Chapter 7: Transnational Crews and Postsocialist Precarity – Globalizing Screen Media Labor in Prague
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Political economists and network theorists offer different assessments of the global relations of motion picture production. While spatially extended webs of productive labor are central to such approaches, neither explains specifically how these webs are constituted or how they operate in peripheral production ecologies. What is more, they do not consider the implications of the knowledge transfers and power hierarchies emerging from such transnational production contexts. By contrast, this chapter offers a concrete analysis of these issues in Prague’s postsocialist film and television industries. It focuses on the segregation of the local work world and on barriers inhibiting transsectoral knowledge...
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7.1: Introduction
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Overview of the chapter focus: analysis of film and television industry labor issues in postsocialist Prague, including the segregation of work cultures, barriers against transsectoral knowledge transfers, and the two-tier production split between international and domestic production.
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7.2: Localized Learning in Global Production Networks
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Distinguishing this chapter's focus on local reasons for labor precarity from the U.S.-dominated neo-Marxist analysis of international production. The process by which Czech workers learn foreign production practices, and the three dimensions of localized learning proposed by Malmberg and Maxwell.
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7.3: Globalizing a Postsocialist Production World – Producers and Production Management as Cultural Interface
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The rise of Prague's foreign services industry since the 1990s. The emphasis on transfer of organizational knowledge and managerial, rather than technical, skills from overseas producers to Czech workers.
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7.4: Multiple Globalizations
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The limitations of knowledge transfer as a result of interaction between Czech and overseas personnel, including the lack of local production reshaping due to the lack of hiring of Czech above-the-line workers or department heads, the limited upward mobility of Czech workers in transnational productions, and the lack of production services companies branching out to original productions.
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7.5: Career Patterns and Precarity in Transnational Project Networks
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Contrasting career patterns: American-born production managers in Prague are fast-tracked compared to their counterparts in Hollywood, while Czech production workers rarely gain promotions to higher creative positions, build internationally known career, or take part in prestigious domestic projects.
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7.6: Conclusion – A Two-Tier, Departmentalized Work World
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The importance of a balanced approach to modeling globalization, that considers knowledge transfers, learning effects, and cultural intermediaries, in analyzing labor issues of the Czech screen industries.
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7.7: Notes
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2.2: A Look Into History
19 th Century
Modern cultural anthropology has its origins in, and developed in reaction to, 19 th -century "ethnology", the comparative study of cultures; it presents analytical generalizations about human culture. Scholars like E.B. Tylor and J.G. Frazer in England worked mostly with materials collected by others – usually missionaries, traders, explorers, or colonial officials – this earned them their current sobriquet of "arm-chair anthropologists".
Ethnologists had a special interest in why people living in different parts of the world often had similar beliefs and practices. In addressing this question, ethnologists in the 19 th century divided into two schools of thought. Some, like Grafton Elliot Smith, argued that different groups must somehow have learned from one another, however indirectly; in other words, they argued that cultural traits spread from one place to another, or "diffused". This way of thinking could be better understood in the context of the school playground; everyone wants to be like the "cool" kid-they see what he has and they want it. This idea can be expanded to an entire culture, people see another group of people doing something better than them, and so they learn the new, more effective way of living.
Other ethnologists argued that different groups had the capability of inventing similar beliefs and practices independently. Some of those who advocated "independent invention", like Morgan, additionally supposed that similarities meant that different groups had passed through the same stages of cultural evolution. Morgan, in particular, acknowledged that certain forms of society and culture could not possibly have arisen before others. For example, industrial farming could have been invented before simple farming, and metallurgy could have developed without previous non-smelting processes involving metals (such as simple ground collection or mining). Morgan, like other 19 th century social evolutionists, believed there was a more or less orderly progression from the primitive to the civilized.
20 th Century
20 th -century anthropologists largely rejected the notion that all human societies must pass through the same stages in the same order, on the grounds that such a notion does not fit the empirical facts. After witnessing such a broad development of human society, we now have the knowledge that cultures change at different rates due to environmental causes, economic resources and educational development. Some 20 th -century ethnologists, like Julian Steward, have instead argued that such similarities reflected similar adaptations to similar environments.
Others, such as Claude Lévi-Strauss (who was influenced both by American cultural anthropology and by French Durkheimian sociology), have argued that apparent patterns of development reflect fundamental similarities in the structure of human thought (see structuralism ). By the mid-20 th century, the number of examples of people skipping stages, such as going from hunter-gatherers to post-industrial service occupations in one generation, were so numerous that 19 th -century evolutionism was effectively disproved.[1]
In the 20 th century, most cultural (and social) anthropologists turned to the crafting of ethnographies. An ethnography is a case study of a culture made by a researcher immersing themself in said culture. Typically, the anthropologist actually lives among another society for a considerable period of time, simultaneously participating in and observing the social and cultural life of the group. This way of studying a culture is a much more unbiased view of the culture, as opposed to the previous method of armchair anthropologists throughout history, these scholars are there interacting with the people. As a way of learning about a culture, these ethnographies are a great resource.
However, any number of other ethnographic techniques have resulted in ethnographic writing or details being preserved, as cultural anthropologists also curate materials, spend long hours in libraries, churches and schools poring over records, investigate graveyards, and decipher ancient scripts. A typical ethnography will also include information about physical geography, climate, and habitat. It is meant to be a holistic piece of writing about the people in question, and today often includes the longest possible timeline of past events that the ethnographer can obtain through primary and secondary research.
Bronisław Malinowski (who conducted fieldwork in the Trobriand Islands and taught in England) developed this method, and Franz Boas promoted it. Boas's students drew on his conception of culture and cultural relativism to develop cultural anthropology in the United States. Simultaneously, Malinowski and A.R. Radcliffe Brown´s students were developing social anthropology in the United Kingdom. Whereas cultural anthropology focused on symbols and values, social anthropology focused on social groups and institutions. Today socio-cultural anthropologists attend to all these elements.
Although 19 th -century ethnologists saw "diffusion" and "independent invention" as mutually exclusive and competing theories, most ethnographers quickly reached a consensus that both processes occur, and that both can plausibly account for cross-cultural similarities. But these ethnographers pointed out the superficiality of many such similarities, and that even traits spread through diffusion often changed their meaning and functions as they moved from one society to another.
Accordingly, these anthropologists showed less interest in comparing cultures, generalizing about human nature, or discovering universal laws of cultural development, than in understanding particular cultures in those cultures' own terms. Such ethnographers and their students promoted the idea of "cultural relativism", the view that one can only understand another person's beliefs and behaviors in the context of the culture in which he or she lived.
In the early 20 th century socio-cultural anthropology developed in different forms in Europe and in the United States. European "social anthropologists" focused on observed social behaviors and on "social structure", that is, on relationships among social roles, (e.g. husband and wife, or parent and child) and social institutions (e.g. religion, economy, and politics).
American "cultural anthropologists" focused on the ways people expressed their view of themselves and their world, especially in symbolic forms (such as art and myths). These two approaches frequently converged (kinship, for example, and leadership function both as symbolic systems and as social institutions), and generally complemented one another. Today almost all socio-cultural anthropologists refer to the work of both sets of predecessors and have an equal interest in what people do and in what people say.
Present Day
Today ethnography continues to dominate socio-cultural anthropology. Nevertheless, many contemporary socio-cultural anthropologists have rejected earlier models of ethnography which they claim treated local cultures as "bounded" and "isolated". These anthropologists continue to concern themselves with the distinct ways people in different locales experience and understand their lives, but they often argue that one cannot understand these particular ways of life solely from a local perspective; they instead combine a focus on the local with an effort to grasp larger political, economic, and cultural frameworks that impact local lived realities. Notable proponents of this approach include Arjun Appadurai, James Clifford, George Marcus, Sidney Mintz, Michael Taussig and Eric Wolf.
A growing trend in anthropological research and analysis seems to be the use of multi-sited ethnography, discussed in George Marcus's article "Ethnography In/Of the World System: the Emergence of Multi-Sited Ethnography". Looking at culture as embedded in macro-constructions of a global social order, multi-sited ethnography uses traditional methodology in various locations both spatially and temporally. Through this methodology, greater insight can be gained when examining the impact of world-systems on local and global communities.
Also, emerging in multi-sited ethnography are greater interdisciplinary approaches to fieldwork, bringing in methods from cultural studies, media studies, science and technology studies, and others. In multi-sited ethnography research tracks a subject across spatial and temporal boundaries. For example, a multi-sited ethnography may follow a "thing," such as a particular commodity, as it transfers through the networks of global capitalism.
Multi-sited ethnography may also follow ethnic groups in diaspora, stories or rumours that appear in multiple locations and in multiple time periods, metaphors that appear in multiple ethnographic locations, or the biographies of individual people or groups as they move through space and time. It may also follow conflicts that transcend boundaries. Multi-sited ethnographies, such as Nancy Scheper-Hughes's ethnography of the international black market for the trade of human organs. In this research she follows organs as they transfer through various legal and illegal networks of capitalism, as well as the rumours and urban legends that circulate in impoverished communities about child kidnapping and organ theft.
Sociocultural anthropologists have increasingly turned their investigative eye on to "Western" culture. For example, Philippe Bourgois, won the Margaret Mead Award in 1997 for In Search of Respect , a study of the entrepreneurs in a Harlem crack-den. Also, growing more popular are ethnographies of professional communities, such as laboratory researchers, Wall Street investors, law firms, or IT computer employees.[2]


13.6: Age Related Changes to the Urinary System
Kidneys
After the age of 40 there is a decrease in the number of cells within the kidney. As this is happening there is a thickening of the connective tissue capsule surrounding the organ and a decrease in the thickness of the cortical region.
The loss of kidney cells is explained mostly by a loss of glomeruli. As glomeruli are responsible for filtration, the loss of cells is associated with a loss of kidney functioning.
Bladder and Urethra
The walls of the bladder and urethra are made of smooth muscle. With age this muscle tissue weakens and is less elastic. This means that the bladder is less able to expand and contract in older people. As a result, the bladders of elderly people have a capacity of approximately one-half of young adults and the bladders are unable to fully evacuate during urination.
Contributors and Attributions
- Age Related Changes to the Urinary System. Authored by : Kelly, Jessica. Provided by : Herkimer College. Located at : NA. Project : AtD Course. License : CC BY: Attribution


5.1: Algebraic Considerations
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- Develop the abstract concept of a vector space through axioms.
- Deduce basic properties of vector spaces.
- Use the vector space axioms to determine if a set and its operations constitute a vector space.
In this section we consider the idea of an abstract vector space. A vector space is something which has two operations satisfying the following vector space axioms.
Definition \(\PageIndex{1}\): Vector Space
A vector space \(V\) is a set of vectors with two operations defined, addition and scalar multiplication, which satisfy the axioms of addition and scalar multiplication.
In the following definition we define two operations; vector addition, denoted by \(+\) and scalar multiplication denoted by placing the scalar next to the vector. A vector space need not have usual operations, and for this reason the operations will always be given in the definition of the vector space. The below axioms for addition (written +) and scalar multiplication must hold for however addition and scalar multiplication are defined for the vector space.
It is important to note that we have seen much of this content before, in terms of \(\mathbb{R}^n\). We will prove in this section that \(\mathbb{R}^n\) is an example of a vector space and therefore all discussions in this chapter will pertain to \(\mathbb{R}^n\). While it may be useful to consider all concepts of this chapter in terms of \(\mathbb{R}^n\), it is also important to understand that these concepts apply to all vector spaces.
In the following definition, we will choose scalars \(a,b\) to be real numbers and are thus dealing with real vector spaces. However, we could also choose scalars which are complex numbers. In this case, we would call the vector space \(V\) complex.
Definition \(\PageIndex{2}\): Axioms of Addition
Let \(\vec{v}, \vec{w}, \vec{z}\) be vectors in a vector space \(V\). Then they satisfy the following axioms of addition:
- Closed under Addition \[\mbox{If}\; \vec{v}, \vec{w} \;\mbox{are in}\; V, \;\mbox{then}\; \vec{v}+\vec{w} \;\mbox{is also in}\; V.\nonumber \]
- The Commutative Law of Addition \[\vec{v}+\vec{w}=\vec{w}+\vec{v}\nonumber \]
- The Associative Law of Addition \[\left( \vec{v}+\vec{w}\right) +\vec{z}=\vec{v}+\left( \vec{w}+ \vec{z}\right)\nonumber \]
- The Existence of an Additive Identity \[\vec{v}+\vec{0}=\vec{v}\nonumber \]
- The Existence of an Additive Inverse \[\vec{v}+\left( -\vec{v}\right) =\vec{0}\nonumber \]
vectorspaceaxiomsaddition
Definition \(\PageIndex{3}\): Axioms of Scalar Multiplication
Let \(a, b \in \mathbb{R}\) and let \(\vec{v}, \vec{w}, \vec{z}\) be vectors in a vector space \(V\). Then they satisfy the following axioms of scalar multiplication:
- Closed under Scalar Multiplication \[\mbox{If}\; a \;\mbox{is a real number, and}\; \vec{v} \;\mbox{is in}\; V, \;\mbox{then}\; a\vec{v} \;\mbox{is in}\; V.\nonumber\]
- \[a \left( \vec{v}+\vec{w}\right) = a \vec{v}+ a \vec{w} \nonumber \]
- \[\left( a + b \right) \vec{v}= a \vec{v}+ b \vec{v} \nonumber \]
- \[a \left( b \vec{v}\right) = (a b) \vec{v} \nonumber \]
- \[1\vec{v}=\vec{v} \nonumber \]
Consider the following example, in which we prove that \(\mathbb{R}^n\) is in fact a vector space.
Example \(\PageIndex{1}\): \(\mathbb{R}^n\)
\(\mathbb{R}^n\), under the usual operations of vector addition and scalar multiplication, is a vector space.
Solution
To show that \(\mathbb{R}^n\) is a vector space, we need to show that the above axioms hold. Let \(\vec{x}, \vec{y}, \vec{z}\) be vectors in \(\mathbb{R}^n\). We first prove the axioms for vector addition.
- To show that \(\mathbb{R}^n\) is closed under addition, we must show that for two vectors in \(\mathbb{R}^n\) their sum is also in \(\mathbb{R}^n\). The sum \(\vec{x} + \vec{y}\) is given by: \[\left[ \begin{array}{c} x_1 \\ x_2 \\ \vdots \\ x_n \end{array}\right] + \left[ \begin{array}{c} y_1 \\ y_2 \\ \vdots \\ y_n \end{array}\right] = \left[ \begin{array}{c} x_1 + y_1 \\ x_2 + y_2 \\ \vdots \\ x_n + y_n \end{array}\right]\nonumber \] The sum is a vector with \(n\) entries, showing that it is in \(\mathbb{R}^n\). Hence \(\mathbb{R}^n\) is closed under vector addition.
- To show that addition is commutative, consider the following: \[\begin{aligned} \vec{x} + \vec{y} &= \left[ \begin{array}{c} x_1 \\ x_2 \\ \vdots \\ x_n \end{array} \right] + \left[ \begin{array}{c} y_1 \\ y_2 \\ \vdots \\ y_n \end{array} \right] \\ &= \left[ \begin{array}{c} x_1 + y_1 \\ x_2 + y_2 \\ \vdots \\ x_n + y_n \end{array} \right] \\ &= \left[ \begin{array}{c} y_1 + x_1 \\ y_2 + x_2 \\ \vdots \\ y_n + x_n \end{array} \right] \\ &= \left[ \begin{array}{c} y_1 \\ y_2 \\ \vdots \\ y_n \end{array} \right] + \left[ \begin{array}{c} x_1 \\ x_2 \\ \vdots \\ x_n \end{array} \right] \\ &= \vec{y} + \vec{x}\end{aligned}\] Hence addition of vectors in \(\mathbb{R}^n\) is commutative.
- We will show that addition of vectors in \(\mathbb{R}^n\) is associative in a similar way. \[\begin{aligned} (\vec{x} + \vec{y}) + \vec{z} &= \left( \left[ \begin{array}{c} x_1 \\ x_2 \\ \vdots \\ x_n \end{array} \right] + \left[ \begin{array}{c} y_1 \\ y_2 \\ \vdots \\ y_n \end{array} \right] \right) + \left[ \begin{array}{c} z_1 \\ z_2 \\ \vdots \\ z_n \end{array} \right] \\ &= \left[ \begin{array}{c} x_1 + y_1 \\ x_2 + y_2 \\ \vdots \\ x_n + y_n \end{array} \right] + \left[ \begin{array}{c} z_1 \\ z_2 \\ \vdots \\ z_n \end{array} \right] \\ &= \left[ \begin{array}{c} (x_1 + y_1) + z_1 \\ (x_2 + y_2) + z_2\\ \vdots \\ (x_n + y_n) + z_n \end{array} \right] \\ &= \left[ \begin{array}{c} x_1 + (y_1 + z_1) \\ x_2 + (y_2 + z_2)\\ \vdots \\ x_n + (y_n + z_n) \end{array} \right ) \\ &= \left ( \begin{array}{c} x_1 \\ x_2 \\ \vdots \\ x_n \end{array} \right] + \left[ \begin{array}{c} y_1 + z_1 \\ y_2 + z_2\\ \vdots \\ y_n + z_n \end{array} \right] \\ &= \left[ \begin{array}{c} x_1 \\ x_2 \\ \vdots \\ x_n \end{array} \right] + \left( \left[ \begin{array}{c} y_1 \\ y_2 \\ \vdots \\ y_n \end{array} \right] + \left[ \begin{array}{c} z_1 \\ z_2 \\ \vdots \\ z_n \end{array} \right] \right) \\ &= \vec{x} + \left( \vec{y} + \vec{z} \right)\end{aligned}\]Hence addition of vectors is associative.
- Next, we show the existence of an additive identity. Let \(\vec{0} = \left[ \begin{array}{c} 0 \\ 0 \\ \vdots \\ 0 \end{array} \right].\) \[\begin{aligned}\vec{x}+\vec{0}&=\left[\begin{array}{c}x_1\\x_2\\ \vdots \\x_n\end{array}\right]+\left[\begin{array}{c}0\\0\\ \vdots \\0\end{array}\right] \\ &=\left[\begin{array}{c}x_1+0 \\ x_2+0 \\ \vdots \\ x_n+0\end{array}\right] \\ &=\left[\begin{array}{c}x_1\\x_2\\ \vdots \\ x_n\end{array}\right] \\ &=\vec{x}\end{aligned}\] Hence the zero vector \(\vec{0}\) is an additive identity.
- Next, we prove the existence of an additive inverse. Let \(-\vec{x} = \left ( \begin{array}{c} -x_1 \\ -x_2 \\ \vdots \\ -x_n \end{array}\right )\). \[\begin{aligned}\vec{x}+(-\vec{x})&=\left[\begin{array}{c}x_1\\x_2\\ \vdots\\x_n\end{array}\right]+\left[\begin{array}{c}-x_1 \\ -x_2\\ \vdots \\ -x_n\end{array}\right] \\ &=\left[\begin{array}{c}x_1-x_1 \\ x_2-x_2 \\ \vdots \\ x_n-x_n\end{array}\right] \\ &=\left[\begin{array}{c}0\\0\\ \vdots\\0\end{array}\right] \\ &=\vec{0}\end{aligned}\] Hence \(-\vec{x}\) is an additive inverse.
We now need to prove the axioms related to scalar multiplication. Let \(a,b\) be real numbers and let \(\vec{x}, \vec{y}\) be vectors in \(\mathbb{R}^n\).
- We first show that \(\mathbb{R}^n\) is closed under scalar multiplication. To do so, we show that \(a\vec{x}\) is also a vector with \(n\) entries. \[a\vec{x} = a\left[ \begin{array}{c} x_1 \\ x_2 \\ \vdots \\ x_n \end{array} \right] = \left[ \begin{array}{c} ax_1 \\ ax_2 \\ \vdots \\ ax_n \end{array} \right]\nonumber \] The vector \(a\vec{x}\) is again a vector with \(n\) entries, showing that \(\mathbb{R}^n\) is closed under scalar multiplication.
- We wish to show that \(a (\vec{x} + \vec{y}) = a\vec{x} + a\vec{y}\). \[\begin{aligned}a(\vec{x}+\vec{y})&=a\left(\left[\begin{array}{c}x_1\\x_2\\ \vdots\\x_n\end{array}\right]+\left[\begin{array}{c}x_1\\x_2\\ \vdots x_n\end{array}\right]\right)\\ &=a\left[\begin{array}{c}x_1+y_1 \\ x_2+y_2 \\ \vdots \\ x_n+y_n\end{array}\right] \\ &=\left[\begin{array}{c}a(x_1+y_1) \\ a(x_2+y_2) \\ \vdots \\ a(x_n+y_n)\end{array}\right] \\ &=\left[\begin{array}{c}ax_1+ay_1 \\ ax_2+ay_2 \\ \vdots \\ ax_n+ay_n\end{array}\right] \\ &=\left[\begin{array}{c}ax_1 \\ ax_2 \\ \vdots \\ ax_n\end{array}\right] +\left[\begin{array}{c}ay_1\\ay_2\\ \vdots\\ay_n\end{array}\right] \\ &=a\vec{x}+a\vec{y}\end{aligned}\]
- Next, we wish to show that \((a+b)\vec{x} = a\vec{x} + b\vec{x}\). \[\begin{aligned}(a+b)\vec{x}&=(a+b)\left[\begin{array}{c}x_1\\x_2\\ \vdots\\x_n\end{array}\right] \\ &=\left[\begin{array}{c}(a+b)x_1 \\ (a+b)x_2 \\ \vdots \\ (a+b)x_n\end{array}\right] \\ &=\left[\begin{array}{c}ax_1+bx_1 \\ ax_2+bx_2\\ \vdots \\ ax_n+bx_n\end{array}\right] \\ &=\left[\begin{array}{c}ax_1 \\ ax_2 \\ \vdots \\ ax_n\end{array}\right]+\left[\begin{array}{x}bx_1 \\ bx_2\\ \vdots \\ bx_n\end{array}\right] \\ &=a\vec{x}+b\vec{x}\end{aligned}\]
- We wish to show that \(a(b\vec{x}) = (ab) \vec{x}\). \[\begin{aligned} a(b\vec{x}) &= a\left(b \left[ \begin{array}{c} x_1 \\ x_2 \\ \vdots \\ x_n \end{array} \right] \right) \\ &= a\left( \left[ \begin{array}{c} bx_1 \\ bx_2 \\ \vdots \\ bx_n \end{array} \right] \right) \\ &= \left[ \begin{array}{c} a(bx_1) \\ a(bx_2) \\ \vdots \\ a(bx_n) \end{array} \right] \\ &= \left[ \begin{array}{c} (ab)x_1 \\ (ab)x_2 \\ \vdots \\ (ab)x_n \end{array} \right] \\ &= (ab) \left[ \begin{array}{c} x_1 \\ x_2 \\ \vdots \\ x_n \end{array} \right] \\ &= (ab)\vec{x}\end{aligned}\]
- Finally, we need to show that \(1\vec{x} = \vec{x}\). \[\begin{aligned} 1\vec{x} &= 1 \left[ \begin{array}{c} x_1 \\ x_2 \\ \vdots \\ x_n \end{array} \right] \\ &= \left[ \begin{array}{c} 1x_1 \\ 1x_2 \\ \vdots \\ 1x_n \end{array} \right] \\ &= \left[ \begin{array}{c} x_1 \\ x_2 \\ \vdots \\ x_n \end{array} \right] \\ &= \vec{x}\end{aligned}\]
By the above proofs, it is clear that \(\mathbb{R}^n\) satisfies the vector space axioms. Hence, \(\mathbb{R}^n\) is a vector space under the usual operations of vector addition and scalar multiplication.
We now consider some examples of vector spaces.
Example \(\PageIndex{2}\): Vector Space of Polynomials
Let \(\mathbb{P}_2\) be the set of all polynomials of at most degree \(2\) as well as the zero polynomial. Define addition to be the standard addition of polynomials, and scalar multiplication the usual multiplication of a polynomial by a number. Then \(\mathbb{P}_2\) is a vector space.
Solution
We can write \(\mathbb{P}_2\) explicitly as \[\mathbb{P}_2 = \left\{ a_2x^2 + a_1x + a_0 | a_i \in \mathbb{R} \; \mbox{for all} \; i \right\}\nonumber \] To show that \(\mathbb{P}_2\) is a vector space, we verify the axioms. Let \(p(x), q(x), r(x)\) be polynomials in \(\mathbb{P}_2\) and let \(a,b,c\) be real numbers. Write \(p(x)=p_2x^2 + p_1x + p_0\), \(q(x)=q_2x^2 + q_1x + q_0\), and \(r(x)=r_2x^2 + r_1x + r_0\).
- We first prove that addition of polynomials in \(\mathbb{P}_2\) is closed. For two polynomials in \(\mathbb{P}_2\) we need to show that their sum is also a polynomial in \(\mathbb{P}_2\). From the definition of \(\mathbb{P}_2\), a polynomial is contained in \(\mathbb{P}_2\) if it is of degree at most \(2\) or the zero polynomial. \[\begin{aligned} p(x) + q(x) &= p_2x^2 + p_1x + p_0 + q_2x^2+ q_1x + q_0 \\ &= (p_2+q_2)x^2 + (p_1+q_1)x + (p_0+q_0) \end{aligned}\] The sum is a polynomial of degree \(2\) and therefore is in \(\mathbb{P}_2\). It follows that \(\mathbb{P}_2\) is closed under addition.
- We need to show that addition is commutative, that is \(p(x)+q(x) = q(x) + p(x)\). \[\begin{aligned} p(x) + q(x) &= p_2x^2 + p_1x + p_0 + q_2x^2 + q_1x + q_0\\ &= (p_2+q_2)x^2 + (p_1+q_1)x + (p_0+q_0) \\ &= (q_2+p_2)x^2 + (q_1+p_1)x + (q_0+p_0) \\ &= q_2x^2 + q_1x + q_0 + p_2x^2 + p_1x + p_0\\ &= q(x) + p(x)\end{aligned}\]
- Next, we need to show that addition is associative. That is, that \((p(x) + q(x)) + r(x) = p(x) + (q(x)+r(x))\). \[\begin{aligned} (p(x) + q(x)) + r(x) &= \left( p_2x^2 +p_1x + p_0 + q_2x^2 + q_1x + q_0 \right) + r_2x^2 +r_1x + r_0 \\ &= (p_2+q_2)x^2 + (p_1+q_1)x + (p_0 +q_0) + r_2x^2 + r_1x + r_0\\ &= (p_2+q_2+r_2)x^2 + (p_1+q_1+r_1)x + (p_0+q_0+r_0) \\ &= p_2x^2 + p_1x + p_0 + (q_2+r_2)x^2 + (q_1+r_1)x + (q_0+r_0) \\ &= p_2x^2 + p_1x + p_0 + \left( q_2x^2 +q_1x + q_0 + r_2x^2 + r_1x + r_0 \right)\\ &= p(x) + \left( q(x) + r(x) \right)\end{aligned}\]
- Next, we must prove that there exists an additive identity. Let \(0(x)=0x^2+0x+0\). \[\begin{aligned} p(x) + 0(x) &= p_2x^2 + p_1x + p_0 + 0x^2 + 0x + 0 \\ &= (p_2 + 0)x^2 + (p_1 + 0)x + (p_0 + 0)\\ &= p_2x^2 + p_1x + p_0 \\ &= p(x)\end{aligned}\] Hence an additive identity exists, specifically the zero polynomial.
- Next we must prove that there exists an additive inverse. Let \(-p(x) = -p_2x^2 - p_1x - p_0\) and consider the following: \[\begin{aligned} p(x) + (-p(x)) &= p_2x^2 + p_1x + p_0 + \left( - p_2x^2 - p_1x - p_0\right) \\ &= (p_2 - p_2)x^2 + (p_1 - p_1)x + (p_0 - p_0) \\ &= 0x^2 + 0x + 0 \\ &= 0(x)\end{aligned}\] Hence an additive inverse \(-p(x)\) exists such that \(p(x) + (-p(x)) = 0(x)\).
We now need to verify the axioms related to scalar multiplication.
- First we prove that \(\mathbb{P}_2\) is closed under scalar multiplication. That is, we show that \(ap(x)\) is also a polynomial of degree at most \(2\). \[ap(x) = a\left( p_2x^2 + p_1x + p_0 \right) = ap_2x^2 +ap_1x+ ap_0\nonumber \] Therefore \(\mathbb{P}_2\) is closed under scalar multiplication.
- We need to show that \(a(p(x) + q(x)) = ap(x) + aq(x)\). \[\begin{aligned} a(p(x) + q(x)) &= a \left( p_2x^2 + p_1x + p_0 + q_2x^2 + q_1x + q_0 \right)\\ &= a \left( (p_2+q_2)x^2 + (p_1+q_1)x + (p_0+q_0) \right)\\ &= a(p_2+q_2)x^2 + a(p_1+q_1)x + a(p_0 + q_0) \\ &= (ap_2 + aq_2)x^2 + (ap_1+aq_1)x + (ap_0 + aq_0) \\ &= ap_2x^2 + ap_1x + ap_0 + aq_2x^2 +aq_1x + aq_0\\ &= ap(x) + aq(x) \end{aligned}\]
- Next we show that \((a+b) p(x) = ap(x) + bp(x)\). \[\begin{aligned} (a+b) p(x) &= (a+b) ( p_2x^2 + p_1x + p_0)\\ &= (a+b)p_2x^2 + (a+b)p_1x + (a+b)p_0 \\ &= ap_2x^2 + ap_1x + ap_0 + bp_2x^2 +bp_1x + bp_0\\ &= ap(x) + bp(x)\end{aligned}\]
- The next axiom which needs to be verified is \(a(bp(x)) = (ab)p(x)\). \[\begin{aligned} a(bp(x)) &= a \left( b \left(p_2x^2 + p_1x +p_0\right)\right) \\ &= a \left( bp_2x^2 +bp_1x + bp_0 \right)\\ &=abp_2x^2+abp_1x+abp_0 \\ &=(ab)(p_2x^2+p_1x+p_0) \\ &=(ab)p(x)\end{aligned}\]
- Finally, we show that \(1p(x) = p(x)\). \[\begin{aligned} 1p(x) &= 1 \left( p_2x^2 + p_1x + p_0\right)\\ &= 1p_2x^2 + 1p_1x + 1p_0\\ &= p_2x^2 + p_1x + p_0\\ &= p(x)\end{aligned}\] Since the above axioms hold, we know that \(\mathbb{P}_2\) as described above is a vector space.
Another important example of a vector space is the set of all matrices of the same size.
Example \(\PageIndex{3}\): Vector Space of Matrices
Let \(\mathbb{M}_{2,3}\) be the set of all \(2 \times 3\) matrices. Using the usual operations of matrix addition and scalar multiplication, show that \(\mathbb{M}_{2,3}\) is a vector space.
Solution
Let \(A, B\) be \(2 \times 3\) matrices in \(\mathbb{M}_{2,3}\). We first prove the axioms for addition.
- In order to prove that \(\mathbb{M}_{2,3}\) is closed under matrix addition, we show that the sum \(A+B\) is in \(\mathbb{M}_{2,3}\). This means showing that \(A+B\) is a \(2 \times 3\) matrix. \[\begin{aligned} A+B &= \left[ \begin{array}{rrr} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23} \end{array} \right] + \left[ \begin{array}{rrr} b_{11} & b_{12} & b_{13}\\ b_{21} & b_{22} & b_{23} \end{array} \right] \\ &= \left[ \begin{array}{rrr} a_{11} + b_{11} & a_{12}+b_{12} & a_{13}+b_{13}\\ a_{21} +b_{21}& a_{22}+b_{22} & a_{23}+b_{23} \end{array} \right]\end{aligned}\] You can see that the sum is a \(2\times 3\) matrix, so it is in \(\mathbb{M}_{2,3}\). It follows that \(\mathbb{M}_{2,3}\) is closed under matrix addition.
- The remaining axioms regarding matrix addition follow from properties of matrix addition. Therefore \(\mathbb{M}_{2,3}\) satisfies the axioms of matrix addition.
We now turn our attention to the axioms regarding scalar multiplication. Let \(A, B\) be matrices in \(\mathbb{M}_{2,3}\) and let \(c\) be a real number.
- We first show that \(\mathbb{M}_{2,3}\) is closed under scalar multiplication. That is, we show that \(cA\) a \(2 \times 3\) matrix. \[\begin{aligned} cA &= c\left[ \begin{array}{rrr} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23} \end{array} \right] \\ &= \left[ \begin{array}{rrr} ca_{11} & ca_{12} & ca_{13}\\ ca_{21} & ca_{22} & ca_{23} \end{array} \right]\end{aligned}\] This is a \(2 \times 3\) matrix in \(\mathbb{M}_{2,3}\) which proves that the set is closed under scalar multiplication.
- The remaining axioms of scalar multiplication follow from properties of scalar multiplication of matrices. Therefore \(\mathbb{M}_{2,3}\) satisfies the axioms of scalar multiplication.
In conclusion, \(\mathbb{M}_{2,3}\) satisfies the required axioms and is a vector space.
While here we proved that the set of all \(2 \times 3\) matrices is a vector space, there is nothing special about this choice of matrix size. In fact if we instead consider \(\mathbb{M}_{m,n}\), the set of all \(m \times n\) matrices, then \(\mathbb{M}_{m,n}\) is a vector space under the operations of matrix addition and scalar multiplication.
We now examine an example of a set that does not satisfy all of the above axioms, and is therefore not a vector space.
Example \(\PageIndex{4}\): Not a Vector Space
Let \(V\) denote the set of \(2 \times 3\) matrices. Let addition in \(V\) be defined by \(A + B = A\) for matrices \(A,B\) in \(V\). Let scalar multiplication in \(V\) be the usual scalar multiplication of matrices. Show that \(V\) is not a vector space.
Solution
In order to show that \(V\) is not a vector space, it suffices to find only one axiom which is not satisfied. We will begin by examining the axioms for addition until one is found which does not hold. Let \(A,B\) be matrices in \(V\).
- We first want to check if addition is closed. Consider \(A+B\). By the definition of addition in the example, we have that \(A+B = A\). Since \(A\) is a \(2 \times 3\) matrix, it follows that the sum \(A+B\) is in \(V\), and \(V\) is closed under addition.
- We now wish to check if addition is commutative. That is, we want to check if \(A + B = B + A\) for all choices of \(A\) and \(B\) in \(V\). From the definition of addition, we have that \(A + B = A\) and \(B + A = B\). Therefore, we can find \(A\), \(B\) in \(V\) such that these sums are not equal. One example is \[A = \left[ \begin{array}{rrr} 1 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right], B = \left[ \begin{array}{rrr} 0 & 0 & 0 \\ 1 & 0 & 0 \end{array}\right]\nonumber \] Using the operation defined by \(A+B=A\), we have \[\begin{aligned}A+B&=A \\ &=\left[\begin{array}{ccc}1&0&0\\0&0&0\end{array}\right] \\ B+A&=B \\ &=\left[\begin{array}{ccc}0&0&0\\1&0&0\end{array}\right]\end{aligned}\] It follows that \(A+B\neq B+A\). Therefore addition as defined for \(V\) is not commutative and \(V\) fails this axiom. Hence \(V\) is not a vector space.
Consider another example of a vector space.
Example \(\PageIndex{5}\): Vector Space of Functions
Let \(S\) be a nonempty set and define \(\mathbb{F}_S\) to be the set of real functions defined on \(S\). In other words, we write \(\mathbb{F}_S: S \mapsto \mathbb{R}\). Letting \(a,b,c\) be scalars and \(f,g,h\) functions, the vector operations are defined as \[\begin{aligned} \left( f+g\right) \left( x\right) &=f\left( x\right) +g\left( x\right) \\ \left( af\right) \left( x\right) &=a\left( f\left( x\right) \right)\end{aligned}\] Show that \(\mathbb{F}_S\) is a vector space.
Solution
To verify that \(\mathbb{F}_S\) is a vector space, we must prove the axioms beginning with those for addition. Let \(f, g, h\) be functions in \(\mathbb{F}_S\).
- First we check that addition is closed. For functions \(f, g\) defined on the set \(S\), their sum given by \[(f+g)(x) = f(x)+g(x)\nonumber \] is again a function defined on \(S\). Hence this sum is in \(\mathbb{F}_S\) and \(\mathbb{F}_S\) is closed under addition.
- Secondly, we check the commutative law of addition: \[\left( f+g\right) \left( x\right) =f\left( x\right) +g\left( x\right) =g\left( x\right) +f\left( x\right) =\left( g+f\right) \left( x\right)\nonumber \] Since \(x\) is arbitrary, \(f+g=g+f\).
- Next we check the associative law of addition: \[\left( \left( f+g\right) +h\right) \left( x\right) = \left( f+g\right) \left( x\right) +h\left( x\right) =\left( f\left( x\right) +g\left( x\right) \right) +h\left( x\right)\nonumber \] \[=f\left( x\right) +\left( g\left( x\right) +h\left( x\right) \right) =\left( f\left( x\right) +\left( g+h\right) \left( x\right) \right) =\left( f+\left( g+h\right) \right) \left( x\right)\nonumber \] and so \(\left( f+g\right) +h=f+\left( g+h\right) .\)
- Next we check for an additive identity. Let \(0\) denote the function which is given by \(0\left( x\right) =0.\) Then this is an additive identity because \[\left( f+0\right) \left( x\right) =f\left( x\right) +0\left( x\right) =f\left( x\right)\nonumber \] and so \(f+0=f\).
- Finally, check for an additive inverse. Let \(-f\) be the function which satisfies \(\left( -f\right) \left( x\right) = -f\left( x\right) .\) Then \[\left( f+\left( -f\right) \right) \left( x\right) = f\left( x\right) +\left( -f\right) \left( x\right) = f\left( x\right) +-f\left( x\right) =0\nonumber \] Hence \(f+\left( -f\right) =0\).
Now, check the axioms for scalar multiplication.
- We first need to check that \(\mathbb{F}_S\) is closed under scalar multiplication. For a function \(f(x)\) in \(\mathbb{F}_S\) and real number \(a\), the function \((af)(x) = a(f(x))\) is again a function defined on the set \(S\). Hence \(a(f(x))\) is in \(\mathbb{F}_S\) and \(\mathbb{F}_S\) is closed under scalar multiplication.
- \[\left( \left( a+b\right) f\right) \left( x\right) = \left( a+b\right) f\left( x\right) =af\left( x\right) +bf\left( x\right) = \left( af+bf\right) \left( x\right)\nonumber \] and so \(\left( a+b\right) f=af+bf\).
- \[\left( a\left( f+g\right) \right) \left( x\right) = a\left( f+g\right) \left( x\right) = a\left( f\left( x\right) +g\left( x\right) \right)\nonumber \] \[=af\left( x\right) +bg\left( x\right) = \left( af+bg\right) \left( x\right)\nonumber \] and so \(a\left( f+g\right) =af+bg\).
- \[\left( \left( ab\right) f\right) \left( x\right) = \left( ab\right) f\left( x\right) =a\left( bf\left( x\right) \right) = \left( a\left( bf\right) \right) \left( x\right)\nonumber \] so \(\left( abf\right) =a\left( bf\right)\).
- Finally \(\left( 1f\right) \left( x\right) = 1f\left( x\right) =f\left( x\right)\) so \(1f=f\).
It follows that \(V\) satisfies all the required axioms and is a vector space.
Consider the following important theorem.
Theorem \(\PageIndex{1}\): Uniqueness
In any vector space, the following are true:
- \(\vec{0}\), the additive identity, is unique
- \(-\vec{x}\), the additive inverse, is unique
- \(0\vec{x}=\vec{0}\) for all vectors \(\vec{x}\)
- \(\left( -1\right) \vec{x}=-\vec{x}\) for all vectors \(\vec{x}\)
- Proof
-
- When we say that the additive identity, \(\vec{0}\), is unique, we mean that if a vector acts like the additive identity, then it is the additive identity. To prove this uniqueness, we want to show that another vector which acts like the additive identity is actually equal to \(\vec{0}\). Suppose \(\vec{0}^{\prime }\) is also an additive identity. Then, \[\vec{0} + \vec{0}^{\prime} = \vec{0}\nonumber \] Now, for \(\vec{0}\) the additive identity given above in the axioms, we have that \[\vec{0}^{\prime} + \vec{0} = \vec{0}^{\prime}\nonumber \] So by the commutative property: \[0 = 0 + 0^{\prime} = 0^{\prime} + 0 = 0^{\prime}\nonumber \] This says that if a vector acts like an additive identity (such as \(\vec{0}^{\prime}\)), it in fact equals \(\vec{0}\). This proves the uniqueness of \(\vec{0}\).
- When we say that the additive inverse, \(-\vec{x}\), is unique, we mean that if a vector acts like the additive inverse, then it is the additive inverse. Suppose that \(\vec{y}\) acts like an additive inverse: \[\vec{x}+\vec{y}=\vec{0}\nonumber \] Then the following holds: \[\vec{y} = \vec{0} + \vec{y} = (-\vec{x} + \vec{x}) + \vec{y} = -\vec{x} + (\vec{x} + \vec{y}) = -\vec{x} + \vec{0} = -\vec{x}\nonumber \] Thus if \(\vec{y}\) acts like the additive inverse, it is equal to the additive inverse \(-\vec{x}\). This proves the uniqueness of \(-\vec{x}\).
- This statement claims that for all vectors \(\vec{x}\), scalar multiplication by \(0\) equals the zero vector \(\vec{0}\). Consider the following, using the fact that we can write \(0=0+0\): \[0\vec{x}=\left( 0+0\right) \vec{x}=0\vec{x}+0\vec{x}\nonumber \] We use a small trick here: add \(-0\vec{x}\) to both sides. This gives \[\begin{aligned} 0\vec{x} + (-0\vec{x})&=0\vec{x}+0\vec{x}+(-\vec{x})\\ \vec{0} + 0 &=0\vec{x} + 0 \\ \vec{0} &= 0\vec{x}\end{aligned}\] This proves that scalar multiplication of any vector by \(0\) results in the zero vector \(\vec{0}\).
- Finally, we wish to show that scalar multiplication of \(-1\) and any vector \(\vec{x}\) results in the additive inverse of that vector, \(-\vec{x}\). Recall from \(2.\) above that the additive inverse is unique. Consider the following: \[\begin{aligned} \left( -1\right) \vec{x}+\vec{x} & =\left( -1\right) \vec{x}+1\vec{x}\\ &=\left(-1+1\right) \vec{x} \\ &=0\vec{x} \\ &=\vec{0}\end{aligned}\] By the uniqueness of the additive inverse shown earlier, any vector which acts like the additive inverse must be equal to the additive inverse. It follows that \(\left( -1\right) \vec{x}=-\vec{x}\).
An important use of the additive inverse is the following theorem.
Theorem \(\PageIndex{2}\)
Let \(V\) be a vector space. Then \(\vec{v} + \vec{w} = \vec{v} + \vec{z}\) implies that \(\vec{w} = \vec{z}\) for all \(\vec{v}, \vec{w}, \vec{z} \in V\)
- Proof
-
The proof follows from the vector space axioms, in particular the existence of an additive inverse (\(-\vec{u}\)). The proof is left as an exercise to the reader.


1.4.1: From The Relation of Alvar Nunez Cabeza de Vaca (1542)
Chapter XV WHAT BEFEL US AMONG THE PEOPLE OF MALHADO.
On an Island of which I have spoken, they wished to make us physicians without examination or inquiring for diplomas.  They ordered that we also should do this, and be of use to them in some way. We laughed at what they did, telling them it was folly, that we knew not how to heal. In consequence, they withheld food from us until we should practice what they required. Seeing our persistence, an Indian told me I knew not what I uttered, in saying that what he knew availed ‘nothing; for stones and other matters growing about in the fields, have virtue, and that passing a pebble along the stomach would take away pain and restore health, and certainly then we who were extraordinary men must possess power and efficacy over all other things. At last, finding ourselves in great want we were constrained to obey; but without fear lest we should be blamed for any failure or success.
Their custom is, on finding themselves sick to send for a physician, and after he has applied the cure, they give him not only all they have, but seek among their relatives for more to give.  They make cauteries with fire, a remedy among them in high repute, which I have tried on myself and found benefit from it. They afterwards blow on the spot, and having finished, the patient considers that he is relieved.
Our method was to bless the sick, breathing upon them, and recite a Paternoster and an Ave-Maria, praying with all earnestness to God our Lord that he would give health and influence them to make us some good return. In his clemency he willed that all those for whom we supplicated, should tell the others that they were sound and in health, directly after we made the sign of the blessed cross over them. For this the Indians treated us kindly; they deprived themselves of food that they might give to us, and presented us with skins and some trifles.
So protracted was the hunger we there experienced, that many times I was three days without eating. The natives also endured as much; and it appeared to me a thing impossible that life could be so prolonged, although afterwards I found myself in greater hunger and necessity, which I shall speak of farther on.
The Indians who had Alonzo del Castillo, Andrés Dorantes, and the others that remained alive, were of a different tongue and ancestry from these, and went to the opposite shore of the main to eat oysters, where they staid until the first day of April, when they returned. The distance is two leagues in the widest part. The island is half a league in breadth and five leagues in length.
The inhabitants of all this region go naked. The women alone have any part of their persons covered, and it is with a wool that grows on trees. The damsels dress themselves in deerskin. The people are generous to each other of what they possess. They have no chief. All that are of a lineage keep together. They speak two languages; those of one are called Capoques, those of the other, Han. They have a custom when they meet, or from time to time when they visit, of remaining half an hour before they speak, weeping; and, this over, he that is visited first rises and gives the other all he has, which is received, and after a little while he carries it away, and often goes without saying a word. They have other strange customs; but I have told the principal of them, and the most remarkable, that I may pass on and further relate what befel us.
Chapter XVI THE CHRISTIANS LEAVE THE ISLAND OF MALHADO.
After Dorantes and Castillo returned to the Island, they brought together the Christians, who were somewhat separated, and found them in all to be fourteen. As I have said, I was opposite on the main, where my Indians had taken me, and where so great sickness had come upon me, that if anything before had given me hopes of life, this were enough to have entirely bereft me of them.
When the Christians heard of my condition, they gave an Indian the cloak of marten skins we had taken from the cacique, as before related, to pass them over to where I was that they might visit me. Twelve of them crossed; for two were so feeble that their comrades could not venture to bring them. The names of those who came were Alonzo del Castillo, Andres Dorantes, Diego Dorantes, Yaldevieso, Estrada, Tostado, Chaves, Gutierrez, Asturiano a clergyman, Diego de Huelva, Estevarico a black, and Benitez; and when they reached the main land, they found another, who was one of our company, named Francisco de Leon. The thirteen together followed along the coast. So soon as they had come over, my Indians informed me of it, and that Hieronymo de Alvaniz and Lope de Oviedo remained on the island. But sickness prevented me from going with my companions or even seeing them.
I was obliged to remain with the people belonging to the island more than a year, and because of the hard work they put upon me and the harsh treatment, I resolved to flee from them and go to those of Charruco, who inhabit the forests and country of the main, the life I led being insupportable. Besides much other labor, I had to get out roots from below the water, and from among the cane where they grew in the ground. From this employment I had my fingers so worn that did a straw but touch them they would bleed. Many of the canes are broken, so they often tore my flesh, and I had to go in the midst of them with only the clothing on I have mentioned.
Accordingly, I put myself to contriving how I might get over to the other Indians, among whom matters turned somewhat more favorably for me. I set to trafficing, and strove to make my employment profitable in the ways I could best contrive, and by that means I got food and good treatment. The Indians would beg me to go from one quarter to another for things of which they have need; for in consequence of incessant hostilities, they cannot traverse the country, nor make many exchanges. With my merchandise and trade I went into the interior as far as I pleased, and traveled along the coast forty or fifty leagues. The principal wares were cones and other pieces of sea-snail, conches used for cutting, and fruit like a bean of the highest value among them, which they use as a medicine and employ in their dances and festivities. Among other matters were sea-beads. Such were what I carried into the interior; and in barter I got and brought back skins; ochre with which they rub and color the face, hard canes of which to make arrows, sinews, cement and flint for the heads, and tassels of the hair of deer that by dyeing they make red. This occupation suited me well; for the travel allowed me liberty to go where I wished, I was not obliged to work, and was not a slave. Wherever I went I received fair treatment, and the Indians gave me to eat out of regard to my commodities. My leading object, while journeying in this business, was to find out the way by which I should go forward, and I became well known. The inhabitants were pleased when they saw me, and I had brought them what they wanted; and those who did not know me sought and desired the acquaintance, for my reputation. The hardships that I underwent in this were long to tell, as well of peril and privation as of storms and cold. Oftentimes they overtook me alone and in the wilderness; but I came forth from them all by the great mercy of God, our Lord. Because of them I avoided pursuing the business in winter, a season in which the natives themselves retire to their huts and ranches, torpid and incapable of exertion.
I was in this country nearly six years, alone among the Indians, and naked like them. The reason why I remained so long, was that I might take with me the Christian, Lope de Oviedo, from the island; Alaniz, his companion, who had been left with him by Alonzo del Castillo, Andrés Dorantes and the rest, died soon after their departure; and to get the survivor out from there, I went over to the island every year, and entreated him that we should go, in the best way we could contrive, in quest of Christians. He put me off every year, saying in the next coming we would start. At last I got him off, crossing him over the bay, and over four rivers in the coast, as he could not swim. In this way we went on with some Indians, until coming to a bay a league in width, and everywhere deep. From the appearance we supposed it to be that which is called Espiritu Sancto. We met some Indians on the other side of it, coming to visit ours, who told us that beyond them were three men like us, and gave their names. We asked for the others, and were told that they were all dead of cold and hunger; that the Indians farther on, of whom they were, for their diversion had killed Diego Dorantes, Valdevieso, and Diego de Huelva, because they left one house for another; and that other Indians, their neighbors with whom Captain Dorantes now was, had in consequence of a dream, killed Esquivel and Mendez. We asked how the living were situated, and they answered that they were very ill used, the boys and some of the Indian men being very idle, out of cruelty gave them many kicks, cuffs and blows with sticks; that such was the life they led.
We desired to be informed of the country ahead, and of the subsistence: they said there was nothing to eat, and that it was thin of people, who suffered of cold, having no skins or other things to cover them. They told us also if we wished to see those three Christians, two days from that time the Indians who had them would come to eat walnuts a league from there on the margin of that river; and that we might know what they told us of the ill usage to be true, they slapped my companion and beat him with a stick, and I was not left without my portion. Many times they threw lumps of mud at us, and every day they put their arrows to our hearts, saying that they were inclined to kill us in the way that they had destroyed our friends. Lope Oviedo, my comrade, in fear said that he wished to go back with the women of those who had crossed the bay with us, the men having remained some distance behind. I contended strongly against his returning, and urged my objections; but in no way could I keep him. So he went back, and I remained alone with those savages. They are called Quevenes, and those with whom he returned, Deaguanes.
Chapter XIX OUR SEPARATION BY THE INDIANS.
When the six months were over, I had to spend with the Christians to put in execution the plan we had concerted, the Indians went after prickly pears, the place at which they grew being thirty leagues off and when we approached the point of flight, those among whom we were, quarreled about a woman. After striking with fists, heating with sticks and bruising heads in great anger, each took his lodge and went his way, whence it became necessary that the Christians should also separate, and in no way could we come together until another year.
In this time I passed a hard life, caused as much by hunger as ill usage. Three times I was obliged to run from my masters, and each time they went in pursuit and endeavored to slay me; but God our Lord in his mercy chose to protect and preserve me; and when the season of prickly pears returned, we again came together in the same place. After we had arranged our escape, and appointed a time, that very day the Indians separated and all went back. I told my comrades I would wait for them among the prickly pear plants until the moon should be full. This day was the first of September, and the first of the moon; and I said that if in this time they did not come as we had agreed, I would leave and go alone. So we parted, each going with his Indians. I remained with mine until the thirteenth day of the moon, having determined to flee to others when it should be full.
At this time Andrés Dorantes arrived with Estevanico and informed me that they had left Castillo with other Indians near by, called Lanegados; that they had encountered great obstacles and wandered about lost; that the next day the Indian’s, among whom we were, would move to where Castillo was, and were going to unite with those who held him and become friends, having been at war until then, and that in this way we should recover Castillo.
We had thirst all the time we ate the pears, which we quenched with their juice. We caught it in a hole made in the earth, and when it was full we drank until satisfied. It is sweet, and the color of must. In this manner they collect it for lack of vessels. There are many kinds of prickly pears, among them some very good, although they all appeared to me to be so, hunger never having given me leisure to choose, nor to reflect upon which were the best.
Nearly all these people drink rain-water, which lies about in spots. Although there are rivers, as the Indians never have fixed habitations, there are no familiar or known places for getting water. Throughout the country are extensive and beautiful plains with good pasturage; and I think it would be a very fruitful region were it worked and inhabited by civilized men. We nowhere saw mountains.
These Indians told us that there was another people next in advance of us, called Camones, living towards the coast, and that they had killed the people who came in the boat of Peñalosa and Tellez, who arrived so feeble that even while being slain they could offer no resistance, and were all destroyed. We were shown their clothes and arms, and were told that the boat lay there stranded. This, the fifth boat, had remained till then unaccounted for. We have already stated how the boat of the Governor had been carried out to sea, and the one of the Comptroller and the Friars had been cast away on the coast, of which Esquevel narrated the fate of the men. We have once told how the two boats in which Castillo, I and Dorantes came, foundered near the Island of Malhado.
Chapter XX OF OUR ESCAPE.
The second day after we had moved, we commended ourselves to God and set forth with speed, trusting, for all the lateness of the season and that the prickly pears were about ending, with the mast which remained in the woods, we might still be enabled to travel over a large territory. Hurrying on that day in great dread lest the Indians should overtake us, we saw some smokes, and going in the direction of them we arrived there after vespers, and found an Indian. He ran as he discovered us coming, not being willing to wait for us. We sent the negro after him, when he stopped, seeing him alone. The negro told him we were seeking the people who made those fires. He answered that their houses were near by, and he would guide us to them. So we followed him. He ran to make known our approach, and at sunset we saw the houses. Before our arrival, at the distance of two cross-bow shots from them, we found four Indians, who waited for us and received us well. We said in the language of the Mariames, that we were coming to look for them. They were evidently pleased with our company, and took us to their dwellings. Dorantes and the negro were lodged in the house of a physician, Castillo and myself in that of another.
These people speak a different language, and are called Avavares. They are the same that carried bows to those with whom we formerly lived, going to traffic with them, and although they are of a different nation and tongue, they understand the other language. They arrived that day with their lodges, at the place where we found them. The community directly brought us a great many prickly pears, having heard of us before, of our cures, and of the wonders our Lord worked by us, which, although there had been no others, were adequate to open ways for us through a country poor like this, to afford us people where oftentimes there are none, and to lead us through imminent dangers, not permitting us to be killed, sustaining us under great want, and putting into those nations the heart of kindness, as we shall relate hereafter.
Chapter XXI OUR CURE OF SOME OF THE AFFLICTED.
That same night of our arrival, some Indians came to Castillo and told him that they had great pain in the head, begging him to cure them. After he made over them the sign of the cross, and commended them to God, they instantly said that all the pain had left, and went to their houses bringing us prickly pears, with a piece of venison, a thing to us little known. As the report of Castillo’s performances spread, many came to us that night sick, that we should heal them, each bringing a piece of venison, until the quantity became so great we knew not where to dispose of it. We gave many thanks to God, for every day went on increasing his compassion and his gifts. After the sick were attended to, they began to dance and sing, making themselves festive, until sunrise; and because of our arrival, the rejoicing was continued for three days.
When these were ended, we asked the Indians about the country farther on, the people we should find in it, and of the subsistence there. They answered us, that throughout all the region prickly pear plants abounded; but the fruit was now gathered and all the people had gone back to their houses. They said the country was very cold, and there were few skins. Reflecting on this, and that it was already winter, we resolved to pass the season with these Indians.
Five days after our arrival, all the Indians went off, taking us with them to gather more prickly pears, where there were other peoples speaking different tongues. After walking five days in great hunger, since on the way was no manner of fruit, we came to a river and put up our houses. We then went to seek the product of certain trees, which is like peas. As there are no paths in the country, I was detained some time. The others returned, and coming to look for them in the dark, I got lost. Thank God I found a burning tree, and in the warmth of it passed the cold of that night. In the morning, loading myself with sticks, and taking two brands with me, I returned to seek them. In this manner I wandered five days, ever with my fire and load; for if the wood had failed me where none could be found, as many parts are without any, though I might have sought sticks elsewhere, there would have been no fire to kindle them. This was all the protection I had against cold, while walking naked as I was born. Going to the low woods near the rivers, I prepared myself for the night, stopping in them before sunset. I made a hole in the ground and threw in fuel which the trees abundantly afforded, collected in good quantity from those that were fallen and dry. About the whole I made four fires, in the form of a cross, which I watched and made up from time to time. I also gathered some bundles of the coarse straw that there abounds, with which I covered myself in the hole. In this way I was sheltered at night from cold. On one occasion while I slept, the fire fell upon the straw, when it began to blaze so rapidly that notwithstanding the haste I made to get out of it, I carried some marks on my hair of the danger to which I was exposed. All this while I tasted not a mouthful, nor did I find anything I could eat. My feet were bare and bled a good deal. Through the mercy of God, the wind did not blow from the north in all this time, otherwise I should have died.
At the end of the fifth day I arrived on the margin of a river, where I found the Indians, who with the Christians, had considered me dead, supposing that I had been stung by a viper. All were rejoiced to see me, and most so were my companions. They said that up to that time they had struggled with great hunger, which was the cause of their not having sought me. At night, all gave me of their prickly pears, and the next morning we set out for a place where they were in large quantity, with which we satisfied our great craving, the Christians rendering thanks to our Lord that he had ever given us his aid.


2.4: Psychosocial Development
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A Look At Self-Concept, Gender Identity, And Family Life
Self-Concept
Early childhood is a time of forming an initial sense of self. A self-concept or idea of who we are, what we are capable of doing, and how we think and feel is a social process that involves taking into consideration how others view us. It might be said, then, that in order to develop a sense of self, you must have interaction with others. Interactionist theorists, Cooley and Mead offer two interesting explanations of how a sense of self develops.
Interactionism and Views of Self
Cooley: Charles Horton Cooley (1964) suggests that our self concept comes from looking at how others respond to us. This process, known as the looking-glass self involves looking at how others seem to view us and interpreting this as we make judgments about whether we are good or bad, strong or weak, beautiful or ugly, and so on. Of course, we do not always interpret their responses accurately so our self-concept is not simply a mirror reflection of the views of others. After forming an initial self-concept, we may use it as a mental filter screening out those responses that do not seem to fit our ideas of who we are. So compliments may be negated, for example. Think of times in your life when you feel self-conscious. The process of the looking-glass self is pronounced when we are preschoolers, or perhaps when we are in a new school or job or are taking on a new role in our personal lives and are trying to gauge our own performances. When we feel more sure of who we are we focus less on how we appear to others.
Mead: Herbert Mead (1967) offers an explanation of how we develop a social sense of self by being able to see ourselves through the eyes of others. There are two parts of the self: the “I” which is the part of the self that is spontaneous, creative, innate, and is not concerned with how others view us and the “me” or the social definition of who we are.
When we are born, we are all “I” and act without concern about how others view us. But the socialized self begins when we are able to consider how one important person views us. This initial stage is called “taking the role of the significant other”. For example, a child may pull a cat’s tail and be told by his mother, “No! Don’t do that, that’s bad” while receiving a slight slap on the hand. Later, the child may mimic the same behavior toward the self and say aloud, “No, that’s bad” while patting his own hand. What has happened? The child is able to see himself through the eyes of the mother. As the child grows and is exposed to many situations and rules of culture, he begins to view the self in the eyes of many others through these cultural norms or rules. This is referred to as “taking the role of the generalized other” and results in a sense of self with many dimensions. The child comes to have a sense of self as student, as friend, as son, and so on.
Exaggerated Sense of Self
One of the ways to gain a clearer sense of self is to exaggerate those qualities that are to be incorporated into the self. Preschoolers often like to exaggerate their own qualities or to seek validation as the biggest or smartest or child who can jump the highest. I wonder if messages given in children’s books or television shows that everyone is special are really meaningful to children who want to separate themselves from others on such qualities. This exaggeration tends to be replaced by a more realistic sense of self in middle childhood.
Erikson: Initiative vs. Guilt
The trust and autonomy of previous stages develop into a desire to take initiative or to think of ideas and initiative action. Children may want to build a fort with the cushions from the living room couch or open a lemonade stand in the driveway or make a zoo with their stuffed animals and issue tickets to those who want to come. Or they may just want to get themselves ready for bed without any assistance. To reinforce taking initiative, caregivers should offer praise for the child’s efforts and avoid being critical of messes or mistakes. Soggy washrags and toothpaste left in the sink pales in comparison to the smiling face of a five year old that emerges from the bathroom with clean teeth and pajamas!
Gender Identity, Gender Constancy and Gender Roles
Another important dimension of the self is the sense of self as male or female. Preschool aged children become increasingly interested in finding out the differences between boys and girls both physically and in terms of what activities are acceptable for each. While 2 year olds can identify some differences and learn whether they are boys or girls, preschoolers become more interested in what it means to be male or female. This self-identification or gender identity is followed sometime later with gender constancy or the knowledge that gender does not change. Gender roles or the rights and expectations that are associated with being male or female are learned throughout childhood and into adulthood.
Freud and the phallic stage: Freud believed that masculinity and femininity were learned during the phallic stage or psychosexual development. During the phallic stage, the child develops an attraction to the opposite sexed parent but after recognizing that that parent is unavailable, learns to model their own behavior after the same sexed parent. The child develops his or her own sense of masculinity or femininity from this resolution. And, according to Freud, a person who does not exhibit gender appropriate behavior, such as a woman who competes with men for jobs or a man who lacks self-assurance and dominance, has not successfully completed this stage of development. Consequently, such a person continues to struggle with his or her own gender identity.
Chodorow and mothering: Chodorow, a neoFreudian, believed that mothering promotes gender stereotypic behavior. Mothers push their sons away too soon and direct their attention toward problem-solving and independence. As a result, sons grow up confident in their own abilities but uncomfortable with intimacy. Girls are kept dependent too long and are given unnecessary and even unwelcome assistance from their mothers. Girls learn to underestimate their abilities and lack assertiveness, but feel comfortable with intimacy.
Both of these models assume that early childhood experiences result in lifelong gender self-concepts. However, gender socialization is a process that continues throughout life. Children, teens, and adults refine and can modify their sense of self based on gender.
Learning through reinforcement and modeling: Learning theorists suggest that gender role socialization is a result of the ways in which parents, teachers, friends, schools, religious institutions, media and others send messages about what is acceptable or desirable behavior as males or females. This socialization begins early-in fact, it may even begin the moment a parent learns that a child is on the way. Knowing the sex of the child can conjure up images of the child’s behavior, appearance, and potential on the part of a parent. And this stereotyping continues to guide perception through life. Consider parents of newborns, shown a 7 pound, 20 inch baby, wrapped in blue (a color designating males) describe the child as tough, strong, and angry when crying. Shown the same infant in pink (a color used in the United States for baby girls), these parents are likely to describe the baby as pretty, delicate, and frustrated when crying. (Maccoby & Jacklin, 1987). Female infants are held more, talked to more frequently and given direct eye contact, while male infants play is often mediated through a toy or activity.
Sons are given tasks that take them outside the house and that have to be performed only on occasion while girls are more likely to be given chores inside the home such as cleaning or cooking that is performed daily. Sons are encouraged to think for themselves when they encounter problems and daughters are more likely to be given assistance even when they are working on an answer. This impatience is reflected in teachers waiting less time when asking a female student for an answer than when asking for a reply from a male student (Sadker and Sadker, 1994).  Of course, the stereotypes of advisors can also influence which kinds of courses or vocational choices girls and boys are encouraged to make.
Friends discuss what is acceptable for boys and girls and popularity may be based on modeling what is considered ideal behavior or looks for the sexes. Girls tend to tell one another secrets to validate others as best friends while boys compete for position by emphasizing their knowledge, strength or accomplishments. This focus on accomplishments can even give rise to exaggerating accomplishments in boys, but girls are discouraged from showing off and may learn to minimize their accomplishments as a result.
Gender messages abound in our environment. But does this mean that each of us receives and interprets these messages in the same way? Probably not. In addition to being recipients of these cultural expectations, we are individuals who also modify these roles (Kimmel, 2008).
How much does gender matter? In the United States, gender differences are found in school experiences (even into college and professional school, girls are less vocal in the classrooms and much more at risk for sexual harassment from teachers, coaches, classmates, and professors), in social interactions and in media messages. The stereotypes that boys should be strong, forceful, active, dominant, and rational and that girls should be pretty, subordinate, unintelligent, emotional, and gabby are portrayed in children’s toys, books, commercials, video games, movies, television shows and music. In adulthood, these differences are reflected in income gaps between men and women where women working full-time earn about 74 percent the income of men, in higher rates of women suffering rape and domestic violence, higher rates of eating disorders for females, and in higher rates of violent death for men in young adulthood. Each of these differences will be explored further in subsequent chapters.
The impact in India: Gender differences in India can be a matter of life and death as preferences for male children have been strong historically and are still held, especially in rural areas. (WHO, 2010). Male children are given preference for receiving food, breast milk, medical care and other resources. It is no longer legal to give parents information on the sex of their developing child for fear that they will abort a female fetus. Clearly, gender socialization and discrimination still impact development in a variety of ways across the globe.


3.8.2: Endocytosis
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Learning Objectives
- Describe endocytosis, including phagocytosis, pinocytosis, and receptor-mediated endocytosis.
Endocytosis is a type of active transport that moves particles, such as large molecules, parts of cells, and even whole cells, into a cell. There are different variations of endocytosis, but all share a common characteristic: the plasma membrane of the cell invaginates, forming a pocket around the target particle. The pocket pinches off, resulting in the particle being contained in a newly-created intracellular vesicle formed from the plasma membrane.
Phagocytosis
Phagocytosis (the condition of “cell eating”) is the process by which large particles, such as cells or relatively large particles, are taken in by a cell. For example, when microorganisms invade the human body, a type of white blood cell called a neutrophil will remove the invaders through this process, surrounding and engulfing the microorganism, which is then destroyed by the neutrophil.
In preparation for phagocytosis, a portion of the inward-facing surface of the plasma membrane becomes coated with a protein called clathrin, which stabilizes this section of the membrane. The coated portion of the membrane then extends from the body of the cell and surrounds the particle, eventually enclosing it. Once the vesicle containing the particle is enclosed within the cell, the clathrin disengages from the membrane and the vesicle merges with a lysosome for the breakdown of the material in the newly-formed compartment ( endosome ). When accessible nutrients from the degradation of the vesicular contents have been extracted, the newly-formed endosome merges with the plasma membrane and releases its contents into the extracellular fluid. The endosomal membrane again becomes part of the plasma membrane.
Pinocytosis
A variation of endocytosis is called pinocytosis. This literally means “cell drinking” and was named at a time when the assumption was that the cell was purposefully taking in extracellular fluid. In reality, this is a process that takes in molecules, including water, which the cell needs from the extracellular fluid. Pinocytosis results in a much smaller vesicle than does phagocytosis, and the vesicle does not need to merge with a lysosome.
Potocytosis, a variant of pinocytosis, is a process that uses a coating protein, called caveolin, on the cytoplasmic side of the plasma membrane, which performs a similar function to clathrin. The cavities in the plasma membrane that form the vacuoles have membrane receptors and lipid rafts in addition to caveolin. The vacuoles or vesicles formed in caveolae (singular caveola) are smaller than those in pinocytosis. Potocytosis is used to bring small molecules into the cell and to transport these molecules through the cell for their release on the other side of the cell, a process called transcytosis.
Receptor-mediated Endocytosis
A targeted variation of endocytosis, known as receptor-mediated endocytosis, employs receptor proteins in the plasma membrane that have a specific binding affinity for certain substances. In receptor-mediated endocytosis, as in phagocytosis, clathrin is attached to the cytoplasmic side of the plasma membrane. If uptake of a compound is dependent on receptor-mediated endocytosis and the process is ineffective, the material will not be removed from the tissue fluids or blood. Instead, it will stay in those fluids and increase in concentration. Some human diseases are caused by the failure of receptor-mediated endocytosis. For example, the form of cholesterol termed low-density lipoprotein or LDL (also referred to as “bad” cholesterol) is removed from the blood by receptor-mediated endocytosis. In the human genetic disease familial hypercholesterolemia, the LDL receptors are defective or missing entirely. People with this condition have life-threatening levels of cholesterol in their blood, because their cells cannot clear LDL particles from their blood.
Although receptor-mediated endocytosis is designed to bring specific substances that are normally found in the extracellular fluid into the cell, other substances may gain entry into the cell at the same site. Flu viruses, diphtheria, and cholera toxin all have sites that cross-react with normal receptor-binding sites and gain entry into cells.
LICENSES AND ATTRIBUTIONS
CC LICENSED CONTENT, SPECIFIC ATTRIBUTION
- OpenStax College, Biology. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44419/latest...ol11448/latest . License : CC BY: Attribution
- neutrophil. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/neutrophil. License : CC BY-SA: Attribution-ShareAlike
- endosome. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/endosome. License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Bulk Transport. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44419/latest...e_05_04_01.jpg . License : CC BY: Attribution
- OpenStax College, Bulk Transport. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44419/latest...e_05_04_02.jpg . License : CC BY: Attribution
- OpenStax College, Bulk Transport. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44419/latest...e_05_04_03.jpg . License : CC BY: Attribution
Key Points
- Endocytosis consists of phagocytosis, pinocytosis, and receptor -mediated endocytosis.
- Endocytosis takes particles into the cell that are too large to passively cross the cell membrane.
- Phagocytosis is the taking in of large food particles, while pinocytosis takes in liquid particles.
- Receptor-mediated endocytosis uses special receptor proteins to help carry large particles across the cell membrane.
Key Terms
- endosome : An endocytic vacuole through which molecules internalized during endocytosis pass en route to lysosomes
- neutrophil : A cell, especially a white blood cell that consumes foreign invaders in the blood.


14.6: Review and Additional Resources
Review
Review and assess your learning. Start with the "Important Terms and Concepts" to ensure you know the terminology related to the topic of the chapter and concepts discussed. Move on to the "Review Questions" to answer critical thinking questions about concepts and processes discussed in the chapter. Finally, test your overall understanding by taking the "Self-assessment quiz".
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- compressional wave
- generate a back-and-forth motion parallel to the direction of travel
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- shear wave
- move up-and-down perpendicular to the direction of wave transmission
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- crust
- outer brittle shell of the Earth; forms the "skin" of the lithosphere. The crust is primarily composed of silicate rocks and ranging in thickness of about 5 to 70 km
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- sima
- basal zone of oceanic crust; primarily composed of a heavy, dark group of basaltic rocks
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- sial
- less dense continental crust; predominate elements are silicon and aluminum
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- lithosphere
- rigid cool layer composed of the crust and the uppermost mantle
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- asthenosphere
- the least rigid portion of the mantle. It is a soft, easily deformed layer that is susceptible to slow convection caused by pockets of increased heat from the decay of radioactive elements
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- mesosphere
- lies between the asthenosphere and core where the pressures are so great the mantle is solid
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- core
- molten outer and rigid inner layers
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- mantle
- over 2900 km thick (1801 mi) and comprises 80% of the Earth's total volume; mainly composed of a dark, dense ultramafic rock called peridotite (rich in iron and magnesium)
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- endogenic force
- forces that are are driven by the Earth's vast heat engine
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- exogenic force
- processes acting at the surface of the earth and primarily driven by solar energy
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- relief
- the difference in elevation between two points
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- first order relief feature
- the tectonic plates
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- second order relief feature
- the result of plate collision or divergence
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- third order relief feature
- created by erosion and deposition of the surface as opposed to the movement of tectonic plates. Individual landforms are considered third order relief features
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- mineral
- a naturally occurring inorganic substance with a unique crystal structure
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- silicate
- a combination of silicon, oxygen, and another element; see Table 14.4.1
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- oxide
- see Table 14.4.1
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- sulfide
- see Table 14.4.1
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- carbonate
- see Table 14.4.1
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- rock cycle
- represents the alteration of rock-forming minerals above and below the Earth's surface
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- rock
- assemblages of minerals
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- magma
- molten rock material
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- sediment
- fragments of weathered rock and the precursor for sedimentary rock
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- igneous rock
- cooled/crystallized magma or lava
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- sedimentary rock
- formed by compaction and cementation of sediments
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- metamorphic rock
- formed by the alteration of pre-existing rocks from exposure to heat and pressure while remaining in a solid form
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- clastic sedimentary rock
- form from the compaction of rock fragments
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- chemically precipitated sedimentary rock
- form by the precipitation of elements
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- country rock
- the pre-existing rock that insulates the magma that has intruded as it cools
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- sill
- feature created when magma intrudes between the layers of rock and solidifies
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- dike
- created when magma cools in near vertical fractures
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- laccolith
- created when the magma solidifies as a pocket of igneous rock that warps the overlying rock
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- batholith
- a huge intrusive igneous rock mass or pluton that when uncovered creates topographic highs in mountainous regions.
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- pluton
- rock mass in which magma has intruded and solidified
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- vesicles
- small holes; void spaces left by escaping gasses
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- stratum
- individual layer of sedimentary rock
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- bedding plane
- separation between each bed; signifies a cessation of deposition at that location for a period of time
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- lithostatic pressure
- the confining pressure created by the material that sits above a particular location; equal in all directions and compresses the volume of rock into a denser material
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- directed pressure
- flattens and lengthens the rock in the direction of greatest pressure; affects the shape and arrangement the minerals
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- burial metamorphism
- occurs in deep basins where sediments or sedimentary rocks have accumulated. At a depth of about 10 kilometers, the confining pressure of the overlying material combined with geothermal heat is great enough to metamorphose rocks.
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- contact metamorphism
- occurs at shallower levels of the crust, where the pressure is relatively low. At those shallow depths, the stresses characteristic of orogenic belts are generally small or absent thus producing metamorphic rocks that lack foliation
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- regional metamorphism
- occurs over broad areas of the crust; occurs in a linear belt in the plate overriding the subducting one due to increasing temperature and pressure as a result of compression, thrusting, folding, and intrusion of magmas from below.
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- dynamothermal metamorphism
- occurs in areas that have undergone deformation during mountain building that have since been eroded to expose the metamorphic rocks. It is caused by the differential stress resulting from plate subduction or collision along plate boundaries
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- foliated metamorphic rock
- minerals in distinct bands
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- nonfoliated metamorphic rock
- lack the banding of minerals
Compare and contrast compressional and shear waves.
- Answer
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Compressional (P) waves generate a back-and-forth motion parallel to the direction of travel. Shear (S) waves move up-and-down perpendicular to the direction of wave transmission. Shear waves do not penetrate molten masses and when they encounter a boundary between two rock types of differing densities, a portion of the wave travels along the boundary while another part returns to the surface.
Compare and contrast the sima and sial.
- Answer
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Sima refers to silica and magnesium, two important elements of the rocks forming the ocean basin like basalt. Sial refers to silica and aluminum, two important elements that comprise the rocks of the continents like granite.
Briefly describe the layers of the mantle.
- Answer
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The uppermost part of the mantle includes part of the lithosphere. Below the lithosphere is the asthenosphere, the least rigid portion of the mantle. Finally the mesosphere is the bottom most portion comprised of solid rock.
Describe the basic structure of the Earth's core.
- Answer
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The core is divided into the inner and outer cores. The inner core is made of solid iron and nickel. The outer core is thought to be molten iron.
Compare and contrast endogenic and exogenic forces. Give examples.
- Answer
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Endogenic forces are those driven by Earth's "heat engine" like volcanoes and earthquakes. Exogenic forces are driven by solar radiation like wind and water erosion.
Compare and contrast first, second, and third order relief features. Give an example for each.
- Answer
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First order relief features are the tectonic plates. Second order relief features are formed by plate interaction, e.g. mountain systems, ocean trenches. Third order relief features are produced by the erosion or deposition e.g., sand dunes, mountain peak.
What is a mineral and how is it different from a rock?
- Answer
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A mineral is an inorganic substance having a unique crystalline structure while a rock is a combination of minerals.
What is the rock cycle?
- Answer
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It is a model of the interrelationships between the three types of rocks and how they form.
Compare and contrast the physical features of intrusive and extrusive igneous rocks.
- Answer
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Extrusive igneous rock has smaller mineral grains and thus finer texture than intrusive igneous rocks.
Briefly describe how a sill, dike, batholith, and laccolith form.
- Answer
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Sill - magma intrudes between layers of host rock and solidifies. Dike - magma solidifies in a near vertical fracture. Batholith - huge subterranean mass of igneous rock. Laccolith - magma intrudes between layers of host rock, then warp the overlying layers.
Compare and contrast the various types of sedimentary rocks. Give examples.
- Answer
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Clastic sedimentary - formed from fragments, example = sandstone. Chemical (nonclastic) - formed from a precipitate. Example = limestone. Biologic sedimentary - Compaction of animal remains. Example = coal.
Compare and contrast the various types of metamorphism.
- Answer
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Contact metamorphism occurs along contact zones between pre-existing rock and a cooling pluton.
Regional metamorphism occurs over broad areas of the crust. There are two basic kinds of regional metamorphism: dynamothermal metamorphism - deformation during mountain building. burial metamorphism - occurs in deep basins where sediments or sedimentary rocks have accumulated.
What is the fundamental difference between foliated and nonfoliated metamorphic rocks.
- Answer
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Foliated metamorphic rocks display banding of minerals, nonfoliated do not.
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Waves of seismic energy propagated as a back-and-forth motion are called
- compressional waves
- shear waves
- surface waves
- none of the above
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The sima is primarily composed of
- granitic-type rocks
- basaltic-type rocks
- limestone-like rocks
- none of the above
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Which of the following layers are, we think, composed of solid nickel and iron?
- The asthenosphere
- The lithosphere
- The outer core
- The inner core
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Which of the following is created by endogenic forces?
- Glacial erosion
- Water erosion
- Wind erosion
- Faulting
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The Himalaya Mountains are a _____ relief feature of the Earth.
- first
- second
- third
- fourth
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The most abundant mineral family is the
- silicates
- oxides
- sulfides
- carbonates
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Metamorphic rocks form from
- sedimentary rocks
- igneous rocks
- other metamorphic rocks
- all the above
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An intrusive igneous rock body formed by the cooling of magma in a nearly vertical fracture is called a
- dike
- sill
- laccolith
- batholith
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Granite is
- an extrusive igneous rock
- a clastic sedimentary rock
- a nonfoliated metamorphic rock
- none of the above
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Quartzite is
- an extrusive igneous rock
- a clastic sedimentary rock
- a nonfoliated metamorphic rock
- none of the above
- Answer
-
- A
- B
- D
- D
- B
- A
- D
- A
- D
- C
Additional Resources
Use these resources to further explore the world of geography
Focus on The Physical Environment : "Earth's Core" Naked Science
Connections : " Evolution of Landscape Change along Clear Creek, Colorado " USGS. A look at the effects of urbanization, aggregate mining and reclamation.
Multimedia
"The Chemistry of Earth" The World of Chemistry video series ( Annenberg/CPB ) "Silicon, a cornerstone of the high-tech industry, is one of the elements of the Earth highlighted in this program." Additional information about Earth structure and mineral formation is included. Go to the The World of Chemistry site and scroll to "The Chemistry of Earth". One-time, free registration may be required to view film.
"Intrusive Igneous Rocks"
Earth Revealed
video series (
Annenberg/CPB
)
Most magma does not extrude onto Earth’s surface but cools slowly deep inside Earth. This magma seeps into crevices in existing rock to form intrusive igneous rocks. Experts provide a graphic illustration of this process and explain the types and textures of rocks such as granite, obsidian, and quartz. Once again, plate tectonics is shown to be involved in the process. Go to the Earth Revealed site and scroll to "Intrusive Igneous Rocks". One-time, free registration may be required to view film.
"Metamorphic Rocks" Earth Revealed video series ( Annenberg/CPB ) "The weight of a mountain creates enough pressure to recrystallize rock, thus creating metamorphic rocks. This program outlines the recrystallization process and the types of rock it can create — from claystone and slate to schist and garnet-bearing gneiss. The relationship of metamorphic rock to plate tectonics is also covered." Go to the Earth Revealed site and scroll to "Metamorphic Rocks". One-time, free registration may be required to view film.
"Sedimentary Rocks": The Key to Past Environments Earth Revealed video series ( Annenberg/CPB ) This program returns to the Grand Canyon: its exposed layers of sedimentary rock allow scientists to peer into the geologic past. The movement of sediment and its deposition are covered, and the processes of lithification, compaction, and cementation that produce sedimentary rocks are explained. Organic components of rock are also discussed. Go to the Earth Revealed site and scroll to "Sedimentary Rocks: The Key to Past Environments". One-time, free registration may be required to view film.


19.1: Care of the Older Adult Introduction
- Consider all aspects of diversity, including age
- Differentiate between normal and abnormal findings for older adults
- Detail specific adaptations in patient care to accommodate the needs of older adults
The needs of the older adult population will continue to influence health care through this century. The aging “baby boomer” population, along with an increased average life span of Americans, has led to an increased number of older adults and is only expected to grow. The U.S. Census Bureau projects that 1 in 5 Americans will be over the age of 65 by 2030, and by 2034, the number of older individuals will outnumber children for the first time in U.S. history. [1]
Each individual ages in their own way, and the physical, psychosocial, and cognitive health of older individuals varies widely. Because of this broad scope of health and illness in the aging population, providing nursing care that meets the needs of each older adult can be challenging. Additionally, although there are common physiological changes that occur with aging, many individuals ignore symptoms by erroneously attributing them to the aging process. For example, many older adults mistakenly believe that pain from arthritis is a normal part of growing older and do not seek treatment, resulting in decreased physical activity that puts them at increased risk for developing chronic disease. Providing individualized nursing care and patient education to older adults can promote effective preventative health care and self-management that maintains and enhances their quality of life. [2] Let’s begin by reviewing basic concepts related to the aging process.
- United States Census Bureau. (2018, March 13). Older people projected to outnumber children for the first time in U.S . history . https://www.census.gov/newsroom/press-releases/2018/cb18-41-population-projections.html ↵
- Sarkisian, C. A., Hays, R. D., Berry, S., & Mangione, C. M. (2002). Development, reliability, and validity of the expectations regarding aging (ERA-38) survey. The Gerontologist, 42 (4), 534-542. https://doi.org/10.1093/geront/42.4.534 ↵


3.4.1: Antibiotics and Selective Toxicity
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Learning Objectives
- Describe selective toxicity
Selective Toxicity in Antibiotics
Synthetic antibiotic chemotherapy as a science and development of antibacterials began in Germany with Paul Ehrlich in the late 1880s. Ehrlich noted that certain dyes would color human, animal, or bacterial cells, while others did not. He then proposed the idea that it might be possible to create chemicals that would act as a selective drug that would bind to and kill bacteria without harming the human host. After screening hundreds of dyes against various organisms, he discovered a medicinally useful drug, the synthetic antibacterial Salvarsan now called arsphenamine.
Antibiotics are commonly classified based on their mechanism of action, chemical structure, or spectrum of activity. More specifically, narrow spectrum antibiotics target specific types of bacteria, such as Gram-negative or Gram-positive bacteria, whereas broad spectrum antibiotics affect a wide range of bacteria. Following a 40-year hiatus in discovering new classes of antibacterial compounds, three new classes of antibacterial antibiotics have been brought into clinical use: cyclic lipopeptides (such as daptomycin), glycylcyclines (such as tigecycline), and oxazolidinones (such as linezolid).
Some antibacterials have been associated with a range of adverse effects. Side-effects range from mild to very serious depending on the antibiotics used, the microbial organisms targeted, and the individual patient. Safety profiles of newer drugs are often not as well established as for those that have a long history of use. Adverse effects range from fever and nausea to major allergic reactions, including photodermatitis and anaphylaxis. Common side-effects include diarrhea, resulting from disruption of the species composition in the intestinal flora, resulting, for example, in overgrowth of pathogenic bacteria, such as Clostridium difficile . Antibacterials can also affect the vaginal flora, and may lead to overgrowth of yeast species of the genus Candida in the vulvo-vaginal area. Additional side-effects can result from interaction with other drugs, such as elevated risk of tendon damage from administration of a quinolone antibiotic with a systemic corticosteroid.
Antibacterial Production
Despite the wide variety of known antibiotics, less than 1% of antimicrobial agents have medical or commercial value. For example, whereas penicillin has a high therapeutic index as it does not generally affect human cells, this is not so for many antibiotics. Other antibiotics simply lack advantage over those already in use, or have no other practical applications. Useful antibiotics are often discovered using a screening process. To conduct such a screen, isolates of many different microorganisms are cultured and then tested for production of diffusible products that inhibit the growth of test organisms. Most antibiotics identified in such a screen are already known and must therefore be disregarded. The remainder must be tested for their selective toxicities and therapeutic activities, and the best candidates can be examined and possibly modified. A more modern version of this approach is a rational design program. This involves screening directed towards finding new natural products that inhibit a specific target, such as an enzyme only found in the target pathogen, rather than tests to show general inhibition of a culture.
Key Points
- Their mechanism of action, chemical structure, or spectrum of activity are ways in which antibiotics are classified.
- Broad spectrum antibiotics affect a wide range of bacteria, while narrow spectrum antibiotics are able to target specific types.
- Antibiotics must go through a screening process, where they are isolated, cultured, and then tested for production of diffusible products that inhibit the growth of specific test organisms.
- Due to potential adverse side effects, antibiotics must also be tested for their selective toxicities.
Key Terms
- antibacterial : A drug having the effect of killing or inhibiting bacteria.
- bactericidal : An agent that kills bacteria.
- bacteriostatic : A drug that prevents bacterial growth and reproduction but does not necessarily kill them. When it is removed from the environment the bacteria start growing again.


3.20: Sentence Fragment
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Sentence fragments always make the list of the most common errors, and they are among the most seriously stigmatizing errors we can make. To put it simply, a sentence fragment is an incomplete sentence that you have punctuated as if it is a complete sentence.
Sometimes, fragments are missing a verb. Sometimes, fragments are missing a subject. Sometimes, a fragment is simply a dependent clause punctuated like a complete sentence. Here are some examples:
You’ll notice that each of these so-called sentences is not a complete sentence. They are both missing parts that would make them complete.
You always have options about how you correct a sentence fragment, but here are some possible corrections for our two sample sentence fragments:
Fragments are among the most serious errors in academic writing. While you may read fiction and informal prose that contain sentence fragments, in academic writing, fragments are generally frowned upon. In fact, research on how errors are perceived by people indicates that fragments are what we call “status marking” errors, which means people will make negative assumptions about the intelligence of the writer when they see fragments in writing.
Of course, making a sentence fragment error has nothing to do with your intelligence. Usually, for native speakers of English, making a sentence fragment error is more about not editing carefully or just not being practiced in the rules.
In this video, the Grammar Professor will review what a fragment is and how you can avoid fragments in your academic writing.