The Mathematics of Persuasive
At first glance, mathematics and persuasive communication – writing,
and particularly public speaking - would seem to have little in
common. After all, mathematics is an objective science, whilst
speaking involves voice quality, inflection, eye contact,
personality, body language, and other subjective components.
However, under the surface they are very similar. Above anything
else, the success of an oral presentation depends on the precision
of its structure. Mathematics is all about precision. It is
therefore not so odd to think that applying some of the concepts of
mathematics to oral presentations could make them substantially more
As they say in the film industry, three key factors go into making a
successful movie: the script, the script, and the script. Likewise,
three key factors go into making a successful speech: the structure,
the structure, and the structure.
Not convinced? Then let's start with something less radical. I
think we can all agree that good speaking is related to good
writing. If you can write a good text, then you are well on your
way to preparing a good oral presentation. Therefore, if you
improve your writing, you will also improve your speaking. To
simplify matters, from now on we will talk mainly about good
writing, because in most cases the same ideas apply directly to good
Know what you are doing: Many commercial companies do not
live up to their potential - and sometimes even go bankrupt -
because they fail to correctly define the business they are in.
Perfume companies, for example, do not sell fragrant liquids, but
rather love, romance, seductiveness, self-esteem, etc. Bio-food
companies do not sell organic produce, but rather honesty, purity,
nature, etc. Automobile manufacturers do not sell transportation,
but rather freedom, adventure, spontaneity, prestige, etc. The fact
is, each industry, even each individual product, may have to
determine what it is truly all about - and there are thousands of
Writers are lucky. There are numerous variations to what we do, but
there are really only two fundamental types of writing. It is
important to recognize this, because not only are they quite
different, in some respects they are exactly opposite. So unless we
clearly recognize which type of writing we are doing - and how it
differs from the other one - we will almost certainly commit serious
errors. What are the two types? And how do they differ?
Texts such as short stories, novels, poems, radio plays,
stage plays, television scripts, film scripts, etc.
The fundamental purpose of creative writing is to
amuse and entertain.
Texts such as memos, reports, proposals, training
manuals, newsletters, research papers, etc.
The fundamental purpose of expository writing is to
instruct and inform.
Essential attitude towards expository writing: Because the
objectives of creative and expository writing are so different,
before striking a key you must adopt the appropriate attitude
towards the type of writing you are doing.
Creative writing attitude: Everyone wants to
read want what you are going to write. After all, who doesn't
want to be amused and entertained?
Expository writing attitude: No one wants to read what
you are going to write. Most people don't like to be instructed and
informed. They probably would much prefer to be doing something
else. The importance of recognizing and adopting the "expository
writing attitude" cannot be over-stated, because it can dramatically
change the very nature of what you are writing. Here are a couple
A. Corporate image brochure: I was once commissioned to
write a corporate image brochure. Two things are certain about
these expensive, glossy booklets:
from the attitude that no one would want to read what I was about to
write, I created a brochure that people not only read. They
actually called the company to request additional copies to give to
friends, clients, and professional colleagues!
B. Stagnating product: On another occasion, I was
commissioned to develop an advertising campaign to revitalize a
product with stagnating sales. Applying the expository writing
attitude, I discovered that three of the product's key benefits were
not being properly exploited. Why? The manufacturer felt that
everything about their product was important, so for
years they had been systematically burying these three key benefits
under an avalanche of other information of less interest to
potential buyers. The new campaign sharply focused on the key
benefits; virtually all other information was moved to the
background or eliminated. As a result, sales shot up some 40% in
the first year.
With some nuances, this self-same expository writing attitude can be
- and should be - applied to speaking, as well.
Essential approach to expository writing: Because creative
writing and expository writing have essentially different objectives
and attitudes, they require essentially different approaches.
Creative writing approach: Play with language to generate
In other words, use your mastery of the language to amuse and
Expository writing approach: Organize information to generate
Clever use of language will never make dull information interesting;
however, you can organize the information to make it interesting.
Forget about literary pyrotechnics. Concentrate on content. We are
now going to leave creative writing, because most of what we write,
and say, is expository.
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 virtually everyone will
agree that it is clear – you must do three things.
Emphasize what is of key importance.
De-emphasize what is of secondary importance.
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. 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-emphasizes 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 organize 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
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:
Short as possible
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:
Density: Density is a less familiar concept than clarity and
conciseness, but is equally important. In mathematical form,
density consists of:
words: D = PL
Importance of precise information: Suppose you enter a room
where there are two other people and say, "It's very hot today.”
One of those people comes from Helsinki; in his mind, he interprets
"hot" to mean about 23°C. The other one comes from Khartoum; to him
"hot" means 45°C.
You are off to a rather bad start, because each one has a different
idea of what you want to say. But suppose you say, "It's very hot
today; the temperature is 28° C.” Now there is no room for
confusion. They both know quite clearly that it is 28° C outside
and that you consider this to be very hot. Using as much precise
information as possible in a text gives the writer two significant
Mind Control: Let's not be embarrassed by the
term "mind control,” because this is precisely what the good
expository writer wants to achieve. He needs for the reader's mind
to go only where he directs it and nowhere else. Because they can
be interpreted in unknown ways, ambiguous terms (so-called "weasel
words") such as "hot,” "cold", "big", "small", "good", "bad", etc.,
allow the reader's mind to escape from the writer's control. An
occasional lapse is not critical; however, too many weasel words in
a text will inevitably lead to reader confusion, boredom, and
Reader Confidence: Using precise information
generates confidence, because it tells the reader that the writer
really knows what he is talking about. Reader confidence is
important in any kind of text, but it is crucial in argumentation.
If you are trying to win a point, the last thing you want is the
reader to challenge your data, but this is the first reaction
imprecise writing will provoke. Precise writing ensures that the
discussion will be about the implications of the information, i.e.
what conclusions should be drawn, not whether the whole thing needs
to go back for further investigation.
Importance of logical linking: Precise data (facts) by
themselves are insufficient. To be meaningful, data must be
organized to create information, to help the reader understand.
There are two important tests to apply when converting data into
Relevance: Is a particular piece of data really
needed? As we have seen, unnecessary data damages understanding and
ultimately undermines confidence. Therefore, any data that do not
either aid understanding or promote confidence should be eliminated.
Misconceptions: The logical link between data
must be made explicit to prevent the reader from coming to false
conclusions. For example: a specific situation may be confused for
a general one; credit for an achievement may seem to belong to only
one person when it really belongs to a group; a company policy may
appear to apply only in very specific circumstances rather than in
all circumstances, etc.
To ensure that a logical link is clear, place the two pieces of data
as close to each other as possible, preferably right next to each
other. When data are widely separated, their logical relationship
is masked and the reader is unlikely to make the connection.
do you want? What do your readers want? I frequently ask
non-professional writers what they are thinking when they sit down
at the keyboard to compose their text. The answer is usually
something like, "How do I want to present my material?” "What tone
and style should I use?” "In what order should I put my key
ideas?” And so on.
However, you must start with the correct attitude. No one wants to
read what you write; your first task is none of these. Ahead of
anything else, you must find reasons why people should spend their
time to read what you write.
In general, you cannot force people to read what they don't want to,
even if they are being paid to do so.
For example, you produce a report defining opportunities for
increased sales and profits. However, if it is not well written,
even people who must read it as part of their job are unlikely to
give it their full attention. On the other hand, if they
immediately see their own self-interest in reading what you have
written, they will do so gladly and with full attention. In fact,
you probably couldn't stop them from reading it!
There are various methods to generate such a strong desire to read,
depending on the type of readers and the type of information.
Whatever the most appropriate device, the crucial thing is to
recognize the imperative need to use it. Until this need is met,
nothing else is of any importance.
Philip Yaffe is a former
reporter/feature writer with The Wall Street Journal and a
marketing communication consultant. He currently teaches a course
in good writing and good public speaking in Brussels, Belgium.
In the 'I' of the Storm is available either in a print version or
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