Mathematics of Communication
Philip Yaffe discusses what writing and public speaking have
in common. Mr. Yaffe also breaks down the fundamentals of clarity
and conciseness in effective writing.
The Mathematics of Persuasive Communication
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
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 effective.
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
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,
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 them!
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 recognise this, because not only are they quite
different, in some respects they are exactly opposite. So unless
we clearly recognise which type of writing we are doing - and
how it differs from the other one - we will almost certainly commit
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
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 recognising 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:
o Almost all companies of any size feel compelled to produce them.
o Virtually no one ever reads them.
Starting 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 revitalise 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
focussed 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
Creative writing approach
Play with language to generate pleasure. In other words, use
your mastery of the language to amuse and entertain.
Expository writing approach
Organise information to generate interest. Clever use of language
will never make dull information interesting; however, you can
organise 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
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. Emphasise what is of key importance.
2. De-emphasise 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 judgement.
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
What about the second element of the formula, de-emphasise 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 emphasise what is of key
importance - via headlines, Italics, underlining, or simply how
you organise the information - then whatever is left over is automatically
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 judgement,
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.
How do you know that a text is concise?
If this once again sounds like a silly question, let's try to
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
clea r- 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:
o Aids clarity by ensuring best structuring of information.
o Holds reader interest by providing maximum information in minimum
Density is a less familiar concept than clarity and conciseness,
but is equally important. In mathematical form, density consists
1. Precise information
2. Logically linked
In other 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"
You are off to a rather bad start, because each one has a totally
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 advantages:
o 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 disinterest.
o 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 organised to create information, i.e. help the reader
There are two important tests to apply when converting data into
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.
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.
What 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, if you start with the correct attitude, i.e. 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
recognise the imperative need to use it. Until this need is met,
nothing else is of any importance.
Editor's note: Reading is an isolated activity and listening
to a speech is a social one. Therefore, whilst the underlying
principles of good writing and good speaking are constant, the
way they are applied can be markedly different. In the 'I' of
the Storm: the Simple Secrets of Writing & Speaking (Almost)
like a Professional, Mr. Yaffe's recently published book, clearly
explains these differences. It also offers several appendices
with cogent examples and pertinent, effective exercises.
About the Author
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 electronic version from Story Publishers in Ghent,
and Amazon (www.amazon.com).
For further information, please contact:
61 avenue des Noisetiers
B -1170 Brussels, Belgium
Tel: +32 (0) 660 04 05
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