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.
Ghica van Emde Boas - Lubsen Bronstee.com Software & Services, Heemstede firstname.lastname@example.org Bonan Zhao Tsinghua University - University of Amsterdam Joint Research Centre for Logic email@example.com Kaibo Xie Institute for Logic Languages and Computation, University of Amsterdam firstname.lastname@example.org Peter van Emde Boas ILLC, FNWI, University of Amsterdam email@example.com
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:
- Pairs of Opposites. A pair of opposites is not an enumeration with two elements. It is used to explain how seemingly opposite or contrary forces may actually be complementary, for example: direct and indirect (chapter 5), empty and solid (chapter 6).
- Enumerations, to clarify reasoning, such as: Thus we may know that there are five essentials for victory (chapter 1). In addition to explicit enumerations, there is mention of numbered things, such as five colors (chapter 5), without saying what they are.
- Conditionals, such as: If victory is long in coming, then men's weapons will grow dull and their ardor will be damped (chapter 2).
- Preference order, as illustrated by the following detail (chapter 3):
- It is better to take a country intact, than to destroy a country;
- It is better to capture an army intact, than to destroy an army;
- It is better to capture a squad, than to kill a squad;
- Implications (故 gù, therefore), with a discussion about its difference in meaning between ancient and modern Chinese.
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.
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":
- It is said that if you know your enemies and know yourself, you will not be imperiled in a hundred battles.
- When we are able to attack, we must seem unable.
- Victorious warriors win first and then go to war, while defeated warriors go to war first and then seek to win.
- It is best to win without fighting.
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.
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 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:
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
See for a more detailed description of mind mapping: https://en.wikipedia.org/wiki/Mind_map .
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:
- Import the original text, chapter by chapter, into a mindmap. We made a separate mind map for each chapter.
- The chapter title becomes the root node in the mindmap for that chapter. Each paragraph becomes a sub-node.
sub-node is split into further sub-nodes. This is a subjective analytical
process, but there were some rules to guide us.
- The occurrence of certain words such as hence or therefore (故 in Chinese) would cause a sub-node to de made. See also the discussion about 故 in the section about conditionals.
- Almost every chapter contains one or more enumerations. These can be shown as sub-nodes of the enumerated concept.
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 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:
- Life and death
- night and day, cold and heat, times and seasons
- great and small; danger and security; open ground and narrow passes
- Deception, see the figure with the final mind map detail in Conditional Statements pattern for paragraph 18.
- intact, destroy
- weak and strong
- direct and indirect
- heaven and earth
- sun and moon
- strength and weakness
- weak points and strong
- at ease and harass
- supplied with food and starve
- encamped and move
- attack and defend
- concentrate and divide
- whole and separate parts
- front and rear, left and right, reinforce and weaken
- avoid strong and strike weak
In almost every chapter Sun Tzu used some form of enumeration of things or concepts, in several chapters even two. For example,
- the seven military considerations in chapter 1,
- the ﬁve essentials for victory in chapter 3,
- the nine varieties of ground in chapter 11,
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
where they occur. As you can see, there are enumerations in all chapters, except 2 and 7. In chapter 5 and 6 Sun
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:
- Five musical notes: the classical Chinese pentatonic scale.
- Five primary colors: blue, yellow, red, white, and black.
- Five cardinal tastes: sour, acrid, salt, sweet, bitter.
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:
- The five elements (water, fire, wood, metal, earth) are not always equally predominant;
- The four seasons make way for each other in turn.
In the remaining chapters, there are also enumerations which we only list here for completeness:
- Chapter 8: 5 Faults of a Commander
- Chapter 9: 4 Useful branches of Military Knowlede
- Chapter 10: 6 Kinds of Terrain
- Chapter 10: 6 Calamities
Chapter 11: 9 Varieties of Ground
- Chapter 12: 5 Ways of Attacking with Fire
- Chapter 12: 5 Possible Developments when Attacking with Fire
- Chapter 13: 5 Types of Spies
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.
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:
- the first one is a condition that describes a status or situation,
- the second one is a condition that should lead to an action.
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:
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:
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:
- The commander makes many calculations in his temple before the battle is fought
- 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.
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:
- 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.
- 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 OrderWe 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 (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:
- It's true that "gù" does not imply strong causal relation as in modern Chinese, but even as "so" in the weak sense, it still reveals information about the implicit logic behind the text. It is not a good idea to omit such a strong indication of a pattern completely from the text.
- Sentences containing gù could express steps towards a conclusion, where the gù marks the start of the description of the conclusion.
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.
- Par. 3, Thus the good fighter is able to secure himself against defeat, but cannot make certain of defeating the enemy.
- Par 4, Hence the saying: One may know how to conquer without being able to do it.
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|
|3||Attack by Stratagem||9|
|6||Weak Points and Strong||14|
|8||Variation in Tactics||5|
|9||The Army on the March||1|
|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:
- Chapter 3:
Hence to fight and conquer in all your battles is not supreme excellence; supreme excellence consists in breaking the enemy's resistance without fighting.
Thus it is that in war the victorious strategist only seeks battle after the victory has been won, whereas he who is destined to defeat first fights and afterwards looks for victory.
Therefore the good fighter will be terrible in his onset, and prompt in his decision.
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.