36.2: America- Utopia or Dystopia?
In the beginning of Letters from an American Farmer , Farmer James claims that America is “the most perfect society now existing in the world. Here, man is as free as he ought to be…” (606). He cites the absence of kings and the feudal system to account for this “perfectness”. Without kings, citizens can own land and keep most of their produce that they farm. Everyone is happy, because everyone can be fed, there are no oppressive rules dictating in the ways people can worship, and there is no ruling class with a large disparity between the wealthy and the poor.
However, later on in the letters, Farmer James recounts the disturbing treatment of African slaves. He paints a very vivid picture of despair, torture, and horror. Right away, he sympathizes with the slaves, pleading to Nature (not God, interesting): “Are not these blacks thy children as well as we?” (616).  This disparity between the citizens and the slaves can be best illustrated in this quote: “The chosen race eat, drink, and live happy, while the unfortunate one grubs up the ground… exposed to a sun full as scorching as their native one; without the support of good food, without the cordials of any cheering liquor” (616).
This seemingly sudden switch in tone from the wonders and magic of America to covering the deepest and darkest trenches is what I think makes it a great example of American literature. These letters depict a newly immigrated European who sees nothing but promise, wealthy, and happiness in the country, but then discovers that not all of it is sunshine and rainbows. Even though the slaves work hard, they will never be able to reach the happiness and transcendence that European immigrants seem to enjoy.
Works Cited
Crevecoeur, J. Hector St. John, et al. J. Hector St. John De Crevecoeur . The Norton Anthology of American Literature , edited by Sandra M. Gustafson, W.W. Norton & Company, 2017, pp. 604–624.


20.6D: Immunological Memory
Immunological memory refers to the ability of B and T cells to produce long-lived memory cells that defend against specific pathogens.
- Describe immunological memory of the immune system
Key Points
- When B and T cells begin to replicate, some offspring will become long-lived memory cells.
- Memory cells remember all specific pathogens encountered during the animal’s lifetime and can thus call forth a strong response if the pathogen ever invades the body again.
- Passive immunity comes from IgG antibodies given through the mother during fetal development and through breast milk. This memory is short term, but protects the infant until its own adaptive immune system is functional.
- During a secondary immune response, memory B and T cells work to rapidly eliminate the pathogen, preventing reinfection by the same pathogen.
- During a vaccination, the antigen of a pathogen is introduced into the body through a weakened form of the pathogen that cannot cause an infection. This stimulates the immune system to develop a specific immunity against that pathogen without actually causing the disease that the pathogen brings.
- Vaccines do not exist for every pathogen due to frequent strain mutations and challenges in producing an immunization strong enough to work, but not strong enough to cause an infection.
Key Terms
- secondary immune response : The act of exposure to the same pathogen after the initial immune response. Memory B and T cells work to rapidly eliminate the pathogen to prevent reinfection.
- vaccination : Inoculation with the weakened form of a pathogen to protect against a particular disease or strain of disease by stimulating the development of immunological memory against that pathogen.
When B and T cells begin to replicate during an adaptive immune response, some offspring become long-lived memory cells. These memory cells remember all specific pathogens encountered during the animal’s lifetime and can thus call forth a stronger response, called the secondary immune response, if the pathogen ever invades the body again. The adaptive immune system is so-named because it is a result of an adaptation to an infection. Immunological memory can either exist in active long-term memory or passive short-term memory.
Immune response : When B and T cells begin to replicate, some of the offspring that they produce will end up becoming long-lived memory cells. These memory cells will remember all specific pathogens encountered during the animal’s lifetime and can thus call forth a strong response if the pathogen ever invades the body again.
Passive Memory
Newborn infants are particularly vulnerable to infections since they have no prior exposure to pathogens. Thus, the mother protects the infant through several layers of passive protection. During pregnancy, IgG, a certain isotype of antibody, is transported to the baby from the mother through the placenta, so even babies have high levels of antibodies with similar antigen specificities as the mother. Even breast milk contains antibodies that are transferred to the infant’s gastrointestinal tract and protect against bacterial infections until the baby is capable of making its own antibodies. Since the fetus isn’t making any memory cells or antibodies, this is called passive immunity. Passive immunity is short-lived, ranging from a couple days to a couple months.
As the infant matures, their thymus and bone marrow work to raise a stock of mature lymphocytes that form the foundation for the infant’s personal adaptive immune system. Because the passive memory comes from antibodies instead of B cells themselves, infants do not inherit long-term immunological memory from the mother. Even if the infant receives antibodies specific to certain diseases from its mother, the infant wouldn’t be able to bolster a long-term memory that would direct antigen exposure and presentation.
Active Memory and Immunization
Following an infection, long-term active memory is acquired by activation of B and T cells. Memory cells derive from their parent B and T cells, and undergo clonal selection following infection, which increases antigen-binding affinity. Following reinfection, the secondary immune response typically eliminates the pathogen before symptoms of an infection can occur. During the secondary immune response, memory T cells rapidly proliferate into active helper and cytotoxic T cells specific to that antigen, while memory B cells rapidly produce antibodies to neutralize the pathogen. Long-term active memory consists of rapid response and form permanent immunological memory so long as those memory cells survive.
Vaccinations take advantage of memory lymphocyte development by artificially-generating active immunity, a process called immunization. During a vaccination, the antigen of a pathogen is introduced into the body and stimulates the immune system to develop a specific immunity against that pathogen. It doesn’t cause the disease that the pathogen brings because the vaccine uses an attenuated form of the pathogen that contains the same antigen but doesn’t have the capacity for replication. This deliberate introduction of the pathogen is successful since it exploits the immune system’s natural specificity and inducibility. Vaccination is an extremely effective manipulation of the immune system that helps fight diseases. Over the course of vaccine development, they have saved countless lives, and diseases like rubella and polio are not the widespread causes of disability they once were.
Despite the effectiveness of vaccines, methods do not yet exist to develop vaccines for every pathogen. Many pathogens undergo mutations that change the expression of their antigens, making immunization attempts fruitless for diseases like the common cold or norovirus. Many parasitic pathogens, such as the plasmodium protist that causes malaria, haven’t successfully been vaccinated against because it is challenging to develop a vaccine that is strong enough to stimulate an immune response (sufficient immunogenicity) without causing a live infection.


1.2.8: Factoring Special Products
By the end of this section, you will be able to:
- Factor perfect square trinomials
- Factor differences of squares
- Factor sums and differences of cubes
Before you get started, take this readiness quiz.
1. Simplify \((3x^2)^3\).
2. Multiply \((m+4)^2\).
3. Multiply \((x−3)(x+3)\).
We have seen that some binomials and trinomials result from special products—squaring binomials and multiplying conjugates. If we recognize these kinds of polynomials, we can use the special products patterns to factor them much more quickly.
Factoring Differences of Squares
One special product we are familiar with is the Product of Conjugates pattern. We use this to multiply two binomials that were conjugates. Here’s an example:
\[(2x-5)(2x+5)=4x^2-25.\nonumber\]
A difference of squares factors to a product of conjugates (in this context, \(a-b\) is said to be conjugate to \(a+b\), and vice versa.)
Difference of Squares Pattern
If \(a\) and \(b\) are (or represent) real numbers,
\[a^2-b^2=(a+b)(a-b).\nonumber\]
Remember, “difference” refers to subtraction. So, to use this pattern we must make sure we have a binomial in which two squares are being subtracted.
Factor \(64y^2−1\).
Solution
Note that \((8y)^2=64y^2\) and \(1^2=1\), so that
\[\begin{align*} &64y^2-1\\ = &(8y)^2-(1)^2 \\ =&(8y+1)(8y-1).\end{align*}\]
Try It \(\PageIndex{2}\)
Factor \(121m^2−1\).
- Answer
-
\((11m−1)(11m+1)\)
Try It \(\PageIndex{3}\)
Factor \(81y^2−1\).
- Answer
-
\((9y−1)(9y+1)\)
Factor Difference of Squares
\(\begin{array} {llll} \textbf{Step 1.} &\text{Does the binomial fit the pattern?} &\qquad &\hspace{5mm} a^2−b^2 \\ &\text{Is this a difference?} &\qquad &\hspace{2mm} \text{____−____} \\ &\text{Are the first and last terms perfect squares?} & & \\ \textbf{Step 2.} &\text{Write them as squares.} &\qquad &\hspace{3mm} (a)^2−(b)^2 \\ \textbf{Step 3.} &\text{Write the product of conjugates.} &\qquad &(a−b)(a+b) \\ \textbf{Step 4.} &\text{Check by multiplying.} & & \end{array}\)
It is important to remember that sums of squares do not factor into a product of binomials . There are no binomial factors that multiply together to get a sum of squares. After removing any GCF, the expression \(a^2+b^2\) can not be factored any further!
The next example shows variables in both terms.
Factor \(144x^2−49y^2\).
Solution
| \(\quad 144x^2−49y^2\) | |
| Is this a difference of squares? Yes. | \(=(12x)^2−(7y)^2\) |
| Factor as the product of conjugates. | \(=(12x−7y)(12x+7y)\) |
| Check by multiplying. | \(=144x^2−49y^2\checkmark\) |
| Conclude. | The factorization is \((12x-7y)(12x+7y)\). |
Try It \(\PageIndex{5}\)
Factor \(196m^2−25n^2\).
- Answer
-
\((16m−5n)(16m+5n)\)
Try It \(\PageIndex{6}\)
Factor \(121p^2−9q^2\).
- Answer
-
\((11p−3q)(11p+3q)\)
As always, we should look for a common factor first whenever we have an expression to factor. Sometimes a common factor may “disguise” the difference of squares and we won’t recognize the perfect squares until we factor the GCF.
Also, to factor the binomial in the next example, we’ll factor a difference of squares twice!
Factor \(48x^4y^2−243y^2\).
Solution
| \(\quad 48x^4y^2−243y^2\) | |
| Is there a GCF? Yes, \(3y^2\) - factor it out! | \(=3y^2(16x^4−81)\) |
| Is the binomial a difference of squares? Yes. | \(=3y^2\left((4x^2)^2−(9)^2\right)\) |
| Factor as a product of conjugates. | \(=3y^2(4x^2−9)(4x^2+9)\) |
| Notice the first binomial is also a difference of squares! | \(=3y^2((2x)^2−(3)^2)(4x^2+9)\) |
| Factor it as the product of conjugates. | \(=3y^2(2x−3)(2x+3)(4x^2+9)\) |
| The last factor, the sum of squares, cannot be factored. | |
| Check by multiplying: |
\(\quad 3y^2(2x−3)(2x+3)(4x^2+9)\) \(=3y^2(4x^2−9)(4x^2+9)\) \(=3y^2(16x^4−81) \) \(=48x^4y^2−243y^2\checkmark\) |
| Conclude. | The factorization is \(3y^2(2x-3)(2x+3)(4x^2+9)\). |
Try It \(\PageIndex{8}\)
Factor \(2x^4y^2−32y^2\).
- Answer
-
\(2y^2(x−2)(x+2)(x^2+4)\)
Try It \(\PageIndex{9}\)
Factor \(7a^4c^2−7b^4c^2\).
- Answer
-
\(7c^2(a−b)(a+b)(a^2+b^2)\)
The next example has a polynomial with 4 terms. So far, when this occurred we grouped the terms in twos and factored from there. Here we will notice that the first three terms form a perfect square trinomial.
Factor \(x^2−6x+9−y^2\).
Solution
Notice that the first three terms form a perfect square trinomial.
| \(x^2−6x+9−y^2\) | |
|
Factor by grouping the first three terms. Use the perfect square trinomial pattern. |
\((x-3)^{2}-y^{2}\) |
| Is this a difference of squares? Yes. | |
| Yes—write them as squares. | (already in that form) |
| Factor as the product of conjugates. | \((x-3-y)(x-3+y)\) |
| Conclude. | The factorization is \((x−y−3)(x+y−3)\). |
Try It \(\PageIndex{11}\)
Factor \(x^2−10x+25−y^2\).
- Answer
-
\((x−5−y)(x−5+y)\)
Try It \(\PageIndex{12}\)
Factor \(x^2+6x+9−4y^2\).
- Answer
-
\((x+3−2y)(x+3+2y)\)
Factoring Perfect Square Trinomials (optional discussion)
Some trinomials are perfect squares. They result from multiplying a binomial times itself. We squared a binomial using the Binomial Squares pattern in a previous chapter.
The trinomial \(9x^2+24x+16\) is called a perfect square trinomial . It is the square of the binomial \(3x+4\).
In this chapter, we will start with a perfect square trinomial and factor it into its as many factors as possible. We could factor this trinomial using the methods described in the last section, since it is of the form \(ax^2+bx+c\). But if we recognize that the first and last terms are squares and the trinomial fits the perfect square trinomials pattern, we will save ourselves a lot of work. Here is the pattern—the reverse of the binomial squares pattern.
Perfect Square Trinomial Pattern
If \(a\) and \(b\) are (or represent) real numbers
\[a^2+2ab+b^2=(a+b)^2,\nonumber\]
\[a^2−2ab+b^2=(a−b)^2.\nonumber\]
To make use of this pattern, we have to recognize that a given trinomial fits it. Check first to see if the leading coefficient is a perfect square, \(a^2\). Next check that the last term is a perfect square, \(b^2\). Then check the middle term—is it the product, \(2ab\)? If everything checks, we can easily write the factors.
The sign of the middle term determines which pattern we will use. When the middle term is negative, we use the pattern \(a^2−2ab+b^2\), which factors to \((a−b)^2\).
The steps are summarized here.
Factoring Perfect Square Trinomials
\(\begin{array} {lllll} \textbf{Step 1.} &\text{Does the trinomial fit the pattern?} &\quad &\hspace{7mm} a^2+2ab+b^2 &\hspace{7mm} a^2−2ab+b^2 \\ &\text{Are the first and last terms perfect squares?} &\quad & &\\ &\text{Write them as squares.} &\quad &\hspace{5mm}(a)^2\hspace{16mm} (b)^2 &\hspace{6mm}(a)^2\hspace{16mm} (b)^2 \\ &\text{Check the middle term. Is it }2ab? &\quad &\hspace{12mm} {\,}^{\searrow}{\,}_{2·a·b}{\,}^{\swarrow} &\hspace{12mm} {\,}^{\searrow}{\,}_{2·a·b}{\,}^{\swarrow} \\ \textbf{Step 2.} &\text{Write the square of the binomial.} &\quad &\hspace{13mm} (a+b)^2 &\hspace{13mm} (a−b)^2 \\ \textbf{Step 3.} &\text{Check by multiplying.} & & & \end{array}\)
Remember the first step in factoring is to look for a greatest common factor. Perfect square trinomials may have a GCF in all three terms and it should be factored out first. And, sometimes, once the GCF has been factored, we will recognize a perfect square trinomial.
The above is for consideration, but we will not give any examples of this here.
- Why might it be useful to recognize the special products?
- Explain why \((x+2)^2\not = x^2+4\).
- Give an example of the difference-of-squares pattern with three variables?
- Use the difference of squares pattern to simplify and factor 49-16.
- Is there a sum of squares formula?
- Demonstrate why \(a^2-b^2=(a-b)(a+b)\).
Factor \(25x^2-16y^6\).
Key Concepts
-
Difference of Squares Pattern:
If \(a\), \(b\) are (or represent) real numbers,
\[a^2-b^2=(a+b)(a-b)\] -
How to factor differences of squares
\(\begin{array} {llll} \textbf{Step 1.} &\text{Does the binomial fit the pattern?} &\qquad &\hspace{5mm} a^2−b^2 \\ &\text{Is this a difference?} &\qquad &\hspace{2mm} \text{____−____} \\ &\text{Are the first and last terms perfect squares?} & & \\ \textbf{Step 2.} &\text{Write them as squares.} &\qquad &\hspace{3mm} (a)^2−(b)^2 \\ \textbf{Step 3.} &\text{Write the product of conjugates.} &\qquad &(a−b)(a+b) \\ \textbf{Step 4.} &\text{Check by multiplying.} & & \end{array}\) -
Perfect Square Trinomials Pattern:
If \(a\) and \(b\) are (or represent) real numbers,
\[\begin{array} {l} a^2+2ab+b^2=(a+b)^2 \\ a^2−2ab+b^2=(a−b)^2\end{array} \nonumber\]
-
How to factor perfect square trinomials
\(\begin{array} {lllll} \textbf{Step 1.} &\text{Does the trinomial fit the pattern?} &\quad &\hspace{7mm} a^2+2ab+b^2 &\hspace{7mm} a^2−2ab+b^2 \\ &\text{Are the first and last terms perfect squares?} &\quad & &\\ &\text{Write them as squares.} &\quad &\hspace{5mm}(a)^2\hspace{16mm} (b)^2 &\hspace{6mm}(a)^2\hspace{16mm} (b)^2 \\ &\text{Check the middle term. Is it }2ab? &\quad &\hspace{12mm} {\,}^{\searrow}{\,}_{2·a·b}{\,}^{\swarrow} &\hspace{12mm} {\,}^{\searrow}{\,}_{2·a·b}{\,}^{\swarrow} \\ \textbf{Step 2.} &\text{Write the square of the binomial.} &\quad &\hspace{13mm} (a+b)^2 &\hspace{13mm} (a−b)^2 \\ \textbf{Step 3.} &\text{Check by multiplying.} & & & \end{array}\)


1.4: The Integers modulo m
In this section, we'll seek to answer the questions:
- What are equivalence relations?
- What is congruence modulo \(m\text{?}\)
- How does arithmetic in \(\mathbb{Z}_m\) compare to arithmetic in \(\mathbb{Z}\text{?}\)
The foundation for our exploration of abstract algebra is nearly complete. We need the basics of one more "number system" in order to appreciate the abstract approach developed in subsequent chapters. To build that number system, a brief review of relations and equivalence relations is required. Recall that given sets \(S\) and \(T\text{,}\) the Cartesian product of \(S\) with \(T\text{,}\) denoted \(S\times T\) ("\(S\) cross \(T\)"), is the set of all possible ordered pairs whose first element is from \(S\) and second element is from \(T\text{.}\) Symbolically,
\begin{equation*} S\times T = \{(s,t) : s\in S, \ t\in T \}. \end{equation*}
Let \(S\) be a nonempty set. A relation \(R\) on \(S\) is a subset of \(S\times S\text{.}\) If \(x,y\in S\) such that \((x,y)\in R\text{,}\) we usually write \(xRy\) and say that \(x\) and \(y\) are related under \(R\) .
The notion of a relation as presented above is extremely open-ended. Any subset of ordered pairs of \(S\times S\) describes a relation on the set \(S\text{.}\) Of course, some relations are more meaningful than others; the branch of mathematics known as order theory studies order relations (such as the familiar \(\lt\)). Our focus will be on equivalence relations , which isolate the important features of \(=\text{.}\)
Let \(S\) be a nonempty set. We say a relation \(\sim\) on \(S\) is an equivalence relation if the following properties hold:
- \(\sim\) is reflexive : if \(a\in S\text{,}\) then \(a\sim a\text{.}\)
- \(\sim\) is symmetric : if \(a,b\in S\) with \(a\sim b\text{,}\) then \(b\sim a\text{.}\)
- \(\sim\) is transitive : if \(a,b,c\in S\) with \(a\sim b\) and \(b\sim c\text{,}\) then \(a\sim c\text{.}\)
Given \(x\in S\text{,}\) the set
\begin{equation*} \overline{x} = \{y\in S: x\sim y\} \end{equation*}
is called the equivalence class of \(x\) . Any element \(z\in \overline{x}\) is called a representative of the equivalence class.
Prove that “has the same birthday as” is an equivalence relation on the set \(P\) of all people.
What other relations can you think of? Write down one example and one non-example of an equivalence relation.
Prove that \(\le\) is not an equivalence relation on \(\mathbb{Z}\text{.}\)
For our purposes, a particularly important equivalence relation is congruence modulo \(m\) on the set of integers.
Let \(a,b\in \mathbb{Z}\) and \(m \in \mathbb{N}\text{,}\) \(m > 1\text{.}\) We say \(a\) is congruent to \(b\) modulo \(m\) if \(m\mid a-b\text{.}\) We write \(a \equiv b\mod m\text{.}\)
Justify the following congruences.
- \(\displaystyle 18 \equiv 6\mod 12\)
- \(\displaystyle 47 \equiv 8\mod 13\)
- \(\displaystyle 71 \equiv 1\mod 5\)
- \(\displaystyle 21 \equiv -1 \mod 11\)
- \(\displaystyle 24 \equiv 0\mod 6\)
Given an integer \(m > 1\text{,}\) congruence modulo \(m\) is an equivalence relation on \(\mathbb{Z}\text{.}\)
Find all of the equivalence classes of \(\mathbb{Z}_5\) and \(\mathbb{Z}_7\text{.}\)
Let \(a,b, c,d\in \mathbb{Z}\) and \(m > 1\) such that \(a\equiv c\mod m\) and \(b\equiv d\mod m\text{.}\) Then \(a+b \equiv c + d \mod m\text{.}\)
Let \(a,b, c,d\in \mathbb{Z}\) and \(m > 1\) such that \(a\equiv c\mod m\) and \(b\equiv d\mod m\text{.}\) Then \(ab \equiv c d\mod m\text{.}\)
Let \(S\) be a set and \(\sim\) an equivalence relation on \(S\text{.}\) Then a statement \(P\) about the equivalence classes of \(S\) is well-defined if the representative of the equivalence class does not matter. That is, whenever \(\overline{x} = \overline{y}\text{,}\) \(P(\overline{x}) = P(\overline{y})\text{.}\)
The previous exercises justify the following definitions.
Let \(m > 1\) and \(a,b\in \mathbb{Z}_m\text{.}\) Then the following are well-defined operations on the equivalence classes:
- Addition modulo \(m\) : \(\overline{a} + \overline{b} := \overline{a+b}\text{.}\)
- Multiplication modulo \(m\) : \(\overline{a}\cdot \overline{b} := \overline{a\cdot b}\text{.}\)
Most elementary propositions about \(\mathbb{Z}_m\) can be recast as statements about \(\mathbb{Z}\text{.}\) For instance, in proving Theorem 1.4.2 you likely proved that if \(m|a-c\) and \(m|b-d\) that \(m|(a+b)-(c+d)\text{.}\) However, as the statements become more complex, repeatedly reshaping statements about \(Z_m\) as statements about \(\mathbb{Z}\) becomes cumbersome and unhelpful. Instead, you are encouraged to become comfortable doing arithmetic modulo \(m\) or, put another way, arithmetic with the equivalence classes of \(\mathbb{Z}_m\) as defined in Definition: Modulo .
Without passing back to \(\mathbb{Z}\text{,}\) find the smallest nonnegative integer representative of the resulting equivalence classes.
- \(\overline{5}+\overline{11}\) in \(\mathbb{Z}_{9}\)
- \(\overline{-3}+\overline{-3}\) in \(\mathbb{Z}_{6}\)
- \(\overline{8}\cdot\overline{3}\) in \(\mathbb{Z}_{19}\)
- \(\overline{-1}\cdot(\overline{3}+\overline{8})\) in \(\mathbb{Z}_{7}\)
- \(\overline{3}\cdot(\overline{5}^2+\overline{3}^3)\) in \(\mathbb{Z}_{20}\)
In the remainder of this section, we investigate fundamental properties of arithmetic in \(\mathbb{Z}_m\text{.}\)
Let \(\overline{a},\overline{b},\overline{c}\in \mathbb{Z}_m\) with \(\overline{c}\ne\overline{0}\) and \(m > 1\text{.}\) If \(\overline{a}\cdot \overline{c} = \overline{b}\cdot \overline{c}\text{,}\) is it true that \(\overline{a} = \overline{b}\text{?}\) If so, prove it. If not, find an example of when the statement fails to hold.
Let \(a,b,c\text{,}\) and \(m\) be integers with \(m > 1\) and \(\gcd(c,m)=1\text{.}\) Then there is some \(x\in \mathbb{Z}\) such that \(\overline{c} \overline{x} = \overline{1}\text{.}\)
Conclude that if \(\overline{a} \cdot\overline{c} = \overline{b}\cdot\overline{c}\) in \(\mathbb{Z}_m\) that \(\overline{a} = \overline{b}\text{.}\)
Let \(p\in \mathbb{N}\) be prime and \(\overline{a},\overline{b},\overline{c}\in \mathbb{Z}_p\) such that \(\overline{c}\ne \overline{0}\text{.}\) Then
- there is some \(\overline{x}\in \mathbb{Z}_p\) such that \(\overline{c}\cdot \overline{x} = \overline{1}\text{;}\) and,
- if \(\overline{a} \cdot\overline{c} = \overline{b}\cdot\overline{c}\text{,}\) \(\overline{a} = \overline{b}\text{.}\)


9.7D: Double-Stranded DNA Bacteriophages
- Describe dsDNA bacteriophages
The Double-Stranded DNA (dsDNA) tailed phages, or Caudovirales, account for 95% of all the phages reported in the scientific literature, and possibly make up the majority of phages on the planet. Nineteen families that infect bacteria and archaea are currently recognized; of these, 15 have double-stranded DNA genomes.
Under the Baltimore classification scheme, the Caudovirales are group I viruses as they have double-stranded DNA (dsDNA) genomes, which can be anywhere from 18,000 base pairs to 500,000 base pairs in length. The virus particles have a distinct shape; each virion has an icosohedral head that contains the viral genome, and is attached to a flexible tail by a connector protein. The order encompasses a wide range of viruses, many of which contain genes of similar nucleotide sequence and function. Some tailed bacteriophage genomes can vary quite significantly in nucleotide sequence, however, even among the same genus. Due to their characteristic structure and possession of potentially homologous genes, it is believed these bacteriophages possess a common origin. There are at least 350 recognized species in this order.
Upon encountering a host bacterium, the tail section of the virion binds to receptors on the cell surface and delivers the DNA into the cell by use of an injectisome-like mechanism (an injectisome is a nanomachine that evolved for the delivery of proteins by type III secretion). The tail section of the virus punches a hole through the bacterial cell wall and plasma membrane and the genome passes down the tail into the cell. Once inside, the genes are expressed from transcripts made by the host machinery, using host ribosomes. Typically, the genome is replicated by use of concatemers, in which overlapping segments of DNA are made, and then put together to form the whole genome.
Viral capsid proteins come together to form a precursor prohead, into which the genome enters. Once this has occurred, the prohead undergoes maturation by cleavage of capsid subunits to form an icosohedral phage head with 5-fold symmetry. After the head maturation, the tail is joined in one of two ways: either the tail is constructed separately and joined with the connector, or the tail is constructed directly onto the phage head. The tails consist of helix-based proteins with 6-fold symmetry. After maturation of virus particles, the cell is lysed by lysins, holins, or a combination of the two.
Because the lack of homology between the amino acid and DNA sequences of these viruses precludes these from being used as taxonomic markers (as is common for other organisms), the three families here are defined on the basis of morphology. This classification scheme was originated by Bradley in 1969 and has since been extended. All viruses in this order have icosahedral or oblate heads, but differ in the length and contractile abilities of their tails. The Myoviridae have long tails that are contractile, the Podoviridae have short noncontractile tails, and the Siphoviridae have long non-contractile tails. Siphoviridae constitute the majority of the known tailed viruses.
Key Points
- The Caudovirales are an order of viruses also known as the tailed bacteriophages. The virus particles have a distinct shape; each virion has an icosohedral head that contains the viral genome, and is attached to a flexible tail by a connector protein.
- The order encompasses a wide range of viruses, many of which contain genes of similar nucleotide sequence and function. Some tailed bacteriophage genomes can vary quite significantly in nucleotide sequence, even among the same genus. There are at least 350 recognized species in this order.
- Because of the lack of homology between the amino acid and DNA sequences of these viruses, the three families here are defined based on morphology: the Myoviridae have long contractile tails, the Podoviridae have short noncontractile tails, and the Siphoviridae have long non-contractile tails.
Key Terms
- Caudovirales : A taxonomic order within the kingdom Virus—the bacteriophages that have tails.


10.1: A Simple Test Apparatus to Verify the Photoresponse of Experimental Photovoltaic Materials and Prototype Solar Cells
Introduction
One of the problems associated with testing a new unproven photovoltaic material or cell design is that significant processing required in order to create a fully functioning solar cell. If it is desired to screen a wide range of materials or synthetic conditions it can be time consuming (and costly of research funds) to prepare fully functioning devices. In addition, the success of each individual cell may be more dependent on fabrication steps not associated with the variations under study. For example, lithography and metallization could cause more variability than the parameters of the materials synthesis. Thus, the result could be to give no useful information as to the viability of each material under study, or even worse a false indication of research direction.
So-called quick and dirty qualitative measurements can be employed to assess not only the relative photoresponse of new absorber layer materials, but also the relative power output of photovoltaic devices. The measurement procedure can provide a simple, inexpensive and rapid evaluation of cell materials and structures that can help guide the development of new materials for solar cell applications.
Equipment Needs
Everything needed for the measurements can be purchased at a local electronics store and a hardware or big box store. Needed items are:
- Two handheld digital voltmeter with at least ±0.01 mV sensitivity (0.001 mV is better, of course).
- A simple breadboard and associated wiring kit.
- A selection of standard size and wattage resistors (1/8 - 1 Watt, 1 - 1000 ohms).
- A selection of wire wound potentiometers (0 - 10 ohms; 0 - 100 ohms; 0 - 1000 ohms) if I-V tracing is desired.
- A light source. This can be anything from a simple flood light to an old slide projector.
- A small fan or other cooling device for “steady state” (i.e., for measurements that last more than a few seconds such as tracing an I-V curve).
- 9 volt battery and holder or simple ac/dc low voltage power supply.
Measurement of the Photo-response of an Experimental Solar Cell
A qualitative measurement of a solar cell’s current-voltage (I-V) characteristics can be obtained using the simple circuit diagram illustrated in Figure \(\PageIndex{1}\). Figure \(\PageIndex{2}\) shows an I-V test setup using a household flood lamp for the light source. A small fan sits to the right just out of the picture.
Driving the potentiometer to its maximum value will place the cell close to open circuit operation, depending on the potentiometer range, so that the open circuit voltage can be simply extrapolated from the I versus V curve. If desired, the circuit can simply be opened to make the actual measurement once the rest of the data have been recorded. Data in this case were simply recorded by hand and later entered into a spreadsheet so an I-V plot could be generated. A sample plot is shown in Figure \(\PageIndex{3}\). Keep in mind that cell efficiency cannot be determined with this technique unless the light source has been calibrated and color corrected to match terrestrial sunlight. The fact that the experimental device actually generated net power was the result sought. The shape of the curve and the very low voltage are the result of very large resistive losses in the device along with a very “leaky” junction.
One improvement that can be made to the above system is to replace the floodlight with a simple slide projector. The floodlight will typically have a spectrum very heavily weighted in the red and infrared and will be deficient in the shorter wavelengths. Though still not a perfect match to the solar spectrum, the slide projector does at least have more output at the shorter wavelengths; at the same time it will have less IR output compared to the floodlight and the combination should give a somewhat more representative response. A typical set up is shown in Figure \(\PageIndex{4}\).
The mirror in Figure \(\PageIndex{5}\) serves two purposes. First, it turns the beam so the test object can be laid flat a measurement bed and second it serves to collimate and concentrate the beam by focusing it on a smaller area, giving a better approximation of terrestrial solar intensity over a range of intensities such as AM2 (air mass 2) through AM0 (Figure \(\PageIndex{5}\)). An estimate of the intensity can be made using a calibrated silicon solar cell of the sort that can be purchased online from any of several scientific hobby shops such as Edmunds Scientific. While still far from enabling a quantitative measurement of device output, the technique will at least provide indications within a ballpark range of actual cell efficiency.
Figure \(\PageIndex{6}\) shows a measurement made with the test device placed at a distance from the mirror for which the intensity was previously determined to be equivalent to AM1 solar intensity, or 1000 watts per square meter. Since the beam passes through the projector lens and reflects from the second surface of the slightly concave mirror, there is essentially no UV light left in the beam that could be harmful to the naked eye. Still, if this technique is used, it is recommended that observations be made through a piece of ordinary glass such as eyeglasses or even a small glass shield inserted for that purpose. The blue area in the figure represents the largest rectangle that can be drawn under the curve and gives the maximum output power of the cell, which is simply the product of the current and voltage at maximum power.
Figure \(\PageIndex{6}\) is a plot of current density, obtained by dividing the current from the device by its area. It is common to normalize the output is this manner.
If the power density of the incident light (P 0 ) is known in W/cm 2 , the device efficiency can be obtained by dividing the maximum power (as determined from I m and V m ) by the incident power density times the area of the cell (A cell ), \ref{1}.
\[ \eta \ =\ I_{m}V_{m}/P_{0}A_{cell} \label{1} \]
Measurement of the Photoconductivity of Experimental Photovoltaic Materials
In many cases it is beneficial to determine the photoconductivity of a new material prior to cell fabrication. This allows for the rapid screening of materials or synthesis variable of a single material even before issues of cell design and construction are considered.
Figure \(\PageIndex{7}\) shows the circuit diagram of a simple photoconductivity test made with a slightly different set up compared to that shown above. In this case a voltage is placed across the sample after it has been connected to a resistor placed in series with the sample. A simple 9 V battery secured with a battery holder or a small ac to dc power converter can be used to supply the voltage. The sample and resistor sit inside a small box with an open top.
The voltage across (in this case) the 10 ohm resister was measured with a shutter held over the sample (a simple piece of cardboard sitting on the top of the box) and with the shutter removed. The difference in voltage is a direct indication of the change in the photoconductance of the sample and again is a very quick and simple test to see if the material being developed does indeed have a photoresponse of some sort without having to make a full device structure. Adjusting the position of the light source so that the incident light power density at the sample surface is 200 or 500 or 1000 W/m2 enables an approximate numerical estimate of the photocurrent that was generated and again can help guide the development of new materials for solar cell applications. The results from such a measurement are shown in Figure \(\PageIndex{8}\) for a sample of carbon nanotubes (CNT) coated with CdSe by liquid phase deposition (LPD).


17.1A: Anatomy of the Heart
The heart is an organ responsible for pumping blood through the blood vessels using rhythmic contractions of cardiac muscle.
- Describe the anatomy of the heart
Key Points
- The heart is a four-chambered muscular organ containing an involuntary conduction system that initiates rhythmic contractions to pump blood throughout the body.
- The heart has its own blood supply and is controlled by self-regulating nerve bundles called nodes.
- The SA and AV nodes send impulses through the Purkinje fibers that cause muscle contractions to the heart.
- The heart is composed of three layers: the epicardium (outer layer) which prevents excess expansion or movement of the heart, the myocardium (middle layer) which initiates contractions driving the cardiac cycle, and the endocardium (inner layer) that lines the cavities and valves.
- The heart contains two upper chambers called atria and two lower chambers called ventricles. The left and right sides of the heart are separated by the septum.
- Valves prevent the backflow of blood and separate the atria from the ventricle and the ventricle from the pulmonary artery or aorta.
Key Terms
- heart : A fist-sized muscular organ in the chest that pumps blood through the body using involuntary contractions of cardiac muscle.
- ventricle : One of two lower chambers of the heart that receives blood from the atria and pumps it out into pulmonary or systemic circulation, depending on side.
- myocardium : The middle of the three layers forming the wall of the heart, containing cardiac muscle tissue. Innervated by the Purkinje fibers.
The human heart is the pump for the circulatory system, and along with the circulatory system is considered to be an organ of the cardiovascular system. It consists of four chambers and pumps blood through both systemic and pulmonary circulation to enable gas exchange and tissue oxygenation. The heart is located in the thoracic cavity between the lungs and protected by the rib cage.
Structure of the Heart
The heart consists of four chambers separated into two sides. Each side contains an atria which receives blood into the heart and flows it into a ventricle, which pumps the blood out of the heart. The atria and ventricle on each side of the heart are linked together by valves that prevent backflow of blood. The wall that separates the left and right side of the heart is called the septum.
The left heart deals with systemic circulation, while the right heart deals with pulmonary circulation. The left side of the heart receives oxygenated blood from the pulmonary vein and pumps it into the aorta, while the right side of the heart receives deoxygenated blood from the vena cava and pumps it into the pulmonary vein. The pulmonary vein and aorta also have valves connecting them to their respective ventricle.
The heart has its own self-sustaining conduction system that sends nervous impulses to cardiac tissue. The sinoatrial (SA) and atrioventricular (AV) nodes are bundles of nerve fibers that form this conduction system. They are located in the left atrial wall of the heart and send nerve impulses to a large, highly specialized set of nerves called the Purkinje fibers, which in turn send those nerve impulses to the cardiac muscle tissue. These nodes can send impulses to the heart without central nervous system stimulation, but may be influenced by nervous stimulation to alter heart rate. The heart also has its own blood supply, the cardiac arteries that provide tissue oxygenation to the heart as the blood within the heart is not used for oxygenation by the heart.
Cardiac Histology
The heart is enclosed in a double-walled protective membrane called the pericardium, which is a mesothelium tissue of the thoracic cavity. The double membrane of pericardium contains pericardial fluid which nourishes the heart and prevents shock. This composite sac protects the heart, anchors it to surrounding structures, and prevents the heart from overfilling with blood.
The wall of the heart is composed of three layers of different tissues. The outer layer is called the epicardium, or visceral pericardium, since it is also the inner wall of the pericardium. The middle layer of the heart, the myocardium, and contains specialized cardiac muscle tissue responsible for contraction. Cardiac muscle tissue is distinct from skeletal or smooth muscle because it pumps involuntarily based on conduction from the AV and SA nodes. The inner layer is called the endocardium and is in contact with the blood that the heart pumps. It also merges with the inner lining of blood vessels and covers heart valves. Cardiac tissue is permanent tissue that does not heal or regenerate when damaged. As a result, is prone to scarring and enlargement due to mechanical stress and injury.
The Mammalian Heart : The position of valves ensures proper directional flow of blood through the cardiac interior. Note the difference in the thickness of the muscled walls of the atrium and the left and right ventricle.


2.2: Eight Cultural Variables
-
- Last updated
- Save as PDF
In this section, we will address eight cultural variables: human nature, time, action, communication, space, power, individualism/collectivism, and competitiveness/cooperativeness. These major variables offer a simple frame of reference for examining culture and understanding its major characteristics.
Human Nature
Cultures may also hold one of three beliefs pertaining to human nature. The first is the belief that people are basically “good”. In these cultures, people will generally believe that you can put the right person in the right position and empower him/ her to perform. The second belief is that people are basically “bad.” These types of cultures put an emphasis on control and monitoring of people. The final belief is that people are a mixture of “good” and “bad.” In these cultures, people believe personal development is possible, and investment in training and professional development is highly desirable.
Time
A culture’s use of time can communicate differences more profoundly than words. Three orientations to time can be seen across cultures. The first is past-orientation, where high value is placed on continuance of traditions. In these cultures, changes and plans are judged according to their fit with history and customs. The second is present-orientation, which is a short-term orientation aimed at quick results. In these cultures, changes and plans are judged on fast pay-off. Finally, future-orientation includes a willingness to trade short-term gains for long-term results. In these cultures, changes and plans are judged on expected future benefit.
In addition, we also see differences in terms of single-focused and multi-focused views of on how time is used and adhered to. Single-focused, also referred to monochronic, uses of time place high concentration on one task or issue and people are committed to schedules. Multiple-focused, or polychronic, uses of time emphasize on multiple tasks, with a priority on relationship building rather than on meeting deadlines.
Action
Cultures, like individuals, can be oriented towards activity or passivity. The first type is a doing culture, where value is placed on action, accomplishments, achieving personal goals and improving one’s standard of living. These cultures follow external standards of measurement and are motivated by promotions, raises, bonuses and recognition.
Conversely, in being cultures, value is placed on working for the moment, release from stress, and experience rather than accomplishment. These cultures put emphasis on job satisfaction and are not motivated by promises of future rewards.
Context and Formality
There are two variables that exist across cultures- high-context/low-context and formal/informal- that deal more directly with the way we send messages back and forth when we interact. The first variable pertains to how much meaning is conveyed through the context surrounding verbal communication. In low-context cultures, information is given primarily in words and meaning is expressed explicitly. In other words, you are expected to say what you mean and mean what you say. Conversely in high-context cultures, information is transmitted not just in words but also through a variety of contexts, such as voice tone, body language, facial expressions, eye contact, speech patterns, use of silence, past interactions, status, common friends, etc. Members of high-context cultures might not say something directly as they may assume other group members will understand the indirect meaning.
The second pertains to how important it is to formally or informally follow rules for self-presentation and for behavior in organizations and social situations. In formal-communication cultures, importance is given to following protocol and social customs. In informal-communication cultures, people feel more comfortable doing business in a more casual way without lots of rituals and ceremonies.
Space
Cultures also differ in regard to how they perceive and use physical spaces, specifically private and public space. In private-space cultures, personal space is valued, and clear borders and boundaries exist between one space and another. Ownership of space is important. Doors are to be closed, and knocking before entering is expected. In public-space cultures, the boundaries between personal and public spaces are weaker and more flexible. Space is shared rather than owned. Doors are to be kept open, and access is free.
Power Distance
The power variable pertains to how much the less powerful members of a society expect and accept that power is distributed unequally. In high-power distance cultures, also referred to as hierarchy cultures, inequality is accepted. Structures are defined and differences in status are seen as normal. This type of culture satisfies a need for dependence and security. In professional settings, members of high-power distance cultures usually prefer groups where clear roles are assigned and there is a designated leader.
In low-power distance cultures, also referred to as equality cultures, inequality is thought to be unsatisfactory. While it may be unavoidable, it is considered correct to minimize it through legal, political, and economic means. In professional settings, members of low-power distance cultures do not accept that a manager has a given right to greater power and all member can participate in decision making.
Individualism and Collectivism
Individualism and collectivism pertain to the extent to which countries elevate the role of the individual over the group. In individualistic cultures, the bonds between individual members are relatively loose. People are independent and expected to take care of themselves, or at most, the nuclear family. Guilt and fear of loss of self-respect are central to social control. The “I” predominates over the “We.” Individual identity is key, and speaking one’s mind is a sign of honesty. Individualist cultures emphasize individual expression and personal responsibility.
In collectivist cultures, individual interests are placed second to group interests. Groups protect their members in exchange for loyalty and obedience. Social control is based on the fear of losing face and the possibility of shame. Identity is therefore based on the social network to which a person belongs. Harmony, rather than speaking one’s mind, is a key value. Laws and rights differ from group to group, and political power is held by interest groups.
Competitiveness and Cooperativeness
Competitiveness pertains to how much achievement and success dominate over caring for others and quality of life. In competitive cultures, achievement, assertiveness and competition are reinforced. In these cultures, social and gender roles also tend to be distinct. Men are expected to be assertive, tough, and driven by material success. Women, on the other hand, are expected to be modest, nurturing, and concerned mainly with the quality of life. When competitiveness is valued, the culture is predominantly materialistic, with an emphasis on assertiveness and acquisition of money, property, goods, etc. High value is placed on ambition, decisiveness, performance, speed and size.
Cooperativeness characterizes cultures in which social and gender roles overlap. Everyone is expected to demonstrate modesty, nurturing, and a concern for the quality of life. Being sympathetic to one’s fellow human beings is important with an emphasis on relationships. High value is placed on consensus and intuition. In a competitive culture, people live to work. In a cooperative culture, people work to live.


6.2: Sexual Orientation
Sexual orientation describes one’s sexual attraction, and there are multiple labels that one can use in order to describe it. There are an infinite number of identities, and it should be noted that the meanings of these labels often change due to social or cultural shifts. Our sexuality is not fixed, but rather, it is fluid; people may identify with different labels at different points in their life. Some people will figure out what term they identify as, and identify that way their whole life, while for others, the labels they use to express their identity may shift. As new definitions and understanding emerge with regard to sexual orientation, people may then redefine themselves.
 Many are organized around specific identities, such as groups that support lesbian, gay, bisexual, pansexual, queer, asexual, etc. In addition to sexual orientation, monogamy and polyqueer identities are other terms to consider in this conversation, as they relate to the expression of sexual orientation.
There is no question that progress has been made in the United States surrounding sexuality and gender equity; however, local, state, and federal governments continue to legislate policy that disadvantages LGBTQIA+ people, while hate crimes and other forms of discrimination persist. This is why LGBTQIA+ is still considered a protected category.


7.1: Overview and Objectives
-
- Last updated
- Save as PDF
Markets vary in ways that affect competition and pricing. In some markets, competition is fierce. In others, it is light. Some firms have broad discretion in setting prices, while others face take-it-or-leave-it market prices. Pricing and competition depend on the structural characteristics of the market. Economists classify markets as monopolies, oligopolies, monopolistically competitive, or perfectly competitive depending on the characteristics of selling firms in the market. A brief overview of each market structure is as follows:
A monopoly is a market with only one seller. The seller (called a monopolist) will often have quite a bit of control over the price that it charges. Earlier in the course, you examined a firm that was a price taker. A monopolist is not a price taker. As the only seller, the monopolist has an incentive to keep its price above its marginal cost. In so doing, it takes surplus from consumers and turns that surplus into profits for itself. Naturally, sellers like to have monopoly power. The problem for the monopolist is to get as much of the consumer surplus as it can. This problem is complicated in that the monopolist faces the market demand curve. Because of the law of demand, the monopolist must lower its price if it wants to sell more, which entails sacrificing its profit margin. On the other hand, if the monopolist attempts to raise price, and thereby increase its profit margin, it sacrifices volume. There is a balancing act here that you have seen before with demand elasticities in Chapter 3. In this chapter, you will see that the demand elasticity facing the monopolist is relevant and can help you solve the monopolist’s problem.
An oligopoly is a market where there are a few sellers. There must be at least two sellers (a duopoly), and there is no magic number on what constitutes the upper limit of a “few” sellers. Like monopolists, oligopolists do have some discretion in setting their prices. However, the problem is further complicated by the fact that the oligopolist must pay attention to the actions of its competitors. Interactions among competitors are of primary interest in oligopoly models.
Monopolistic competition refers to situations where there are generally many sellers (again, there is no magic number that divides “few sellers” from “many sellers”). A key feature of monopolistic competition is that products are differentiated in the minds of consumers and/or transactions costs give rise to varied perceptions among consumers as to the advantages or disadvantages of patronizing one firm over another. Because products are differentiated, sellers are not price takers. Like the monopolist, firms in monopolistic competition face a downward sloping demand curve. In fact, you will see that the individual firm’s problem in monopolistic competition has the same set-up as the monopolist’s problem.
Perfect competition refers to situations where there are many sellers. Products are homogeneous or differ only in ways that readily apparent to all buyers. The actions of any single seller has no effect on the market price. Firms under perfect competition are price takers. The price taking assumption was introduced earlier in Chapter 2. This assumption is the one key feature of perfect competition. While the market demand curve slopes downward, the firm does not face the market demand curve; it only sees the prevailing market price. It can sell all that it wants (or all that it can produce) at the going market price. If the firm attempts to raise its price, there are no buyers. For this reason, it can be said that the firm faces an elasticity of demand that is negative infinity.
This chapter is about competition and market outcomes under these different market structures. The specific learning objectives for the chapter are as follows:
- Describe and explain characteristics of different market structures on the selling side of the market.
- Use the MR = MC profit maximizing condition to find profit maximizing solutions under different market structures.
- Explain the strategic interactions in duopoly models, distinguish between Cournot and Bertrand models of duopoly, and explain how each is an example of the prisoners’ dilemma
- Explain the folk theorem and the ability of firms to avoid prisoners’ dilemma outcomes in price competition over time.
- Understand the economic welfare implications of imperfectly competitive market structures relative to the perfectly competitive benchmark.


3.3: Sources of Criminal Law - Federal and State Constitutions
-
- Last updated
- Save as PDF
- Alison S. Burke, David Carter, Brian Fedorek, Tiffany Morey, Lore Rutz-Burri, & Shanell Sanchez
- Southern Oregon University via OpenOregon
Where do you look to see if something you want to do violates some criminal law? The answer is “in many places.” Criminal law originates from many sources. Some criminal law is the result of constitutional conventions, so you would need to review federal and state constitutions. Other criminal laws result from the legislative or initiative process, so you will need to review state statutes or congressional acts. Other criminal law results from the work of administrative agencies, so you need to review state and federal administrative rules. Other criminal law, called case law, originates from appellate court opinions written by judges. These court opinions, called “decisions”, are published in both official and unofficial reporters, but thanks to the Internet, they are now easy to find if you know the parties’ names. Much of our criminal law descended from the English common law. This law developed over time, through custom and tradition, and it is a bit more difficult to locate, but it is mentioned in treatises and legal “hornbooks” (like legal encyclopedias) and is often referred to in case decisions.
The federal constitution—The Constitution of the United States
Although the United States Constitution recognizes only three crimes (counterfeiting, piracy, and treason), it nevertheless plays a significant role in the American criminal justice system. Most importantly, the Constitution establishes limits on certain types of legislation or substantive law, and it provides significant procedural constraints on the government when it seeks to prosecute individuals for crimes. The Constitution also establishes federalism (the relationship between the federal government and state governments), requires the separation of powers between the three branches of government (the judicial branch, the legislative branch, and the executive branch), and limits Congress’s authority to pass laws not directly related to either its enumerated powers (listed in the Constitution) or implied powers (inferred because they intertwined with the enumerated powers).
Constitutional Limitations on Criminal Law and Procedure
The drafters of the federal Constitution were so concerned about two historic cases of abuse by English Parliament (ex post facto laws and bills of attainder) that they prohibited Congress from passing these types of laws in the original body of the Constitution. (See, Article I Section 9 of the Constitution.) Ex post facto laws are laws that are retroactively applied, or punishments retroactively increased, or changes in the amount and types of evidence that is required of the government in order to successfully prosecute an individual. B ills of attainders are laws that are directed at named individual or group of individuals and has the effect of declaring them guilty without a trial.
Most of the other limitations are found within the Bill of Rights, the first ten amendments to the U.S. Constitution. The states adopted the Bill of Rights in 1791. The statesmen had opposing viewpoints concerning how strong the national government should be and how strong state governments should be. Even as the original federal constitution was being circulated and ratified, the framers were thinking about the provisions that became known as the Bill of Rights.
Music & Law Exercise
For a novel way to explore this dispute, listen to the soundtrack from Alexander Hamilton, the Broadway Musical composed by Lin-Manuel Miranda.
The First Amendment limits Congress’s ability to pass laws that limit free speech, freedom of religion, freedom of assembly and association. The Second Amendment limits Congress’s ability to outlaw the personal possession of firearms. The Fourth, Fifth, Sixth and Eighth Amendments have provisions that govern criminal procedure during the investigative, pretrial, and trial phases. The Eighth Amendment sets limits on the government’s ability to impose certain types of punishments, impose excessive fines, and set excessive bail. The Due Process Clauses of the Fifth and Fourteenth Amendment require that criminal justice procedures be fundamentally fair. The Fourteenth Amendment’s Equal Protection Clause requires that, at a minimum, there be some rational reason for treating people differently. For example, states can pass laws prohibiting minors from purchasing and consuming alcohol because states have a reasonable interest in protecting the health and welfare of its citizens. These amendments discussed more fully below, added several constraints on Congress. The impact of the Bill of Rights was to place substantial checks on the federal government’s ability to define crimes.
The Incorporation Debate
When drafted and passed, the U.S. Constitution and the Bill of Rights applied only to the federal government. Individual states each had their own guarantees and protections of individuals’ rights found in the state constitutions. (See below.) Since 1868, the Fourteenth Amendment has become an important tool for making states also follow the provisions of the Bill of the Rights. It was drafted to enforce the Civil Rights Act passed in 1866 in the post-Civil War states. Section 1 of the Fourteenth Amendment enjoins the states from depriving any person of life, liberty, or property, without due process of law. It prohibits states from adopting any laws that abridge the privileges and immunities of the citizens of the United States and requires that states not deny any person equal protection under the law. U.S. Const. amend. XIV, § 2.
The practice of making the states follow provisions of the Bill of Rights is known as incorporation. Over decades, the Supreme Court debated whether the Bill of Rights should be incorporated all together, in one-fell-swoop, called total incorporation, or piece-by-piece, called selective incorporation. The case-by-case, bit-by-bit approach won. In a series of decisions, the Supreme Court has held that the Due Process Clause of the Fourteenth Amendment makes enforceable against the states those provisions of the Bill of Rights that are “implicit in the concept of ordered liberty.” [1] For example, in 1925 the Court recognized that the First Amendment protections of free speech and free press apply to states as well as to the federal government. [2] In the 1960s, the Court selectively incorporated many of the procedural guarantees of the Bill of Rights. The Court also used the Fourteenth Amendment to extend substantive guarantees of the Bill of Rights to the states. Most recently, on February 20th, 2019 the Court incorporated the right to be free from excessive fines guarantee found in the Eighth Amendment to the states in Timbs v. Indiana , ___ U.S. ___ (2019).
First Amendment Limitations
Under the First Amendment, Congress cannot create laws that limit individuals’ speech. The Court has recognized symbolic speech (for example, wearing black armbands) and expressive conduct (for example, picketing) as protected under the First Amendment’s guarantee that Congress shall not abridge freedom of speech. The Court struck down a law banning flag burning. Texas v. Johnson, 491 U.S. 397 (1989). The Court upheld a local ordinance prohibiting public indecency when applied to business establishment wishing to provide totally nude dancing. Barnes v. Glen Theater, 501 U.S. 560 (1991). The Court has recognized political speech and commercial speech as protected by the First Amendment as well. See, e.g., Citizens United v. Federal Election Commission , 558 U.S. 310 (2010). The Court has, however, deemed some speech not worthy of protection, and consequently may be limited. According to the Court, non-protected speech includes libel and slander, fighting words, words that present a clear and present danger when spoken, obscenity and profanity. See, Chaplinsky v. New Hampshire , 315 U.S. 568 (1942) “There are certain well-defined and narrowly limited classes of speech, the prevention, and punishment of which have never been thought to raise any constitutional problem. These include the lewd and obscene, the profane, the libelous, and the insulting or fighting words—those which by their very utterance inflict injury or tend to incite an immediate breach of peace.” Similarly, the Court has said anti-hate crime statutes permissibly limit individuals’ speech to the extent they are directed at conduct rather than the content of the speech. See, e.g., Rav v. City of St. Paul , 505 U.S. 377 (1992) and Wisconsin v. Mitchell , 508 U.S. 476 (1993).
The First Amendment limits Congress’s authority to legislate in the realm of religion as well. Congress cannot make laws that either create a religion (these violate the Establishment Clause) or target and interfere with a person’s exercise of their own religion (these violate the Free Exercise Clause). Finally, the First Amendment guarantees that people have the right to freely associate and assemble with others. Thus, Congress cannot make laws that completely limit people’s ability to gather together peaceably. However, the Court has indicated that the government can place reasonable time and manner limitations based on the location in which the gathering is to take place. See, e.g., Cox v. Louisiana, 379 U.S. 536 (1965).
Second Amendment Limitations
Legislatures can place restrictions on weapons and ammunition purchase and possession, but they cannot completely restrict people’s ability to possess guns for the purpose of self-defense. See, District of Columbia v. Heller , 554 U.S. 570 (2008) (an individual’s right to possess a weapon is unconnected with service in the military). According to the Court, the Second Amendments’ protections apply equally to the states. See, McDonald v. Chicago , 561 U.S. 742 (2010).
Fourth Amendment Limitations
The Fourth Amendment limits the government’s ability to engage in searches and seizures. Under the least restrictive interpretation, the Amendment requires that, at a minimum, searches and seizures be reasonable. Under the most restrictive interpretation, the Amendment requires that government officers need a warrant any time they do a search or a seizure. The Court has interpreted the Fourth Amendment in many cases and, the doctrine of stare decisis notwithstanding, search and seizure law is subject to the Court’s constant refinement and revision. One thing is clear, the Court has never embraced the most restrictive interpretation of the Fourth requiring a warrant for every search and seizure conducted.
Fifth Amendment Limitations
The Fifth Amendment protects against self-incrimination (having to disclose information that could ultimately harm you) in that it states that no person “shall be compelled in a criminal case to be a witness against himself.” Defendants have the right to not testify at trial and the right to remain silent during a custodial interrogation. See, Miranda v. Arizona , 384 U.S. 436 (1966). The Fifth Amendment also provides for a grand jury in federal criminal prosecutions, prohibits double jeopardy, demands due process of law, and prohibits taking private property for public use (a civil action). The Court has incorporated the double jeopardy provision through the Fourteenth Amendment, making states also prohibited from subjecting a person to double jeopardy. However, it has not held that states must provide a grand jury review. The Fifth Amendment’s grand jury provision is one of two clauses of the Bill of Rights that has not been incorporated to the states, but most states do use the grand jury at least for some types of cases. The Fifth Amendment also entitled citizens prosecuted by the federal government to the due process of law. This is discussed more fully below as a Fourteenth Amendment right.
Sixth Amendment Limitations
The Sixth Amendment guarantees a criminal defendant: the right to a speedy trial, the right to a public trial, the right to a jury trial, the right to have his or her trial in the district where the crime took place, the right to be told what charges have been filed, the right to confront witnesses at trial, the right to compel witnesses to testify at trial, and the right to assistance of counsel. This Amendment governs the federal court process, but because of the Fourteenth Amendment’s Due Process Clause, these rights also apply to defendants in state criminal cases.
Eighth Amendment Limitations
Legislatures cannot make laws that make the punishment for a crime “cruel or unusual.” This means that punishments cannot be either barbaric (causing needless pain) or disproportionate (i.e., too severe to fit the crime). In addition to the prohibition against cruel and unusual punishment, the Eighth Amendment also prohibits the imposition of excessive bail and excessive fines. The Court has dealt with excessive fines in terms of whether the fine is disproportionate to the crime. See, e.g., Timbs v. Indiana (above) (forfeiting defendant’s $42,000 land rover was excessive compared to the maximum fine he could get for his crime ($10,000.) The prohibition against excessive bail does not mean that courts must set bail in every case, but rather, when courts do set bail, it must not be excessive. Bail is excessive when it is an amount more than necessary to assure the defendant’s reappearance. Stack v. Boyle , 342 U.S. 1 (1951). *
Fourteenth Amendment limitations
The Fourteenth Amendment mandates that states do not deny their citizen’s due process of law. Due process can be summarized as making sure that the government treats people fairly. Part of fairness is giving people fair warning as to what behaviors are permitted and what behaviors are not permitted—putting people on notice of what the law is. Thus, legislators must be very careful when making new laws. They cannot make laws that are so poorly drafted such that a person of ordinary intelligence would not understand the law or that would allow police too much discretion in how they will interpret and apply the law because such a law would be considered void for vagueness.
The Fourteenth Amendment also guarantees equal protection of the law. Generally, legislatures cannot make laws that treat people differently unless the laws are rationally related to a legitimate government interest. When legislatures attempt to pass laws that treat people differently based on sex, then the court reviews the law with heightened scrutiny — the law must be designed to achieve an important government interest and the differential treatment must be based on an actual physiological difference between the sexes and not based on archaic stereotypes. When legislatures attempt to pass laws that treat people differently based upon their race or ethnicity, then they have to have even a more compelling reason to do so, and even then, the courts, employing “strict scrutiny” are likely to declare such laws unconstitutional.
Limitations Found in the “Penumbra” of the Constitution
Sometimes the Constitution doesn’t explicitly state protection or right that the courts have nevertheless found to be inherent or found within the Constitution. Justice Douglas, writing the majority opinion in Griswold v. Connecticut , 381 U.S. 479 (1965), stated
“[The] . . . specific guarantees in the Bill of Rights have penumbras, formed by emanations from those guarantees that help give them life and substance. … Various guarantees create zones of privacy. The right of association contained in the penumbra of the First Amendment is one, as we have seen. The Third Amendment in its prohibition against the quartering of soldiers ‘in any house’ in time of peace without the consent of the owner is another facet of that privacy. The Fourth Amendment explicitly affirms the ‘right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures.’ The Fifth Amendment in its Self-Incrimination Clause enables the citizen to create a zone of privacy which government may not force him to surrender to his detriment. The Ninth Amendment provides: ‘The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people.’
The Fourth and Fifth Amendments were described … as protection against all governmental invasions ‘of the sanctity of a man’s home and the privacies of life.’ We recently referred in Mapp v. Ohio , 367 U. S. 643, 656, to the Fourth Amendment as creating a ‘right to privacy, no less important than any other right carefully and particularly reserved to the people.’ (Footnote omitted).” 381 U.S. at 484-485.
Thus, legislatures cannot make laws that allow the government to invade people’s privacy, even though no specific amendment can be pointed to. The constitutional right to privacy must often be balanced against the state’s compelling interests such as promoting public safety. The courts have found the right to privacy in the context of reproductive freedom (See, e.g., Roe v. Wade , 410 U.S. 113 (1972) (right to abortion), Eisenstadt v. Baird , 405 U.S. 438 (1972) (the right of married persons to possess contraceptives), Griswold v. Connecticut, 381 U.S. 479 (1965) (declaring invalid the ban on contraceptives), Stanley v. Georgia, 394 U.S. 557 (1969) (the right to view and possess adult pornography), and the right of adults to engage in consensual sexual contact), and Lawrence v. Texas, 539 U.S. 558 (2003) (the right of adults to engage in consensual sexual contact).
State Constitutions
States’ constitutions, similar to the federal constitution, set forth the general organization of state government and basic standards governing the use of governmental authority. Although the federal constitution is preeminent because of the Supremacy Clause, state constitutions are still significant. State constitutional rules are supreme as compared to any other rules coming from all other state legal sources (statutes, ordinances, administrative rules) and prevail over such laws in cases of conflict. The federal constitution sets the floor of individual rights, but states are free to provide more individual freedoms and protections that are granted by the federal constitution. State constitutions are defined and interpreted by state courts, and even identical provisions in both the state and federal constitution may be interpreted differently. For example, the state constitution’s guarantee to be free from unreasonable searches and seizures may mean that, under state law, roadblocks established to identify impaired, intoxicated drivers are impermissible, but under the federal constitution, these roadblocks are permitted and are not deemed to be unreasonable seizures.
Comparing Cases Exercise
Compare the U.S. Supreme Court holding in Michigan Department of State Police v. Sitz , 496 U.S. 444 (1990) to the Michigan Supreme Court holding interpreting the same case under Michigan Constitution, 506 N.W.2d 209 (Mich. 1993).
Rule of Law, Constitutions and Judicial Review
One of the key features of the American legal system has been its commitment to the rule of law . Rule of law has been defined as a “belief that an orderly society must be governed by established principles and known standards that are uniformly and fairly applied.” [3] Reichel identified a three-step process by which countries can achieve rule of law. [4] The first step is that a country must identify core, fundamental values. The second step is for the values to be reduced to writing and written somewhere that people can point to them. The final step is to establish a process or mechanism whereby laws or governmental actions are tested to see if they are consistent with the fundamental values. When laws or actions embrace the fundamental values, they are considered valid, and when the laws or actions conflict with the fundamental values, they are invalid.
Applying this three-step process to America’s approach to law one can see that Americans have recognized fundamental values, such as the right to freedom of speech, the right to privacy, and the right to assemble. Second, we have reduced these fundamental values to writing and, for the most part, have compiled them in our constitutions (both federal and state). Third, we have a mechanism, that of judicial review, by which we judge whether our laws and our government actions comply with or violate our fundamental values found within our constitutions. Judicial review is the authority of the courts to determine whether a law (a legislative action) or action (an executive or judicial action) conflicts with the Constitution. Judicial review can be traced to the case of Marbury v. Madison , 5 U.S. 137 (1803), in which Chief Justice John Marshall wrote, “It is emphatically the province and duty of the judicial department to say what the law is. Those who apply the rule to particular cases, must of necessity expound and interpret that rule. If two laws conflict with each other, the courts must decide on the operation of each.”
- Palko v. Connecticut , 302 U.S. 319 (1937). ↵
- Gitlow v. New York , 268 U.S. 652 (1925) ↵
- Feldmeier, J. P., & Schmalleger, F. (2012). Criminal Law and Procedure for Legal Professionals . Prenice Hall. ↵
- Reichel, P. (2018) Comparative Criminal Justice Systems: A Topical Approach. New York, NY: Pearson. ↵


39.11: Breathing - The Work of Breathing
- Explain the roles played by surfactant, flow-resistive and elastic work, and lung resistance and compliance in breathing
The Work of Breathing
The number of breaths per minute is the respiratory rate; under non-exertion conditions, the human respiratory rate averages around 12–15 breaths/minute. The respiratory rate contributes to the alveolar ventilation, or how much air moves into and out of the alveoli, which prevents carbon dioxide buildup in the alveoli. There are two ways to keep the alveolar ventilation constant: increase the respiratory rate while decreasing the tidal volume of air per breath (shallow breathing), or decrease the respiratory rate while increasing the tidal volume per breath. In either case, the ventilation remains the same, but the work done and type of work needed are quite different. Both tidal volume and respiratory rate are closely regulated when oxygen demand increases.
There are two types of work conducted during respiration: flow-resistive and elastic work. Flow-resistive work refers to the work of the alveoli and tissues in the lung, whereas elastic work refers to the work of the intercostal muscles, chest wall, and diaphragm. When the respiratory rate is increased, the flow-resistive work of the airways is increased and the elastic work of the muscles is decreased. When the respiratory rate is decreased, the flow-resistive work is decreased and the elastic work is increased.
Surfactant
The air-tissue/water interface of the alveoli has a high surface tension, which is similar to the surface tension of water at the liquid-air interface of a water droplet that results in the bonding of the water molecules together. Surfactant is a complex mixture of phospholipids and lipoproteins that works to reduce the surface tension that exists between the alveoli tissue and the air found within the alveoli. By lowering the surface tension of the alveolar fluid, it reduces the tendency of alveoli to collapse.
Surfactant works like a detergent to reduce the surface tension, allowing for easier inflation of the airways. When a balloon is first inflated, it takes a large amount of effort to stretch the plastic and start to inflate the balloon. If a little bit of detergent were applied to the interior of the balloon, then the amount of effort or work needed to begin to inflate the balloon would decrease; it would become much easier. This same principle applies to the airways. A small amount of surfactant on the airway tissues reduces the effort or work needed to inflate those airways and is also important for preventing collapse of small alveoli relative to large alveoli. Sometimes, in babies that are born prematurely, there is lack of surfactant production; as a result, they suffer from respiratory distress syndrome and require more effort to inflate the lungs.
Lung Resistance and Compliance
In pulmonary diseases, the rate of gas exchange into and out of the lungs is reduced. Two main causes of decreased gas exchange are compliance (how elastic the lung is) and resistance (how much obstruction exists in the airways). A change in either can dramatically alter breathing and the ability to take in oxygen and release carbon dioxide.
Examples of restrictive diseases are respiratory distress syndrome and pulmonary fibrosis. In both diseases, the airways are less compliant and stiff or fibrotic, resulting in a decrease in compliance because the lung tissue cannot bend and move. In these types of restrictive diseases, the intrapleural pressure is more positive and the airways collapse upon exhalation, which traps air in the lungs. Forced or functional vital capacity (FVC), which is the amount of air that can be forcibly exhaled after taking the deepest breath possible, is much lower than in normal patients; the time it takes to exhale most of the air is greatly prolonged. A patient suffering from these diseases cannot exhale the normal amount of air.
Obstructive diseases and conditions include emphysema, asthma, and pulmonary edema. In emphysema, which mostly arises from smoking tobacco, the walls of the alveoli are destroyed, decreasing the surface area for gas exchange. The overall compliance of the lungs is increased, because as the alveolar walls are damaged, lung elastic recoil decreases due to a loss of elastic fibers; more air is trapped in the lungs at the end of exhalation. Asthma is a disease in which inflammation is triggered by environmental factors, obstructing the airways. The obstruction may be due to edema, smooth muscle spasms in the walls of the bronchioles, increased mucus secretion, damage to the epithelia of the airways, or a combination of these events. Those with asthma or edema experience increased occlusion from increased inflammation of the airways. This tends to block the airways, preventing the proper movement of gases. Those with obstructive diseases have large volumes of air trapped after exhalation. They breathe at a very high lung volume to compensate for the lack of airway recruitment.
Key Points
- Both flow-resistive and elastic work are conducted during the act of respiration; flow-resistive work involves the alveoli and tissues, while elastic work involves the intercostal muscles, chest wall, and diaphragm.
- These types of work function in an inverse relationship; for example, increasing the rate of respiration results in an increase in the flow-resistive work and a decrease in the elastic work.
- Surfactant is a phospholipid and lipoprotein substance produced in the lungs that functions similarly to a detergent: it reduces the surface tension between alveoli tissue and air within the alveoli, thereby reducing the work needed for airway inflation.
- Lung resistance plays a key role in the ability to efficiently exchange gases; if there is obstruction (resistance) within the airways, the result will be decreased gas exchange.
- Lung compliance plays a key role in the ability to efficiently exchange gases; if there is too much of an increase or decrease in elasticity of the lung, the result will be disruption of gas exchange, which will cause obstructive or restrictive diseases.
Key Terms
- surfactant : a lipoprotein in the tissues of the lung that reduces surface tension and permits more efficient gas transport
- tidal volume : the amount of air breathed in or out during normal respiration


9.8.7: Mapping With Three-Point Crosses
-
- Last updated
- Save as PDF
- Ying Liu
- City College of San Francisco
A particularly efficient method of mapping three genes at once is the three-point cross , which allows the order and distance between three potentially linked genes to be determined in a single cross experiment (Figure \(\PageIndex{12}\)). This is particularly useful when mapping a new mutation with an unknown location to two previously mapped loci. The basic strategy is the same as for the dihybrid mapping experiment; pure breeding lines with contrasting genotypes are crossed to produce an individual heterozygous at three loci (a trihybrid), which is then testcrossed to determine the recombination frequency between each pair of genes.
One useful feature of the three-point cross is that the order of the loci relative to each other can usually be determined by a simple visual inspection of the F 2 segregation data. If the genes are linked, there will often be two phenotypic classes that are much more infrequent than any of the others. In these cases, the rare phenotypic classes are usually those that arose from two crossover events, in which the locus in the middle is flanked by a crossover on either side of it. Thus, among the two rarest recombinant phenotypic classes, the one allele that differs from the other two alleles relative to the parental genotypes likely represents the locus that is in the middle of the other two loci. For example, based on the phenotypes of the pure-breeding parents in Figure \(\PageIndex{12}\), the parental genotypes are aBC and AbC (remember the order of the loci is unknown, and it is not necessarily the alphabetical order in which we wrote the genotypes). Because we can deduce from the outcome of the testcross (Table \(\PageIndex{2}\)) that the rarest genotypes were abC and ABc , we can conclude that locus A that is most likely located between the other two loci, since it would require a recombination event between both A and B and between A and C in order to generate these gametes. Thus, the order of loci is BAC (which is equivalent to CAB ).
|
tail phenotype |
fur phenotype |
whisker phenotype |
number of progeny |
gamete from trihybrid |
genotype of F 2 from test cross |
loci A, B |
loci A, C |
loci B, C |
|---|---|---|---|---|---|---|---|---|
|
short |
brown |
long |
5 |
aBC |
aaBbCc |
P |
R |
R |
|
long |
white |
long |
38 |
AbC |
AabbCc |
P |
P |
P |
|
short |
white |
long |
1 |
abC |
aabbCc |
R |
R |
P |
|
long |
brown |
long |
16 |
ABC |
AaBbCc |
R |
P |
R |
|
short |
brown |
short |
42 |
aBc |
aaBbcc |
P |
P |
P |
|
long |
white |
short |
5 |
Abc |
Aabbcc |
P |
R |
R |
|
short |
white |
short |
12 |
abc |
aabbcc |
R |
P |
R |
|
long |
brown |
short |
1 |
ABc |
AaBbcc |
R |
R |
P |
Recombination frequencies may be calculated for each pair of loci in the three-point cross as we did before for one pair of loci in our dihybrid (Figure 7. 8).
\[\begin{alignat}{2} \textrm{loci A,B R.F.} = &\dfrac{1+16+12+1}{120} &&= 25\%\\ \textrm{loci A,C R.F.} = &\dfrac{1+5+1+5}{120} &&= 10\%\\ \textrm{loci B,C R.F.} = &\dfrac{5+16+12+5}{120} &&= 32\%\\ \textrm{(not corrected for double}\\ \textrm{crossovers)}\hspace{40px} \end{alignat}\]
However, note that in the three point cross, the sum of the distances between A-B and A-C (35%) is less than the distance calculated for B-C (32%)(Figure \(\PageIndex{13}\)). this is because of double crossovers between B and C, which were undetected when we considered only pairwise data for B and C. We can easily account for some of these double crossovers, and include them in calculating the map distance between B and C, as follows. We already deduced that the map order must be BAC (or CAB ), based on the genotypes of the two rarest phenotypic classes in Table \(\PageIndex{2}\). However, these double recombinants, ABc and abC, were not included in our calculations of recombination frequency between loci B and C . If we included these double recombinant classes (multiplied by 2, since they each represent two recombination events), the calculation of recombination frequency between B and C is as follows, and the result is now more consistent with the sum of map distances between A-B and A-C.
\[\begin{align} \textrm{loci B,C R.F.} &= \dfrac{5+16+12+5+2(1)+2(1)}{120} = 35\%\\ \textrm{(corrected for double}&\\ \textrm{recombinants)}& \end{align}\]
Thus, the three point cross was useful for:
- determining the order of three loci relative to each other,
- calculating map distances between the loci, and
- detecting some of the double crossover events that would otherwise lead to an underestimation of map distance.
However, it is possible that other, double crossovers events remain undetected, for example double crossovers between loci A,B or between loci A,C. Geneticists have developed a variety of mathematical procedures to try to correct for things like double crossovers during large-scale mapping experiments.
As more and more genes are mapped a better genetic map can be constructed. Then, when a new gene is discovered, it can be mapped relative to other genes of known location to determine its location. All that is needed to map a gene is two alleles, a wild type allele (e.g. A) and a mutant allele (e.g. 'a').


6.1: Pitch (class)
Tonality is highly charged system where scale degrees are endowed with a magnetic or gravitational pull towards other tones. Within the key of C major, B-natural is attracted to the tonic C, other members of the dominant triad are attracted to the tonic triad, and other scale degrees have functions as well. Spelling is extremely important within common-practice tonality. A-flat — as lowered scale degree 6 — leads to G, but G-sharp — as raised scale degree 5 — leads to A. Underlying “scale degree” and “spelling” are two important concepts that will influence our study of post-tonal music.
Octave Equivalence
”Scale degree” implies an equivalence between pitches that are spelled the same but any number of octaves apart. C4 is the same as C3 is the same as C9, and so on. The concept of scale degree, then, has the idea of octave equivalence embedded within it.
Enharmonic Equivalence
Though octave equivalence is central to our understanding of tonal music, enharmonic equivalence often is not. In the key of C major, A-flat and G-sharp are not equivalent, though in isolation they sound the same. Spelling often indicates tendency: A-flat falls to G and G-sharp rises to A.
In post-tonal music, enharmonic equivalence is often assumed — with exceptions of course. Because many composers no longer felt constrained by a tonal center, the same gravitational relationships amongst tones that we find in tonal music aren’t important. A-flat and G-sharp, therefore, can be treated as representations of the same thing.
Pitch
Pitches are discrete tones with individual frequencies. The concept of pitch, then, does not imply octave equivalence. C4 is a pitch, and it is not the same pitch as C3.
Pitch class
Pitch classes are pitches under octave equivalence that are also spelled the same. A4, A3, A2, etc. are all members of the pitch class A.
Pitch Space
Integer notation
When analyzing post-tonal music where assuming octave equivalence and enharmonic equivalence is appropriate, we can use integers to represent pitch class. All C’s and any notes that are enharmonically-equivalent to C (B-sharp, for example) are pitch class 0. All C-sharps’s and any notes that are enharmonically-equivalent to C-sharp (D-flat, for example) are pitch class 1. And so on: C = 0, C-sharp = 1, D = 2, D-sharp = 3, E = 4, F = 5, F-sharp = 6, G = 7, G-sharp = 8, A = 9, B-flat = 10 (T), and B = 1 1 (E).
This type of pitch-class, which assumes octave and enharmonic equivalence is easily visualized on a clock-face diagram, like the one below.
Pitch-Class Space
Disclaimer!
Post-tonal music is extremely various. Composers have individual compositional styles, aesthetic goals, and unique conceptions of pitch. All this is to say that you must approach a composition with flexibility. For example: because it is quasi-tonal, Debussy’s music often benefits from a view that does not assume enharmonic equivalence. But sometimes it does. You must rely on your musical intuitions when analyzing this music, and you should also be willing to approach pitch in these compositions from multiple perspectives until you find one that seems most appropriate.


8.6: Comparaciones
-
- Last updated
- Save as PDF
Objetivos
Compare two things using comparative expressions
Comparaciones de igualdad
¿What grammatical structures do we use to compare two people or things that have equal or similar qualities? In English we use the formula “as” + adjective/adverb + “as.” Here is the formula and some examples in Spanish:
Tan + (adjetivo/adverbio) + como
- Un enfermero es tan importante como un médico. ( A nurse is as important as a doctor. )
- Gina Rodríguez actúa tan bien como America Ferrera. ( Gina Rodriguez acts just as well as America Ferrera. )
Spanish and English follow a similar pattern for adjectives and adverbs but comparing nouns is different. The formula is similar, but now instead of “tan” we use the word “tanto”. “Tanto” is functioning as an adjective and as we learned in Unidad 2, adjectives need to agree in gender and in number with the nouns that they modify. Therefore, the formula is as follows:
| tanto + | (masculine singular noun) + | como |
| tanta + | (feminine singular noun) + | como |
| tantos + | (masculine plural noun) + | como |
| tantas + | (feminine plural noun) + | como |
- El músico tiene tantos instrumentos como el cantante. ( The musician has as many instruments as the singer .)
- El ingeniero tiene tantas máquinas como el mecánico. ( The engineer has as many machines as the mechanic .)
- El trabajador social tiene tanta paciencia como el psicólogo. ( The social worker has as much patience as the psychologist. )
To compare two actions, the structure is simply:
(Verbo) + tanto como
Comparaciones de desigualdad
In English, we typically add “-er” to an adjective and combine it with the word “than” to make unequal comparisons between two items. But if we have an adjective with more than two syllables in English we have to add “more.”
This is similar to Spanish where you always add “más” ( more ) in front of the adjective, the quality that is the point of comparison. However, we do not need to limit ourselves to saying “más”, we can also use “menos”. And instead of “than” we’ll use “que”. ¡Ojo! There’s no accent mark on “que” in comparisons, these are not questions. Therefore, the formula for comparisons of inequality is as follows:
más
+ (
adjective
) +
que
menos
+ (
adjective
) +
que
As always, there are no hard-and-fast grammar rules: there are some irregular adjectives when making comparisons.
joven:
menor
(
younger
)
viejo:
mayor
(
older
)
Ejemplos:
- Eva Longoria es más baja que Jennifer Lopez. ( Eva Longoria is shorter than Jennifer Lopez. )
- Camila Cabello es menor que mi hermano menor. ( Camila Cabello is younger than my younger brother .)
The same formula works for adverbs as well in comparisons of inequality:
más
+ (
adverb
) +
que
menos
+ (
adverb
) +
que
And of course, there are some “irregular” adverbs when making comparisons.
bien:
mejor
(
better
)
mal:
peor
(
worse
)
Ejemplos:
- Yo ahorro dinero más lentamente que mi hermana. ( I save money slower than my sister. )
- Esa peluquera me corta el pelo peor que mi mamá. ( That hairdresser cuts my hair worse than my mother. )
Nouns are compared in the same way:
más
+ (
noun
) +
que
menos
+ (
noun
) +
que
Ejemplos:
- Rita Moreno tiene más premios que Sofía Vergara. ( Rita Moreno has more awards than Sofia Vergara. )
- La enfermera estudia menos años que la médica. ( The nurse studies for fewer years than the doctor .)
For inequality with verbs, be sure to switch the order of the words, as below:
verbo +
más que
verbo +
menos que
Ejemplos:
- Ella camina más que yo. ( She walks more than I do .)
- La secretaria cobra menos que la abogada. ( The secretary charges less than the lawyer. )
When we compare nouns with numbers, using the number as a reference point for the more or less statement, we switch the “que” to “de”.
más de
+ número
menos de
+ número
Ejemplos:
Attributions
- Authored by : SUNY Oneonta with Lumen Learning. License : CC BY: Attribution
- Espau00f1a: Tan singular como plural. Located at : https://www.youtube.com/watch?v=W-O9futG7O4 . License : All Rights Reserved . License Terms : Screen grab / Fair Use