JiscMail Logo
Email discussion lists for the UK Education and Research communities

Help for MEDIEVAL-RELIGION Archives


MEDIEVAL-RELIGION Archives

MEDIEVAL-RELIGION Archives


MEDIEVAL-RELIGION@JISCMAIL.AC.UK


View:

Message:

[

First

|

Previous

|

Next

|

Last

]

By Topic:

[

First

|

Previous

|

Next

|

Last

]

By Author:

[

First

|

Previous

|

Next

|

Last

]

Font:

Proportional Font

LISTSERV Archives

LISTSERV Archives

MEDIEVAL-RELIGION Home

MEDIEVAL-RELIGION Home

MEDIEVAL-RELIGION  October 1997

MEDIEVAL-RELIGION October 1997

Options

Subscribe or Unsubscribe

Subscribe or Unsubscribe

Log In

Log In

Get Password

Get Password

Subject:

re: dustboard

From:

Otfried Lieberknecht <[log in to unmask]>

Reply-To:

[log in to unmask]

Date:

Thu, 02 Oct 1997 03:03:45 +0100

Content-Type:

text/plain

Parts/Attachments:

Parts/Attachments

text/plain (147 lines)

Dear Bella,

Sorry to be so late to take this thread up again, but for some stupid
technical reason (after a temporary absence I had forgotten to resume my
listmail...) I had missed all the med-rel postings since 16 September. So
here I am back again, at least for the moment.

>A belated but heartfelt thank-you for all three responses to my
>dust-board query, which I have been following up. Otfried's lucid
>disentanglement of the abacus (in the modern sense) from the dust-board
>led me to ask why I had got them entangled in the first place, and this
>helped me towards an answer to the problem of the disappearing
>dust-board. It seems to be as much as anything a linguistic difficulty.
>There were two ways of describing the dust-board in antiquity, as an
>'abacus' (a Latinization of Gk. 'abax', genitive 'abakos') or as
>'pulvis' (or the diminutive form 'pulvisculus'). Two successive problems
>arising from this nomenclature: i) since the usual phrasing associated
with the use
>of a dust-board is 'in pulvere', it's often hard to tell whether the
>reference is to a dust-board, unless the context is unambiguous; what
>Cicero called 'pulvis
>eruditus' becomes indistinguishable from ordinary dust [a salutary
>warning to academics against the pride of life?]. ii) once the counter
>abacus is introduced, again it's often hard to tell whether 'abacus' is
>being used in its older or its newer sense.

The few counting-boards extant from Greek and Roman antiquity are all
boards with or for counters, not dustboards. To the best of my knowledge,
written sources from this time don't describe the dustboard as a
counting-board. There is only the Greek name "abakos" to infer that at some
early stage no distinction was made between the dust-board (for drawing and
eventually writing) and the counting-board (for reckoning with counters),
because somehow the name of the first must have been transferred to the
latter. The Latin words  "pulvis" and "pulvisculus" will normally refer to
the dust-board (for drawing), not to the counting-board ("calculator"). As
literary motivs, both stand for erudition in geometry (dust-board) and
arithmetic (counting-board).

 However, a search of the
>Middle English Dictionary turned up some usefully explicit LME glosses
>for the ignorant. The South English Legendary Life (c. 1300) of St Edmund of
>Abingdon, telling the story I cited before from the canonization
>proceedings, explains what Edmund was doing teaching arithmetic at
>Oxford: 'Arsmetrike is a lore that of figurs al is, And of draughtes as
>me draweth in poudre [=dust], and in numbre iwis' (EETS 236, 2.500,
>lines 227-8). And in the late C14 John of Trevisa, translating Higden's
>_Polychronicon_, which draws here on William of Malmesbury, glosses the
>claim that Gerbert of Aurillac took the 'abacus' [here = arithmetic?]
>from the Saracens, 'Abacus is a table with the whiche schappes beth
>portrayed and i-peynt in poudre, and abacus is a craft of geometrie'.

What Gerbert (although it is possible that he was not the first) imported
from the Arabs in Spain was the counting-board with **numbered** counters
and the specific numerals used to number them. The counters on the ancient
counting-board were **not** numbered, and this ancient counting board was
no longer in use during the early middle ages, but was known only by
hearsay (as in Isidore's _Etymologiae_). It was reintroduced (first as a
new variant with non-decimal columns for monetary units) in the 12th/13th
centuries.

>What both quotations suggest, I think, is that academics at any rate were
using
>dustboards in England into the late Middle Ages, certainly for geometry
>and possibly for other kinds of calculation. But I'd welcome any other
>evidence or comments...

I would not put much weight on the passage in Trevisa, because the
dust-board as an instrument and standard attribute of Geometria was common
knowledge in the tradition of Martianus Capella, but this does not
necessarily mean that it was actually used. Chalk-boards and wax-boards
would have been a much better choice for precise geometric drawings. The
passage in St. Edmunds seems more interesting to me, but it speaks of
"drawing" in dust, not of writing the numbers (or the columns and dots of
an abacus) in dust.  

It was only after having written my earlier message that I re-read Paul
Acker, _The Emergence of an Arithmetical Mentality in Middle English
Literature_, in: The Chaucer Review 28,3 (1994), p.293-302, who writes on
p.296:

    According to Steele [Robert Steele, _The Earliest Arithmetics
    in English_, London 1922 (= EETS, Extra Series 128), p.xv], algo-
    ristic reckoning was first carried out using "a board 
    [covered] with fine sand," similar, apparently, to the Greek sand
    tray described by Martianus Capella and Trevisa. Such a board may
    be the intended referent in a remarkably early (?a 1200) and 
    unlikely context, the <i>Ancrene Wisse</i>. Here, in a somewhat
    complicated simile, we learn that a covetous man is like a 
    fire-tender; in the ashes he makes "figures of augrim, as thes
    rikeneres doth the habbeth muche to rikenin." These "figures of
    augrim" are Arabic numerals, and here we find our earliest known
    Middle English reference to them. But in this passage they serve
    only to improve the reckoning abilities of the devil's 
    accountant; such associations with the mercantile world only
    added to the taint suffered by arithmetic.

I don't know which sources are adduced by Steele to support his claim, but
if there is only the passage in the Life of St. Edmund in the SEL (written
when algorism had already been diffused in Europe for more than a century)
to support it, I would hesitate to be convinced. There is also Leonardo da
Pisa ('Fibonacci'), who in his _Liber abaci_ (which has nothing to do with
the counting-board, but introduces reckoning with Indo-Arabic numerals, and
was written ca. 1200, revised in the only extant version 1228) frequently
mentions a 'tabula' or 'tabula dealbata' where intermediary results are to
be noted, and this 'tabula' has been interpreted by Andre/ Allard
(_Muhammad Ibn Musa Al-Khwarizmi, Le calcul indien: Algorismus. Histoire
des textes, e/dition critique, traduction et commentaire des plus anciennes
versions latines remanie/es du XIIe sie\cle_, Paris: Blanchard, 1992, p.85;
beware, I am quoting from second hand!) as a dust-board, whereas Heinz
Lu"neburg (see his _Bemerkungen zu Abacus und Algorismus_ at his website:
http://www.mathematik.uni-kl.de/~luene, and see also his _Leonardi Pisani
Liber Abbaci, oder Lesevergnu"gen eines Mathematikers, Darmstadt: BI
Wissenschaftliche Verlagsgesellschaft, 2nd ed. 1993) argues for a wax-board
or chalk-board. I would say that 'tabula dealbata' in fact is very likely
to refer to a chalk board (a wooden board covered with a layer of dried
chalk, to be washed after use and covered with a new layer).

A good place to look for further info on medieval dust-boards might be
Robert Fossier, _Polyptiques et censiers_, Turnhout: Brepols, 1978 (=
Typologie des Sources du Moyen Age, 28).

So much for tonight,

  Otfried

---------------------------------------------------------------------------
Otfried Lieberknecht, Schoeneberger Str. 11, D-12163 Berlin
Tel.: ++49 30 8516675 (fax on request), E-mail: [log in to unmask]
  Homepage for Dante Studies:
http://members.aol.com/lieberk/welcome.html
  ORB Dante Alighieri - A Guide to Online Resources:
http://orb.rhodes.edu/encyclop/culture/lit/Italian/Danindex.html
---------------------------------------------------------------------------
 







>Many thanks,
>Bella Millett


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Top of Message | Previous Page | Permalink

JiscMail Tools


RSS Feeds and Sharing


Advanced Options


Archives

November 2019
October 2019
September 2019
August 2019
July 2019
June 2019
May 2019
April 2019
March 2019
February 2019
January 2019
December 2018
November 2018
October 2018
September 2018
August 2018
July 2018
June 2018
May 2018
April 2018
March 2018
February 2018
January 2018
December 2017
November 2017
October 2017
September 2017
August 2017
July 2017
June 2017
May 2017
April 2017
March 2017
February 2017
January 2017
December 2016
November 2016
October 2016
September 2016
August 2016
July 2016
June 2016
May 2016
April 2016
March 2016
February 2016
January 2016
December 2015
November 2015
October 2015
September 2015
August 2015
July 2015
June 2015
May 2015
April 2015
March 2015
February 2015
January 2015
December 2014
November 2014
October 2014
September 2014
August 2014
July 2014
June 2014
May 2014
April 2014
March 2014
February 2014
January 2014
December 2013
November 2013
October 2013
September 2013
August 2013
July 2013
June 2013
May 2013
April 2013
March 2013
February 2013
January 2013
December 2012
November 2012
October 2012
September 2012
August 2012
July 2012
June 2012
May 2012
April 2012
March 2012
February 2012
January 2012
December 2011
November 2011
October 2011
September 2011
August 2011
July 2011
June 2011
May 2011
April 2011
March 2011
February 2011
January 2011
December 2010
November 2010
October 2010
September 2010
August 2010
July 2010
June 2010
May 2010
April 2010
March 2010
February 2010
January 2010
December 2009
November 2009
October 2009
September 2009
August 2009
July 2009
June 2009
May 2009
April 2009
March 2009
February 2009
January 2009
December 2008
November 2008
October 2008
September 2008
August 2008
July 2008
June 2008
May 2008
April 2008
March 2008
February 2008
January 2008
December 2007
November 2007
October 2007
September 2007
August 2007
July 2007
June 2007
May 2007
April 2007
March 2007
February 2007
January 2007
December 2006
November 2006
October 2006
September 2006
August 2006
July 2006
June 2006
May 2006
April 2006
March 2006
February 2006
January 2006
December 2005
November 2005
October 2005
September 2005
August 2005
July 2005
June 2005
May 2005
April 2005
March 2005
February 2005
January 2005
December 2004
November 2004
October 2004
September 2004
August 2004
July 2004
June 2004
May 2004
April 2004
March 2004
February 2004
January 2004
December 2003
November 2003
October 2003
September 2003
August 2003
July 2003
June 2003
May 2003
April 2003
March 2003
February 2003
January 2003
December 2002
November 2002
October 2002
September 2002
August 2002
July 2002
June 2002
May 2002
April 2002
March 2002
February 2002
January 2002
December 2001
November 2001
October 2001
September 2001
August 2001
July 2001
June 2001
May 2001
April 2001
March 2001
February 2001
January 2001
December 2000
November 2000
October 2000
September 2000
August 2000
July 2000
June 2000
May 2000
April 2000
March 2000
February 2000
January 2000
December 1999
November 1999
October 1999
September 1999
August 1999
July 1999
June 1999
May 1999
April 1999
March 1999
February 1999
January 1999
December 1998
November 1998
October 1998
September 1998
August 1998
July 1998
June 1998
May 1998
April 1998
March 1998
February 1998
January 1998
December 1997
November 1997
October 1997
September 1997
August 1997
July 1997
June 1997
May 1997
April 1997
March 1997
February 1997
January 1997
December 1996
November 1996
October 1996
September 1996
August 1996
July 1996
June 1996
May 1996
April 1996


JiscMail is a Jisc service.

View our service policies at https://www.jiscmail.ac.uk/policyandsecurity/ and Jisc's privacy policy at https://www.jisc.ac.uk/website/privacy-notice

Secured by F-Secure Anti-Virus CataList Email List Search Powered by the LISTSERV Email List Manager