Pete's Blog

The following are the first twenty terms of a sequence:

1, 2, 3, 1, 5, 6, 7, 2, 1, 10, 11, 3, 13, 14, 15, 1, 17, 2, 19, 5, . . .

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.

I think this is the toughest one I've posted so far, so you'll probably need a hint. If it hasn't been solved by Thursday, I'll give a hint then. 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, 1, 2, 1, 2, 2, 3, 1, 2, 2, . . .) was the number of 1s in the binary expression of the decimal number. E.g., a(7)=3, since 7₁₀=111₂. T solved it.

Update: I've added five more terms to the sequence. It originally only had the first ten terms.

Update: I've added another five more terms to the sequence.

If you're a fan of Driscoll, or if you're an avid inspector of Piper's resource site (Desiring God), you might be aware of a talk Piper gave at one of Driscoll's pastors' conferences. It was titled "Why I Trust the Scriptures." In it Piper gave an amazing illustration of why Christians should be concerned about know why they believe. It goes something like this:

Suppose a man walks up to, hands you a briefcase, telling you there's a million dollars in it, and asks you to take it to the bank. You ask him why he chose you, and he responds that he picked you at random. Do you feel trusted? No.

Now, suppose the same situation happens—a man walks up to, hands you a briefcase, telling you there's a million dollars in it, and asks you to take it to the bank. This time, though, after you ask him why he's given you the money, he says that it's because he knows you. He's studied your behaviour over the course of months. "I know that you treat your boss fairly, that when you say you're going to do something, you'll do it, that your friends have complete trust in you. I know your character. I have every confidence that if you take this briefcase from me it will get to the bank." You feel trusted from this person.

Likewise, is it glorifying to God is you only trust Him because it's better than nothing? Maybe. But if you trust Him because He's clearly the only choice, because it makes a difference, because He has made you confident in Him, He is very glorified.

I'm not saying every Christian needs to be able to respond to Dawkins, Dennett, Harris and Hitchens (today's four horsemen of atheism), but it's good to know why you trust God. I think that God will be most glorified simply at our words to Him, "Why did I trust your Son? I knew Him." But don't insinuate that confidence in the Truth of the Gospel is about as important as a coin toss by spending as much time thinking about arguments for the faith as you would watching the fate of the flip fall with the coin.

The following are the first ten terms of a sequence:

1, 1, 2, 1, 2, 2, 3, 1, 2, 2, . . .

It may be of interest, though probably unhelpful in determining the pattern, that the limit at infinity of the sequence does not exist, though max_{nє{1,2,3,4, . . .}}{a(n)}=∞. Therefore, it follows that the derivative of the mystical curve of best fit is also non-existent at infinity.

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.

This one's easy, but, if it hasn't been solved by Thursday, I'll give a hint then. 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, 2, 3, 2, 5, 3, 7, 2, 3, 5, . . .) was the greatest prime that divided the placeholder, with the first term defined as 1, that is, a(1)=1. E.g., a(30)=5, since the primes that divide 30 are 2, 3 and 5, and 5 is the highest of them. T solved it. No one remarked that the first term needed to be defined apart from the pattern.

The following are the first forty terms of a sequence:

1, 2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 3, 13, 7, 5, 2, 17, 3, 19, 5, 7, 11, 23, 3, 5, 13, 3, 7, 29, 5, 31, 2, 11, 17, 7, 3, 37, 19, 13, 5, . . .

It may be of interest, though probably unhelpful in determining the pattern, that the limit at infinity of the sequence does not exist, though max_{nє{1,2,3,4, . . .}}{a(n)}=∞. Therefore, it follows that the derivative of the mystical curve of best fit is also non-existent at infinity.

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.

This one's easy, but, if it hasn't been solved by Thursday, I'll give a hint then. 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, 1, 1, 1, 1, 2, 1, 1, 1, 2, . . .) was the number of distinct primes that divided the placeholder. E.g., a(30)=3, since the primes that divide 30 are 2, 3 and 5. KWTsui solved it.

Why should a Christian go to his church's worship service on Sunday? Maybe your first instinct is to go to Hebrews 10:24, 25 ("And let us consider how to stir up one another to love and good works, not neglecting to meet together, as is the habit of some, but encouraging one another, and all the more as you see the Day drawing near"). Applying it to this question it says, "Gather with your whole congregation on a regular basis," but it doesn't apply to why a person should go to Sunday morning worship every week. Realistically, in the whole Bible there's probably no explicit command to do so.

I say "probably" because the fourth Commandment is to work six days and to rest one day. One of the things that the Israelites would do on the seventh day was to gather for corporate worship. So some Christians, particularly those following the Westminster Divines as their standard confession of faith (e.g., Presbyterians), would use the fourth Commandment as a justification to say that worship must be a weekly event. They're called sabbatarians. This isn't the camp I fall in. But, if sabbatarianism were true, then it would be explicit that Christians should go to corporate worship on a weekly basis.

One option would be to argue from apostolic example that we should corporately worship every Sunday. For example, the church was gathered in Ephesus on Sunday for worship in Acts 20:7 ("On the first day of the week, when we were gathered together to break bread, Paul talked with them, intending to depart on the next day, and he prolonged his speech until midnight"). And Paul said that the collection was to be taken from the church in Corinth on Sunday in 1 Corinthians 16:1, 2 ("Now concerning the collection for the saints: as I directed the churches of Galatia, so you also are to do. On the first day of every week, each of you is to put something aside and store it up . . ."). I find this compelling, but it's difficult to argue. If this were the only way, I would use it, but I think that there's still a simpler way.

Hebrews 13:17 says, "Obey your leaders and submit to them, for they are keeping watch over your souls, as those who will have to give an account. Let them do this with joy and not with groaning, for that would be of no advantage to you." You say, then, that the leaders of the church, the elders, have said that worship on Sunday is the most important program that the church runs every week so all are required (i.e., not optional) to go. QED.

Here's a possible objection. A disobedient person might say that the elders of a local church aren't his leaders. Is he a member of a visible church that other brothers might be able to bring him before if he's in sin ("tell it to the church . . . if he refuses to listen even to the church. . ." [Mt. 18:17])? If he isn't, then he's being disobedient for not being a member in covenant with a local church. If he is a member of a local church, then it's even easier to counter. "So I exhort the elders among you, as a fellow elder and a witness of the sufferings of Christ, as well as a partaker in the glory that is going to be revealed: shepherd the flock of God that is among you, exercising oversight, not under compulsion, but willingly, as God would have you; not for shameful gain, but eagerly; not domineering over those in your charge, but being examples to the flock" (1P. 5:1-3, emphasis added). Seems pretty obvious that the elders are leaders.

Another objection might be to say that leaders are only allowed to enforce biblical commands. The response to that is to go back to Hebrews 10:24, 25 and say that it is left at the elders' discretion how often the congregation needs to meet in order to not neglect meeting. This is similar to how it is at the elders' discretion how often to celebrate the Lord's Supper—whether it be weekly, monthly or quarterly (though quarterly seems too infrequently in my estimation).

In summary, the argument why a person should go to the main corporate worship service their church has (not just the second service in the evening, if it's a second sermon, different from the morning sermon) is be he is told to by his elders.

--

Loving theology, I am compelled to state where my foot falls concerning sabbatarianism. I'm not a sabbatarian. The only defense (two parts: 1, 2) of the position that I've ever heard was by Dr. John Frame, professor of systematic theology at Reformed Theological Seminary. I found it compelling, but not convincing enough. Colossians 2:16 says, "Therefore let no one pass judgment on you in questions of food and drink, or with regard to a festival or a new moon or a Sabbath." So, it seems clear to me that it's not wrong to not practice the Sabbath. Despite Dr. Frame saying that the Colossians passage is the most difficult challenge to his position, more compelling than the Romans one, I find Romans 14:5 even more compelling than the Colossians passage. It reads, "One person esteems one day as better than another, while another esteems all days alike. Each one should be fully convinced in his own mind." This comes up in a passage where Paul is talking about amoral questions (i.e., questions that aren't morally binding one way or another, see a previous blog post to expand on this). Thus, it stands to reason that neither celebrating the Sabbath is wrong, nor is keeping each day as equally important is wrong. That's why I'm not a sabbatarian.

I think that the Bible would be invaluable in counselling. Suppose you have a man who's feeling depressed. He's with a nonchristian counsellor and the latter's trying to figure out why he feels that way. Meanwhile, the man is cheating on his wife. This is how I imagine their conversation going:

"What sort of things are going on in your life right now and over the past few months? Have there been any significant changes?"

"Well, two months ago I began an affair with my secretary from work," the man reported shamelessly. "Other than that, nothing different really that I can think of."

"And you don't think this affair's affecting you?"

"How could it? My wife doesn't have a clue and it's just for fun, so why should it be affecting me? I'm not hurting anyone so I shouldn't feel guilty."

I wonder what a professional, certified psychiatrist would say to that. Since the best answer that an evolutionary worldview can produce to account for morality is that immorality is, by their definition, the cause of unnecessary pain, adultery in this cause would not, by definition, be immoral. The best response, I think, that the counsellor could give, would be to say, "Are you sure your wife doesn't know?" Because, if he's not sure, then he might be anxious that she'll find out. But that's not the point.

The first thing the Christian should say to the man is, "REPENT! You're hurting your soul, most importantly." But the humanist psychiatrist can't go there. He needs to look for something else going on. And then, if he fails to find something else, blame it on an alleged chemical imbalance. (If you're interested in this stuff, then listen to this lecture from the 2001 Shepherd's Conference on medicating psychological illness, given by a former pharmacologist gone pastor.)

Not off the above topic, though indeed changing focus, Carey Hardy, the pastor I referenced above, talked briefly about placebos in his lecture and even more briefly on dream interpretation. What a neat subject the mind is. As much as the Bible talks about the nature of man which comes in very helpful in the subject of counselling, it doesn't talk a lot about medication and dreams.

I wonder where dreams come from. Are they somehow spiritual (e.g., do only our bodies rest when we sleep our do our souls shut down as well?)? Do they have any relevance to our lives? On the Wikipedia article on dreams, there is lots of hypothesis but next to no certainty. I wonder whether God has locked the science of the mind to shame the futile efforts of godless scientists.

And as for placebos (a medically inert substance given under the pretence of being a medical drug), remarkable things happen by the power of suggestion. Let me quote part of the Wikipedia article:

Placebo effects can last for a long time: over 8 weeks for panic disorder, 6 months for angina pectoris, and two and half years for rheumatoid arthritis. Placebo effects after verbal suggestion for mild pain can be robust and still exist after being repeated 10 times even if they have no actual pharmacological pain killing action[.]

That's amazing.

I've had a few thoughts about this myself. First, I think that this explains why people of every religion who pray are more likely to get better than those who don't pray. They (we, maybe) are suggestion to themselves that there is hope of getting better, and this suggestion upon the mind has a placebo effect, causing them to get better. Second, I think this would explain why people get sick a lot. Because they psychosomatically inflict it upon themselves, making themselves more vulnerable to real infection.

I'm not a doctor, I can't verify either of those things. But I think they're true.

The problem I have in stating these is that I fear I am granting too much power to the mind. The Bible is clear that the human mind is not lord over the body which is God's creation, He is. So the idea of the mind healing the person still seems an inadequate explanation to me. Yet, the evidence for the utility of placebos seems strong. And it answers how prayer can appear to work for nonchristians in the case of healing. Another problem that I have with this is that it seems very "name it and claim it." Bad theology.

Anyway, things to consider where science hasn't even begun to scratch the surface.

Starting t Today (Update: awkward wording fixed) will start tradition of uncertain length, where I'll post sequences. I'll post the answers on the following week's sequence.

Anyway, the follow following (Update: conjugated the verb) are the first forty terms of a sequence:

0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, . . .

It may be of interest, though probably unhelpful in determining the pattern, that the limit at infinity of the sequence does not exist, though max_{nє{1,2,3,4, . . .}}{a(n)}=∞. Therefore, it follows that the derivative of the mystical curve of best fit is also non-existent at infinity.

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.

It's pretty tricky. I think you'll need a hint. So, if it hasn't been solved by Thursday, I'll give a hint then. Also, if you ask a polar question (i.e., a yes/no question), I will probably answer it if it relates to this sequence.

Update: Hint: Think prime numbers.

No effort whatsoever was made to ensure historical reliability of this story. The societal conditions in this story are purely there for the sake of advancing the moral of the story, not for advocating a certain societal hierarchy or suppression of opportunities for some.

Wade Crawford was a boy who was picked on for many of his early school years. His father was severely injured in a farming accident when he was young. It was difficult for his mother to find work, as women didn't have many opportunities back in those days. But the community knew what had happened to Mr. Crawford and compassionately gave her a position at the school. (It was very fortunate that Mrs. Crawford came from a wealthy background so she had the rare chance of being well educated and a woman, so she was actually qualified to teach.)

This didn't make it easy on Wade. It was bad enough that he was teased regularly for his father not working, but he was also teased for being the teacher's son. He hated it. He would go home crying from school, so his father would ask what was going on, but would be of little help. So when Mrs. Crawford would arrive home later from school, Mr. Crawford would tell her that Wade was upset, and she would go see him.

She would try to console him, saying, "You don't deserve this; it's not your fault."

Sometimes Wade would retort, "Mom, how can everyone be so mean to me? I don't understand why there isn't anyone who helps me."

"They're not all against you. They're scared of becoming the new targets. So they go along with the crowd. I'm sure that most of them would be good kids if you got to know them apart from the group as a whole."

"I wish someone were mean to them so they could know how it feels."

"Wade, you have such a good heart. I know you don't mean that. When you see someone hurting, though, remember how you feel now and try to help him. Someday you can be a hero if you help someone else. Don't be like those followers who stand with a crowd doing the wrong thing."

"Not now, Mom," he said in protest to her soothe-and-teach combination.

"Wade," she replied sternly. "I know you're hurting, but it's really important to remember that everything happens for a reason. So use this tough time to learn to stand up to bullies."

"I know, Mom. I will. Could we stop talking about this now?"

Wade really did take the lesson to heart, though. He would come to the realization that people broke into two categories, the bullies and the bullied. He wanted to stand for the bullies bullied (Updated).

With his father out of the picture for working on the farm, that put him and his three brothers on the front lines of doing what they could. So it was natural that they were always the strongest boys for their respective ages. And with his mother teaching, Wade had also developed a strong mind. He decided to practice law. He became very competent at his profession.

One day along his career, Frank, the owner and sole employee of an apple orchard came to him asking for his help. Frank (short for François), explained that he and Mrs. Kurt, a lady who had a stand in the local market selling pies, had reached a disagreement. His friends seemed to be doing very well, one had bought a new horse, another had taken his wife on a long voyage to visit England, and another had just acquired a field where he was planning on planting a vineyard. Seeing his friends' advancements, he thought that it might be time to raise the prices on his apples. Mrs. Kurt, who was his main customer, said that if he raised his prices, she would go to another orchard, since he wasn't the only one in the business.

Frank and Wade were friends so the former knew the latter's background, thus he appealed to Wade's sentiment, "We'd been in business this long, and this is how she reacts when I act on behalf of my business? It unfair. She's treating me like I'm disposable and insignificant. If I lose her, how will I provide for my family?" Strangely, Wade was persuaded by this. He saw Mrs. Kurt as the bully, and Frank and as the bullied.

He went to Mrs. Kurt and, using all the gimmicks he'd learned in his profession to be persuasive, he informed her that breaking business with Frank would result in significant legal repercussions. To add to the deception Frank had over Wade, Mrs. Kurt believed Wade. And she sought out the apples that Frank was selling, indeed, at the higher price, for fear of the punishment of not so doing.

--

I'm a poor writer so I suspect many of the details of the story don't seem plausible. For example, how could Wade be manipulated so easily, and how could Mrs. Kurt be so easily duped? And isn't it typical in stories for the person who's picked on in the beginning to be the protagonist in the end? I'm not deluded to think that the contents of this fiction are believable. But the essence of it is happening in our contemporary society with a twist.

The market price for manual labour is below what the workers' unions deem reasonable. So, with the protection of the provincial government, they threaten their employers. For example, if workers go on strike, an employer is not allowed to dismiss those workers and hire new ones. Imagine Frank had said that he wouldn't sell Mrs. Kurt any apples until she paid a higher price per pound of apples, and she wasn't allowed to go to any of the other orchards because of the sway of Wade Crawford. That's so unfair. It is likewise with unions getting the government to take their side against their employers and management. It's an unfair fight when it's the government plus the union versus the employer. In the end, the customer loses because prices go up, adjusting for the union's demands.