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Powers of Ten (film series)

Powers of Ten (film series) is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Powers of Ten (film series) rather than just read about it. In short: The Powers of Ten are two short American documentary films written and directed by Charles and Ray Eames. Both works depict the relative scale of the universe according to an order of magnitude (or logarithmic scale) based on a factor of ten, first expanding out from the Earth until the entire universe is surveyed, then reducing inward until a single atom and its quarks are observed.

Powers of Ten (film series) — main illustration
Powers of Ten (film series) — illustration

Key takeaways

  • Powers of Ten (film series) belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Powers of Ten (film series) to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Powers of Ten (film series) from memory before moving on to harder problems.

Reference excerpt

The Powers of Ten are two short American documentary films written and directed by Charles and Ray Eames. Both works depict the relative scale of the universe according to an order of magnitude (or logarithmic scale) based on a factor of ten, first expanding out from the Earth until the entire universe is surveyed, then reducing inward until a single atom and its quarks are observed.

History and background The first film, A Rough Sketch for a Proposed Film Dealing with the Powers of Ten and the Relative Size of Things in the Universe, was a prototype and was completed in 1968; the second film, Powers of Ten: A Film Dealing with the Relative Size of Things in the Universe and the Effect of Adding Another Zero, was completed in 1977. The Powers of Ten films were adaptations of the book Cosmic View (1957) by Dutch educator Kees Boeke. Both films, and a book based on the second film, follow the form of the Boeke original, adding color and photography to the black and white drawings employed by Boeke in his seminal work. The 1977 film has a number of changes from the prototype, including being entirely in color, moving the starting location from Miami to Chicago, removing the relativistic (time) dimension, introducing an additional two powers of ten at each extreme, a change in narrator from Judith Bronowski to Philip Morrison, and much-improved graphics.

Synopsis

1968 version This version of the film has two clocks in the corner showing the comparison between the viewer's time and that of Earth time. As the viewer's speed increases, Earth time, relative to the viewer, also increases. It was installed in the Smithsonian Institution's National Air and Space Museum's Life in the Universe gallery at the time of the museum's opening in 1976, until the gallery's closure in 1978. There is also a 1968 National Film Board of Canada film entitled Cosmic Zoom which covers the same subject using animation. It is wordless, using sped-up music during the return trips to normal size.

1977 version The film begins with an overhead view of a man and woman picnicking in a park at the Chicago lakefront — a 1-meter (3.3 ft) overhead image of the figures on a blanket surrounded by food and books they brought with them, one of them being The Voices of Time by J. T. Fraser. The man (played by Swiss designer Paul Bruhwiler) then sleeps, while the woman (played by Eames staffer Etsu Garfias) starts to read one of the books. The viewpoint, accompanied by expository voiceover by Philip Morrison, then slowly zooms out to a view 10 meters (33 ft) across (or 101 meters in scientific notation). The zoom-out continues (at a rate of one power of ten per 10 seconds), to a view of 100 meters (330 ft) (where they are shown to be in Burnham Park, near Soldier Field, then 1 kilometer (3,300 ft) (where we see the entirety of Chicago), and so on, increasing the perspective and continuing to zoom out to a field of view of 1024 meters, or a field of view 100 million light years across. The camera then zooms back in at a rate of a power of ten per 2 seconds to the picnic, and then slows back down to its original rate into the man's hand, to views of negative powers of ten: 10 centimeters (10−1 meters), and so forth, revealing a white blood cell and zooming in on it—until the camera comes to quarks in a proton of a carbon atom at 10−16 meters.

Reception and legacy Physicist Robbert Dijkgraaf noted: "It is a brilliant short documentary [...]. If I wanted to show an alien how we view the world, I would show this movie". In 1998, Powers of Ten, the 1977 version, was selected for preservation in the United States National Film Registry by the Library of Congress as being "culturally, historically, or aesthetically significant".

Related books Morrison, Philip; Morrison, Phylis Morrison (1994) [1982]. Powers of Ten: A Book About the Relative Size of Things in the Universe and the Effect of Adding another Zero. Scientific American Library. ISBN 978-0-7167-6008-5.

Related films Cosmic Zoom (1968), the aforementioned eight-minute short from Canada. Cosmic Voyage (1996), the Oscar-nominated loose remake of Powers of Ten in IMAX format for the National Air and Space Museum. Our Universe is SO big, it's mindblowing! (2021)

See also Cosmic Eye (2012), remake of Powers of Ten Orders of magnitude Earth's location in the universe

References

Worked examples

Example 1 — a first encounter with Powers of Ten (film series)

Start with the simplest possible case. Write down what Powers of Ten (film series) claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Powers of Ten (film series) before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Powers of Ten (film series) ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Powers of Ten (film series)

In research
Powers of Ten (film series) appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Powers of Ten (film series) in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Powers of Ten (film series) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1968 American films, 1968 English-language films, 1968 films, so understanding it makes those chapters shorter.
In everyday life
Look for Powers of Ten (film series) outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Powers of Ten (film series) in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Powers of Ten (film series) means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Powers of Ten (film series) out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Powers of Ten (film series) in simple terms?

The Powers of Ten are two short American documentary films written and directed by Charles and Ray Eames. Both works depict the relative scale of the universe according to an order of magnitude (or logarithmic scale) based on a factor of ten, first expanding out from the Earth until the entire univ…

Why does Powers of Ten (film series) matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Powers of Ten (film series)?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Powers of Ten (film series).

Tags

  • 1968 American films
  • 1968 English-language films
  • 1968 films
  • 1968 short documentary films
  • 1977 American films
  • 1977 English-language films
  • 1977 films
  • 1977 short documentary films
  • American short documentary films
  • Documentary films about mathematics
  • Documentary films about science
  • English-language short documentary films

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