Sun Tzu and the Rules of Victorious Warriors

This paper describes work in progress that has been presented at the conference The Making of the Humanities VII, University of Amsterdam, November 15-17, 2018.

Full details can be found on the website: http://suntzu.squaringthecircles.com. In addition to the description of the patterns as presented in this paper, the site shows mind maps for all chapters, English and Chinese text. For the first 6 chapters you can see the modifications we made to the translation.

Authors

Ghica van Emde Boas - Lubsen
Bronstee.com Software & Services, Heemstede
emdeboas@bronstee.com

Bonan Zhao
Tsinghua University - University of Amsterdam Joint Research Centre for Logic
zbn.dale@gmail.com

Kaibo Xie
Institute for Logic Languages and Computation, University of Amsterdam
xiekaibozju@gmail.com

Peter van Emde Boas
ILLC, FNWI, University of Amsterdam
peter@bronstee.com

Abstract

We examine an ancient Chinese work on strategy and warfare: Sun Tzu, “The Art of War”, from the perspectives of logic, mathematics, and computer science. Making use of contemporary mind mapping methods, we show how logic can be extracted from this 2500 year old text.

A hierarchical decomposition of the text, as constructed using mind maps, allows us to highlight patterns and structures in the text. We will look at: Our work is based on the translation of Lionel Giles, made in 1910, and on comparisons with the original Chinese text. We found that mind maps enable us to bring back some of the rhythm and visual structure of this book which are obscured in many translations, because the translators tried to produce a readable narrative.

Introduction

In this study we are looking at Sun Tzu, "the Art of War", An ancient Chinese work on strategy and warfare.

This famous book, which is very popular in business circles today, was written about 500 BC. Scientists or translators studying "the Art of War" are in general looking from the perspective of history, military science, philosophy, or linguistics. The background of the authors of this study is quite different: mathematics, computer science, and logic. We think that this new perspective provides new insights, particularly about the logic used by Sun Tzu.

The use of mind maps adds a visual dimension to the text and can therefore provide a substantially new insight as shown by the results: finding logical structures in Sun Tzu's work that we have not seen before in such a systematic way.

Why is the visual dimension important? Consider the well know saying that "a picture is worth a thousand words". Think also of the problem of solving a Sudoku puzzle. Try to imagine solving a Sudoku in your head, without the visual representation of a square divided into 81 little squares in front of you!

"The Art of War" contains 13 chapters, where the first 6 chapters are considered more theoretical and the last 7 chapters are more practical. In our work, we look primarily at the first 6 chapters.

"The Art of War" was translated into English by Lionel Giles in 1910. Although there are many, and better, translations made later, this is still the most used translation because it has no copyright. You can find the text here: http://www.gutenberg.org/ebooks/132, or the text without commentary can be found here: http://www.gutenberg.org/ebooks/17405.

Famous Quotes

Here is a short list of famous quotes that many people know about, even if they never heard of Sun Tzu and his book "The art of War":

Maybe you noticed that these quotes all concern war and fighting. However, in Sun Tzu's book there is other content that would be worth mentioning in any list of quotes. For example, this poetic text:

There are not more than five musical notes, yet the combinations of these five give rise to more melodies than can ever be heard. There are not more than five primary colors, yet in combination they produce more hues than can ever been seen. There are not more than five cardinal tastes, yet combinations of them yield more flavors than can ever be tasted.

Our interpretation of this text is that there are always unlimited possibilities even with limited means.

To explain how we found this quote, we start from the quote, put it into a mind map form, then we look at the complete mind map of chapter 5, were we found this quote, to arrive finally at the original text.

Then we go back to the details to explain how the mind map are made. This is detailed in the section about the use of mind maps. In this section we show a few mind maps that are intuitively understood, we hope.

The annotated quote rendered as mind map.
In the translation of L. Giles, the five ingredients for infinite possibilities are given. In the original Chinese text, these are omitted, maybe because every Chinese person is supposed to know the five ingredients for each category.

Next we look at how this mind map fits into the larger mind map of chapter 5:

The mind map of chapter 5. Some of the structures are collapsed to get a better overview.

The yellow colored part shows our from five to infinity text. If we look for that part in the original text, we see that it does not stand out:

The original text of chapter 5, as translated by L. Giles.

If you look back to our larger mind map and relate that to the original text, you see that all text is still there, but that structure is added, which makes it easier to see what this chapter contins and is trying to tell us. In the section about how to create the mind maps you will see our method of making them.

Mind Maps and Patterns

The text of Sun Tzu's book is very structured. In the Chinese text this is more visible than in the English translations that we studied. With the help of mind maps we try to highlight this structure again and find the reasoning that Sun Tzu used.

What is a Mind Maps

A mind map is a way to visualize information in an organizational and hierarchical structure. Visual methods to help brainstorming, problem solving, structuring of a subject and so on is quite old, and in IT-circles several charting methods have been in use. In business circles graphical brainstorming methods are made popular again by Tony Buzan in the 1970-ies.
See for a more detailed description of mind mapping: https://en.wikipedia.org/wiki/Mind_map .

Example of a mindmap.

http://mindmapping.bg [CC BY-SA 2.5], via Wikimedia Commons


When it became possible to show graphics on computer screens, a multitude of tools to create mind maps were developed, such as Freemind, which we used to develop our mind maps.

Freemind, as the name suggests, is a free, open source tool to create mind maps. We like the very simple representation it allows, without colors, bells and whistles, which makes it possible to show the structure of the text.

Feemind did not allow to import directly the semi-structured text we created from the "Art of War" in the Gutenberg edition of the translation by L. Giles. We used a tool named iThoughts that allowed this import and had an export facility into Freemind format (https://www.toketaware.com/).

The tool that allows us to show the mind maps in an interactive way on the web, My Mind (https://github.com/ondras/my-mind) is fine on a PC, but not on a tablet, therefore you will find in addition to the interactive maps, also the expanded mind maps as images, both in English and Chinese, one mind map per chapter.

Analyzing Text Using Mind Maps

A digital mind map is essentially text formatted in a tree structure. We tried to keep the formatting as simple as possible: although the tools allow pictures, colors, various shapes of nodes and more, we thought that this would not enhance the clarity of our analysis. We did not add any text to the mind map, except for some categorizations, as explained below. Sometimes we removed text, when it seemed duplicate or not adding meaning after text restructuring. The process of analyzing text using a mind map is roughly as follows:

To give an impression of what the result of our mind mapping work could be, we colored the mind map of chapter 1, to show the patterns we found.

The mind map of chapter 1.

The coloring cannot be completely exact: for example, we were not able to show opposite pairs clearly. See also the deception category, where on almost every line there is a pair of opposites, but they are colored green because of the conditions that are expressed. One reason is that Freemind does not allow us to color part of a node. Another reason is the overlap of patterns used.

In the sections for each pattern: Pairs of Opposites, Enumerations, Conditional Sentences, Preference Order and Implications, we describe each of them, with examples. For the first six chapters these examples should give a complete overview of what we found.

Pairs of Opposites

Opposite pairs are groups of two items which have meaning that is opposite, like regular and irregular, front and back, and so on. This must be related to the yin-yang principle of ancient China, which stems from roughly the same era. Yin and yang describes how seemingly opposite or contrary forces may actually be complementary, interconnected, and interdependent in the natural world, and how they may give rise to each other as they interrelate to one another. (source: Wikipedia).

We scanned the first six chapters of "the Art of War" to find pairs of opposites. Below you see a list of what we found.

Chapter 1: Chapter 3: Chapter 5: Chapter 6:

Enumerations

In almost every chapter Sun Tzu used some form of enumeration of things or concepts, in several chapters even two. For example,

There are 15 enumerations in total in Sun Tzu's book, look in the details section for snippets from mind maps and for more explanation.
In addition to explicit enumerations, there is mention of numbered things, such as five colors (chapter 5), without saying what they are.

A very different kind of grouping that occurs in Sun Tzu's book are groups of two, used as pairs of opposites. We think that the special meaning and frequent use of those pairs warrants description as a separate pattern.

The enumerations found in Sun Tzu's book are shown in the following mind map, together with a number of the chapter where they occur. As you can see, there are enumerations in all chapters, except 2 and 7. In chapter 5 and 6 Sun Tzu mentions numbered items without enumerating them explicitly.
This shows that Sun Tzu found it useful to clarify his reasoning by summing up circumstances or subjects of his rules.


Here is an overview of the enumerations we found:

Chapter 1: 5 Constant Factors

(1) The Moral Law; (2) Heaven; (3) Earth; (4) The Commander; (5) Method and discipline.

Chapter 1: 7 Deliberations



Chapter 3: 3 Ways of Misfortune



Chapter 3: 5 Essentials for Victory



Chapter 4: 5 Factors for Military Method

The original English text reads like this:

17. In respect of military method, we have,
    firstly, Measurement; secondly, Estimation of quantity; thirdly, Calculation;
    fourthly, Balancing of chances; fifthly, Victory.
18. Measurement owes its existence to Earth;
    Estimation of quantity to Measurement;
    Calculation to Estimation of quantity;
    Balancing of chances to Calculation;
    and Victory to Balancing of chances.

This enumeration posed an interesting problem of putting it in a mind map. Most translations refer to the previous enumerated item backwards: Analysis is determined by Earth, and so on.

However, this does not look good in a mind map and more careful study of the chinese text leads us to believe that forward reference is much better and more true to the original text.

Therefore we constructed the texts as: Earth determines Analaysis, and so on. This is reflected in the Chinese mind map detail below. It also shows that mind maps can be helpful in finding the right translation.




To make the enumeration more clear, we could represent the text also like this:



Chapter 5: From Five to Infinity

This is an example of grouping where the items are not explicitly given, presumably because they are considered well known. From the commentary of the old Chinese scholars we know now what they are and also Giles mentioned them by name in his translation.



The items in these groups are:

Sun Tzu is explaining here that there are an infinite number of strategies that can be used for warfare, even if the components of such a strategy are limited.

Chapter 6: 5 Elements and Seasons

The last paragraph in this chapter starts with:


In the remaining chapters, there are also enumerations which we only list here for completeness:

As this list shows, Sun Tzu has a preference for the number five, which according to the translator Peter Harris, caused by its prevalence in early Chinese culture, see his comment at the end of chapter 4 of his Sun Tzu translation.

Conditional Sentences

Sun Tzu frequently employs reasoning in his text, like this:
If victory is long in coming, then men's weapons will grow dull and their ardor will be damped.

This is an example of a conditional sentence. Basically, conditionals may be of two types:

Here are a few examples from chapter 1 that show conditional sentences used by Sun Tzu:

Chapter 1, sentence 15.

The English mind map detail:

The Chinese mind map detail:

This discusses two conditions of a general: (1) the generals that follow your command, and (2) the generals that do not follow your command. For (1), you keep them, and for (2) you dismiss them. Sun Tzu also gives reasons for why you react differently to these two groups of generals - for (1) they will conquer, and for (2) they will suffer defeat.

This is a very neat thumb-rule for evaluating your generals, using a clear one-cut separation.

Chapter 1, Sentence 19-24.

Sun Tzu considers in paragraph 18-25, at how to deceive the enemy and when. The text as given by Giles, looks like this:
 18. All warfare is based on deception.
 19. Hence, when able to attack, we must seem unable; when using our
 forces, we must seem inactive; when we are near, we must make the
 enemy believe we are far away; when far away, we must make him
 believe we are near.
 20. Hold out baits to entice the enemy. Feign disorder, and crush him.
 21. If he is secure at all points, be prepared for him. If he is in
 superior strength, evade him.
 22. If your opponent is of choleric temper, seek to irritate him.
 Pretend to be weak, that he may grow arrogant.
 23. If he is taking his ease, give him no rest. If his forces are united, separate them.
 24. Attack him where he is unprepared, appear where you are not expected.
 25. These military devices, leading to victory, must not be divulged beforehand.
 

This could be structured as follows:


Deception

The first pass mind map detail.

Looking at the Chinese version, we see this:

We notice that the English translation makes use of different expressions to translate this list of conditions: when, to, if, where. In the original Chinese text, as you can see from the Chinese mind map, these sentences all follow a clear structure:

(in case of) A, do B.

A is some possible condition of your enemy: able to attack, using their forces, getting close etc., and B is what Sun Tzu suggest you to do under each condition: make them unable, make them unable to use their forces, get away from them, etc.

The 而 (ér) character indicates the logical relation between condition A and your reaction B, and the character 之 (zhī) is the Chinese work refers to the enemy.

The improved English translation and structure looks like this in a mind map:


The final mind map detail.

Chapter 1, Sentence 26.

The English text is as follows:

26. Now, the commander who wins a battle makes many calculations in his temple before the battle is fought. The commander who loses a battle makes only few calculations beforehand. Thus do many calculations lead to victory, and few calculations to defeat.
What if there are no calculation at all! It is by attention to this point that I can foresee who is likely to win or lose.


This text is transformed into the following mind map detail in English:

And this is the Chinese mind map detail:


This paragraph contains both conditions and preference orders.

First two conditions are distinguished:
  1. The commander makes many calculations in his temple before the battle is fought
  2. He makes few calculations beforehand.

Condition (1) leads to victory, and condition (2) leads to defeat. From these two observations, Sun Tzu asks the rhetorical question that, since more calculations leads to victory and less to defeat: what would happen if you do not make any calculations at all?

As we will see in the section about the preference order pattern, Sun Tzu structures the text in such a way that the most desirable option is mentioned first, a less desirable option next, and a condition that should not happen at all, last.

Preference Order

Preferences are conditional statements which assume a certain order in their execution. Sun Tzu uses this construct at several occasions, indicating good and not-so-good ways of performing warfare.

Definition of Preference Order

In logic and mathematics, preference is usually defined as an ordering of given elements in a set. These elements can be some objects, or possible outcomes of certain actions, and the ordering is usually defined by a utility function that weights how preferable an element is. An element A is more preferable than element B if and only if A's utility is higher than B's.

In the context of Sun Tzu, the author does not explicitly define preferences in such a rigid way. However, when multiple possible situations are being articulated, Sun Tzu indeed gives them a preference order.

We call this ordering preference order mainly for two reasons:
  1. For each of the element being mentioned, you can always find a preference relation, and there's no circle-back.
    If A is more preferable than B, B is more preferable than C, then it implies that A is more preferable than C.
  2. They are in coherence with Sun Tzu's general philosophy of war. Sun Tzu is not ordering these possible outcomes randomly, but follows his reasoning in evaluating these conditions.

Examples of Preference Order

We show here some examples of sentences using a preference order.

Chapter 01, sentence 26.

 Now the general who wins a battle makes many calculations in his temple before the battle is fought.
The general who loses a battle makes but few calculations beforehand.
Thus,
	do many calculations lead to victory,
	and few calculations to defeat:
	how much more no calculation at all!
        

There are three conditions to order. The most preferable one is to do many calculations that lead to victory, and the second prefer one is to do few calculations (which leads to defeat). The least preferable one, is to do no calculation at all.

Chapter 03, sentence 1.

    In the practical art of war, 
        the best thing of all is to take the enemy's country whole and intact;
        to shatter and destroy it is not so good.
    So, too, it is better to recapture an army entire than to destroy it,
        to capture a regiment, a detachment or a company entire than to destroy them.
        

This example orders five elements: 國,軍,旅,卒,伍。These five terms refer to five organizational units in the ancient Chinese armies. 國 is the entirely country, 軍 is the full army of the country, 旅 is one sub-unit of the country, the the rest two are smaller units.

For each of the elements, to keep it intact is better than to destroy it.

Taking all the five elements into consideration, to keep the higher oredered one is preferable than to keep the lower ones.

This constructs a nested preference order of the five elements.

This analysis allows us now to improve the English mind map and the translated text.

2. Chapter 3, Sentence 3.

Thus the highest form of generalship is to balk the enemy's plans;
    the next best is to prevent the junction of the enemy's forces;
    the next in order is to attack the enemy's army in the field;
        and the worst policy of all is to besiege walled cities.

This one orders four strategies. The most preferred is from the planning perspective, then the forces, then the army, and last to besiege a city.

The world is not a perfect one, therefore when the best scenario cannot happen, Sun Tzu lists a second-best one, and then the next, thus one doesn’t have to drop to the worst option immediately. By preference order, Sun Tzu provides a more refined granular view of strategies. It is not about A or not A, but we can rate from the the more preferable to the least preferable, and the possibility to make each sub-optimal scenario to happen.

Implications

Implications (故 gù, therefore), are used to find rules and reasoning.

Discussion of 故 (gù, therefore)

From our look at the word-for-word translation in Zieger, Sun Tzu’s Original Art of War, there appears to be an issue that needs to be clarified. Zieger says that this Chinese character in modern Chinese may indeed mean hence or therefore, but that in classical Chinese this word is much weaker and just means a comma, or at its best so. Therefore he omits gù in his translation.

If we read Zieger's translation of chapter 4, we think that the meaning of the text is less visible and it is more difficult to find the categories that we found for the mind map.

Our investigation and communication with our Chinese contacts lets us conclude this:

In Xizhou (1046BC - 771 BC), 故 is already taken as a cause-and-effect conjunction.

In bronze inscriptions researchers found four appearances of 故 that clearly refers to ‘therefore’, ‘hence,’ ‘so’. In ancient written classics that recorded Xizhou inscriptions, there are also two occurrences of gu that serves as the cause-and-effect conjunction.

Some researchers claim that sometimes 故 just refers to the next sentence, without a cause-and-effect indication. This occurs later, during the Qin and Han dynasty. This usage of 故 is also rare, while in the majority of cases gu serves as the cause-and-effect conjunction. Shi-gu (是故) indicates strong and clear cause-and-effect relation between two sentences, and this point is a common agreement among scholars in ancient Chinese studies.

Let us look at two examples of the usage of 故 (gù) in chapter 4, in the Giles translation.

There is a clear causal correlation with the paragraph before: To secure ourselves against defeat lies in our own hands, but the opportunity of defeating the enemy is provided by the enemy himself.

Later in this chapter there is the sentence To lift an autumn hair is no sign of great strength, in Chinese: 故舉秋毫不為多力. Here the use of 故 is much less directly related with the previous sentence, which states that there is no merit in easy victories.

Our conclusion is that interpreting the use 故 for causal reasoning will be mostly fine, while in some cases we do not understand well enough what was intended to be able to judge.

For more information, see the articles from Zhigang Mao and Cheng Zhang.

Survey of the occurrence of 故 in "The Art of War"

With help of the search facility of ctext.org we could create the following table showing the frequency of occurrence of 故 in the book, adding up to a total of 102.

ch. Title nr. of 故
1 Start Planning 3
2 Waging War 8
3 Attack by Stratagem 9
4 Tactical Dispositions 10
5 Energy 6
6 Weak Points and Strong 14
7 Maneuvering 14
8 Variation in Tactics 5
9 The Army on the March 1
10 Terrain 7
11 The Nine Situations 13
12 The Attack by Fire 3
13 The Use of Spies 9

The stronger combination, 是故 (shi-gu) occurs 16 times. Looking at the first 6 chapters, our focus chapters for this study, the occurrence of 是故 coincides with some famous quotes:

A quick survey of the other chapters show a much less convincing pattern. Half of all occurrences (8) of 是故, appear in chapter 11, The Nine Situations. There are 4 more occurrences of 故 without 是 in this chapter. Why the text in this chapter contains so much more reasoning than the rest of the book would be an interesting subject of further study.

Translations of Sun Tzu, the Art of War, into English

The history of the translations is interesting in itself, because most translators seem to be of the opinion that they improved significantly on what their predecessors did.

The first known translation into English was done by Captain E.F. Calthrop in 1905, with improvements in 1908  . Lionel Giles must be the second translator, motivated to do this translation because he thought that the translation by Calthrop was “excessively bad"  . Giles has abundant notes and explanations in his text.

Dr. Giles, in justifying his translation, wrote: "It was not undertaken out of any inflated estimate of my own powers; but I could not help feeling that Sun Tzu deserved a better fate than had befallen him, and I knew that, at any rate, I could hardly fail to improve on the work of my predecessors."

It would take about 50 years before another translation was made by Samuel B. Griffith .

More recent translations were done by: Cleary (1988) , Ames (1993) , Sawyer (1994) , Wu Rusong (1999) , Minford (2002) , Lin Wusun (2003) , Mair (2007) , Zieger (2010)  and Harris (2018).

The translations are substantially different and it is difficult to decide whether the exact concepts from the old text are used. Moreover, the source text is of course written in ancient Chinese, yielding additional problems, also for modern native Chinese scholars.

We use mainly the translation into English by Lionel Giles, one of the oldest translations, made in 1910. This text is available as part of the Gutenberg project  and is therefore freely available without copyright restrictions. Although there are later translations based on more modern research and on Chinese texts that were found during later excavations, notably in 1972, we think that the Giles translation is most suitable for our purpose: the translation is highly structured and because of its unrestricted availability we can transform the text to highlight this structure and the rules behind it. We consulted newer translations to check that understanding of the text is not completely dependent on the Giles translation.

Finding the right meaning and translate it the right way remains tricky, as is illustrated by three different translations of a famous sentence in chapter 4:

We can conclude from these examples that the word bing has been translated to single soldier, commander or the whole army. It can also mean weapons, or military. The use of the translation warrior in this context only appears in the Cleary edition  where it occurs in a commentary to the final sentence of chapter 1, ascribed to Zhang Yu, a commentator who lived during the Sung Dynasty (960-1279 AD). Therefore the quote in the Civilization IV game is actually a quote of an ancient commentator and not of Sun Tzu himself. In Liu An , sect. 15.8 we find a similar sentence about soldiers.

A comprehensive discussion of the diversity of the translations is given by Yang Ming.

Conclusions

At the third conference for the forthcoming handbook on the History of logic in China, in Tianjin, 2014, one of our co-authors of the handbook expressed his opinion that the Sun Tzu's Art of War is a logic text. Subsequently, we included in our chapter about "Logical and Game Theoretical aspects of Strategy Theory in ancient China", an investigation of Sun Tzu's work using mindmap, with a focus on chapter 4.
In the work presented here we took a more thorough look at the first 6 chapters of The Art of War, refining the mind maps, describing all logical patterns we could find and with help of these patterns we looked at the English translations. find

We hope to have given evidence that there is a substantial amount of logical structure hidden in the text, which can be made explicit by rendering the text as mind maps. This structure exhibits itself even stronger if you return to the Chinese source text. That it becomes less visible in the translated versions should be considered a consequence of the targets the editors and translators had in mind, aiming for the cultural and historical meaning, and the philosophy underneath the text. Even word-for-character translation like the one of Ziegler is aimed at the language, rather than the logical structure of the text.

The use of mind maps makes it possible to uncover this logical structure even for researchers like the European authors missing a thorough background in Chinese language or philosophy. Moreover the implementation of our ideas in the Sun Tzu website affiliated with this paper, https://suntzu.squaringthecircles.com/ presents to the public access to the text in a manner unprecedented in the literature.

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