Pete's Blog

This has been fun. I think Mondays will become Sequences Day on my blog.

Anyway, the follow are the first twenty terms of a sequence:

1, 1, 1, 2, 1, 3, 1, 4, 6, 1, 5, 10, 1, 6, 15, 20, 1, 7, 21, 35, . . .

Same idea as the past two days. Describe the pattern of the sequence. Once you figure out the pattern, help me out with the behaviour of the mystical curve of best fit for this sequence at infinity. Is it infinity, or does it not exist? The derivative of the mystical curve of best fit, at infinity, like the function itself, is either infinite or does not exist.

If you use a search engine, please don't submit it in the comments. If it hasn't been solved at the time, Thursday I'll post a hint in the comments section, and Friday, I'll post in the comments section the solution.

If you ask a polar question (i.e., a yes/no question), I will probably answer it if it relates to this sequence.

Since the previous one was solved so quickly, I figured I'd put up a new one. Here are the first ten terms of a sequence.

1, 3, 7, 12, 18, 26, 35, 45, 56, 69, . . .

Same idea as yesterday, describe the pattern of the sequence. Also, since I'm not stating it this time, what would the magical curve of best fit for this one do at infinity? What would its limit be? What would its derivative's limit be?

If you use a search engine, please don't submit it in the comments. Thursday night, I'll post in the comments section the solution.

If you ask a polar question (i.e., a yes/no question), I will probably answer it if it relates to this sequence.

The following is a list of the first 106 (hint: note, not the first 100) terms of a sequence, {a(n)}.

1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 21, . . .

The pattern this sequence employs, if it is to contain each of the positive integers, must take on the form above, with no variation. However, if you were to deviate slightly, and neglect that rule, the sequence would be constructed purely on how you define a(1).

Three possibly interesting, yet useless, characteristics:

• The sequence is non-decreasing, that is, a(k)≤ a(k+1).
  
• The limit of the sequence at infinity is infinity, that is, lim_n→∞a(n)=∞.
  
• The sequences flatten as it approaches infinity, that is, in calculus speak, if a magical, continuous curve of best-fit could be drawn for the sequence, its derivative would be zero at infinity, lim_x→∞f'(x)=0, where f(x) is the function of the magical curve of best fit.
  

Describe the pattern of the sequence.

If you use a search engine, please don't submit it in the comments. Tomorrow, if no one's solved it, I'll post in the comments section a sequence that follows the same pattern, but not following the strict rule of containing all of the positive integers. I think you'll find it helpful. Wednesday night, I'll post in the comments section the solution.

If you ask a polar question (i.e., a yes/no question), I will probably answer it if it relates to this sequence.

I love math.

From Blog and Mablog:

[F]eminism, far from liberating women to compete with men on a level playing field, has actually resulted in a removal of many ancient constraints that provided protection for women—protection from one another. Feminism has not liberated women to get in there to race with the big dogs. But it has succeeded in multiplying the cat fights. Women don't compete with men. But they can be prevailed upon to compete with other women, in the presence of men, for the approval of men, or for the men themselves.

I took the quote out of context, though, it does speak for itself. Read the whole thing.

The proposal of the quote seems both logical and plausible, but not infallible. I can imagine a feminist saying, "That's simply not true." Anyway, I wonder about its validity. Plus, it was written by a man.

--

Doug Wilson, the author of Blog and Mablog, one of my favourite blogs, among other things, writes interesting narratives, they're parables. That's where this quote came from. He's a pastor, a professor, and an apologist. He did a series of debates with Christopher Hitchens (here's the only one with free audio that I know of, three parts: 1, 2, 3, and there's a transcript of all some of their written back and forth).

I am a conservative. As such, I am capitalistic in my thinking, though not a complete libertarian capitalist. Following are some of the truths which make me lean in such a direction. It is a quick list. I might think of others at another point.

1. Capitalism promotes wealth distribution based on merit.
   
2. Labour and natural resources are not the only economic resources in calculations of merit (e.g., a good idea can be very valuable, yet not cost a person a nickel).
   
3. Economics is not a zero-sum game.
   
4. A higher price in one (geographic) place (e.g., in one country) over another (e.g., the higher cost of medical care in the US over Canada, ignoring that the provinces catch the bill in Canada for its citizens) does not imply inefficiencies in the former.
   
5. Money not spent on consumption (e.g., what Bill Gates didn't spend in a year back when he was pulling in an income), and corporate profits are still productive, and can cause economic growth which includes job creation.
   
6. When the economy hurts, most feel it, rich and poor. (Refer to 3.)
   
7. Taxing the rich disproportionately to the rest of the population is a disincentive for working hard. (Refer to 1.)
   
8. The economy has a natural way of setting prices and wages: supply and demand.
   
9. When the government intervenes (e.g., minimum wages, price fixing typically taking the form of ceilings, subsidizing an industry) it creates inequalities which cause the economy to unnaturally shift, distributing wealth where the government deems fit, not where it is merited.
   
10. Government programs (e.g., running a war, universal healthcare, Universities), whether they're good or bad, do not maximize economic productivity. (This one needs a clarification. I haven't looked into this, but many economists have argued that WWII ended the Great Depression. I've never heard someone dissent from this conclusion. Government programs spend money. So they naturally stimulate the economy. The problem is that the government needs to make an assessment of where to spend the money. Individuals are better at making that decision than the government, which is I why I am a proponent of tax cuts across the board to handouts.)
    
11. Capitalism provides an incentive for people to work hard and give their all, while giving natural consequences for laziness and idleness.
    

Some further considerations. As stated above, I'm not a complete capitalist, in fact, I'm a Christian (surprise, surprise) and that has significant implications on the way I think about economics and politics. I know that there are drawbacks to capitalism. I will list some.

1. Since an economy produces maximum human employment when consumption is high, it can tend to promote consumerism, where people store up treasures on earth, blinding them from the greater treasures in heaven found in Christ.
   
2. Capitalism relies on the self-interest of individuals to keep the economy rolling, which can lead to self-absorption and self-obsession, and thus, neglect for other individuals.
   
3. People, though all created in the image of God, are not created equally able to earn wealth, for example, a mentally handicapped person has much less capacity to produce wealth than the average person, yet he should still be provided for, being an image bearer of God. (Actually it's really interesting to think about how God's image is reflected in someone who isn't able to think and communicate above a three-year-old's ability. Maybe it's the way that they are fascinated by everything. Maybe it's the way they are gentler than others. Any other ideas?)
   
4. Capitalism can easily give people an unnatural measure of success and a life well lived. People are on earth to glorify God, not inherently to make money.
   
5. Capitalism has no natural way of punishing immorality (e.g., murder, stealing, racism), so several government programs are necessary, in my mind, such as police departments, prisons and, more abstractly, a government to make law.
   
6. Self-interest could cause a person to live with a scarcity mentality, so his consumption would be lower than it could be, and if every individual behaved in this way, the whole economy would slow down, causing unemployment and poor wealth creation. (This is why WWII was effective at ending the Great Depression. It forced consumption where not enough was happening. I am willing to concede that a government stimulus package can work, but it depends on the situation.)
   
7. If an individual is rightly following his own self-interest, he would realize that having children, and taking care of a child once one is born, is disadvantageous, so capitalism is not able to naturally provide for children. (The question of how much the government should intervene, going against the parents' will, in a child's life is debateable, but I think in certain cases it's necessary. I will blog about this sometime in the near future.)
   

When all has been said and done, there are still two more reasons to go for a more capitalistic system than a more socialistic system for a country's economic policy. First, whether or not you have public healthcare (e.g., in Canada) or private healthcare (e.g., in the U.S.), or high taxes (e.g., France) or low taxes (e.g., the Caymen Islands), as long as people are choosing where to apply for work, where they're going to spend their money, what brand of shoes to buy, the economy is fundamentally capitalistic. There may be more or less socialistic intervention, but the fundamentals are capitalistic. Authoritarian communism failed in the U.S.S.R. and is being marginalized in China (every year I end up reading at least one article saying that China is becoming more and more capitalistic). Like Churchill saying, "democracy is the worst form of Government except all those other forms that have been tried from time to time," capitalism, while it has some dangerous implications, is the only winner so far. (See the YouTube video below.)

Second, an economic system which is more capitalistic, as opposed to less, by implication minimizes the size of the government. In Christianity, we acknowledge that people are sinful, and whenever power is concentrated in certain institutions (e.g., governments) or individuals (e.g., dictators) dangerous outcomes may occur. Have you read 1^st and 2^nd Kings? It's something to consider, at least.

In terms of resources, the only one that immediately jumps to mind that I would recommend is a talk by Wayne Grudem on Why Do Poor Nations Remain Poor? There is also a handout to go along with it. Grudem also wrote a book on the issue called, Business for the Glory of God.

I guess upon second thought I think of a YouTube video that Justin Taylor showed on his blog a few days ago by Milton Friedman. Friedman's a libertarian and he's not a Christian (I'd argue that the two are mutually incompatible). Nevertheless, he and I would have a ton in common to talk about if we were in a room together. His mannerism reminds me of one of my math profs at Carleton, Professor Sam Melkonian. Here's a video of him talking about the benefit of applying capitalistic principles in economic policy:

A paedobaptist is one who says that the baptism of children is legitimate. In my experience, it's not very common in Canadian evangelicalism. It's more common in the US than it is here, especially among Calvinists.

They make many arguments, but I really only find two compelling. One is the origin of infant baptism. If the NT is thoroughly credobaptistic (i.e., the conviction of believer's baptism), where did infant baptism come from, especially since we have records of infant baptism going back to the mid-second century? This isn't the argument I want to challenge, but to direct a word against it, if the early Church were struggling as much as it was on justification by faith alone, the deity of Christ, the supposed eternal virginity of Mary, and other things in Scripture, it's no surprise they erred on baptism.

The other is the connection of circumcision and baptism. That is, the paedobaptist would argue, if children were circumcised in Israel, and since "you were circumcised . . . having been buried with him in baptism" (Co. 2:11-12), i.e., baptism is New Covenant circumcision, children should be baptized. I don't want to deal exhaustively with this one either, but here's a word about this argument: Do paedobaptists baptize their children on the eighth day? Do they only baptize boys? No. Yes, there's continuity between baptism and circumcision, but even the paedobaptist must acknowledge there's also discontinuity.

Also, paedobaptists say that the Lord's Supper corresponds to the Passover (at least reformed paedobaptists do). The whole family, children and all, ate the Passover meal in Israel. But who's allowed to eat the Lord's Supper? Only believers. So it would seem logical that the rites the Israelites practiced that correspond to New Covenant ordinances are reserved for the Church, believers only. But, I've now spent more time on this than I wanted to.

The objection that paedobaptists make to credobaptists that I want to deal with here is another argument from history. They say that children have been baptized for centuries and that only baptizing adults is a (relatively) new invention. I at one time found this argument convincing. Thinking upon it recently, though, I realized the poverty of the argument. For I would say back to them that their view of baptism is a relatively new invention as well.

In the NT, in Catholic teachings, in Luther's writings, and now in credobaptists' theology, a baptized person is always a saved person (or, at least someone thought to be saved). The Catholics believed that baptism saved its recipients. And Luther was simultaneously a paedobaptist and a credobaptist. He said that baptism was a sign of the faith of a person, but indeed, he baptized babies. Seem inconsistent? Almost. He believed in infant faith.

Their position is no less historically novel than the credobaptist's is. In fact, before Luther's day ended, there were Anabaptists (the historical root of the modern day Mennonites, surprisingly, not the modern day Baptists) he was responding to who were practicing what he and the Catholics called re-baptism (Anabaptists are re-baptists since the prefix "ana" is Greek for again). So there's as much historical precedence for credobaptism as paedobaptism.

This isn't a positive argument for credobaptism. In fact, only the connection between the Passover meal and circumcision with the Lord's Supper and baptism that I pointed out here is a positive argument for credobaptism. The others are answers to arguments that paedobaptists make. For a positive statement, read Piper on baptism. For other resources, read this blog interview between Justin Taylor and Steve Wellum on the relationship between baptism and the covenants (long, but so helpful). Also, listen to the three part (1, 2 and 3) debate between Tom Schreiner (credo) and David VanDrunen (paedo).

If you're interested here's a list of contemporary figures and their stance on baptism:

• Credobaptists:
  
  • Mark Dever;
    
  • Al Mohler;
    
  • John Piper;
    
  • John MacArthur;
    
  • Wayne Grudem;
    
  • C.J. Mahaney;
    
  • Mark Driscoll;
    
• Paedobaptists:
  
  • R.C. Sproul;
    
  • Ligon Duncan;
    
  • J.I. Packer;
    
  • Tim Keller;
    
  • Sinclair Ferguson;
    
  • John Stott;
    
  • Derek Thomas.
    

Perhaps, also of interest, here is the position of some historical figures (thus demonstrating my limited knowledge of Church history):

• Augustine (paedo);
  
• Anselm (paedo);
  
• Aquinas (paedo);
  
• John Calvin (paedo);
  
• Huldrich Zwingli (paedo);
  
• John Owen (paedo);
  
• Richard Baxter (paedo);
  
• John Bunyan (credo);
  
• Jonathan Edwards (paedo);
  
• Charles Finney (paedo);
  
• George Whitefield (paedo);
  
• J. Gresham Machen (paedo);
  
• D. Martyn Lloyd-Jones (credo);
  
• William Carey (credo);
  
• Adoniram Judson (credo).

I wonder how long I could convincingly pretend to be colour blind.

I doubt I could for very long pretend to be deaf, physically disabled or completely blind (remember the challenge it was for Ziyi Zhang, in House of Flying Daggers?), but pretending to be colour blind might be doable. I wonder what fumbles would be the first give aways.

Maybe you've seen it already, but a new article has been released criticizing the ministry of Pastor Mark Driscoll. It rides on the heels of a column that Pastor John MacArthur wrote a while back, sometime in 2006 (one of the biggest problems with MacArthur's ministry's website is that none of the resources have dates on them). I don't want to quote much from either of these. By and large, I don't think they're helpful. They're primarily arguments from authority, that is, they pronounce judgment, maybe state a Bible verse, and then leave their word in the lap of the reader, not explaining why what Pastor Driscoll is doing is wrong.

For example, in the article I mention, Mrs. Cathy Mickels' article, her primary accusation against Driscoll is that he talks about sex. The whole time I was reading her article, I was wondering, Why does she have a problem with him talking about sex if the Bible talks about sex? It was true, he does talk about sex, but there's nothing wrong with that. That's why I don't want to quote too much from them.

At the same time, I find myself hesitant to endorse Driscoll, mostly because of the contempt he shows for his opponents, and the quantity of humour that he uses, from the pulpit. That said, I find it really easy to see faults in people, while looking past their strengths. And I certainly do that with Driscoll. So, I'm going to try to do the exact opposite hear by sharing what I respect in him.

He's frequently being praised for being theologically conservative, and I could join in that choir, talking about how the four doctrines I used to most enjoy talking about (baptism, spiritual gifts, God's sovereignty and gender) he and I would agree on—which I do greatly appreciate, but I want to point out another strength of his which goes less spoken.

The things that Driscoll is being criticized for are things that he thinks aren't forbidden in the Bible, which others might. He sees no evidence in Scripture that humour is wrong, so he tells lots of jokes from the pulpit. He sees Jesus insulting the Pharisees, so he openly mocks his critics and opponents from his pulpit (to be fair, I've never heard him do it by name). That said, he has an amazing confidence in the sufficiency of the Scriptures alone. If the Bible doesn't say it's wrong, it ain't wrong. We don't need tradition or culture to tell us what's right and wrong, or to tell us about God. Only the Bible has authority to speak on God, faith and practice.

I'll give an example. The Southern Baptists, whom Driscoll frequently praises, in most corners of their ministry have a vow of temperance (abstinence from alcohol). Driscoll says that since Jesus made wine, he's going to feel free to drink.

Another example. Many reformed pastors (e.g., Mohler, Piper) speak of not making pictures or paintings of Jesus because it borders on violating the Second Commandment, not to make an image of God (Ex. 20:4-6). Driscoll on the other hand, has worn T-shirts with Jesus' face on the front, saying that since God did have a face at one point, it's not blasphemy to try to capture that face in art.

Agree or disagree, Driscoll's example shows that the Scriptures are enough. That Truth changes everything. It means that you don't need to worry about whether it's wrong to have a vacation. You don't need to wonder whether you're sinning by taking two days off per week instead of one. Driscoll does a fantastic job of making that clear. He understands the relationship between the sufficiency of Scripture and the believer's freedom in Christ. I admire his desire to do only what the Bible tells him to do.

--

The title of this entry is not meant to imply that I am less of a sinner than Driscoll. I'm certain the opposite is true. But, as I'm sure he'd agree, he's also a sinner. In this post I'm trying to not focus on where I disagree with Driscoll, thus seeing the good in the sinner.

Update: There's been a bit of controversy on this post in the comments section, particularly over my assertion that Dr. MacArthur's column is largely an argument from authority. So please refer to the comments. If I haven't already, I will soon respond.

Update: I scratched off a chunk of the entry because it was unfair. See the comments for why this came about.