Tag Archives: scientific exposition

exposition, language, math

The revolution in technical exposition II

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In the last post I talked about the bad side of much technical exposition and the better aspects of popular science writing (exemplified by Priestley).   These two streams have continued to the present. Stuffy, formal, impersonal technical exposition has continued to be the norm for works intended for academic credit.  Math and science expositions written for the public have been much looser and some have been remarkably good.  I described two of them in a previous post.

The revolution mentioned in the title of this post is that some aspects of the style of popular science writing have begun infiltrating writing in academic journals. Consider these sentences from Jody Azzouni's essay in [1]:

It's widely observed that, unlike other cases of conformity, and where social practices really are the source of that conformity, one finds in mathematical practice nothing like the variability found cuisine, clothing, or metaphysical doctrine. (p. 202).

Add two numbers fifteen times, and you do something different each time — you do fifteen different things that (if you don't blunder) are the same in the respect needed; the sum you write down at the end of each process is the same (right) one. (p. 210).

Written material gives the reader many fewer clues as to the author's meaning in comparison with a lecture.  Azzouni increases the comprehensibility of his message by doing things that would have been unheard of in a scholarly book on the philosophy of math thirty years ago.

  • He uses italics to emphasis the thrust of his message.
  • He uses abbreviations such as "it's".
  • He says "you" instead of "one":  He does not say "If one adds two numbers fifteen times, one does something different each time…"  This phrase would probably have been nominalized to incomprehensibility thirty years ago: "A computation with fifteen repetitions of the process of numerical addition of a fixed pair of integers involves fifteen distinct actions."

In abstractmath.org I deliberately adopt a style that is similar to Azzouni's, including "you" instead of "one", "it's" instead of "it is" (and the like), and many other tricks, including bulleted prose, setting off proclamations in purple prose, and so on. (See [2].)  One difference is that I too use italics a lot (actually bold italics), but with a difference of purpose:  I use it for phrases that I think a student should mark with a highlighter.

My discussion of modus ponens from the section Conditional Assertions illustrates some of these ideas:

Method of deduction: Modus ponens

The truth table for conditional assertions may be summed up by saying: The conditional assertion “If P, then Q” is true unless P is true and Q is false.

This fits with the major use of conditional assertions in reasoning:

Method of deduction

  • If you know that a conditional assertion  is true and
  • you know that its hypothesis is true,
  • then you know its conclusion is true.

In symbols:

When “If P then Q” and P are both true,

______________________________________

then Q must be true as well.

This notation means that if the statements above the line are true, the statement below the line has to be true too.

This fact is called modus ponens and is the most used  method of deduction of all.

Remark

That modus ponens is valid is a consequence of the truth table:

  • If  P is true that means that one of the first two lines of the  truth table holds.
  • If the assertion “If P then Q” is true, then one of lines 1, 3 or 4 must hold.

The only possibility, then, is  that Q is true.

Remark

Modus ponens is not a method of proving conditional assertions. It is a method of using a conditional assertion in the proof of another assertion.  Methods for proving conditional assertions are found in the chapter on forms of proof.

This section also includes a sidebar (common in magazines) that says:  "The first statement of modus ponens does not require pattern recognition.  The second one (in purple) does require it."

Informality, bulleted lists, italics for emphasis, highlighted text, sidebars, and so on all belong in academic prose, not just in popular articles and high school textbooks.  There are plenty of other features about popular science articles that could be used in academic prose, too, and I will talk about them in later posts.

Note: Some features of popular science should not be used in academic prose, of course, such as renaming technical concepts as I discussed in the post of that name.  An example is referring to simple groups as "atoms of symmetry", since many laymen would not be able to divorce their understanding of the words "simple" and "group" from the everyday meanings:  "HOW can you say the Monster Group is SIMPLE??? You must be a GENIUS!"

References

[1] 18 Unconventional Essays on the Nature of Mathematics, by Reuben Hersh. Springer, 2005.  ISBN 978-0387257174

[2] Attitude, in abstractmath.org.

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exposition

Joseph Priestley

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The Invention of Air, by Steven Johnson.  Riverhead Books, 2008.  978-1-59448-852-8.   This is a biography of Joseph Priestly:

  • He discovered that, although animals put in a closed box with no source of air died pretty quickly, plants put in a similar box did not die.  This led him to conceive a primitive form of the idea of the cycle of nature. (Note 1.)
  • He discovered oxygen (apparently not really based on the previous discovery above), but did not understand what he discovered.  He continued to believe in phlogiston to the end of his life.
  • He invented soda water because he lived near a brewery.
  • He cofounded the first Unitarian Church in England and wrote extensively about the corruptions of Christianity such as the Trinity.
  • He supported America’s independence and the French Revolution.  Concerning the latter, he exhibited considerable naiveté.
  • Because of the last two things listed, a mob burned down his house and laboratory, his church and the house of one of his supporters.  In consequence he moved to America.
  • He engaged in much correspondence with Thomas Jefferson with the result that Jefferson was relieved to find that he could still consider himself a Christian, of the Unitarian variety, of course.  (Nowadays Unitarians don’t consider themselves Christian but then they did.)
  • He wrote a bunch of sharp attacks on John Adams, in particular accusing him of dastardly behavior in signing the Alien and Sedition Act, and of opposing further advances of science.  Guess which attack made Adams the most furious.  (The latter.)
  • Thomas Jefferson and John Adams were bitter enemies for many years, but engaged in an extensive and reasonably polite correspondence during the last years of their lives.  Much of the correspondence involved Adams defending himself against Priestley’s criticisms.

They never taught me all that in school!  By the way, I probably got all sorts of things wrong in the summary above.  So you’d better read the book from cover to cover.

Scientists should read this book, too; it gives them a new sense of how important they were regarded by the politicians in England, America and France, in comparison to these days.  Politicians should read this book as well, but they won’t.

Popular science

The author claims (pp. 34-35) that Priestley’s work (Note 2) explaining the wonderful new discoveries about electricity constitute the first popular science book (at least of the narrative kind.)

Note

1.  See Priestley’s Experiments and Observations on Different Kinds of Air, Volume III, Book 9, Part 1. (1790).

2.  Joseph Priestley, The History and Present State of Electricity, with Original Experiments (1775).

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