Pete's Blog

Al Mohler recently commented on the attention the media's given to Jimmy Carter's relationship with the Southern Baptist Convention. Though his column has now been making the rounds of the net for a few days, perhaps it's not too late to refer you to it. It's not a significant issue; Jimmy Carter is old news, and, as much as I love the Southern Baptists, the SBC is still insignificant in our Canadian lives. That said, I thought Mohler made a funny observation in it against Jimmy Carter: "[President Carter] straightforwardly rejects what he admits some texts of the Bible teach. Then, he opens and closes his article by citing as his main authority the Universal Declaration of Human Rights, adopted by the United Nations in 1948" (emphasis added). I found it a funny read, even if it's irrelevant to most of us, because Dr. Mohler points out a number of strange things in the way the story's recently been covered.

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The story of Numbers 13-14, where the twelve Israelites go to spy out Canaan and see if it's conquerable (though God's already promised the land to them) and the reaction of Israel to the spies' report, this, is summarized by Dan Phillips (in passing—this is not what his post was primarily about) as:

God said "Go"

They said "No"

So God said "No go"

They said "Woe!"

(Some tried...

...they died)

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Unborn babies can learn and use their memories in the womb!

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In Harry Potter V: The Order of the Phoenix, the Minister of Magic (the highest ranking official in the magical world), Cornelius Fudge, is paranoid that Dumbledore is fabricating the return of Voldemort. Interestingly, Rowling (the author) paralleled Fudge's paranoia to an historical figure, concerning the rise of the Nazis. She said, "My model of the world after Voldemort's return was, directly, the government of Neville Chamberlain in Great Britain during the Second World War, when he tried to minimize the menace of the Nazi regime for political convenience."

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Frank Leahy: "Egotism is the anaesthetic that dulls the pain of stupidity."

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Aaron Menikoff at 9 Marks: "Yes, the Gospel is offensive and we can't think we have to 'earn' the right to share it. But our evangelism should be robust enough that our lives really are overlapping with non-Christians. We really should be getting to know them." After having read the title of the entry, A Challenge to Evangelism, it took me a while while reading the entry to realize he meant "challenge" in the C4C way.

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Taken from The Amateur Etymologist:

Awhile is an adverb used after a verb. Its definition is "after a short period of time". Example:

After the heavy lunch, Roger snuck into the bedroom and slept awhile before resuming his chores.

A while, on the other hand, is a construction meaning "an indefinite period of time". Example:

• The family settled in Shanghai for a while.
  
• After a while, the car drove off.
  

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One friend recently said he wasn't sure how to interpret 1 Timothy 2:15, "Yet [a woman] will be saved through childbearing—if they continue in faith and love and holiness, with self-control." So I figured I'd make reference to a good blog entry by Dr. Andreas Kostenberger on the verse.

Here's the conclusion: "In v. 15, Paul addresses the question, 'How can women today avoid the mistake made by Eve?' The answer: By adhering to their God-given boundaries and tending to their God-given responsibilities."

What's really valuable about this entry is that afterwards there is dialogue between Dr. Kostenberger and Dr. Ben Witherington in the comments section. Dr. Witherington is a staunch egalitarian. In fact, he said that he really liked the ESV Study Bible except for the lack of female and ethnic scholars among the contributors. (They're complementarian, so in this case, the editors decided to allow men to fulfill this role of teaching. As for the charge of too many white guys, my guess, though I can't substantiate this, is that they're not conceding to affirmative action. They probably took the best men in each of the fields, and each of those men happened to be white.)

Despite all the literature out there on this verse, I'm still not sure why Paul goes from the third person singular feminine ("she will be saved . . .") to the third person plural ("if they continue . . .").

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In Isaiah 43:6 God calls Himself the "King of Israel": "Thus says the LORD, the King of Israel and his Redeemer, the LORD of hosts: 'I am the first and I am the last; besides me there is no god.'" I wonder whether this was the main reason why the Jews didn't want Pilate to put the inscription above Jesus' head on the cross that He was King of the Jews in John 19:19-21. Of course, they may simply have wanted to deny that He the rightful inheritor of the throne of David.

Also, there's more evidence in the Isaiah verse of the deity of Christ: God calls Himself "the first and the last." Given that the book of Revelation is loaded to the brim with Old Testament allusions and quotations (e.g., Revelation 12:9 and 20:2, "ancient serpent" compared with Genesis 3's serpent, or Revelation 14:14, "behold, a white cloud, and seated on the cloud one like a son of man," compared with Daniel 7:13, "behold, with the clouds of heaven there came one like a son of man"), John probably wasn't ignorant of Isaiah's language when he recorded Jesus saying of Himself, "I am the Alpha and the Omega, the first and the last, the beginning and the end" (Revelation 22:13, refer to v. 16 to see that it is Jesus making this statement).

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Is it possible for a legitimately democratic government (as opposed to the ancient monarchies, and the current communist regimes and Islamic theocracies) to steal from its people?

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Mohler's a "Mac guy" (as opposed to a PC, I'm not talking about MacArthur) (00:47).

The following are the first fifty terms of a sequence:

1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, 103, 109, 129, 130, 133, 139, 167, 176, 188, 190, 192, 193, 203, 208, 219, 226, 230, 236, 239, 262, 263, 280, 291, 293, 301, 302, 310, 313, 319, 320, . . .

Same idea as the other sequences. Describe the pattern of the sequence. If you use a search engine, please don't submit it in the comments.

On Wednesday, if it hasn't been solved yet, I'll give a hint (yes, earlier than usual). This one is very tough. I don't know how helpful the hint I'm planning on offering is going to be, so if it's not enough, on Friday I'll post a big hint which will be enough to get it solved.

To give you a starting point, this is a list of numbers that meet a criterion. So considering the absent numbers is as important as considering the present terms. The criterion involves the sum of the squares of the digits of the positive numbers. I don't expect this to be particularly helpful, though. Also, if you ask a polar question (i.e., a yes/no question), I will probably answer it if it relates to this sequence.

I'll post the solution on next week's sequence.

Last week's sequence (1, 4, 9, 16, 25, 36, 49, 64, 81, 1, . . .) was the sum of the squares of the digits. E.g., a(18)=1²+8²=1+64=65. KWTsui solved it.

Update: First Hint: The criterion is one of convergence. And this convergence is related to the sum of the square of the digits of the positive numbers.

Update: Second Hint: Iterate the process of finding the sum of the squares of the digits of the numbers. Do it first for the first few terms of this sequence until you think you see what happens, then do the same iteration process for the positive integers absent from this sequence and confirm that is why they are absent.

The following are the first fifty terms of a sequence:

1, 4, 9, 16, 25, 36, 49, 64, 81, 1, 2, 5, 10, 17, 26, 37, 50, 65, 82, 4, 5, 8, 13, 20, 29, 40, 53, 68, 85, 9, 10, 13, 18, 25, 34, 45, 58, 73, 90, 16, 17, 20, 25, 32, 41, 52, 65, 80, 97, 25, . . .

Same idea as the other sequences. Describe the pattern of the sequence. If you use a search engine, please don't submit it in the comments.

If it hasn't been solved by Thursday, I'll give a hint. Also, if you ask a polar question (i.e., a yes/no question), I will probably answer it if it relates to this sequence.

I'll post the solution on next week's sequence.

Last week's sequence (3, 11, 21, 33, 47, 63, 81, 101, 123, 147, . . .) was defined explicitly a(n)=n²+5n-3. KWTsui solved it.

The following are the first ten terms of a sequence:

3, 11, 21, 33, 47, 63, 81, 101, 123, 147, . . .

Same idea as the other sequences. Describe the pattern of the sequence. If you use a search engine, please don't submit it in the comments.

If it hasn't been solved by Thursday, I'll give a hint. Also, if you ask a polar question (i.e., a yes/no question), I will probably answer it if it relates to this sequence.

I'll post the solution on next week's sequence.

Last week's sequence (0, 2, 4, 6, 8, 10, 11, 12, 14, 16, . . .) was the list of all integers that are the sum of a nonnegative integer plus the integer with its digits reversed. E.g., 71+17=88. E.g., 100+001=101. E.g., 2+2=4. It was not solved.

In an interview Mark Dever did with John Piper, Dr. Dever suggested two books to defend the doctrine of Limited Atonement, Redemption Accomplished and Applied by John Murray and The Difficult Doctrine of the Love of God by D. A. Carson. So when I saw that it was free online I downloaded it right away.

It's not heavy on the argument for the scope of the atonement (which I was fine with). It was a great little read (at only 95 pages from cover to cover). Dr. Carson is a very gifted writer.

One of the benefits of reading a PDF was that it's very easy to quote. Surprisingly, I didn't find it anymore difficult to read than a paperback, and much easier to hold. So, here are some excerpts:

To begin with, I chose the title for this blog entry based on this excerpt: "[I]s the biblical teaching on the love of God maintaining its shape when the meaning of 'God' dissolves in mist?" (p. 12). Saying that "God is love" (1J. 4:8, 16) is meaningless if you don't have the One, True, Living God in mind. It would be like saying, "My breakfast cereal is love."

I've heard many people talk about John 3:16 and the implications it has on God's election. Read how Dr. Carson deals with the verse: "[W]orld in John does not so much refer to bigness as to badness. In John's vocabulary, world is primarily the moral order in willful and culpable rebellion against God. In John 3:16 God's love in sending the Lord Jesus is to be admired not because it is extended to so big a thing as the world, but to so bad a thing; not to so many people, as to such wicked people" (p. 17).

When I read the following quote, I finally realized why so many Arminians have difficulty accepting Limited Atonement. "We have already reflected a little on attempts to strip God's love of affective content and make it no more than willed commitment to the other's good" (p. 46). No Christian can deny that God loves everyone (Mt. 5:45). So if you think that the definition of love is working exclusively for the receiver's good, and since God loves everyone, in the atonement, He must have been working for everyone's good in an equal way.

But God's love varies person to person. Carson argues that God's love manifests in at least five ways (pp. 16-19). (This list is probably the most profitable portion of the book.) I'm not saying that all Arminians make this mistake, but I think that if you're arguing for a universal atonement theologically (as opposed to biblically), you either need to believe one size of love fits all, or you need to believe in an atonement with a limited scope of intended effectiveness.

One of the texts those defending a universal atonement would refer to is 1 John 2:2. Dr. Carson has done much scholarship on the Johannine corpus, so he has some helpful thoughts to bear on this verse:

As far as I can see, a text such as 1 John 2:2 states something about the potential breadth of the Atonement. As I understand the historical context, the proto-gnostic opponents John was facing thought of themselves as an ontological elite who enjoyed the inside track with God because of the special insight they had received.2 But when Jesus Christ died, John rejoins, it was not for the sake of, say, the Jews only or, now, of some group, gnostic or otherwise, that sets itself up as intrinsically superior. Far from it. It was not for our sins only, but also for the sins of the whole world. The context, then, understands this to mean something like "potentially for all without distinction" rather than "effectively for all without exception"—for in the latter case all without exception must surely be saved, and John does not suppose that that will take place. (pp. 76-77)

For the last quote dealing with the extent of the atonement, Dr. Carson cautions that belief in a universal atonement may lead to boasting: "[T]o preserve the notion of particular redemption proves pastorally important for many reasons. If Christ died for all people with exactly the same intent, as measured on any axis, then it is surely impossible to avoid the conclusion that the ultimate distinguishing mark between those who are saved and those who are not is their own decision, their own will. That is surely ground for boasting" (pp. 78-79).

Anyway, going back to the discussion of what love means, where some people think that loving someone involves working only for their good, Carson gives a practical example where loving someone doesn't necessarily end with the expected results:

If for no good reason my teenagers do not get home by the time I have prescribed, the least they will experience is a bawling out, and they may come under some restrictive sanctions. There is no use reminding them that I am doing this because I love them. That is true, but the manifestation of my love for them when I ground them and when I take them out for a meal or attend one of their concerts or take my son fishing or my daughter on an excursion of some sort is rather different in the two cases. Only the latter will feel much more like remaining in my love than falling under my wrath. (p. 20)

I've recorded two quotes demonstrating Dr. Carson's humour. Here's the first one, and I save the second one for last:

Jesus says, "You are my friends if you do what I command. I no longer call you servants, because a servant does not know his master's business. Instead, I have called you friends, for everything that I learned from my Father I have made known to you" (15:14-15).

Observe that Jesus makes a distinction between slaves (douvloi; not "servants") and friends. But the distinction initially surprises us. We are Jesus' friends if we do what he commands. This sounds rather like a definition of a slave. (p. 41)

Often times when I think about the nature of God I over anthropomorphize Him (I make Him out to be too much like a human). For example, I try to understand how it's possible that I have my own decision making mind, that is completely responsible for its action, while at the same time, God ordains all things. It's possible with God because He's not man. Another apparent contradiction I get confused about sometimes is wondering how it's possible for God to be unchanging, yet create something, interact with those creatures, and even have one person of His essence take on a temporal body (i.e., the Incarnation, Jesus). If God sometimes talks, and sometimes doesn't talk, it sounds like He's changing. Somehow it's possible with God.

Anyway, reading Carson, it was helpful to be remind that, "[I]n certain respects God's love does not function exactly like ours. How could it? God's love emanates from an infinite Being whose perfections are immutable [unchanging]. But this way of wording things guards the most important values in impassibility [in humans, dispassionate, in God, more like not driven by unbalanced emotions] and still insists that God's love is real love, of the same genus as the best of love displayed by God's image-bearers" (p. 61). It's refreshing to be reminded not to think narrowly in the categories assigned to God.

This is great for showing how God is different from us: "God does not 'fall in love' with the elect; he does not 'fall in love' with us; he sets his affection on us. He does not predestine us out of some stern whimsy; rather, in love he predestines us to be adopted as his sons (Eph. 1:4-5). The texts themselves tie the love of God to other perfections in God" (emphasis Carson's, p. 61).

This time, how we are supposed to love like God:

John's point in 1 John 4, "God is love," is that those who really do know God come to love that way too. Doubtless we do not do it very well, but aren't Christians supposed to love the unlovable—even our enemies? Because we have been transformed by the Gospel, our love is to be self-originating, not elicited by the loveliness of the loved. For that is the way it is with God. He loves because love is one of his perfections, in perfect harmony with all his other perfections. (pp. 63-64)

Second last. Here, Dr. Carson talks about the unpopular notion of God hating people: "A difference must be maintained between God's view of sin and his view of the sinner. Nevertheless the cliché (God hates the sin but loves the sinner) is false on the face of it and should be abandoned. Fourteen times in the first fifty psalms alone, we are told that God hates the sinner, his wrath is on the liar, and so forth. In the Bible, the wrath of God rests both on the sin (Rom. 1:18ff.) and on the sinner (John 3:36)" (p. 69).

Lastly, a blunt funny one:

Picture Charles and Susan walking down a beach hand in hand at the end of the academic year. The pressure of the semester has dissipated in the warm evening breeze. They have kicked off their sandals, and the wet sand squishes between their toes. Charles turns to Susan, gazes deeply into her large, hazel eyes, and says, "Susan, I love you. I really do."

What does he mean?

Well, in this day and age he may mean nothing more than that he feels like testosterone on legs and wants to go to bed with her forthwith. . . .

What he most certainly does not mean is something like this: "Susan, quite frankly you have such a bad case of halitosis it would embarrass a herd of unwashed, garlic-eating elephants. Your nose is so bulbous you belong in the cartoons. Your hair is so greasy it could lubricate an eighteen-wheeler. Your knees are so disjointed you make a camel look elegant. Your personality makes Attila the Hun and Genghis Khan look like wimps. But I love you!" (pp. 61-62)

It was a really good book and I recommend it for all, even if my review was poorly written.

The following are the first forty terms of a sequence:

0, 2, 4, 6, 8, 10, 11, 12, 14, 16, 18, 22, 33, 44, 55, 66, 77, 88, 99, 101, 110, 121, 132, 141, 143, 154, 161, 165, 176, 181, 187, 198, 201, 202, 221, 222, 241, 242, 261, 262, 281, . . .

Same idea as the other sequences. Describe the pattern of the sequence. If you use a search engine, please don't submit it in the comments.

If it hasn't been solved by Thursday, I'll give a hint. Also, if you ask a polar question (i.e., a yes/no question), I will probably answer it if it relates to this sequence.

I'll post the solution on next week's sequence.

Update: Hint: This is a list, so the sequence is not dependent on the index. Now, for positive integer i there exist nonnegative integers c_i and d_i (c_i greater than or equal to d_i) such that a(i)=c_i+d_i. Obviously, there are ½a(i)+1 choices for the pair (c_i, d_i) if a(i) is even, and ½(a(i)+1) choices for the pair (c_i, d_i) if a(i) is odd, but to be more specific, for a certain pair dependent on a(i) (and for full disclosure, even this pair might not be unique), there is an almost one-to-one relationship between c_i and d_i, that is to say, if you choose the correct c_i you get d_i, and most of the time if you have the correct d_i
you get c_i. An instance where knowing d_i will not give you c_i is for a(19); if you have c_i you get d_i
but if you have d_i
there are an infinite number of choices for c_i. To give some substance to this hint, think mirror for the relationship between the two elements of the pair. (This is a very strong hint, provided you don't over extend the properties of a mirror relationship.)

Update: I've added twenty more terms to the sequence. This is not to denote difficulty. Something worth noting happens at a(33) so I decided to list to the nearest multiple of ten that was greater than 33. (A similar thing happened at a(11).)

Last week's sequence (5, 13, 17, 25, 29, 37, 41, 53, 61, 65, . . .) was the set of hypotenuses of primitive Pythagorean Triples. Suppose you have integers a, b and c. They form a primitive Pythagorean Triple if 1. a²+b²=c², and 2. a and b are coprime (i.e., they share no prime factors, i.e., their greatest common denominator is 1). For the triple a, b and c that satisfies the previous equation, we say that c is the hypotenuse because it is the longest side, and it is opposite the right angle. E.g., 5 is in the sequence because 5²=3²+4², and 3 and 4 share no prime factors. E.g., 37²=12²+35², and 12 and 35 share no prime factors.

Alternatively, last week's sequence is the list of terms from the sequence two weeks ago (0, 1, 2, 4, 5, 8, 9, 10, 13, 16, . . .) with some excluded. Suppose we have a term from two weeks ago, say a(i) for some i=1, 2, 3, . . ., where a(i)= c²+d² for some integers c and d. Then a(i) is excluded from last week's sequence if and only if c and d share a prime factor or c and d are both odd or one of c and d is 0. I mentioned in the hint last week that Euclid's formula generates these terms. Suppose you have odd integer c and even integer d who share no prime factor. These generate the primitive Pythagorean Triple 2cd, |c²-d²| and c²+d². E.g., 0=0²+0², c=d=0. But 0 and 0 share an infinite number of prime factors, so 0 was not in last week's sequence.

Practically speaking, the exclusion statements in the previous paragraph exclude three categories of terms in the sequence from two weeks ago (this is not an exhaustive list):

1. The term is a square, say k² for some integer k. Then k²=k²+0². Obviously 0's in this construction, so all terms that are squares are excluded.
   
2. The term is a square doubled, say 2k² for some k=2, 3, 4, . . . . Then 2k²=k²+k². Obviously k shares at least one prime factor with itself so all the double squares are excluded.
   
3. The term is an hypotenuse of a Pythagorean Triple, but it is not of a primitive Pythagorean Triple. A Pythagorean Triple has the form (ma) ²+(mb) ²=(mc) ² where a, b and c are integers greater than 1, and a and b share no prime factors. The primitive case is for m=1. (An example of a Pythagorean Triple than is not primitive is 45. 45²=27²+36². But 27 and 36 share the prime factor 3, so 45 is a Pythagorean Triple, but is not primitive.) These are the toughest to identify for the purposes of excluding.
   

So, e.g., exclude 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, the rest of the squares, as they fit in the first category.

E.g, exclude 8, 18, 32, 50, the rest of the double squares, as they fit in the second category.

E.g., exclude 10, 20, 26, 34 the rest of the non-primitive Pythagorean Triples, as they fit in the third category.

Real examples: E.g., 2=1²+1². Obviously 1 and 1 are both odd, so 2 is excluded. E.g., 5=1²+2². Considering 1 and 2, they share no prime factors, 2 is even so they're not both odd, and neither number is 0, so there's no reason to exclude 5. Thus, 5 is the first candidate to go into last week's sequence. E.g., 13=2²+3². Considering 2 and 3, they share no prime factors, 2 is even so they're not both odd, and neither number is 0, so there's no reason to exclude 13. It is the second candidate to go into last week's sequence.

It was not solved.