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The Mathematics of Persuasive Communication: Part I

By Philip Yaffe |

Author's Note: Many articles on effective communication (writing and speaking) offer lists of "do's" and "don'ts". These tips and suggestions can be fully useful only when the writer/speaker understands the foundations from which they are derived.

This three-part series explores persuasive communication with almost mathematical rigour.

  • Part 1 strips away the superficialities to reveal the bedrock underneath, i.e. what persuasive communication is truly all about.
  • Part 2 then shows how simple mathematical concepts can be used to significantly improve both clarity and conciseness.
  • Part 3 examines "density", a crucial but often overlooked aspect 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 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 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 good speaking.

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 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 serious errors.

What are the two types? And how do they differ?

Creative Writing

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.

Expository Writing

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 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 of examples.

A. Corporate image brochure

I was once commissioned to write a corporate image brochure. Two things are certain about these expensive, glossy booklets:

  • Almost all companies of any size feel compelled to produce them.
  • 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 approaches.

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.

The expository writing attitude and the expository writing approach form the bedrock of persuasive communication. So now that we clearly understand what we need to do, the question is: How do we do it?

This is the subject of Part II of this series.

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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