves like the contours of a natural coastline or, by other suitable arbitrary andrandom curves. The curves joining our grammatical and aesthetic vertices mayrepresent the various forms of art, literature (including mathematical literature),technology and science; the curves joining the aesthetic and mathematical verticesmay represent mathematical imagination and creativity in the various fields ofmathematics and in the mathematized disciplines; and, the curves joining themathematical and grammatical vertices may represent various kinds ofmathematical and stochastic context free grammars, mathematical and statisticalsoft wares , computational linguistics etc. etc.

The probable grammatical, aesthetic and, mathematical networks of the Lusosphereof today and tomorrow may be more competently handled by future investigatorswith the aid of insights, images and metaphors generated by the ongoing study ofthe culturomics [Michel et al, 2011] and, that of the statistics and analysis of naturaland random fractals [Gao et al, 2012]. Similar investigations may also be conductedabout the various components of the Sinosphere, Hispanosphere, Anglosphere,Hindosphere, Arabosphere, Bengalosphere [Phani et al, 2012], Russosphere,Francosphere, and Persosphere among others. It is thus very likely that a futuretreatment of the theme of the present paper will carry a very different title.

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Shastri, Haraprasad [1901], Intervention in a discussion on Bangla Vyakaran held atthe Bangiya Sahitya Parisad, Kolkata on 10 December, in: Haraprasad Shastri

Rachana-Sangraha [Collected Works of Haraprasad Shastri], Volume 2 (1981): 617;Kolkata: Paschimbanga Rajya Pustak Parsat.

__ (Ed.) [1916], Hajar Bachharer Purano Bangala Bhashay Bauddha Gan O Doha[Buddhist Songs and Couplets in a Thousand Years Old Bengali Language]; Kolkata:Bangiya Sahitya Parisad.

Truschke, Audrey. [2012] Defining the Other: An Intellectual History of SanskritLexicons and Grammars of Persian, Journal of Indian Philosophy (2012) 40: 635-668.

Vyakarana: http://en.wikipedia.org/wiki/Vy%C4%81kara%E1%B9%87aWilliams, Mukesh [2007], The Unpublished Poems of Henry Derozio 1825-29.

Available at:

http://libir.soka.ac.jp/dspace/bitstream/10911/1242/1/KJ00005437126.pdf

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http://tamilnation.co/conferences/cnfTN68/rajamanickam.htmhttp://scholar.googleusercontent.com/scholar?q=cache:QKsitCAk8vAJ:scholar.google.com/&hl=en&as_sdt=0,5http://scholar.googleusercontent.com/scholar?q=cache:QKsitCAk8vAJ:scholar.google.com/&hl=en&as_sdt=0,5http://www.cimm.ucr.ac.cr/ciaem/documentos/historiaCiaem/Scott,%20mesa%20%20plenaria%202.pdfhttp://www.cimm.ucr.ac.cr/ciaem/documentos/historiaCiaem/Scott,%20mesa%20%20plenaria%202.pdfhttp://archive.org/details/notesonthebengal035527mbphttp://en.wikipedia.org/wiki/Vy%C4%81kara%E1%B9%87ahttp://libir.soka.ac.jp/dspace/bitstream/10911/1242/1/KJ00005437126.pdfhttp://tamilnation.co/conferences/cnfTN68/rajamanickam.htmhttp://scholar.googleusercontent.com/scholar?q=cache:QKsitCAk8vAJ:scholar.google.com/&hl=en&as_sdt=0,5http://scholar.googleusercontent.com/scholar?q=cache:QKsitCAk8vAJ:scholar.google.com/&hl=en&as_sdt=0,5http://www.cimm.ucr.ac.cr/ciaem/documentos/historiaCiaem/Scott,%20mesa%20%20plenaria%202.pdfhttp://www.cimm.ucr.ac.cr/ciaem/documentos/historiaCiaem/Scott,%20mesa%20%20plenaria%202.pdfhttp://archive.org/details/notesonthebengal035527mbphttp://en.wikipedia.org/wiki/Vy%C4%81kara%E1%B9%87ahttp://libir.soka.ac.jp/dspace/bitstream/10911/1242/1/KJ00005437126.pdf


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__ [2008 a], Henry Derozios Manifesto of the New Indian Aesthetics, 1830.

Available at:

http://ci.nii.ac.jp/els/110007145049.pdf?id=ART0009089314&type=pdf&lang=en&host=cinii&order_no=&ppv_type=0&lang

_sw=&no=1335434918&cp=

__ [2008 b], Henry Derozio and the Making of Indian Modernity: Togetherwith a Discussion ofThe Fakeer of Jungheera, 1828. Available at:

http://libir.soka.ac.jp/dspace/bitstream/10911/1069/1/KJ00005448762.pdf

Yaskacharya [c. 500 B.C.E.], The Nighantu and the Nirukta, Ed. by Lakshman Sarup;London: H. Milford 1920-29. Available at:

http://archive.org/details/nighantuniruktao00yaskuoft

Young Bengal:

http://www.banglapedia.org/HT/Y_0008.HTM

Zvelebil, Kamil [1974], Tamil Literature, Wiesbaden: Otto Harrassowitz.

Zwartjes, Otto [2011], Portuguese Missionary Grammars in Asia, Africa andBrazil, 1550-1800. Amsterdam: John Benjamins Publishing Company.

Links to some Illustrations:

Links to the photos of the church of St. Nicolao of Tolentino [St. Nicholas ofTorentino], at Naagari, Gazipur, in Faridpur, Bangladesh, where Manoel daAssumpam became Rector in 1742:

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http://ci.nii.ac.jp/els/110007145049.pdf?id=ART0009089314&type=pdf&lang=en&host=cinii&order_no=&ppv_type=0&lang_sw=&no=1335434918&cp=http://ci.nii.ac.jp/els/110007145049.pdf?id=ART0009089314&type=pdf&lang=en&host=cinii&order_no=&ppv_type=0&lang_sw=&no=1335434918&cp=http://ci.nii.ac.jp/els/110007145049.pdf?id=ART0009089314&type=pdf&lang=en&host=cinii&order_no=&ppv_type=0&lang_sw=&no=1335434918&cp=http://libir.soka.ac.jp/dspace/bitstream/10911/1069/1/KJ00005448762.pdfhttp://archive.org/details/nighantuniruktao00yaskuofthttp://www.banglapedia.org/HT/Y_0008.HTMhttp://www.flickr.com/photos/jalal61/6059659594/in/set-72157627252599804http://www.flickr.com/photos/jalal61/6059668858/in/set-72157627252599804http://ci.nii.ac.jp/els/110007145049.pdf?id=ART0009089314&type=pdf&lang=en&host=cinii&order_no=&ppv_type=0&lang_sw=&no=1335434918&cp=http://ci.nii.ac.jp/els/110007145049.pdf?id=ART0009089314&type=pdf&lang=en&host=cinii&order_no=&ppv_type=0&lang_sw=&no=1335434918&cp=http://ci.nii.ac.jp/els/110007145049.pdf?id=ART0009089314&type=pdf&lang=en&host=cinii&order_no=&ppv_type=0&lang_sw=&no=1335434918&cp=http://libir.soka.ac.jp/dspace/bitstream/10911/1069/1/KJ00005448762.pdfhttp://archive.org/details/nighantuniruktao00yaskuofthttp://www.banglapedia.org/HT/Y_0008.HTMhttp://www.flickr.com/photos/jalal61/6059659594/in/set-72157627252599804http://www.flickr.com/photos/jalal61/6059668858/in/set-72157627252599804


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Links to the photos of Henry Louis Vivian Derozios:

Bust: ; and,

Tomb: , at Kolkata, WestBengal, India.

Link to a photo of Ubiratan DAmbrosio, 2007:

http://www.rbhm.org.br/Festschrift%20-%20Ubi.html

Kolkata

30 September 2013

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http://www.flickr.com/photos/jalal61/6059081727/in/set-72157627252599804http://commons.wikimedia.org/wiki/File:Kolkata_Derozio_statue.jpghttp://commons.wikimedia.org/wiki/File:Derogio2.JPGhttp://www.rbhm.org.br/Festschrift%20-%20Ubi.htmlhttp://www.flickr.com/photos/jalal61/6059081727/in/set-72157627252599804http://commons.wikimedia.org/wiki/File:Kolkata_Derozio_statue.jpghttp://commons.wikimedia.org/wiki/File:Derogio2.JPGhttp://www.rbhm.org.br/Festschrift%20-%20Ubi.html

A Lusospherical Triangle [Draft]

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