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The Mathematics of Persuasive Communication: Part II

By Philip Yaffe |


Author's note
Part 1 of this three-part series striped away the superficialities of persuasive communication to reveal the bedrock underneath, i.e. what persuasive communication is truly all about. Part 2 now shows how simple mathematical concepts can be used to significantly improve both clarity and conciseness.

What do we mean by "good writing"?

We are now ready to return to the notion of how mathematics applies to good writing, and by extension to good speaking.

When someone reads an expository text or listens to an expository speech, they are likely to judge it as good or not good. You probably do this yourself. But what do you actually mean when you say a text or a speech is "good".

After some struggling, most people will usually settle on two criteria: clear and concise.

Mathematics depends on unambiguous definitions; if you are not clear about the problem, you are unlikely to find the solution. So we are going to examine these criteria in some detail in order to establish objective definitions - and even quasi-mathematical formulae - for testing whether a text or a presentation truly is "good".

A. Clarity

How do you know that a text is clear?

If this sounds like a silly question, try to answer it. You will probably do something like this:

Question: What makes this text clear?
Answer: It is easy to understand.
Question: What makes it easy to understand?
Answer: It is simple.
Question: What do you mean by simple?
Answer: It is clear.

You in fact end up going around in a circle. The text is clear because it is easy to understand . . . because it is simple . . . because it is clear.

"Clear", "easy to understand", and "simple" are synonyms. Whilst synonyms may have nuances, they do not have content, so you are still left to your own subjective appreciation. But what you think is clear may not be clear to someone else.

This is why we give "clear" an objective definition, almost like a mathematical formula. To achieve clarity -i.e. virtually everyone will agree that it is clear - you must do three things.

  1. Emphasize what is of key importance.
  2. De-emphasize what is of secondary importance.
  3. Eliminate what is of no importance.

In short: CL = EDE

Like all mathematical formulae, this one works only if you know how to apply it, which requires judgment.

In this case, you must first decide what is of key importance, i.e. what are the key ideas you want your readers to take away from your text? This is not always easy to do. It is far simpler to say that everything is of key importance, so you put in everything you have. But there is a dictum that warns: If everything is important, then nothing is. In other words, unless you first do the work of defining what you really want your readers to know, they won't do it for you. They will get lost in your text and either give up or come out the other end not knowing what it is they have read.

What about the second element of the formula, de-emphasize what is of secondary importance?

That sounds easy enough. You don't want key information and ideas to get lost in details. If you clearly emphasize what is of key importance - via headlines, Italics, underlining, or simply how you organise the information - then whatever is left over is automatically de-emphasized.

Now the only thing left to do is eliminate what is of no importance.

But how do you distinguish between what is of secondary importance and what is of no importance? Once again, this requires judgment, which is helped by the following very important test.

Secondary importance is anything that supports and/or elaborates one or more of the key ideas. If you judge that a piece of information in fact does support or elaborate one or more key ideas, then you keep it. If not, you eliminate it.

B. Conciseness

How do you know that a text is concise?

If this once again sounds like a silly question, let's try to answer it.

Question: What makes this text concise?
Answer: It is short.
Question: What do you mean by short?
Answer: It doesn't have too many words.
Question: How do you know it doesn't have too many words?
Answer: Because it is concise.

So once again we end up going around in a circle. The text is concise because it is short . . . because it doesn't have too many words . . . because it is concise.

Once again, we have almost a mathematical formula to solve the problem. To achieve conciseness, your text should meet two criteria. It must be as:

  1. Long as necessary
  2. Short as possible

In symbols: CO = LS

If you have fulfilled the criteria of "clarity" correctly, you already understand "as long as necessary". It means covering all the ideas of key importance you have identified, and all the ideas of secondary importance needed to support and/or elaborate these key ideas.

Note that nothing is said here about the number of words, because it is irrelevant. If it takes 500 words to be "as long as necessary", then 500 words must be used. If it takes 1500 words, then this is all right too. The important point is that everything that should be in the text is fully there.

Then what is meant by "as short as possible"?

Once again, this has nothing do to with the number of words. It is useless to say at the beginning, "I must not write more than 300 words on this subject", because 500 words may be the minimum necessary.

"As short as possible" means staying as close as you can to the minimum. But not because people prefer short texts; in the abstract the terms "long" and "short" have no meaning. The important point is that all words beyond the minimum tend to reduce clarity.

We should not be rigid about this. If being "as long as necessary" can be done in 500 words and you use 520, this is probably a question of individual style. It does no harm. However, if you use 650 words, it is almost certain that the text will not be completely clear--and that the reader will become confused, bored or lost.

In sum, conciseness means saying what needs to be said in the minimum amount of words. Conciseness:

  • Aids clarity by ensuring best structuring of information.
  • Holds reader interest by providing maximum information in minimum time.


Editor's note

This series of three articles is based on Philip Yaffe's recent book In the "I" of the Storm: the Simple Secrets of Writing & Speaking (Almost) like a Professional. For a full description of the book, follow the links to:

Go to The Mathematics of Persuasive Communication:

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