Quantitative concepts: big numbers, exponential growth and decay
Deep Time - the geologic time scaleby Jennifer M. Wenner, Geology Department, University of Wisconsin-Oshkosh
Jump down to: Relative vs. Numerical age | Timescales | How do we know? | Religion | Examples & Exercises
Essential ConceptsThere are 5 main concepts with which students struggle when thinking about Deep Time - the concept that Earth has a multi-billion year history:
- imagining or comprehending big numbers,
- the difference between relative and numerical age,
- the concept of "timescales",
- the ways we know about the age of the Earth and other materials, and
- resolving perceived issues with religious beliefs
Big numbers - How many zeros?!?When we tell students that the Earth is 4.6 billion years old, that number may have no meaning to them. Even when they are told that a number that large has 10 digits, they cannot comprehend anything that large (particularly that amount of time). It is even difficult for many geoscientists to really come to a true understanding of how long 4,600,000,000 years really is.
In fact, many geologists find that it is easier to think about numbers (ages) like millions of years relative to the total age of the Earth or the length of geologic time. To understand the time since the Earth's inception, we need to put it into perspective that we can understand. To do this we often use analogies for the length of time rather than the absolute value of that time. Here are a few examples in which significant events in Earth history are plotted relative to some known (and easily comprehended) quantity or object:
- The roll of toilet paper: Imagine that all of geologic time is represented by a 1,000 sheet roll of toilet paper (Scott tissue works well) - each sheet is 4,500,000 years. Unroll the toilet paper and mark off significant events in the history of the Earth. (This can be a delicate operation but if the paper rips, tape can be used to fix it.)
- Trip across the country: Imagine that all 4.5 billion years of geologic time are represented by a roadtrip from Washington, DC, to Seattle - about 4500 km. Mark out specific time periods in geologic time along your route across the country.
- The football field: Imagine that all 4.5 billion years of geologic time are represented by the length of a football field. Mark out specific time periods in geologic time along its length.
- The calendar year: Imagine that the deep time of Earth's history is compressed into one year. Calculate (to the fraction of a second) when significant events in geologic history happened. Assume that January 1 is the formation of Earth and milliseconds before midnight on December 31 is present day.
- The yard/meter stick: Imagine that geologic time is represented by the length of a yard, or better yet a meter, stick. Make a scale model of the geologic time scale to within fractions of inches or centimeters.
- The beer glass: Imagine that geologic time is represented in the volume of a beer glass (it works well to imagine Guinness in a 20 ounce imperial pint - each ounce represents 230,000,000 years). Calculate the volume (this can also be done by %) of beer that represents time before present to significant geologic events.
- The clothes line: Stretch out a clothes line of known length. Have students calculate the where they should place a clothespin on the clothesline for a specific geologic event.
- Length of the hallway: With a measuring tape, have students measure the hallway outside the classroom as the geologic time scale with one end representing present day and the other end, Earth's birth. Give each student a geologic event (with its age) and have them stand at the appropriate distance from "present day".
Clearly, there are numerous analogies out there for deep time, make sure you choose one to which your students can relate. Or, let your students choose the one that makes the most sense to them.
Relative vs. Numerical AgeSome students have difficulty with the concept of relative vs. numerical* age. Particularly that the geologic time scale was first conceived through an understanding of the relative age of fossils. For many years, the geologic time scale had no units of 'time' attached to it. Only with the discovery of radioactivity could geologists attach numerical ages to time periods.
*Often numerical age is called absolute age - however, "absolute" is misleading because numerical ages have associated errors and geologic ages are adjusted as new techniques are developed.
Relative time/ageBecause we understand and observe the effects of physical forces acting on earth materials (e.g., gravity), we can infer stories about the sedimentary rocks found on Earth.
Suppose I gave you a list of "Relative" events:
- My mother's birth
- My maternal grandmother meets my maternal grandfather
- My father meets my mother
- My mother's birth
- I graduate from high school
- My maternal grandmother's birth
With a few clues, could you reasonably put them in chronological order? How did you do it? There are certain conditions that must be true in order for a sequential event to occur (e.g., my grandmother must be born and know my grandfather before my mother can be born). The same is true for geologic events - there is a well understood set of principles that govern the deposition of sediments that can help a geologist tell a story about the history of the rocks.
Numerical time/ageDespite the fact that you can put the above events into a relative chronological order, you have no idea how much time occurs between each of the events. Are they spaced evenly from the first event to the last (i.e., 25 years betweeen each event)? Are the years between them the same for each person (e.g., did we all start 1st grade when we were exactly 6 years old?)
- My maternal grandmother's birth - June 20, 1918
- My maternal grandmother meets my maternal grandfather - September, 1936
- My mother's birth - May 30, 1944
- My father meets my mother - October, 1964
- My birth - May 6, 1970
- I graduate from high school - June, 1988
Although your "relative" list should be in exactly the same order as mine, the "age" of the events will not be the same. This is the concept of numerical age. You can put "relatives" in chronological order just by knowing their relationship to one another; however, when you have done that, you have no idea what the numerical age of any of those relatives is.
Ways of representing geologic time
The geologic columnToday, the geologic timescale has numbers associated with the boundaries between eons, epochs, periods, etc.
- The sedimentary principles are:
In this image, A is younger than C (superposition), C is younger than I (inclusions), I is younger than D, E and B (cross-cutting), D is younger than E and B (cross-cutting), H, F, K and J have been tilted or folded (original horizontality), G is younger than B, H, F, K and J (baked contacts). In order from youngest to oldest, the sequence is as follows: A, C, I, D, E, G, B, tilting, H, F, K. J.
- principle of uniformitarianism:
- physical processes acting today also acted in the past at comparable rates -- the present is the key to the past;
- principle of superposition:
- younger sedimentary rocks overlie older rocks because a layer of sediment cannot accumulate unless there is already a substrate on which it can collect
- principle of original horizontality:
- sedimentary rocks are deposited relatively horizontally because they settle out of fluid in a gravitational field -- folds and tilted beds indicate deformation that postdates deposition;
- principle of original continuity:
- sedimentary rock units accumulate in continuous sheets, a layer exposed on one side of a canyon likely spanned the canyon at one time;
- principle of cross-cutting relationships:
- a feature that cuts across another is younger than that it cuts;
- principle of inclusions:
- igneous and sedimentary rocks that contain inclusions of other rocks must be younger than the rocks they include;
- principle of baked contacts:
- an igneous intrusion "bakes" the rock surrounding it.
- definitions modified from Earth: Portrait of a Planet by Stephen Marshak
- one piece of bread was there for me to spread the PB (or J) on (principle of superposition);
- the bread had to be (relatively) flat for me to spread the peanut butter on it (principle of original horizontality);
- the peanut butter probably covered the entire piece of bread (principle of original continuity);
- if I slice the sandwich, all those layers (PB, J and bread) had to be there for me to cut through them (principle of cross cutting relationships;
- if there is jelly in my peanut butter, I put the jelly on first - and vice versa (principle of inclusions).
- Some grains of sand in Australia have been dated at 4.2-4.4 billion years - this suggests that there were rocks around at that time even if they are no longer there,
- Rocks collected from the Moon have yielded ages as old as 4.6 billion years old,
- Nearly every meteorite that has the same composition as the Earth has an age of 4.6 billion years.
- That would be like polling the University and having 90% of the students have exactly the same birthday! How likely is that?
- For more information about teaching to Creationist students, SERC's Starting Point has a number of pages on addressing Creationism.
- Geologic timescale with 1000 sheet roll of toilet paper contains teaching notes for using this as a demonstration in class, a modifiable table and possible assessment techniques. Also included are links to other pages with information about using this activity in class.
- Geologic timescale using a pre-measured length of calculator tape contains teaching notes for using this as an activity for small groups.
Students can relate to the making of a peanut butter and jelly sandwich - this is a great way to help students understand the sedimentary principles listed above:
When I make a PB and J sandwich, I can say that:
The geologic timescale
The numerical geologic time scale is in a constant state of flux as geochronologists (geologists who date rocks) find (or bracket) more precise ages for the fossiliferous rocks used to construct the original geologic column. The discovery of radioactivity allowed us to put a scale on the geologic column.