Time and Space Across Time and Space

This curriculum module encourages students to think about the concepts of time and space by showing them how they have been viewed at different times in history and in different cultures--including the Igbo culture of Nigeria.

This curriculum module was developed as part of a project sponsored by SciMath-MN and The Bakken Museum and Library. Click to see other modules using history and philosophy of science.

Teaching Time and Space

• What is space?
• What is time?
• How do different people perceive space and time?
• What are the ways different people measured space and time?
• Is there a standard way to measure space and time?
• How was our understanding of space and time shaped by Galileo, Newton, and Einstein?

This approach to teaching space and time is based on the premise that time and space are particularly suitable as a framework for a general cultural history because they are comprehensive, universal and essential. Everybody knows that time flows, equally without relation to anything external--a view expanded by Isaac Newton. Space-time is both objective and subjective but nonetheless universal. A calendar arranges space-time in an orderly manner. The Calendar concept views time-space as continuously moving forward in consonance with Newton's classical theory of irreversibility of space-time. No occurrence in material world could affect the flow of time. Yet space-time is adjusted in the calendar as shown by number of days/months--indications of the interaction between space-time and matter (Einstein's theory of relative space-time).

Objectives -- Students should understand/know that:

1. Motion (change in position in time and space) is both relative and absolute.
2. Einstein's theory of relativity and thus the emergence of reference frames of motion does not necessarily invalidate Newton's classical theory of absolute motion but extends and improves our understanding of changes in space and time.
3. The excitement/"magic" in both theories lies in the "ordinariness" of natural phenomena and the process of observation.
4. Without using only mathematical symbols or complex experiments and using the historico- socio-cultural phenomena, we can at the same conclusions Newton and Einstein arrived at.
5. The people involved in the development of scientific theories often operated from cultural view point and therefore are real.

Lesson I: Introducing Motion

• How fast you walked (speed)
• How far you walked (distance)
• How long you walked (time)
• Where you walked (space)

Task 3:
Repeat exercise 1 stopping briefly at each turn. Using a stopwatch and a meter stick measure and record the time (in seconds); distance (meters); speed (distance/time) at each stop. What is your average speed and total time?

Theme to Highlight:
No two walks are quite the same. This individuality is typical of most events occurring in nature.

Assessment Product:

1. Students database/computer spreadsheet showing space, time, distance, speed.
2. Original device constructed by students to measure time and distance.

Lesson 2: The Historical Development of the Concept of Motion

Theme to Highlight:
Science concepts develop over time. Theories are modified based on prior experience.

Assessment Product:
Students time lines which must show date, period in history, names of people involved and concept of motion held.

Lesson 3: Factors in Scientific Discovery

• Galileo Galilei
• Isaac Newton
• Albert Einstein

Theme: Great discoveries begin with processes of observation, patience, hard work, favorable attitude and perseverance.

Assessment Product: At least a 2-page typed report either contained in form of a table or paragraphs--each section showing lives and works of the people involved.

LESSON 4: New Year in Another Culture

Theme:
Everyone is moving through time/space. We move through time at certain hours per day. Though we may not seem to be moving, we move through space with reference to any point outside the planet.

Assessment: A written report. (Special Note: The students could present their report in form of a video report and present the video to class.)

Lesson 5: Conceptions of space-time among different cultures with reference to relativity of space-time.

The IGBO calendar consists of a week (IZU) made up of four (4) days (Ubochi); a month (Onwa) of 28 days or seven native weeks (IZU asaa); a year or afo made up of 91 weeks (IZUS) or 13 months (Onwa). Incidentally, Onwa means moon in the Igbo language so the month is a lunar month. Below, the Igbo week (Izu), month (Onwa) and year (Afo, or Eye):

The Priests of each community are the time keepers, and the process of time keeping is called Igu afo (also called aro or eye). The lunar months dictate major feasts and celebrations in Igboland as it is in most other African ethnic groups.

The days (Ubochi) are individually called in Igbo language Eke, Orie (or Oye), Afo and Nkwo (E,O,A and N in the figure below). Markets are associated with these days and derive their names accordingly.

What the calendar represents are natural movements. The day, for instance, is determined by the rotation of the earth on its axis; the month represents the time or period the moon takes to revolve around the earth; while the year follows the revolution of the earth around the sun. All time reckoning is based on these natural phenomena since their movements are constant.

The resultant Igbo calendar with a 4-day week and 28-day month can be represented as follows:
Month = 4 (days) x 7 (weeks) = 28 days
Year = 28 (days) x 13 (months) = 364 days.
Recently an adjustment is made to add 1 day.
Years add together in blocks of five years to make a century:

(Some native time keepers got confused with simultaneous use of the Gregorian (or the Egyptian) calendar and substituted the 4-day week with an 8-day week. The 8-day week was derived by adding Ukwu (big) and Nta (small) to the 4 days of Eke, Orie, Afo and Nkwo. Thus the 8-day week named individually becomes Eke Ukwu, Eke nta, Orie Ukwu, Orie Nta, Afo Ukwu, Afo Nta, Nkwo Ukwu and Nkwo nta. With an 8-day week, the data is as follows:
Month = 8 (days) x 4 (weeks) = 32 days.
Year = 32 (days) x 12 (months) = 384 days.
or 32 (days) x 13 (Lunar months) = 416 days.
Since the idea of a 384-day year or 416 day year is most unlikely, this calendar is unlikely to be found in Igboland.) The numbers 4 and 7 and the difference (3) arising thereof are sacred in Igbo rituals because of their relations to the calendar. The use of the 4-day week across many countries of West Africa up to the Congo basin suggest a shared historical and cultural experience.

Origin of Igbo Calendar
There are lots of legends and propositions about the origin of the calendar. From these legends and propositions run a central conception that there are four corners of the earth-represented by 4 days. Eke corresponds to the East; Orie to the West; Afo to the North and Nkwo to the south. The sun and the moon transverse the earth in different directions (across the length and breadth of the earth). The point of intersection between the movement of the sun and the moon symbolizes the center of the earth-the meeting point of all forces (natural and supernatural). This center which is a constant symbolizes cosmic equality.

Comparison between the Igbo Calendar and the Gregorian (or Egyptian) Calendar
The Egyptians adopted a seven-day week from the names of five planets plus the sun and the moon. The Romans and the rest of Europe used the Egyptian names for their days and week. Thus they have the names strictly based on the planetary names. However, the English made some changes of the names adapting them to those of their local gods. The Spanish and French still maintain these planetary names as we illustrate in the following chart.

So far in the world chronologies, and particularly in Africa, a number of nations and cultures use either the seven-day week or the four-day week; but both paradigms of the calendar have African origins, namely the Egyptians and the Igbo. Until research presents other calendrical paradigms or models, the four-day and seven-day weeks show amazing coincidence. A close look at the Egyptian calendar in it natural stage, coinciding with the natural order, shows that it operates within the frame of the numbers four and seven as is the case in the Igbo four-day week:

Igbo Time and Space
The Igbo have a linear (and some argue, a cyclic) concept of time. There are evidences in Igbo land to buttress both viewpoints. The Age Grade system and the idea of reincarnation or cyclic agricultural seasons are indications of both linear and cyclic conceptions of time. Within this linear or cyclic framework, it is interesting to note that points in time are regarded as intervals along the linear continuum or the four corners of earth. 

This conception of time is therefore at variance with the atomistic nature of time made popular by Newton's calculus which conceive of time as a sum of infinitesimally small but discrete units.

The Igbo space is associated with continuity, dimensionality, connectedness and orientability. These are especially manifested at cross-roads, market places, and the interaction of the sky (elu), the earth (Ala) and the underworld (Ala Mmuo).

Measuring Time and Space
The Igbo measure time with motion-the moon phase, the season, night and day, shadows across sundial, ocean tide among others. It is not uncommon for children to use evaporation of drops of water or spit. The motion associated with these events is regular and orderly and therefore constitutes index of time associated with science.

Space is measured with foot lengths, strides, landmarks or time of journey (similar to using light year as an estimate of distance). All these are associated with motion. Observations of motion in space and time are certain/absolute (Newtonian motion) and also dependent on who/what is being observed (Einstein's relativity of motion).

The Igbo also hold the view that things/events/people move through space-time while space- time remains constant-hence seasons come and go, people live and die, the sun rises and sets but there is Ndudu gandu nile, ebebe ebebe (world without end).

Bibliography

• Davis, P.C.W. (1977). Space & Time in the Modern Universe, Cambridge Univ. Press, London.
• Kern, Steven (1983). The Culture of Time and Space 1880-1918, Harvard Univ. Press.
• Meadows, Jack (1994). The Great Scientists. Oxford Univ Press, London.
• Sciana, D.W. (1969). The Physical Foundations of General Relativity, Doubleday and Company.
• Toulmin S. and Goodfield J. (1965) The Discovery of Time. Harper & Row.
• Ukaegbu, J. O. (1991). Igbo Identity and Personality vis-a-vis Igbo Cultural Symbols, Snaap Press, Enugu Nigeria.

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© The Bakken Updated: April 6, 2007