History of Mathematics Project | Midewiwin Birchbark Scroll

History of
Mathematics

Project

around 1800

Midewiwin Birchbark Scroll

Sequential counting on a birchbark scroll

The birchbark (wiigwaasabak) master scroll De-1 depicts the four lodges of the Midewiwin (Grand Medicine Society) in which the Ojibwe Native Americans conducted curing ceremonies. Sequences of dots appearing in the upper-left-hand corner of each lodge give the counting numbers 1, 2, 3, 4, which correspond to the principal shaman and his assistants. Various other sequences of dots, tally marks and diagonal T-shaped extensions depicted in the scroll represent other numerical aspects of Midewiwin ceremonies.

In addition to the sequences of 1, 2, 3, 4 dots in the upper-left corner of each lodge corresponding to the principal shaman and his assistants, the sequence 4, 9, 12, 21 of tally marks along the lower half of the processional path represents the Mide officials. Additionally, the sequence 2, 3, 4, 5 of dots in the central portion symbolized sacred fire and 1, 2, 3 or 4 sacred posts. Finally, the outer edges of the lodges contain T-shaped extensions that give the series 4, 6, 8, 10, representing the numbers of evil spirits trying to influence the candidate taking part in the curing ceremony.

Artifact origin

Northern Midwestern United States

Catalog number

Master scroll De-1

Timeline

Interactive Content

Computational Explanation

The Ojibwe, also known as Ojibwa, Ojibway, Chippewa or Saulteaux, are a native people of southern Canada and the northern Midwestern United States. They spoke the Ojibwe traditional language, which is a branch of the Algonquian language family. The bark of the birch tree found extensive use in the daily life of the Ojibwe, who used it in the construction of birchbark canoes and as the writing medium for birchbark scrolls. The Ojibwe, together with other indigenous peoples of the Maritime Provinces of Eastern Canada and the New England and Great Lakes regions of the United States, practiced a secretive religion known as the Midewiwin or Grand Medicine Society. Midewiwin practitioners are known as Midew (sometimes translated into English as "medicine man"), and the practices of Midewiwin are referred to as Mide. In addition to performing ceremonies, Midew leaders served as the keepers of detailed scrolls that were used to record events, oral history, songs, maps, memories, stories and mathematics.

This birchbark master scroll De-1 depicts the four lodges of the Midewiwin in which the Ojibwe conducted curing ceremonies. It is straightforward to construct the various graphical elements appearing on the scroll using the Wolfram Language. For example, to construct a single lodge, let x be the left-edge horizontal position, dx the length of the horizontal lips on either side of doors, dh the half-height of the door openings, t the wall thickness, h the vertical distance from the lodge center to the top of the outer wall, w the half-width from the left exterior side of the inner rectangle to the right, y the half-height from the top exterior side of the inner rectangle to the bottom and color the wall color. Using some simple geometry and a few graphics primitives allows the following function to be written:

In[]:=

lodge[x_,dx_,dh_,t_,h_,w_,y_,color_]:=Module[{lines=Table[Line/@{{{x,sdh},{x+dx,sdh}},{{x+1-dx,sdh},{x+1,sdh}}},{s,{-1,1}}],outerwall=Table[Polygon[{{x+dx,sdh},{x+dx,sh},{x+1-dx,sh},{x+1-dx,sdh},{x+1-dx-t,sdh},{x+1-dx-t,s(h-t)},{x+dx+t,s(h-t)},{x+dx+t,sdh}}],{s,{-1,1}}],innerwall=Rectangle[{x+1/2-w,-y},{x+1/2+w,y}],innerwallhole={White,Rectangle[{x+1/2-w+t,-y+t},{x+1/2+w-t,y-t}]}},{lines,FaceForm[color],EdgeForm[Black],outerwall,innerwall,innerwallhole}]

… that can be used to draw a single lodge:

In[]:=

Graphics[lodge[0,.05,.1,.07,.3,.3,.15,LightYellow]]

Out[]=

Several lodges can then be placed adjacent to one another simply by specifying multiple horizontal positions:

In[]:=

Graphics[Table[lodge[1.1x,.05,.1,.07,.3,.3,.15,LightYellow],{x,0,3}],ImageSizeLarge]

Out[]=

To complete the construction of the lodge complex, add central walls connecting adjacent lodges:

simpleconnectedlodges[n_,spc_,dx_,dh_,t_,h_,w_,y_,color_]:={Table[lodge[spci,dx,dh,t,h,w,y,color],{i,n}],{FaceForm[color],EdgeForm[color],Table[Rectangle[{ispc+1/2+w,-t/2},{(i+1)spc+1/2-w,t/2}],{i,n-1}]},Table[Line[{{ispc+1/2+w,st/2},{(i+1)spc+1/2-w,st/2}}],{s,{-1,1}},{i,n-1}],}

In[]:=

Graphics[simpleconnectedlodges[4,1.1,.05,.1,.07,.3,.3,.15,LightYellow],ImageSizeLarge]

Out[]=

The T-shaped extensions representing evil spirits trying to influence the candidate can also be defined programmatically. As it turns out, this shape is known in the Wolfram Knowledgebase as the "SquareTBeam":

In[]:=

Entity["Lamina","SquareTBeam"]["Region"]

Out[]=

Function{b.,d.,h.,t.},RegionUnionRectangle-

,0,

,h.,Rectangle-

,h.,

,d.

… a particular instance of which can be visualized as follows:

In[]:=

Graphics[EntityInstance[Entity["Lamina","SquareTBeam"],{t..1,b..5,d..8,h..7}]["Region"],ImageSizeSmall]

Out[]=

However, because the shape is so simple, it is just as straightforward to define it directly as a polygon, including an offset and tilt angle:

post[xy_,t_,w_,h_,ang_]:=TranslateRotatePolygon0,-

,0,

,h-t,

,h,

,h,-

,h-t,-

,ang,{0,0},xy

In[]:=

Graphics[Table[post[{x,0},.1,.5,1,50Degree],{x,5}]]

Out[]=

Combining these elements together with dot sequences as depicted in the original scroll provides a graphical output:

… that, with the omission of fish and other animals surrounding the perimeter, give a quite reasonable reproduction of the original:

Additional Reading

Closs, M. P. "Tallies and the Ritual Use of Number in Ojibwe Pictography." Ch. 7 in Native American Mathematics (Ed. M. P. Closs). Austin, TX: University of Texas Press, pp. 203–205, 1996.
Copway, G. The Traditional History and Characteristic Sketches of the Ojibway Nation. Boston, MA: B. F. Mussey & Co., 1851.
Densmore, F. Fig. 12 in Chippewa Customs. Bulletin 86 of the Smithsonian Institution, Bureau of American Ethnology. Washington, DC: Government Printing Office, pp. 90–92 and pl. 34, 1929. Reprinted by Minnesota Historical Society Press, 1979.
Dewdney, S. The Sacred Scrolls of the Southern Ojibway. Toronto, Canada: University of Toronto Press, 1975.
Nelson, R. E. "Inscribed Birch Bark Scrolls and Other Objects of the Midewiwin." Algonquin Papers/Les Actes du Congres des Algonquinistes, Vol. 14, pp. 219–238, 1983.

Midewiwin Birchbark Scroll

Timeline

Interactive Content

Computational Explanation

Additional Reading

Additional Links