2.7: Summarizing and Paraphrasing
- Summarize a passage of reading
- Paraphrase a passage of reading
Have you ever heard, “the best way to learn something is to teach it to someone else”?
Writing a summary of a source is a very similar process to teaching someone the content—but in this case, the student you’re teaching is yourself.
Summarizing , or condensing someone else’s ideas and putting it into your own shortened form, allows you to be sure that you’ve accurately captured the main idea of the text you’re reading. When reading, summarizing is helpful for checking your understanding of a longer text and remembering the author’s main ideas. When writing, summarizing is critical when reviewing, writing an abstract, preparing notes for a study guide, creating an annotated bibliography, answering essay questions, recording results of an experiment, describing the plot of a fictional work or film, or writing a research paper.
How to Write Summary Statements
Use these processes to help you write summary statements:
- Underline important information and write keywords in the margin.
- Record ideas using a two-column note-taking system. Record questions you have about the text concepts in the left column and answers you find in the reading in the right column.
- Identify how concepts relate to what you already know.
- Add examples and details
For retaining key ideas as you read, write a summary statement at the end of each paragraph or section. For capturing the major ideas of the entire work, write a summary paragraph (or more) that describes the entire text.
For longer, overall summary projects that capture an entire reading, consider these guidelines for writing a summary:
- A summary should contain the main thesis or standpoint of the text, restated in your own words. (To do this, first find the thesis statement in the original text.)
- A summary is written in your own words. It contains few or no quotes.
- A summary is always shorter than the original text, often about 1/3 as long as the original. It is the ultimate fat-free writing. An article or paper may be summarized in a few sentences or a couple of paragraphs. A book may be summarized in an article or a short paper. A very large book may be summarized in a smaller book.
- A summary should contain all the major points of the original text , and should ignore most of the fine details, examples, illustrations or explanations.
- The backbone of any summary is formed by crucial details (key names, dates, events, words and numbers). A summary must never rely on vague generalities.
- If you quote anything from the original text, even an unusual word or a catchy phrase, you need to put whatever you quote in quotation marks (” “).
- A summary must contain only the ideas of the original text. Do not insert any of your own opinions, interpretations, deductions or comments into a summary.
Watch this video to see a walk-through explanation on how to summarize.
You can view the transcript for “Summarizing” here (opens in new window).
Paraphrasing
Paraphrasing is the act of putting an author’s ideas into your own words. When reading, paraphrasing is helpful for checking your understanding of what you read as well as remembering what you read. When writing, paraphrasing is an important skill to have when constructing a research paper and incorporating the ideas of others alongside your own.
Click to view the transcript for “Paraphrasing” here (opens in new window) .
paraphrasing : rewriting a passage of text in your own words
summarizing : condensing someone else’s ideas and putting it into your own shortened form
Contributors and Attributions
- Modification, adaptation, and original content. Provided by : Lumen Learning. License : CC BY: Attribution
- PQRST Script. Provided by : Lethbridge College. Located at : www.lethbridgecollege.net/elearningcafe/index.php/pqrst-script. Project : eLearning Cafe. License : CC BY: Attribution
- Summarizing. Provided by : Excelsior College. Located at : https://owl.excelsior.edu/orc/what-to-do-after-reading/summarizing/ . License : CC BY: Attribution
- Why Use Quotes?. Authored by : The News Manual. Provided by : Media Helping Media. Located at : www.mediahelpingmedia.org/training-resources/journalism-basics/659-how-to-use-quotes-in-news-stories-and-features. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
- How to Write an A-plus Summary of a Text. Authored by : Owen M. Williamson. Provided by : The University of Texas at El Paso. Located at : http://utminers.utep.edu/omwilliamson/engl0310/summaryhints.htm . License : Public Domain: No Known Copyright


1.10: The Friedmann Equation
Sticking with our Newtonian expanding universe, we will now derive the Friedmann equation that relates the mass/energy density to the rate of change of the scale factor.
We will proceed by using the Newtonian concept of energy conservation. (You may be surprised to hear me call this a Newtonian concept, but the fact is that energy conservation does not fully survive the transition from Newton to Einstein).
Box \(\PageIndex{1}\)
Assume the universe is filled with a fluid with mass density \(\rho\), that is flowing in a manner consistent with Hubble's law. Consider a test particle of mass \(m\) a distance \(a(t)\ell\) away from the origin of the coordinate system, that moves along with the fluid; i.e., all of its motion relative to the origin is due to the changing of the scale factor. We take the origin of the coordinate system to be at rest.
Exercise 10.1.1: Express the test particle's kinetic energy as a function of \(\dot a, \ell\) and \(m\).
Exercise 10.1.2: Calculate the test particle's potential energy. Do so by considering just the mass interior to a sphere centered on the origin, with radius \(a(t)\ell\), as is justified for spherical mass distributions in Newtonian mechanics.
Exercise 10.1.3: Add these two together and set them equal to a constant. Call the constant \(\kappa\).
 Because the other two terms in the equation are constant in space, we can conclude that the third term is also constant in space. Since \(\frac{1}{a^2}\) is also constant in space, the combination \(2\kappa/(ml^2)\) that precedes it must also be constant in space. We are free to simplify this term by introducing a new space-time constant that we will call \(-k\) so the Friedmann equation becomes:
\[\left(\frac{\dot a}{a}\right)^2 = \frac{8\pi G \rho}{3} - \frac{k}{a^2}.\]
In general relativity this constant, \(k\), is the same as the curvature constant in the FRW invariant distance equation. Of course we cannot use Newtonian physics to derive this fact, as curvature is a non-Newtonian concept. We simply state it here with no proof.
To fully have a handle on the dynamics, what's left is to determine how \(\rho\) changes as \(a\) changes, a subject we will address in the next few chapters. For now, to explore some consequences of the Friedmann equation, we assume \(\rho \propto a^{-3}\). This is a model that most cosmologists, over 25 years ago, thought was probably an excellent approximation to reality. With this assumption, there becomes a connection between the geometry of space, and the fate of the universe. If \(k > 0\) the expansion eventually halts and becomes contraction. If \(k < 0\) or if \( k =0\) the expansion rate remains positive, approaching but never reaching zero.
Note that the Friedmann equation gives us another means of inferring the curvature constant \(k\). All we need to do is determine the expansion rate today, \(H_0\) and the density of matter today, \(\rho_0\) and plug them in to the Friedmann equation and solve for \(k\). We've already seen, in principle, how to infer \(H_0\) by measuring luminosity distances and redshifts for objects at low redshift and using \(cz =H_0 d_{\rm lum}\). Measuring \(\rho_0 \), is trickier, and a subject we may not get to in this course. However, cosmologists have been attempting to measure \(\rho_0\) for decades, in order to then infer \(k\). Because they also used to believe \(\rho \propto a^{-3}\), this meant a density measurement could be used to infer the fate of the universe. This situation is the origin of the statement "density is destiny." As we will see, the surprising discovery of cosmic acceleration ( \( \ddot a > 0\) ) destroyed this notion.
HOMEWORK Problems
Note : Unless directed otherwise, in these first 3 problems assume that \(k = 0\) and \(\rho \propto a^{-3}\).
Problem \(\PageIndex{1}\)
- What is the age of the universe as a function of \(H\)?
- If there were some non-zero curvature, would the magnitude of its contribution to the expansion rate, relative to that of the energy density, increase or decrease over time?
Problem \(\PageIndex{2}\)
What is the furthest physical distance a signal could travel if it started at the beginning? Express your answer as a function of \(H\). To be clear, the distance I mean is the physical distance, at the time when the expansion rate is \(H\), between the particle's actual spatial location and the spatial location it would have had if it had been stationary since the beginning.
Problem \(\PageIndex{3}\)
Is there any limit to the comoving distance we can send a signal, if we send one now and are willing to wait an arbitrarily long amount of time? This is equivalent to asking, are there galaxies out at sufficient distance, that a light signal we send to them now will never get to them, even given an infinite amount of time?
Problem \(\PageIndex{4}\)
Show that if \(\rho \propto a^{p} \) with \(p < -2\), then \(\ddot a < 0.\) Do not assume \(k = 0\).


9.2: Renaissance Music
Introduction
Renaissance music is music written in Europe during the Renaissance. Consensus among music historians–with notable dissent–has been to start the era around 1400, with the end of the medieval era, and to close it around 1600, with the beginning of the baroque period, therefore commencing the musical Renaissance about a hundred years after the beginning of the Renaissance as understood in other disciplines. As in the other arts, the music of the period was significantly influenced by the developments which define the early modern period: the rise of humanistic thought; the recovery of the literary and artistic heritage of ancient Greece and Rome; increased innovation and discovery; the growth of commercial enterprise; the rise of a bourgeois class; and the Protestant Reformation. From this changing society emerged a common, unifying musical language, in particular the polyphonic style of the Franco-Flemish school.
The invention of the Gutenberg press made distribution of music and musical theory possible on a wide scale. Demand for music as entertainment and as an activity for educated amateurs increased with the emergence of a bourgeois class. Dissemination of chansons, motets, and masses throughout Europe coincided with the unification of polyphonic practice into the fluid style which culminated in the second half of the sixteenth century in the work of composers such as Palestrina, Lassus, Victoria and William Byrd. Relative political stability and prosperity in the Low Countries, along with a flourishing system of music education in the area’s many churches and cathedrals, allowed the training of hundreds of singers and composers. These musicians were highly sought throughout Europe, particularly in Italy, where churches and aristocratic courts hired them as composers and teachers. By the end of the sixteenth century, Italy had absorbed the northern influences, with Venice, Rome, and other cities being centers of musical activity, reversing the situation from a hundred years earlier. Opera arose at this time in Florence as a deliberate attempt to resurrect the music of ancient Greece.
Music, increasingly freed from medieval constraints, in range, rhythm, harmony, form, and notation, became a vehicle for new personal expression. Composers found ways to make music expressive of the texts they were setting. Secular music absorbed techniques from sacred music, and vice versa. Popular secular forms such as the chanson and madrigal spread throughout Europe. Courts employed virtuoso performers, both singers and instrumentalists. Music also became more self-sufficient with its availability in printed form, existing for its own sake. Many familiar modern instruments (including the violin, guitar, lute and keyboard instruments), developed into new forms during the Renaissance responding to the evolution of musical ideas, presenting further possibilities for composers and musicians to explore. Modern woodwind and brass instruments like the bassoon and trombone also appeared; extending the range of sonic color and power. During the fifteenth century the sound of full triads became common, and towards the end of the sixteenth-century the system of church modes began to break down entirely, giving way to the functional tonality which was to dominate western art music for the next three centuries.
From the Renaissance era both secular and sacred music survives in quantity, and both vocal and instrumental. An enormous diversity of musical styles and genres flourished during the Renaissance, and can be heard on commercial recordings in the twenty-first century, including masses, motets, madrigals, chansons, accompanied songs, instrumental dances, and many others. Numerous early music ensembles specializing in music of the period give concert tours and make recordings, using a wide range of interpretive styles.
One of the most pronounced features of early Renaissance European art music was the increasing reliance on the interval of the third (in the Middle Ages, thirds had been considered dissonances). Polyphony became increasingly elaborate throughout the fourteenth century, with highly independent voices: the beginning of the fifteenth century showed simplification, with the voices often striving for smoothness. This was possible because of a greatly increased vocal range in music–in the Middle Ages, the narrow range made necessary frequent crossing of parts, thus requiring a greater contrast between them.
The modal (as opposed to tonal) characteristics of Renaissance music began to break down towards the end of the period with the increased use of root motions of fifths. This later developed into one of the defining characteristics of tonality.
The main characteristics of Renaissance music are the following:
- Music based on modes
- Richer texture in four or more parts
- Blending rather than contrasting strands in the musical texture
- Harmony with a greater concern with the flow and progression of chords
Polyphony is one of the notable changes that mark the Renaissance from the Middle Ages musically. Its use encouraged the use of larger ensembles and demanded sets of instruments that would blend together across the whole vocal range.
Principal liturgical forms which endured throughout the entire Renaissance period were masses and motets, with some other developments towards the end, especially as composers of sacred music began to adopt secular forms (such as the madrigal) for their own designs.
Common sacred genres were the mass, the motet, the madrigale spirituale, and the laude.
During the period, secular music had an increasing distribution, with a wide variety of forms, but one must be cautious about assuming an explosion in variety: since printing made music more widely available, much more has survived from this era than from the preceding medieval era, and probably a rich store of popular music of the late Middle Ages is irretrievably lost.
Secular music was music that was independent of churches. The main types were the German Lied, Italian frottola, the French chanson, the Italian madrigal, and the Spanish villancico. Other secular vocal genres included the caccia, rondeau, virelai, bergerette, ballade, musique mesurée, canzonetta, villanella, villotta, and the lute song. Mixed forms such as the motet-chanson and the secular motet also appeared.
Purely instrumental music included consort music for recorder or viol and other instruments, and dances for various ensembles. Common instrumental genres were the toccata, prelude, ricercar, and canzona. Dances played by Instrumental ensembles included the basse danse, tourdion, saltarello, pavane, galliard, allemande, courante, bransle, canarie, and lavolta. Music of many genres could be arranged for a solo instrument such as the lute, vihuela, harp, or keyboard. Such arrangements were called intabulations.
Towards the end of the period, the early dramatic precursors of opera such as monody, the madrigal comedy, and the intermedio are seen.
Theory and Notation
According to Margaret Bent, “Renaissance notation is underprescriptive by our standards; when translated into modern form it acquires a prescriptive weight that overspecifies and distorts its original openness.”
Renaissance compositions were notated only in individual parts; scores were extremely rare, and bar lines were not used. Note values were generally larger than are in use today; the primary unit of beat was the semibreve, or whole note. As had been the case since the Ars Nova, there could be either two or three of these for each breve (a double-whole note), which may be looked on as equivalent to the modern “measure,” though it was itself a note value and a measure is not. The situation can be considered this way: it is the same as the rule by which in modern music a quarter-note may equal either two eighth-notes or three, which would be written as a “triplet.” By the same reckoning, there could be two or three of the next smallest note, the “minim,” (equivalent to the modern “half note”) to each semibreve.
These different permutations were called “perfect/imperfect tempus” at the level of the breve–semibreve relationship, “perfect/imperfect prolation” at the level of the semibreve–minim, and existed in all possible combinations with each other. Three-to-one was called “perfect,” and two-to-one “imperfect.” Rules existed also whereby single notes could be halved or doubled in value (“imperfected” or “altered,” respectively) when preceded or followed by other certain notes. Notes with black noteheads (such as quarter notes) occurred less often. This development of white mensural notation may be a result of the increased use of paper (rather than vellum), as the weaker paper was less able to withstand the scratching required to fill in solid noteheads; notation of previous times, written on vellum, had been black. Other colors, and later, filled-in notes, were used routinely as well, mainly to enforce the aforementioned imperfections or alterations and to call for other temporary rhythmical changes.
Accidentals were not always specified, somewhat as in certain fingering notations (tablatures) today. However, Renaissance musicians would have been highly trained in dyadic counterpoint and thus possessed this and other information necessary to read a score, “what modern notation requires [accidentals] would then have been perfectly apparent without notation to a singer versed in counterpoint.” A singer would interpret his or her part by figuring cadential formulas with other parts in mind, and when singing together musicians would avoid parallel octaves and fifths or alter their cadential parts in light of decisions by other musicians.
It is through contemporary tablatures for various plucked instruments that we have gained much information about what accidentals were performed by the original practitioners.
For information on specific theorists, see Johannes Tinctoris, Franchinus Gaffurius, Heinrich Glarean, Pietro Aron, Nicola Vicentino, Tomás de Santa María, Gioseffo Zarlino, Vicente Lusitano, Vincenzo Galilei, Giovanni Artusi, Johannes Nucius, and Pietro Cerone.
Time Line of Renaissance Composers
Contributors and Attributions
- Renaissance music. Provided by : Wikipeida. Located at : https://en.Wikipedia.org/wiki/Renaissance_music . License : CC BY-SA: Attribution-ShareAlike
- Concert in an Egg. Provided by : Wikimedia. Located at : https://commons.wikimedia.org/wiki/File:Concert_in_the_Egg.jpg . License : Public Domain: No Known Copyright
- Chansonnier by Heinrich Isaac. Provided by : Wikimedia. Located at : https://commons.wikimedia.org/wiki/File:Isaac_pallepalle.jpg . License : Public Domain: No Known Copyright
- Cyprien de Rore manuscript. Provided by : Wikimedia. Located at : https://commons.wikimedia.org/wiki/File:Hans_Mielich_-_Cyprien_de_Rore.jpg . License : Public Domain: No Known Copyright


6.2: Defining mass
What is the mass of an object? Newton’s second law tells us that if there is a constant force \(\overrightarrow{\boldsymbol{F}}_{\text {ref }}\) acting on the object, and we measure an acceleration vector \(\overrightarrow{\boldsymbol{a}}_{i}\), the object’s mass is given by:
\[m_{i} \equiv \frac{\left|\overrightarrow{\boldsymbol{F}}_{\mathrm{ref}}\right|}{\left|\overrightarrow{\boldsymbol{a}}_{i}\right|} \tag{6.2} \label{6.2}\]
where we used the \(\equiv\) sign to indicate that this is the definition of the mass, or inertial mass, of the object.
The object’s mass obeys Equation 6.2 irrespective of the properties of the force \(\overrightarrow{\boldsymbol{F}}_{\text {ref }}\), and is thus an intrinsic property of the object that normally does not change. To assign a value to the mass we use the international systems of units, the SI units. The previous equation tells us that if we apply a force of \(1 \mathrm{~N}\) and observe an acceleration of \(1 \mathrm{~m} / \mathrm{s}^{2}\), the mass of the object is \(1 \mathrm{~kg}\).
6.2.1 Weight of a mass
Since measuring accelerations is not always easy, in practice we often determine the mass of an object via the gravitational force acting on the object, e.g. by using a weighing scale. This is possible because it was experimentally determined that the gravitational force on earth is proportional to the mass of the object: \(\overrightarrow{\boldsymbol{F}}_{i, g}=m_{i} \overrightarrow{\boldsymbol{g}}\). The magnitude of the gravitational force on the object on earth’s surface is defined as the weight \(W\) of the object, so we can write:
\[W_{i} \equiv m_{i}|\overrightarrow{\boldsymbol{g}}| \tag{6.3} \label{6.3}\]
Here, the gravitational acceleration vector \(\overrightarrow{\boldsymbol{g}}\) has a magnitude of approximately \(9.8 \mathrm{~m} / \mathrm{s}^{2}\) on earth and points towards the center of the earth. The gravitational mass of an object can be determined using the equation \(m_{i}=W_{i} /|\overrightarrow{\boldsymbol{g}}|\) and has experimentally been found to be equal to its inertial mass as determined from Newton’s second law.
6.2.2 Point mass
A point mass \(i\) is an object that behaves like a mathematical point in space at position vector \(\overrightarrow{\boldsymbol{r}}_{i}\) and has mass \(m_{i}\).
Since it is located at a single point, a point mass can only have a single position, velocity and acceleration vector. The point mass is an important concept, because Newton’s laws strictly only hold for point masses. Moreover, the smallest known particles, the elementary particles, behave very similar to point masses, and all larger objects are made out of elementary particles. Also, as we will see, the dynamics of larger objects can often still be well approximated by treating them as a point mass, therefore the term point mass is also used for larger objects that move like a point mass, e.g. because they do not rotate.


15.8: Review Questions
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1.
According to the free radical theory, what contributes to physical aging?
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accelerating cellular clocks
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shortening of telomeres
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unstable oxygen molecules
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genetics influences
2 .
________ is an age-related decline in bone mass, while ________ is an age-related loss of muscles mass.
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osteoporosis; sarcopenia
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arthritis; presbyopia
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sarcopenia; osteoporosis
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presbyopia; arthritis
3.
Cognitive decline that is associated with dementia is an example of what type of aging?
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normative
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primary
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secondary
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tertiary
4 .
What is one of the most significant predictors of life expectancy in the United States?
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body mass index
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cultural background
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intelligence
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socioeconomic status
5.
Older adults are more likely to experience ________ conditions but less likely to experience ________ conditions.
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acute; chronic
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respiratory; heart
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heart; respiratory
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chronic; acute
6 .
What is the relationship between age and the likelihood of experiencing anxiety and depression?
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Anxiety and depression are both more common and more devastating for older adults.
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Older adults are at increased risk of depression but less likely to experience anxiety.
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Older adults are at increased risk of anxiety but less likely to experience depression.
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Both depression and anxiety become less common in older age.
7.
According to recent data (2020–2021), which chronic condition was the leading cause of death in the United States for people over age forty-five years?
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cancer
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COVID-19
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heart disease
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complications of diabetes
8 .
What is a characteristic of autobiographical memories?
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They include episodic memories only.
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They tend to get more positive with age.
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They include semantic memories only.
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They are very high in accuracy.
9.
Which type of memory does not appear to be affected by aging?
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short-term
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working
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episodic
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implicit
10 .
Which type of memory has been found to overlap considerably with crystallized intelligence even though retrieval problems may increase with age?
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episodic
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autobiographical
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flashbulb
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semantic
11.
What is the most common type of dementia, accounting for 50 to 70 percent of dementia cases?
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Alzheimer’s disease
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Lewy body dementia
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dementia due to Parkinson’s disease
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vascular dementia
12 .
What term describes general cognitive decline that is more severe than normative but below the threshold for a dementia-related diagnosis?
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amnestic delirium
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transient ischemic attack
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cerebrovascular accident
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mild cognitive impairment
13.
In what type of dementia can cognitive declines stop and later improve if the underlying cause of symptoms is identified and treated?
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Alzheimer’s disease
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Lewy body dementia
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Parkinson’s disease
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vascular dementia
14 .
The primary neurological changes associated with Alzheimer’s disease are the formation of which of the following?
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Lewy bodies and Golgi snares
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amyloid plaques and neurofibrillary tangles
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meninges and neuroblastomas
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bacterial and viral infections
15.
Increased activity in the ________ lobe may be an early indicator of Alzheimer’s disease as this part of the brain tries to compensate for damage in other areas.
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parietal
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temporal
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frontal
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occipital
16 .
How can we best describe the declines associated with normative cognitive aging?
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large global declines that make it difficult for older adults to function without help
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arising only after dementia symptoms become obvious
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subtle and typically not interfering with the ability to live independently
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abrupt transitions from high functioning to low functioning
17.
Characteristics that protect against dementia by delaying onset and reducing symptoms are known as which of the following?
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cognitive reserve
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neurological redundancy
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neuroplasticity
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synaptic pruning
18 .
When solving problems, older adults tend to use ________ abilities, while younger adults tend to use ________ abilities.
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fluid; crystallized
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crystallized; fluid
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convergent; divergent
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divergent; convergent
19.
Research has found that as much as 40 percent of dementia cases were caused by
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telomere death and free readical acceleration in the brain
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abnormalities in endocrine functioning and hormonal disruption
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sleep inadequacies, like insomnia and obstructive apnea
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modifiable behaviors, like high blood pressure and obesity


5.5: Continental Drift
INTRODUCTION
The continental drift hypothesis was developed in the early part of the 20 th century, mostly by Alfred Wegener. Wegener said that continents move around on Earth’s surface and that they were once joined together as a single supercontinent. While Wegener was alive, scientists did not believe that the continents could move.
THE CONTINENTAL DRIFT IDEA
Find a map of the continents and cut each one out. Better yet, use a map where the edges of the continents show the continental shelf. That’s the true size and shape of a continent. Can you fit the pieces together? The easiest link is between the eastern Americas and western Africa and Europe, but the rest can fit together too (figure 1).
Figure 1. The continents fit together like pieces of a puzzle. This is how they looked 250 million years ago.
Alfred Wegener proposed that the continents were once united into a single supercontinent named Pangaea, meaning all earth in ancient Greek. He suggested that Pangaea broke up long ago and that the continents then moved to their current positions. He called his hypothesis continental drift.
EVIDENCE FOR CONTINENTAL DRIFT
Besides the way the continents fit together, Wegener and his supporters collected a great deal of evidence for the continental drift hypothesis.
- Identical rocks, of the same type and age, are found on both sides of the Atlantic Ocean. Wegener said the rocks had formed side-by-side and that the land had since moved apart.
- Mountain ranges with the same rock types, structures, and ages are now on opposite sides of the Atlantic Ocean. The Appalachians of the eastern United States and Canada, for example, are just like mountain ranges in eastern Greenland, Ireland, Great Britain, and Norway (figure 2). Wegener concluded that they formed as a single mountain range that was separated as the continents drifted.
Figure 2. The similarities between the Appalachian and the eastern Greenland mountain ranges are evidences for the continental drift hypothesis.
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Ancient fossils of the same species of extinct plants and animals are found in rocks of the same age but are on continents that are now widely separated (figure 3). Wegener proposed that the organisms had lived side by side, but that the lands had moved apart after they were dead and fossilized. He suggested that the organisms would not have been able to travel across the oceans.
- Fossils of the seed fern Glossopteris were too heavy to be carried so far by wind.
- Mesosaurus was a swimming reptile but could only swim in fresh water.
- Cynognathus and Lystrosaurus were land reptiles and were unable to swim
Figure 3. Wegener used fossil evidence to support his continental drift hypothesis. The fossils of these organisms are found on lands that are now far apart.
- Grooves and rock deposits left by ancient glaciers are found today on different continents very close to the equator. This would indicate that the glaciers either formed in the middle of the ocean and/or covered most of the Earth. Today glaciers only form on land and nearer the poles. Wegener thought that the glaciers were centered over the southern land mass close to the South Pole and the continents moved to their present positions later on.
- Coral reefs and coal-forming swamps are found in tropical and subtropical environments, but ancient coal seams and coral reefs are found in locations where it is much too cold today. Wegener suggested that these creatures were alive in warm climate zones and that the fossils and coal later had drifted to new locations on the continents.
Take a look at this animation showing that Earth’s climate belts remain in roughly the same position while the continents move and this animation showing how the continents split up.
Although Wegener’s evidence was sound, most geologists at the time rejected his hypothesis of continental drift. Why do you think they did not accept continental drift?
Scientists argued that there was no way to explain how solid continents could plow through solid oceanic crust. Wegener’s idea was nearly forgotten until technological advances presented even more evidence that the continents moved and gave scientists the tools to develop a mechanism for Wegener’s drifting continents.
MAGNETIC POLARITY EVIDENCE
Puzzling new evidence came in the 1950s from studies on the Earth’s magnetic history (figure 4). Scientists used magnetometers , devices capable of measuring the magnetic field intensity, to look at the magnetic properties of rocks in many locations.
Figure 4. Earth’s magnetic field is like a magnet with its north pole near the geographic North Pole and the south pole near the geographic South Pole.
Magnetite crystals are like tiny magnets that point to the north magnetic pole as they crystallize from magma. The crystals record both the direction and strength of the magnetic field at the time. The direction is known as the field’s magnetic polarity.
Magnetic Polarity on the Same Continent with Rocks of Different Ages
Geologists noted important things about the magnetic polarity of different aged rocks on the same continent:
- Magnetite crystals in fresh volcanic rocks point to the current magnetic north pole (figure 5) no matter what continent or where on the continent the rocks are located.
Figure 5. Earth’s current north magnetic pole is in northern Canada.
- Older rocks that are the same age and are located on the same continent point to the same location, but that location is not the current north magnetic pole.
- Older rock that are of different ages do not point to the same locations or to the current magnetic north pole.
In other words, although the magnetite crystals were pointing to the magnetic north pole, the location of the pole seemed to wander. Scientists were amazed to find that the north magnetic pole changed location through time (figure 6).
Figure 6. The location of the north magnetic north pole 80 million years before present (mybp), then 60, 40, 20, and now.
There are three possible explanations for this:
- The continents remained fixed and the north magnetic pole moved.
- The north magnetic pole stood still and the continents moved.
- Both the continents and the north pole moved.
Magnetic Polarity on Different Continents with Rocks of the Same Age
Geologists noted that for rocks of the same age but on different continents, the little magnets pointed to different magnetic north poles.
- 400-million-year-old magnetite in Europe pointed to a different north magnetic pole than the same-aged magnetite in North America.
- 250 million years ago, the north poles were also different for the two continents.
The scientists looked again at the three possible explanations. Only one can be correct. If the continents had remained fixed while the north magnetic pole moved, there must have been two separate north poles. Since there is only one north pole today, the only reasonable explanation is that the north magnetic pole has remained fixed but that the continents have moved.
To test this, geologists fitted the continents together as Wegener had done. It worked! There has only been one magnetic north pole and the continents have drifted (figure 7). They named the phenomenon of the magnetic pole that seemed to move but actually did not apparent polar wander.
Figure 7. On the left: The apparent north pole for Europe and North America if the continents were always in their current locations. The two paths merge into one if the continents are allowed to drift.
This evidence for continental drift gave geologists renewed interest in understanding how continents could move about on the planet’s surface.
LESSON SUMMARY
- In the early part of the 20th century, scientists began to put together evidence that the continents could move around on Earth’s surface.
- The evidence for continental drift included the fit of the continents; the distribution of ancient fossils, rocks, and mountain ranges; and the locations of ancient climatic zones.
- Although the evidence for continental drift was extremely strong, scientists rejected the idea because no mechanism for how solid continents could move around on the solid earth was developed.
- The discovery of apparent polar wander renewed scientists interest in continental drift.
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Contributors and Attributions
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Original content from Kimberly Schulte (Columbia Basin College) and supplemented by Lumen Learning . The content on this page is copyrighted under a Creative Commons Attribution 4.0 International license.


13.3: Images, Quantitatively
It sounds a bit odd when a scientist refers to a theory as “beautiful,” but to those in the know it makes perfect sense. One mark of a beautiful theory is that it surprises us by being simple. The mathematical theory of lenses and curved mirrors gives us just such a surprise. We expect the subject to be complex because there are so many cases: a converging mirror forming a real image, a diverging lens that makes a virtual image, and so on for a total of six possibilities. If we want to predict the location of the images in all these situations, we might expect to need six different equations, and six more for predicting magnifications. Instead, it turns out that we can use just one equation for the location of the image and one equation for its magnification, and these two equations work in all the different cases with no changes except for plus and minus signs. This is the kind of thing the physicist Eugene Wigner referred to as “the unreasonable effectiveness of mathematics.” Sometimes we can find a deeper reason for this kind of unexpected simplicity, but sometimes it almost seems as if God went out of Her way to make the secrets of universe susceptible to attack by the human thought-tool called math.
Contributors and Attributions
Benjamin Crowell (Fullerton College). Conceptual Physics is copyrighted with a CC-BY-SA license.