Strange Maps

Here is my favourite map, which I encountered doing research for my book:

It's a traditional "stick chart" from the Marshall Islands (from here). The shells are islands, and the sticks show wave patterns used for navigation. This essay explains the basic idea, and Page 34 of this PDF article explains the chart in the photo. Bikini Atoll, site of the US nuclear tests, is near the top left corner of the map.

I want one!

Happy Euler Day!

I'd completely forgotten that yesterday (April 15) was the 300th anniversary of Leonhard Euler's birth.

As well as being perhaps the greatest mathematician of all time, Euler was a committed Christian (and a P.K.).

In the midst of life...

I was invited to two funerals today. One was for a younger brother in Christ who I didn't know, but who is closely related to people I do know. The other was for a dear elder sister in Christ who was a frequent visitor to this blog.

Both people were fans of the Narnia books, and both are now, I am certain, praising the Lion of those books (who is also the Lamb, and our Lord) in the place where there is no more death:

Then one of the elders said to me, "Do not weep! See, the Lion of the tribe of Judah, the Root of David, has triumphed...

Then I saw a Lamb, looking as if it had been slain, standing in the center of the throne, encircled by the four living creatures and the elders...

Then I looked and heard the voice of many angels, numbering thousands upon thousands, and ten thousand times ten thousand. They encircled the throne and the living creatures and the elders. In a loud voice they sang:

"Worthy is the Lamb, who was slain, to receive power and wealth and wisdom and strength and honor and glory and praise!" (Rev 5:5a,6a,11-12)

But both people left others behind who will need strength from God to deal with their loss, and I pray that they will receive it.

Peter's Denial and Reinstatement

Reading the Passion narrative over Easter, I noticed something about Peter's denial:

John 18:17 "You are not one of his disciples, are you?" the girl at the door asked Peter. He replied, "I am not." ... 25 As Simon Peter stood warming himself, he was asked, "You are not one of his disciples, are you?" He denied it, saying, "I am not." 26 One of the high priest's servants, a relative of the man whose ear Peter had cut off, challenged him, "Didn't I see you with him in the olive grove?" 27 Again Peter denied it, and at that moment a rooster began to crow.

The NIV translates this well - the first two questions use the Greek μη, which expects the answer "no," while the last question uses ουκ, which expects the answer "yes."

Peter's own version of events has three statements, with the last also particularly challenging:

Mark 14:66 While Peter was below in the courtyard, one of the servant girls of the high priest came by. 67 When she saw Peter warming himself, she looked closely at him. "You also were with that Nazarene, Jesus," she said. 68 But he denied it. "I don't know or understand what you're talking about," he said, and went out into the entryway. 69 When the servant girl saw him there, she said again to those standing around, "This fellow is one of them." 70 Again he denied it. After a little while, those standing near said to Peter, "Surely you are one of them, for you are a Galilean." 71 He began to call down curses on himself, and he swore to them, "I don't know this man you're talking about."

This pattern is followed again in John 21, where Jesus uses the word αγαπαω twice (the NIV translates "truly love"), and the weaker (and therefore more challenging) word φιλεω the third time:

John 21:15 When they had finished eating, Jesus said to Simon Peter, "Simon son of John, do you truly love me more than these?"
"Yes, Lord," he said, "you know that I love you."
Jesus said, "Feed my lambs."
16 Again Jesus said, "Simon son of John, do you truly love me?"
He answered, "Yes, Lord, you know that I love you."
Jesus said, "Take care of my sheep."

17 The third time he said to him, "Simon son of John, do you love me?"
Peter was hurt because Jesus asked him the third time, "Do you love me?" He said, "Lord, you know all things; you know that I love you."

18 Jesus said, "Feed my sheep. I tell you the truth, when you were younger you dressed yourself and went where you wanted; but when you are old you will stretch out your hands, and someone else will dress you and lead you where you do not want to go." 19 Jesus said this to indicate the kind of death by which Peter would glorify God. Then he said to him, "Follow me!"

Easter Vigil 6: For New Christians

The last traditional readings (yes, I've skipped a few) are from Daniel (later Colossians was added as well). They are aimed at the new Christians about to be baptised as Easter dawns. The passage about being persecuted for not worshipping pagan idols meant a lot to early Christians -- they faced the same problem.

But there are more metaphorical fires facing the new (and indeed, mature) Christian, and the reminder to "set your minds on things above, not on earthly things" is always apposite.

1 King Nebuchadnezzar made an image of gold, ninety feet high and nine feet wide, and set it up on the plain of Dura in the province of Babylon. 2 He then summoned the satraps, prefects, governors, advisers, treasurers, judges, magistrates and all the other provincial officials to come to the dedication of the image he had set up. 3 So the satraps, prefects, governors, advisers, treasurers, judges, magistrates and all the other provincial officials assembled for the dedication of the image that King Nebuchadnezzar had set up, and they stood before it.
4 Then the herald loudly proclaimed, "This is what you are commanded to do, O peoples, nations and men of every language: 5 As soon as you hear the sound of the horn, flute, zither, lyre, harp, pipes and all kinds of music, you must fall down and worship the image of gold that King Nebuchadnezzar has set up. 6 Whoever does not fall down and worship will immediately be thrown into a blazing furnace."

7 Therefore, as soon as they heard the sound of the horn, flute, zither, lyre, harp and all kinds of music, all the peoples, nations and men of every language fell down and worshiped the image of gold that King Nebuchadnezzar had set up.

8 At this time some astrologers came forward and denounced the Jews. 9 They said to King Nebuchadnezzar, "O king, live forever! 10 You have issued a decree, O king, that everyone who hears the sound of the horn, flute, zither, lyre, harp, pipes and all kinds of music must fall down and worship the image of gold, 11 and that whoever does not fall down and worship will be thrown into a blazing furnace. 12 But there are some Jews whom you have set over the affairs of the province of Babylon—Shadrach, Meshach and Abednego—who pay no attention to you, O king. They neither serve your gods nor worship the image of gold you have set up."

13 Furious with rage, Nebuchadnezzar summoned Shadrach, Meshach and Abednego. So these men were brought before the king, 14 and Nebuchadnezzar said to them, "Is it true, Shadrach, Meshach and Abednego, that you do not serve my gods or worship the image of gold I have set up? 15 Now when you hear the sound of the horn, flute, zither, lyre, harp, pipes and all kinds of music, if you are ready to fall down and worship the image I made, very good. But if you do not worship it, you will be thrown immediately into a blazing furnace. Then what god will be able to rescue you from my hand?"

16 Shadrach, Meshach and Abednego replied to the king, "O Nebuchadnezzar, we do not need to defend ourselves before you in this matter. 17 If we are thrown into the blazing furnace, the God we serve is able to save us from it, and he will rescue us from your hand, O king. 18 But even if he does not, we want you to know, O king, that we will not serve your gods or worship the image of gold you have set up."

19 Then Nebuchadnezzar was furious with Shadrach, Meshach and Abednego, and his attitude toward them changed. He ordered the furnace heated seven times hotter than usual 20 and commanded some of the strongest soldiers in his army to tie up Shadrach, Meshach and Abednego and throw them into the blazing furnace. 21 So these men, wearing their robes, trousers, turbans and other clothes, were bound and thrown into the blazing furnace. 22 The king's command was so urgent and the furnace so hot that the flames of the fire killed the soldiers who took up Shadrach, Meshach and Abednego, 23 and these three men, firmly tied, fell into the blazing furnace.

24 Then King Nebuchadnezzar leaped to his feet in amazement and asked his advisers, "Weren't there three men that we tied up and threw into the fire?"
They replied, "Certainly, O king." (Daniel 3:1-24)

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1 Since, then, you have been raised with Christ, set your hearts on things above, where Christ is seated at the right hand of God. 2 Set your minds on things above, not on earthly things. 3 For you died, and your life is now hidden with Christ in God. 4 When Christ, who is your life, appears, then you also will appear with him in glory. (Col 3:1-4)

Easter Vigil 5: The Passover Lamb and Jonah

The Passover lamb is of course the most obvious type of Christ. A little less obvious is Jonah, who provides types of Christ's resurrection after three days, of baptism (water again), and of the gospel being given to the Gentiles:

1 The LORD said to Moses and Aaron in Egypt, 2 "This month is to be for you the first month, the first month of your year. 3 Tell the whole community of Israel that on the tenth day of this month each man is to take a lamb for his family, one for each household. 4 If any household is too small for a whole lamb, they must share one with their nearest neighbor, having taken into account the number of people there are. You are to determine the amount of lamb needed in accordance with what each person will eat. 5 The animals you choose must be year-old males without defect, and you may take them from the sheep or the goats. 6 Take care of them until the fourteenth day of the month, when all the people of the community of Israel must slaughter them at twilight. 7 Then they are to take some of the blood and put it on the sides and tops of the doorframes of the houses where they eat the lambs. 8 That same night they are to eat the meat roasted over the fire, along with bitter herbs, and bread made without yeast. 9 Do not eat the meat raw or cooked in water, but roast it over the fire—head, legs and inner parts. 10 Do not leave any of it till morning; if some is left till morning, you must burn it. 11 This is how you are to eat it: with your cloak tucked into your belt, your sandals on your feet and your staff in your hand. Eat it in haste; it is the LORD's Passover. (Exodus 12:1-11)

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1 Then the word of the LORD came to Jonah a second time: 2 "Go to the great city of Nineveh and proclaim to it the message I give you."
3 Jonah obeyed the word of the LORD and went to Nineveh. Now Nineveh was a very important city—a visit required three days. 4 On the first day, Jonah started into the city. He proclaimed: "Forty more days and Nineveh will be overturned." 5 The Ninevites believed God. They declared a fast, and all of them, from the greatest to the least, put on sackcloth.

6 When the news reached the king of Nineveh, he rose from his throne, took off his royal robes, covered himself with sackcloth and sat down in the dust. 7 Then he issued a proclamation in Nineveh:
"By the decree of the king and his nobles:
Do not let any man or beast, herd or flock, taste anything; do not let them eat or drink. 8 But let man and beast be covered with sackcloth. Let everyone call urgently on God. Let them give up their evil ways and their violence. 9 Who knows? God may yet relent and with compassion turn from his fierce anger so that we will not perish."

10 When God saw what they did and how they turned from their evil ways, he had compassion and did not bring upon them the destruction he had threatened. (Jonah 3:1-10)

Easter Vigil 4: Crossing the Red Sea

Crossing the Red Sea is a type of conversion, and the waters are another type of baptism. As the Jews were led through the Red Sea, across the desert, to the promised land, we are led through the Christian life to Heaven:

24 During the last watch of the night the LORD looked down from the pillar of fire and cloud at the Egyptian army and threw it into confusion. 25 He made the wheels of their chariots come off so that they had difficulty driving. And the Egyptians said, "Let's get away from the Israelites! The LORD is fighting for them against Egypt."

26 Then the LORD said to Moses, "Stretch out your hand over the sea so that the waters may flow back over the Egyptians and their chariots and horsemen." 27 Moses stretched out his hand over the sea, and at daybreak the sea went back to its place. The Egyptians were fleeing toward it, and the LORD swept them into the sea. 28 The water flowed back and covered the chariots and horsemen—the entire army of Pharaoh that had followed the Israelites into the sea. Not one of them survived.

29 But the Israelites went through the sea on dry ground, with a wall of water on their right and on their left. 30 That day the LORD saved Israel from the hands of the Egyptians, and Israel saw the Egyptians lying dead on the shore. 31 And when the Israelites saw the great power the LORD displayed against the Egyptians, the people feared the LORD and put their trust in him and in Moses his servant.

15:1 Then Moses and the Israelites sang this song to the LORD:

"I will sing to the LORD,
for he is highly exalted.
The horse and its rider
he has hurled into the sea. (Exodus 14:24-15:1)

Easter Vigil 3: Isaac

Genesis 22 describes the Abrahamic covenant. Abraham's only son is a type of Christ, as is the ram sacrificed in Isaac's place. The wood Isaac carries is a type of the Cross:

1 Some time later God tested Abraham. He said to him, "Abraham!"

"Here I am," he replied.

2 Then God said, "Take your son, your only son, Isaac, whom you love, and go to the region of Moriah. Sacrifice him there as a burnt offering on one of the mountains I will tell you about."

3 Early the next morning Abraham got up and saddled his donkey. He took with him two of his servants and his son Isaac. When he had cut enough wood for the burnt offering, he set out for the place God had told him about. 4 On the third day Abraham looked up and saw the place in the distance. 5 He said to his servants, "Stay here with the donkey while I and the boy go over there. We will worship and then we will come back to you."

6 Abraham took the wood for the burnt offering and placed it on his son Isaac, and he himself carried the fire and the knife. As the two of them went on together, 7 Isaac spoke up and said to his father Abraham, "Father?"
"Yes, my son?" Abraham replied.
"The fire and wood are here," Isaac said, "but where is the lamb for the burnt offering?"

8 Abraham answered, "God himself will provide the lamb for the burnt offering, my son." And the two of them went on together.

9 When they reached the place God had told him about, Abraham built an altar there and arranged the wood on it. He bound his son Isaac and laid him on the altar, on top of the wood. 10 Then he reached out his hand and took the knife to slay his son. 11 But the angel of the LORD called out to him from heaven, "Abraham! Abraham!"
"Here I am," he replied.

12 "Do not lay a hand on the boy," he said. "Do not do anything to him. Now I know that you fear God, because you have not withheld from me your son, your only son."

13 Abraham looked up and there in a thicket he saw a ram caught by its horns. He went over and took the ram and sacrificed it as a burnt offering instead of his son. 14 So Abraham called that place The LORD Will Provide. And to this day it is said, "On the mountain of the LORD it will be provided."

15 The angel of the LORD called to Abraham from heaven a second time 16 and said, "I swear by myself, declares the LORD, that because you have done this and have not withheld your son, your only son, 17 I will surely bless you and make your descendants as numerous as the stars in the sky and as the sand on the seashore. Your descendants will take possession of the cities of their enemies, 18 and through your offspring all nations on earth will be blessed, because you have obeyed me."

19 Then Abraham returned to his servants, and they set off together for Beersheba. And Abraham stayed in Beersheba. (Genesis 22:1-19)

Easter Vigil 2: Noah

Noah is of course a type of Christ, and the floodwaters are a type of baptism ("this water symbolizes baptism that now saves you also" -- 1 Peter 3:21), because in both cases the waters represent separation from the sinful world and salvation for the elect.

5:31 Altogether, Lamech lived 777 years, and then he died.

32 After Noah was 500 years old, he became the father of Shem, Ham and Japheth.

6:1 When men began to increase in number on the earth and daughters were born to them, 2 the sons of God saw that the daughters of men were beautiful, and they married any of them they chose. 3 Then the LORD said, "My Spirit will not contend with man forever, for he is mortal; his days will be a hundred and twenty years."
4 The Nephilim were on the earth in those days—and also afterward—when the sons of God went to the daughters of men and had children by them. They were the heroes of old, men of renown.

5 The LORD saw how great man's wickedness on the earth had become, and that every inclination of the thoughts of his heart was only evil all the time. 6 The LORD was grieved that he had made man on the earth, and his heart was filled with pain. 7 So the LORD said, "I will wipe mankind, whom I have created, from the face of the earth—men and animals, and creatures that move along the ground, and birds of the air—for I am grieved that I have made them." 8 But Noah found favor in the eyes of the LORD.

9 This is the account of Noah.

Noah was a righteous man, blameless among the people of his time, and he walked with God. 10 Noah had three sons: Shem, Ham and Japheth.

11 Now the earth was corrupt in God's sight and was full of violence. 12 God saw how corrupt the earth had become, for all the people on earth had corrupted their ways. 13 So God said to Noah, "I am going to put an end to all people, for the earth is filled with violence because of them. I am surely going to destroy both them and the earth. 14 So make yourself an ark of cypress wood; make rooms in it and coat it with pitch inside and out. 15 This is how you are to build it: The ark is to be 450 feet long, 75 feet wide and 45 feet high. 16 Make a roof for it and finish the ark to within 18 inches of the top. Put a door in the side of the ark and make lower, middle and upper decks. 17 I am going to bring floodwaters on the earth to destroy all life under the heavens, every creature that has the breath of life in it. Everything on earth will perish. 18 But I will establish my covenant with you, and you will enter the ark—you and your sons and your wife and your sons' wives with you. 19 You are to bring into the ark two of all living creatures, male and female, to keep them alive with you. 20 Two of every kind of bird, of every kind of animal and of every kind of creature that moves along the ground will come to you to be kept alive. 21 You are to take every kind of food that is to be eaten and store it away as food for you and for them."

22 Noah did everything just as God commanded him.

... 7:6 Noah was six hundred years old when the floodwaters came on the earth.

... 11 In the six hundredth year of Noah's life, on the seventeenth day of the second month—on that day all the springs of the great deep burst forth, and the floodgates of the heavens were opened. 12 And rain fell on the earth forty days and forty nights.

13 On that very day Noah and his sons, Shem, Ham and Japheth, together with his wife and the wives of his three sons, entered the ark. 14 They had with them every wild animal according to its kind, all livestock according to their kinds, every creature that moves along the ground according to its kind and every bird according to its kind, everything with wings.

... 18 The waters rose and increased greatly on the earth, and the ark floated on the surface of the water. 19 They rose greatly on the earth, and all the high mountains under the entire heavens were covered. 20 The waters rose and covered the mountains to a depth of more than twenty feet. 21 Every living thing that moved on the earth perished—birds, livestock, wild animals, all the creatures that swarm over the earth, and all mankind.

... 23 Every living thing on the face of the earth was wiped out; men and animals and the creatures that move along the ground and the birds of the air were wiped from the earth. Only Noah was left, and those with him in the ark.

24 The waters flooded the earth for a hundred and fifty days.

8:1 But God remembered Noah and all the wild animals and the livestock that were with him in the ark, and he sent a wind over the earth, and the waters receded. 2 Now the springs of the deep and the floodgates of the heavens had been closed, and the rain had stopped falling from the sky. 3 The water receded steadily from the earth. At the end of the hundred and fifty days the water had gone down,

... 6 After forty days Noah opened the window he had made in the ark 7 and sent out a raven, and it kept flying back and forth until the water had dried up from the earth. 8 Then he sent out a dove to see if the water had receded from the surface of the ground. 9 But the dove could find no place to set its feet because there was water over all the surface of the earth; so it returned to Noah in the ark. He reached out his hand and took the dove and brought it back to himself in the ark. 10 He waited seven more days and again sent out the dove from the ark. 11 When the dove returned to him in the evening, there in its beak was a freshly plucked olive leaf! Then Noah knew that the water had receded from the earth. 12 He waited seven more days and sent the dove out again, but this time it did not return to him.

... 15 Then God said to Noah, 16 "Come out of the ark, you and your wife and your sons and their wives. 17 Bring out every kind of living creature that is with you—the birds, the animals, and all the creatures that move along the ground—so they can multiply on the earth and be fruitful and increase in number upon it."

18 So Noah came out, together with his sons and his wife and his sons' wives. 19 All the animals and all the creatures that move along the ground and all the birds—everything that moves on the earth—came out of the ark, one kind after another.

20 Then Noah built an altar to the LORD and, taking some of all the clean animals and clean birds, he sacrificed burnt offerings on it. 21 The LORD smelled the pleasing aroma and said in his heart: "Never again will I curse the ground because of man, even though every inclination of his heart is evil from childhood. And never again will I destroy all living creatures, as I have done. (Gen 5-8, selections)

Easter Vigil 1: Creation

From the earliest times, the Church has gathered the night before Easter to celebrate the Passion of Christ. Candles were lit to celebrate the Light of the World, new Christians were baptised, and 12 prophetic passages from the Old Testament were read.

The first is from Genesis, describing creation. Redemption is, of course, just as miraculous.

1 In the beginning God created the heavens and the earth.

2 Now the earth was formless and empty, darkness was over the surface of the deep, and the Spirit of God was hovering over the waters.

3 And God said, "Let there be light," and there was light. 4 God saw that the light was good, and He separated the light from the darkness. 5 God called the light "day," and the darkness he called "night." And there was evening, and there was morning—the first day.

6 And God said, "Let there be an expanse between the waters to separate water from water." 7 So God made the expanse and separated the water under the expanse from the water above it. And it was so. 8 God called the expanse "sky." And there was evening, and there was morning—the second day.

9 And God said, "Let the water under the sky be gathered to one place, and let dry ground appear." And it was so. 10 God called the dry ground "land," and the gathered waters he called "seas." And God saw that it was good.

11 Then God said, "Let the land produce vegetation: seed-bearing plants and trees on the land that bear fruit with seed in it, according to their various kinds." And it was so. 12 The land produced vegetation: plants bearing seed according to their kinds and trees bearing fruit with seed in it according to their kinds. And God saw that it was good. 13 And there was evening, and there was morning—the third day.

14 And God said, "Let there be lights in the expanse of the sky to separate the day from the night, and let them serve as signs to mark seasons and days and years, 15 and let them be lights in the expanse of the sky to give light on the earth." And it was so. 16 God made two great lights—the greater light to govern the day and the lesser light to govern the night. He also made the stars. 17 God set them in the expanse of the sky to give light on the earth, 18 to govern the day and the night, and to separate light from darkness. And God saw that it was good. 19 And there was evening, and there was morning—the fourth day.

20 And God said, "Let the water teem with living creatures, and let birds fly above the earth across the expanse of the sky." 21 So God created the great creatures of the sea and every living and moving thing with which the water teems, according to their kinds, and every winged bird according to its kind. And God saw that it was good. 22 God blessed them and said, "Be fruitful and increase in number and fill the water in the seas, and let the birds increase on the earth." 23 And there was evening, and there was morning—the fifth day.

24 And God said, "Let the land produce living creatures according to their kinds: livestock, creatures that move along the ground, and wild animals, each according to its kind." And it was so. 25 God made the wild animals according to their kinds, the livestock according to their kinds, and all the creatures that move along the ground according to their kinds. And God saw that it was good.

26 Then God said, "Let us make man in our image, in our likeness, and let them rule over the fish of the sea and the birds of the air, over the livestock, over all the earth, and over all the creatures that move along the ground."

27 So God created man in his own image,
in the image of God he created him;
male and female he created them.

28 God blessed them and said to them, "Be fruitful and increase in number; fill the earth and subdue it. Rule over the fish of the sea and the birds of the air and over every living creature that moves on the ground."

29 Then God said, "I give you every seed-bearing plant on the face of the whole earth and every tree that has fruit with seed in it. They will be yours for food. 30 And to all the beasts of the earth and all the birds of the air and all the creatures that move on the ground—everything that has the breath of life in it—I give every green plant for food." And it was so.

31 God saw all that he had made, and it was very good. And there was evening, and there was morning—the sixth day.

2:1 Thus the heavens and the earth were completed in all their vast array.

2 By the seventh day God had finished the work he had been doing; so on the seventh day he rested from all his work. (Gen 1:1-2:2)