Paragraphs Purpose and structure

Paragraphs have multiple uses: BUT ALWAYS... each paragraph makes one coherent point To give evidence for some point To develop an example To shift an argument's direction Etc.

Finance has rich time series

They show universal features

Finance has rich time series They show universal features Mandelbrot deserves credit for starting all this

Finance has rich time series They show universal features Mandelbrot deserves credit for starting all this His most important point is that we should learn from the data

Paragraphs have multiple uses: BUT ALWAYS... each paragraph makes one coherent point To give evidence for some point To develop an example To shift an argument's direction Etc.

Watson & Crick First paragraph:

Watson & Crick Second paragraph:

Watson & Crick Third paragraph:

Watson & Crick Fourth paragraph:

Watson & Crick Fifth paragraph:

Overall structure: 1. We propose a structure for DNA 2. A structure proposed by X doesn't work because A structure proposed by Y also fails 4. We propose a structure with helical chains etc. (gives details)‏ 5. This structure is open...

This is true of all writing: newspapers ‏ magazines and books blogs etc. even much spoken language

Thirty-plus years ago, when I was a graduate student in economics, only the least ambitious of my classmates sought careers in the financial world. Even then, investment banks paid more than teaching or public service — but not that much more, and anyway, everyone knew that banking was, well, boring. First paragraph Making Banking Boring Paul Krugman, New York Times

In the years that followed, of course, banking became anything but boring. Wheeling and dealing flourished, and pay scales in finance shot up, drawing in many of the nation’s best and brightest young people (O.K., I’m not so sure about the “best” part). And we were assured that our supersized financial sector was the key to prosperity. Second Paragraph A small portion of each paragraph makes its key point. The rest gives detail.

Third Paragraph Instead, however, finance turned into the monster that ate the world economy. Even one sentence can be an effective paragraph

Each paragraph makes one coherent point Next question: How do paragraphs achieve such focus?

Second exercise

1. Bio-mathematics has been a runaway success 2. An exception is sympatric speciation 3. At first glance, it seems simple to understand In sexual populations, the problem is... Good summary sentences make the logical skeleton of the argument OBVIOUS... they act as labels for the paragraphs...

A simple technique: topic sentences One sentence of a paragraph should state the main point; this is called the “topic sentence” and is usually the first sentence. Other sentences in the paragraph support or explore the point made by this topic sentence.

Another example.....

1. Introduction Recent investigations have uncovered large, consistent deviations from the predictions of the textbook presentation of Homo economicus. One problem appears to lie in economists' assumption that individuals are entirely self-interested; in addition to their own material payoffs, many experimental subjects appear to care about fairness and reciprocity... First paragraph

..... Fundamental questions remain unanswered. Are the deviations from the canonical model evidence of universal patterns of behaviour, or do the individuals' economic and social environments shape behaviour?... Second paragraph

..... Existing research cannot answer such questions because virtually all subjects have been university students.... To address the above questions, we and our collaborators undertook a large cross-cultural study... in twelve countries on four continents... Third paragraph

..... We can summarize our results as follows. First, the canonical model is not supported in any society studied. Second, there is considerably more behavioural variability across groups than had been found in previous cross-cultural research and... Fourth paragraph

Recent experiments suggest that people aren't as greedy as economists have always assumed (details about why) But big questions remain unanswered (...such as..) Here we do some experiments to answer these questions (+ details on the experiments) We can summarize our results as follows. (gives details) All together...

A simple technique: topic sentences One sentence of a paragraph should state the main point; this is called the “topic sentence” and is usually the first sentence. Other sentences in the paragraph support or explore the point made by this topic sentence.

Exercises on topic sentences

Making contact with the real world

Cells can switch identity several times during development. How do they decide to switch? There is much debate about the extent to which identity switching is a cell-autonomous decision as opposed to being driven by environmental signals. In a paper published on... First paragraph Here these two sentences act like one: “Cells often switch during development, but the mechanisms that control switching remain unknown." Then the next sentence backs this up and adds detail...

The authors grew B. subtilis in a microfluidic device consisting of several channels, each designed to support bacterial growth... Second paragraph Here there is NO topic sentence! It could have been something like "the study rests on a clever experimental design," but this isn't really necessary... the authors do without...

Norman and colleagues’ detailed and precise characterization of hundreds of switching events reveals a critical difference in the transition from the motile to the sessile state and the switch in the other direction. The shift from the motile to the sessile state seems to be... Third paragraph A clear topic sentence, then supporting detail... Later paragraphs all have this structure

Linking sentences together Sentences should present new information AND should tie it to what has gone before Why? Because readers begin reading a new sentence with expectations of what might come next. Linking new information to old gives a feeling of order and comfort.

On summer holiday, we went to Lake Geneva. Poor:

On summer holiday, we went to Lake Geneva. We spent the day with 3 inches of water at our feet. Poor:

On summer holiday, we went to Lake Geneva. We spent the day with 3 inches of water at our feet. We were happy to come home. Poor:

On summer holiday, we went to Lake Geneva. We spent the day with 3 inches of water at our feet. We were happy to come home. We took a boat trip, and with cold and soggy feet enjoyed the day as best we could. Poor:

On summer holiday, we went to Lake Geneva. We spent the day with 3 inches of water at our feet. We were happy to come home. We took a boat trip, and with cold and soggy feet enjoyed the day as best we could. But we don't know why the boat leaked. Poor:

On summer holiday, we went to Lake Geneva.. Better:

On summer holiday, we went to Lake Geneva. We took a boat trip. Better:

On summer holiday, we went to Lake Geneva. We took a boat trip. During the trip, the boat began leaking. Better:

On summer holiday, we went to Lake Geneva. We took a boat trip. During the trip, the boat began leaking. What caused the leak, we do not know, but soon there were 3 inches of water at our feet. Better:

On summer holiday, we went to Lake Geneva. We took a boat trip. During the trip, the boat began leaking. What caused the leak, we do not know, but soon there were 3 inches of water at our feet. With cold and soggy feet we enjoyed the day as best we could. Better:

On summer holiday, we went to Lake Geneva. We took a boat trip. During the trip, the boat began leaking. What caused the leak, we do not know, but soon there were 3 inches of water at our feet. With cold and soggy feet we enjoyed the day as best we could. At the day's end, we were happy to come home. Better:

On summer holiday, we went to Lake Geneva. We took a boat trip. During the trip, the boat began leaking. What caused the leak, we do not know, but soon there were 3 inches of water at our feet. With cold and soggy feet we enjoyed the day as best we could. At the day's end, we were happy to come home. Better:

Before 1930, banking was an exciting industry featuring a number of larger-than-life figures, who built giant financial empires (some of which later turned out to have been based on fraud). This high-flying finance sector presided over a rapid increase in debt. Household debt as a percentage of G.D.P. almost doubled between World War I and Linking sentences together Krugman again:

Before 1930, banking was an exciting industry featuring a number of larger-than-life figures, who built giant financial empires (some of which later turned out to have been based on fraud). This high-flying finance sector presided over a rapid increase in debt. Household debt as a percentage of G.D.P. almost doubled between World War I and Linking sentences together Krugman again: This topic sentence establishes expectations

Before 1930, banking was an exciting industry featuring a number of larger-than-life figures, who built giant financial empires (some of which later turned out to have been based on fraud). This high-flying finance sector presided over a rapid increase in debt. Household debt as a percentage of G.D.P. almost doubled between World War I and Linking sentences together Krugman again: These phrases introduce no new information, but serve as clear ties linking back to the previous sentence.

Another example (from Nature)‏ The malaria mosquito, Anopheles gambiae, is an accessory to the deaths of about one million humans every year. To acquire nutrients for their offspring, female mosquitoes feed on human blood. While sucking their victim’s blood using contaminated, needle-like mouth parts, these mosquitoes unwittingly transmit the malaria-causing parasite that threatens half of the world’s population. Globally, the number of people who get malaria each year is greater than the population of the United States. It is unclear how the perpetrators of these crimes find their victims, but it is known that human-derived odorants have a key role — for example, female mosquitoes find the odour of patients with malaria particularly attractive. Understanding odorant reception by the malaria mosquito is therefore of paramount importance, because it could lead to the development of olfactory-based strategies for controlling the insects, and so to a reduction in the number of mosquito bites....

Linking sentences together The malaria mosquito, Anopheles gambiae, is an accessory to the deaths of about one million humans every year. To acquire nutrients for their offspring, female mosquitoes The first part of the sentence refers only to old, known information

Linking sentences together The malaria mosquito, Anopheles gambiae, is an accessory to the deaths of about one million humans every year. To acquire nutrients for their offspring, female mosquitoes feed on human blood. Remainder of this sentence then links new information to the old Exercise on remainder

Linking sentences together The malaria mosquito, Anopheles gambiae, is an accessory to the deaths of about one million humans every year. To acquire nutrients for their offspring, female mosquitoes feed on human blood. While sucking their victim’s blood

Linking sentences together The malaria mosquito, Anopheles gambiae, is an accessory to the deaths of about one million humans every year. To acquire nutrients for their offspring, female mosquitoes feed on human blood. While sucking their victim’s blood using contaminated, needle-like mouth parts,

Linking sentences together The malaria mosquito, Anopheles gambiae, is an accessory to the deaths of about one million humans every year. To acquire nutrients for their offspring, female mosquitoes feed on human blood. While sucking their victim’s blood using contaminated, needle-like mouth parts, these mosquitoes

Linking sentences together The malaria mosquito, Anopheles gambiae, is an accessory to the deaths of about one million humans every year. To acquire nutrients for their offspring, female mosquitoes feed on human blood. While sucking their victim’s blood using contaminated, needle-like mouth parts, these mosquitoes unwittingly transmit the malaria-causing parasite that threatens half of the world’s population.

Linking sentences together The malaria mosquito, Anopheles gambiae, is an accessory to the deaths of about one million humans every year. To acquire nutrients for their offspring, female mosquitoes feed on human blood. While sucking their victim’s blood using contaminated, needle-like mouth parts, these mosquitoes unwittingly transmit the malaria-causing parasite that threatens half of the world’s population. Globally, the number of people who get malaria

Linking sentences together The malaria mosquito, Anopheles gambiae, is an accessory to the deaths of about one million humans every year. To acquire nutrients for their offspring, female mosquitoes feed on human blood. While sucking their victim’s blood using contaminated, needle-like mouth parts, these mosquitoes unwittingly transmit the malaria-causing parasite that threatens half of the world’s population. Globally, the number of people who get malaria each year is greater than the population of the United States.

Linking sentences together The malaria mosquito, Anopheles gambiae, is an accessory to the deaths of about one million humans every year. To acquire nutrients for their offspring, female mosquitoes feed on human blood. While sucking their victim’s blood using contaminated, needle-like mouth parts, these mosquitoes unwittingly transmit the malaria-causing parasite that threatens half of the world’s population. Globally, the number of people who get malaria each year is greater than the population of the United States. It is unclear how the perpetrators of these crimes find their victims,

Linking sentences together The malaria mosquito, Anopheles gambiae, is an accessory to the deaths of about one million humans every year. To acquire nutrients for their offspring, female mosquitoes feed on human blood. While sucking their victim’s blood using contaminated, needle-like mouth parts, these mosquitoes unwittingly transmit the malaria-causing parasite that threatens half of the world’s population. Globally, the number of people who get malaria each year is greater than the population of the United States. It is unclear how the perpetrators of these crimes find their victims, but it is known that human-derived odorants have a key role —

Linking sentences together The malaria mosquito, Anopheles gambiae, is an accessory to the deaths of about one million humans every year. To acquire nutrients for their offspring, female mosquitoes feed on human blood. While sucking their victim’s blood using contaminated, needle-like mouth parts, these mosquitoes unwittingly transmit the malaria-causing parasite that threatens half of the world’s population. Globally, the number of people who get malaria each year is greater than the population of the United States. It is unclear how the perpetrators of these crimes find their victims, but it is known that human-derived odorants have a key role — for example, female mosquitoes find the odour of patients with malaria particularly attractive.

Linking sentences together The malaria mosquito, Anopheles gambiae, is an accessory to the deaths of about one million humans every year. To acquire nutrients for their offspring, female mosquitoes feed on human blood. While sucking their victim’s blood using contaminated, needle-like mouth parts, these mosquitoes unwittingly transmit the malaria-causing parasite that threatens half of the world’s population. Globally, the number of people who get malaria each year is greater than the population of the United States. It is unclear how the perpetrators of these crimes find their victims, but it is known that human-derived odorants have a key role — for example, female mosquitoes find the odour of patients with malaria particularly attractive. Understanding odorant reception by the malaria mosquito is therefore of paramount importance,

Old information links sentences together Linking sentences together The malaria mosquito, Anopheles gambiae, is an accessory to the deaths of about one million humans every year. To acquire nutrients for their offspring, female mosquitoes feed on human blood. While sucking their victim’s blood using contaminated, needle-like mouth parts, these mosquitoes unwittingly transmit the malaria-causing parasite that threatens half of the world’s population. Globally, the number of people who get malaria each year is greater than the population of the United States. It is unclear how the perpetrators of these crimes find their victims, but it is known that human-derived odorants have a key role — for example, female mosquitoes find the odour of patients with malaria particularly attractive. Understanding odorant reception by the malaria mosquito is therefore of paramount importance, because it could lead to the development of olfactory-based strategies for controlling the insects, and so to a reduction in the number of mosquito bites....

We read with expectations Reading new material with no clear link to anything yet mentioned creates tension and confusion Linking sentences together

Generally aim to begin sentences with “old information” linking to what has gone before New information should tend to arrive later, with the sentence acting to link it to the old information To achieve good linking:

Finishing off: paragraph structure You need: Topic sentences One idea per paragraph Strong linking between sentences

A problematic paragraph Large earthquakes along a given fault segment do not occur at random intervals because it takes time to accumulate the strain energy for the rupture. The rates at which tectonic plates move and accumulate strain at their boundaries are approximately uniform. Therefore, in first approximation, one may expect that large ruptures of the same fault segment will occur at approximately constant time intervals. If subsequent main shocks have different amounts of slip across the fault, then the recurrence time may vary, and the basic idea of periodic mainshocks must be modified. For great plate boundary ruptures the length and slip often vary by a factor of 2. Along the southern segment of the San Andreas fault the recurrence interval is 145 years with variations of several decades. The smaller the standard deviation of the average recurrence interval, the more specific could be the long term prediction of a future mainshock.

“This is the kind of passage that in subtle ways can make readers feel badly about themselves. The individual sentences give the impression of being intelligently fashioned: They are not especially long or convoluted... and they are free of grammatical and dictional errors. On first reading, however, many of us arrive at the paragraph's end without a clear sense of where we have been or where we are going. When that happens, we tend to berate ourselves for not having paid close enough attention.”

Disentangling confused prose is a messy job Such prose usually results from sloppy thinking at the time of writing, resulting in logical gaps in the written argument There's no solution but paying careful attention to the logic of your argument -- “if it doesn't hurt, you're probably not trying hard enough.” Writing Logically