Introduction - settling the debate on structure
We are up to Matthew in our Through the Bible Series. Before I dig into the text I want to say a few words about the incredible structure of the book of Matthew. As you know, I don't always agree with the Bible Project's analysis of books. Sometimes they do a great job and sometimes the video is weak. But if you are a highly visual person, I highly recommend that you look at their two videos on Matthew. The two videos together are about 15 minutes, and are extremely well done. That video shows a foundational block at the beginning and a climax block at the end, with five blocks of teachings in between that parallel the five books of the Pentateuch and establish the renewal of the kingdom by the Prophet like Moses and the King like David. It's one of the ways that several people have seen this book as being structured.
Of course, that is not the only structure that scholars have found. Anyone who has studied Matthew knows that there has been huge debate on what structures Matthew. And each one thinks that their structure is the real one. It is my contention that most of those insights from scholars are not mutually exclusive - they are all true. This is a beautifully written book that intricately weaves several structural devices together in order to emphasize different layers of truth.
For example, is it biographical and therefore chronologically structured? Well, to some degree, yes. But scholars point out that it is more than simply biographical. It is also topically arranged. And almost everyone admits that some things are topically grouped together. But because this is a literal history, we would expect chronological order.
Does the whole book recapitulate the history of Israel, as many scholars claim? Yes. And it does so in remarkable ways to show that Jesus is forming a new Israel and establishing a new kingdom. Indeed, Matthew shows Jesus to be the Israel encapsulated into one person. So that is another lens through which to view the book. That lens helps you to avoid the Dispensational error.
Others have recognized that this book has geographical movement in the major five portions from the mountain top, down to a town, down to the water, then back up to a town, and back up to a mountain. Thematically these parallel His descent into death and back up into resurrection. But if you overlay that over the other structures that people see, you find remarkable parallels.
This is even true of the chiastic structure given by Mago Nagasawa. You would think that would be mutually exclusive of the other structures, but it is not. I think he has shown layer upon layer of perfect parallels in the book that form a thematic chiasm, with the growth of the kingdom in chapter 13 being at the heart of it. The whole book is about the kingdom of Jesus, but those parables keep us from being surprised at the opposition to the kingdom in its early stages. It starts off small and almost unnoticed but eventually grows to fill the earth. It's a marvelous correction to ideas of instant perfection. But anyway, most of these structures take us to chapter 13 as the center.1
Other authors have pointed out that Matthew clearly structures the entire book around sections of Isaiah. And it is true. But he does so as an overlay to other structures. But wow, does Isaiah ever open up the book of Matthew!
Others have noticed that Matthew is beautifully organized in a back and forth interplay between story, teaching, story, teaching, story, teaching, with each section ending with the words, "when Jesus had finished saying these things." And they argue that this is the only way to structure the book. But when you overlay that structure with other structures, it accomplishes the same thing. This too focuses the entire book on the parables of the kingdom in chapter 13. And all you have to do in order to recognize this particular back and forth structuring is to read Matthew in a red letter bible. I'm not a fan of red letter bibles since the black words are just as much His words. But in this case it does give good visual cues.
And I won't get into all of the other structural fights that are out there. If the Bible was inspired by God Himself, we ought not to be surprised that there are layers upon layers of structure and complexities that we wouldn't expect out of a normal person. It's an inspired book.
Now, I say all of that because I don't want you to think that the structure I will be using is the only structure you can see in this book. But in one sermon I think it is the simplest way of handling such a complex book. So this morning I am going to simply divide the book up into ten progressive parts, with each part giving another aspect of Jesus and His kingdom.
- Chapters 1-3 deal with the coming of the King.
- Chapter 4 deals with testing of the King.
- Chapters 5-7 deal with the manifesto of the kingdom. It properly interprets the Old Testament law of God. And without a law, you don't have a kingdom.
- Chapters 8-10 are filled with miracles and in many different ways showcase the power of the kingdom. Without power to back it up, you really don't have a kingdom.
- Chapters 11-12 deal with various reactions to the kingdom - some hostile to Jesus and some embracing Him as the Christ.
- Chapter 13 gives parables of the kingdom’s gradual growth - something that the Jews apparently were not expecting. They wanted it suddenly. But when you realize that the kingdom grows gradually, it gives you hope during difficult times. This is the center and heart of Matthew. Chapter 13 is a huge corrective to Amil and Premil eschatologies. Most people focus on the Olivet Discourse, but chapter 13 is even more key.
- Chapters 14-20 gives repeated calls to have faith and to live by faith as they apply kingdom principles to every area of life.
- And they would need that faith to deal with the next section, the clash of two kingdoms in chapters 21-22.
- Chapters 26-27 then show how Jesus fulfilled all the prophecies about a suffering Messiah who would lay down His life for His people. And without that suffering, you do not have a kingdom.
- And chapter 28 shows us the risen and conquering King commanding His troops to advance His kingdom until the end of the age.
It really is a marvelous book with a very logical structure.
Overview of the book
The coming of the King (Matt. 1-3)
So let's begin at chapter 1. And the way that Matthew introduces us to Jesus in the first chapter is a little bit curious - at least in the Greek. The first words, "the book of the genealogy," are just two words in Greek - Βίβλος γενέσεως. Those are the exact words used for the title of the Greek translation for the book of Genesis - Βίβλος γενέσεως; "the book of Genesis," or "the book of beginnings."
In their commentary, Davies and Allison give seven reasons why this should not be translated as "the book of the genealogy," and should instead be seen as the title for the whole book of Matthew - "The book of beginnings." They are going to be different beginnings than began in Genesis, but this will be the New Testament book of beginnings - the Genesis of the New Creation.
I'll only give three of their seven reasons why this is true. First, they point out that the word "book" is never used to describe genealogies - sorry; a book is a book. That word "book" is not just referring to the next few verses; it is referring to the whole book of Matthew. Second, the literal rendering is "beginnings," not genealogies. Third, the Jews of that day would have immediately recognized the first two words as the title page for their book of Genesis - the book of beginnings. That commentary gives several pages of proofs that I will not get into2 that Matthew intended to trigger thoughts of Genesis in our minds, but explicitly make us think that this is another book of beginnings that answers the problems in the first book. And it is.
This book records the beginning of the New Covenant, the New Creation, and the making of all things new. Where Genesis shows the beginnings of the old creation, Matthew shows the beginnings of the new creation. Where Genesis ties us to the Old Adam, Matthew ties us to the New Adam, Jesus.
And in a rapid-fire way the next words set up Jesus as the long expected Jewish Messiah. The very next word, "Jesus," is really the Greek name for Joshua. Joshua and Jesus are the same word in Greek. Jesus will be the new Joshua who will lead His people in a new conquest. And that's why Matthew ends his book with Christ's call for the church to engage in the conquest of the nations with the Great Commission and with the sword of the Word and promising, "Lo I am with you always, even to the end of age." And Matthew even ties a connection between the Exodus he was calling Jews to in the first century and the 40 years or generation to follow and the original Exodus and the original 40 years before the conquest of Canaan.
The next word is "Christ," which is the Greek word for the Messiah. So Matthew doesn't beat around the bush and make you guess as to who Jesus is. No, he says right up front that Jesus is the fulfillment of all the hundreds of Messianic prophecies of the Old Testament. And Matthew will be packed full of quotes from Old Testament books that looked forward to what Jesus would do. So He is the Messiah; the Christ.
The next words are "the son of David." That immediately clues us into the fact that He is Israel's long anticipated King - who was to be the son of David. And of all the Gospels, Matthew lays the most emphasis upon the fact that Jesus is the son of David, the King of Israel. Being the earliest Gospel (at least in my view and the view of the ancient church - but being the earliest Gospel), this all makes sense. Matthew is the perfect introduction to the New Testament and it beautifully ties the two testaments together as one work. Anyway, the term, "the son of David," was a phrase constantly used by the rabbis of the first century to refer to the coming Messiah. So again, he is not beating around the bush. He is going to do everything he can in this book to establish this initial claim.
And that there are not two Messiahs (a kingly Messiah and a suffering Messiah, like some rabbis thought), Matthew adds, "the Son of Abraham." The Messiah who was to be the son of Abraham was a suffering Messiah. So the kingly Son of David is exactly the same Messiah spoken of by Abraham and the prophets before him - a Messiah who would suffer and die. This too would have been a shock to some rabbis who insisted that there were two Messiahs, not one.
But commentaries point out that the reference to Abraham also makes it clear that Jesus is the Messiah of Gentiles, and not just of the Jews. After all, Abraham was saved as a Gentile, wasn't he? And the book begins the pattern of writing every New Testament book in Greek, rather than in Hebrew. That too is a clue that the kingdom has gone to the Gentiles.
And the genealogy of Jesus will also make the same point. While most of the names in this list are names of Jews, Matthew makes it clear that this Messiah identifies with Gentiles, with the broken, the hurting, and the outcast. I'll just give you some hints, starting in verse 2:
Matt. 1:2 Abraham begot Isaac, Isaac begot Jacob, and Jacob begot Judah and his brothers. 3 Judah begot Perez and Zerah by Tamar...
While Jacob and Judah had plenty of other problems, his daughter-in-law, Tamar, is an embarrassing piece of history for the Jewish leaders who prided themselves in their pedigree. Tamar was a Gentile daughter-in-law of Judah whom he impregnated. Perez was the result of incest.
Verse 5 shows that Rahab the harlot was also in Christ's genealogy. Not only was she saved out of prostitution, but she was saved out of the cursed Canaanites who had been doomed to destruction. God identified with Gentiles and sinners by putting them into Christ's genealogy.
Verse 6 places Jesus as a descendant of Bathsheba, the wife of Uriah the Hittite. And though there are many other chaotic problems that this genealogy goes through, none of it was by accident. Verse 17 shows a sovereignly governed symmetry.
17 So all the generations from Abraham to David are fourteen generations, from David until the captivity in Babylon are fourteen generations, and from the captivity in Babylon until the Christ are fourteen generations.
That’s almost too neat for some people to find it believable, and yet it is true. And if you want, I can show you how that divides up.3 Every person begotten in this genealogy was perfectly prepared by God to be part of the process of producing the Messiah. Not one more or one less would do. Every one was essential. Every one was counted. Certainly there was a lot of chaos that can be seen in this genealogy, but God also intended there to be a symmetry in the midst of all the chaos. Let me quote from William Hendriksen on the significance of these numbers. He says,
In Scripture seven frequently indicates the totality ordained by God. Fourteen, which is twice seven, also bring out this idea. [And I would add that fourteen is a double witness of perfection. He goes on.] So, it would seem, does three times fourteen = forty-two. This is equal to six sevens, and immediately introduces the seventh seven, reduplicated completeness, perfection. (p. 110)
Christ of course is the reduplicated completeness of perfection. And accordingly, the Gospels tell us that He started His ministry on a Sabbath day, in a Sabbath year, and during a Jubilee year, which is the year of release and Liberty that happens once every 49 years. And William Hendriksen gives a lot of Scripture and 24 pages of exposition to further describe the symbolism of these three fourteens and the people in it. When you dig into this it is really marvelous. Christ came in the fullness of time.
And just as the Holy Spirit hovered over the formless earth to make the original creation, the beginning of the new creation was wrought by the Holy Spirit in this chapter as well. Jesus was miraculously formed from Mary just as Eve was miraculously formed from Adam. And there are a lot of other parallels that Matthew is beautifully crafting into this story.
So chapters 1-2 show the Incarnation of Jesus and His young childhood. He was a real man, not simply a gnostic figment who appeared one day. Without His manhood He would not be our Mediator. But unless He was divine, He could not be our Mediator either.
And chapter 3 shows that this King was properly prepared for by John the Baptist. He was the herald of the King. John quotes Isaiah 40:3 and applies it to Jesus. And since John the Baptist was very respected by the people, John's affirmation that Jesus was the Messiah was powerful. John gave Jesus a baptism into priesthood. Every priest in the Old Testament had to be baptized at the age of 30 before becoming a priest, and Jesus needed to fulfill the law in that respect as well. So all three chapters deal with the coming of the King to Israel.
The testing of the King (4)
The second section, chapter 4, shows the testing of the King. Satan threw everything at Jesus that he could to destroy Him morally, but Christ came out victorious.
And by the way, all four of these chapters introduce in tiny cameos many of the themes of the book as a whole and show how Jesus alone could replace the first Adam as the perfect Man. Other cameos that come up are:
- Jesus beginning in obscurity yet being sought by the magi or rulers of the East anticipates the fact that His kingdom will start small and in obscurity but will eventually be entered by all the nations of the earth.
- The unsuccessful opposition that His kingdom will later have is already anticipated in chapter 2 by Herod's hatred of Him and attempt to kill Him.
- Christ's leaving Israel for Egypt anticipates in a small way that Israel will be rejected and the Gentiles received.
- Indeed, a new Exodus from Israel will happen under John the Baptist just as there was an exodus out of Egypt in the Pentateuch.
- Just as Joshua came out of the Jordan River to face the opposition of the Canaanites, Jesus came out of the Jordan river to face the opposition of the Jewish leaders.
All of these (and many others) are marvelous glimpses or hints of how the King and the kingdom will be portrayed in the rest of the book. In chapter 4:17 Jesus began to preach, "Repent, for the kingdom of heaven is at hand." If it is at hand, it can't be 2000 years later.
The manifesto of the kingdom (5-7)
The third section, chapters 5-7, are recognized by almost everyone as being the manifesto of the kingdom. And if all three chapters are the manifesto of the kingdom, then the beatitudes constitute the distillation of this upside-down kingdom that looks like no other and has a power like no other. No one can keep the principles of this manifesto without being regenerate and being filled with the Spirit of God. It's impossible for a Pharisee to think that he measures up after reading the Sermon on the Mount. It takes supernatural grace to love those who hate you and persecute you. It takes supernatural grace to have joy in those circumstances.
So the kingdom is not a list of rules of how to get into the kingdom. Where does he start in chapter 5:3? "Blessed are the poor in spirit, for theirs is the kingdom of heaven." You can't buy your way into the kingdom; you've got to start off bankrupt. And he goes on to talk about mourners, meek, the hungry and thirsty. Too many people have approached the Sermon on the Mount moralistically. They try to be in the kingdom by trying to act like a believer should. And that is approaching it backwards. Christ gave this sermon to devastate the Pharisees in their self-righteousness and to give comfort and hope to the true believers. If we see this as a means of entering the kingdom then we will cause people to either give up hope or to become self-righteous. This sermon:
- Starts With Emptiness and Moves to Fullness and Overflowing.
- Starts With Inability and Moves to Deeds of Righteousness
- Starts With God and Moves to Man
Every religion known to man does the opposite. They recognize that we are alienated from God, but that causes them to think that they must supply what is lacking. World religion is the story of man seeking to do what God alone can do; of man seeking after God. That's what the Pharisees were doing. But Jesus said in Matthew 5:20, "unless your righteousness exceeds the righteousness of the scribes and Pharisees, you will be no means enter the kingdom of heaven." Only the perfect Christ can give us a righteousness that exceeds the righteousness of the scribes and Pharisees. So there is a sense in which the beatitudes crystallize the entire sermon on the mount in just a few words.
The power of the kingdom (8-10)
So it is no wonder that the next section, chapters 8-10, give illustration after illustration of the need for the supernatural power of God's kingdom. Jesus healed many, cast out demons (it appears, for the first time in history), commanded the wind and the waves to obey Him, converted Matthew the tax collector (that's another miracle, right?), raised people from the dead, healed the blind and the mute. He is a God of impossibilities.
But the interesting thing is that after doing all that, He sent out His twelve to do exactly the same impossible things. But they didn't do it in their own power; they did those miracles in the name of Jesus.
So there is a logical development in this book. We first of all have to recognize the king, believe that He is perfect, embrace His laws of the kingdom, and experience the power of the kingdom.
The reactions to the kingdom (11-12)
And the book shows that not everybody does that. The fifth section, chapters 11-12, shows the reactions of people to Jesus. He's just given the Manifesto of the Kingdom and shown that without Him you can do nothing, but that the reverse is also true - "I can do all things through Christ who strengthens me." That's kingdom living. He has shown them that.
But having confronted Israel with the nature of this kingdom, there are three reactions people have. Some believe and submit to Him and they join His kingdom in faith and baptism. Some still question whether He could really be the One prophesied. And most of the leaders hate Him and plot to kill Him.
Interestingly, John the Baptist, who had earlier affirmed him, began to wonder himself whether Jesus was the Messiah. Now I think it is so cool that Matthew includes that in there so that we are not surprised by similar reactions in the early stages of the kingdom.
Chapter 11:20-24 shows two cities that had rejected His message and that passage shows Jesus pronouncing woes upon them. I think I would be motivated to leave those cities, if I were a citizen there.
Chapter 12 shows the scribes and Pharisees engaging in the unpardonable sin by blaspheming the Holy Spirit and ascribing to Satan what Jesus had done by the Holy Spirit. But Christ's casting out of demons was a proof positive that the kingdom of heaven had come. And so we begin to have a stronger and stronger realization of man's depravity, and that apart from sovereign grace, no one would believe. But we also begin to get a stronger and stronger sense that the Messianic kingdom can break through all of that.
The parables of the kingdom’s growth (13)
And all of these reactions are totally consistent with the next section (chapter 13), which gives several parables to illustrate the initial stages of the kingdom. It may start as small as a grain of mustard seed, but over time it will grow into a huge bush. It may start off as a tiny bit of leaven in the dough, but it will eventually leaven the whole lump. That chapter completely contradicts the Dispensational ideas of how the kingdom comes.
A call to faith and to faithful living (14-20)
The next section, chapters 14-20, is a call to faith and to faithful living. How many times does Christ rebuke his disciples for little faith and call them to live by faith. Story after story shows that citizens of His kingdom can do the impossible if they will only live by faith. It takes faith to make Simon's confession of Christ as the Messiah in chapter 16. And it takes faith to answer Christ's call to take up your cross and follow Me, and to be willing to die for Me in the same chapter. The disciples were rebuked for having little faith when they could not cast out a demon out of a young boy in chapter 17. And throughout this section you see every area of life being intersected with a call to stop living by the world's wisdom and to live out the kingdom principles by faith. That involves how we interact with civic authorities (17:24-27). It takes faith to live humbly and to forgive as Christ calls us to forgive in chapter 18, but all who are in the kingdom have access to that supernatural power. And if we refuse to forgive as the kingdom commands, then the chapter ends by saying that the kingdom of Satan triumphs over us. It takes faith to live out Christ's call for kingdom marriage in chapter 19. That call seemed impossible to His disciples, but Jesus expects all kingdom citizens to obey that call because we have access to kingdom power by faith. He calls us to faith and faithful living in chapter 19 in our interactions with young children and in our stewardship of wealth. And chapter 20 is the ultimate call to faithful stewardship of kingdom resources.
There are two feedings of huge crowds with a few fish and a few loaves. And both feedings challenged His disciples' faith. The first feeding is in chapter 14 and the second feeding is in chapter 15. He first fed 5000 Jewish men plus women and children and there were twelve baskets left over - far more than what they had started with. The second feeding was in the Gentile country of Tyre. It was way outside of Israel. After healing many Gentiles, he fed 4000 men plus women and children and had seven baskets left over. They are obviously two quite different groups of people, but they illustrate that Jesus was sent to minister to Jew and Gentile, and He was the bread of the world.
The clash of two kingdoms (21-25)
Now all of those calls to faith were needed to be able to get through the next section, which outlines the clash of two kingdoms. Christ's kingdom is not unopposed. And the eighth section, chapters 21-25, really gets intense as these two kingdoms clash in an overt way. It is clear by this time in the book that the leaders of Israel are not in the kingdom of God. John the Baptist had excommunicated them from the kingdom. Instead, they represent the kingdom of Satan. And boy do those two kingdoms clash.
In chapter 21 Christ rides into Jerusalem on a donkey to declare that He is the fulfillment of Zechariah and the other prophets; that He is the King of Israel. He proceeds to cleanse the temple a second time, calling the leaders thieves. That shows His authority over the temple. And while this section welcomed the praises of children and infants, it has one scathing denunciation after another of the hypocrisy of the scribes and Pharisees. If you want your ears to burn, read all the bold woes that Christ shouted at the scribes and Pharisees in chapter 23. Anyone who thinks being like Jesus means being sweet, nice, and mild-mannered needs to read those chapters. He was holy, but He was anything but nice. There is a vast difference between pleasant niceness and holy zeal that is good.
And of course you know the long Olivet discourse in chapters 24-25 that pronounced judgments upon Israel and which show Jesus to be not only a Judge, but a King who would take over the whole world. But He does so through redemptive judgments. It is par excellence a clash of two kingdoms.
The suffering Servant who lays down His life for His people (26-27)
That leads the religious leaders in the next section to plot to kill Him. And all of chapters 26-27 portray Him as the fulfillment of the Old Testament prophecies about the Suffering Messiah.
That section begins with the threat of His death, a woman pouring perfume over His head as a symbol of His burial, Judas betraying Him, and His arrest, scourging, trials by both the Jewish leaders and Pilate, and despite His innocence, being put to death on the cross. But the way Matthew constantly quotes Old Testament prophecies as being fulfilled, he makes it clear that Jesus orchestrated this. He was not a victim. Chapter 26:5 shows them trying to avoid killing him on the Passover. But Jesus is in control and they don't have a choice.
And in the midst of that, Jesus celebrated a meatless Passover one day early with His disciples, showing them that this was what His whole life was leading Him to. The Passover prophesied this hour of suffering and death. Just as the Passover lamb had to be slain to save the people, He had to be slain in order to redeem His people. Jesus knew that His death was not a tragedy, but was instead the means to His victory. Jesus deliberately climbed the cross. He was not a victim.
The risen and conquering King advances His kingdom (28)
But that leads to the last section of the book, chapter 28, which describes the resurrection of Christ and the Great Commission. This portrays the risen and conquering King commanding His footsoliders to advance His Kingdom until all nations are baptized and are obeying all things found in the Word of God. Those are our marching orders. We may not quit until that is accomplished.
When you read the book from this bird's eye view, you see a beautiful and victorious plan. The King has invaded the world, successfully challenged the world, and is now claiming the world as His own. So that is the overview of the whole book.
Additional applications of Matthew
Let me end by giving four additional applications. And my first one is that this book was written to do more than simply inform you about a beautiful plan. It was written with the intention of transforming you. This morning I have had to give you a framework for understanding the book, but you should read the book with an eye to obeying it by God's power. Whether you are looking at the angel's interactions with Mary and Joseph, or the Wise Men's worship of Jesus, or His casting out of demons, every chapter is relevant to how we live out the kingdom today. If Jesus faced demonic attack in chapter 4 through fasting, we should not think that we are beyond fasting in our spiritual warfare. His instructions on divorce and remarriage are not obsolete. They are binding rules in His kingdom. If His resurrection gave power and boldness to the disciples, it should give power and boldness to us. None of this is theory. God wants the book to change us. It is the book of beginnings - kingdom beginnings that each generation must expand upon and live out more and more consistently.
Second, all the core doctrines can be found in the book of Matthew. Numerous quotes from the Old Testament show Matthew teaching the inspiration and authority of the Bible. He teaches us about the virgin birth of Jesus, His humanity, deity, sinlessness, and roles as prophet, priest, and king - especially king. It is rich in the doctrine of the Trinity - perhaps not as rich as the Gospel of John, but it is there. If you go through all of the fundamental doctrines, you will find them in this book.
Third, this is a book that upholds the entire moral law of the Old Testament. Which makes sense - you don't have a kingdom without a law. In Matthew 5:17-19 Jesus said that the Old Testament moral laws (including the least important of the case laws - not taking a mother bird with her young) continues to have authority in His kingdom throughout history. And over and over Jesus castigated the Pharisees for both adding to the Old Testament law as well as taking away from the Old Testament law. If you can read Matthew without coming away a whole-Bible-Christian who loves the law of God, you have not read it with open eyes. It is a book that internalizes the law to everything inside of us and externalizes the law by applying it to every area of life - to marriage, to civics, to child-rearing, to economics, and to other areas. Of course, it does so in seed form, much like Genesis does - it is after all the Book of beginnings.
And finally, if you are discouraged over the state of the kingdom today, read chapter 13 and regain courage and hope. We are still in the beginning stages of the kingdom, and Christ's kingdom will grow until the entire world is leavened by His grace. Amen.
Appendix A - the Generations of Matthew 1
From Floyd Nolan Jones, *Chronology of the Old Testament: A Return to the Basics," (Woodlands, TX: KingWord Press, 1999), pp. 43-44.
The one exception would be Michael Bull's intricate structure of Matthew around the covenantal pattern developed by Ray Sutton. http://www.biblematrix.com.au/the-shape-of-matthews-gospel-overview/ ↩
W. D. Davies and Dale C. Allison Jr., A Critical and Exegetical Commentary on the Gospel according to Saint Matthew, vol. 1, International Critical Commentary (London; New York: T&T Clark International, 2004), 149-155. ↩
See appendix A ↩