Pete's Blog

The following are the first twenty terms of a sequence:

4, 6, 9, 10, 14, 15, 21, 25, 35, 49, 121, 143, 169, 187, 209, 221, 247, 253, 289, 299, . . .

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.

Solutions to the sequences of the previous post:

1. The Tribonacci sequence. Each term is the sum of the previous three terms. E.g., a(3)=1, a(4)=1, a(5)=2, so a(6)=4. Jer solved it.
   
2. The sequence of primes who were the sum of two primes. E.g., 2 and 17 are prime so 19=2+17 is in the sequence, i.e., a(4)=19. It was not solved.
   
3. The sequence of non-square free numbers. That is, numbers who have at least one prime factor with multiplicity. E.g., 21=(3)(7) has no prime factors with multiplicity so it is not in the sequence. E.g., 18=(2)(3²) has the prime factor 3 with a multiplicity of 2. So 18 is in the sequence, i.e., a(6)=18. It was not solved.
   
4. I'll repeat that this was not an easy one. The term a(n) was the largest exponent such that 2^a(n) divided 2n. E.g., take the index n=5. Then 2n=10. 2¹ divides 10, but 2² does not. So, a(5)=1. It was not solved.
   
5. First, define a(1)=1. For the rest of the sequence a(n) was the smallest positive integer that hadn't been used yet which shared a prime factor with a(n-1). E.g., consider n=7. Since a(6)=9, a(7) must be a multiple of 3, since the only prime factor of 9 is 3. Is a(7)=3? No, because 3 has already been used by a(5). Is a(7)=6? No, because 6 has already been used by a(3). Obviously a(7)≠9 since that's what a(6) is. Is a(7)=12? Since 12 hasn't appeared in the sequence yet, yes, a(7)=12. It was not solved.
   
6. Of the seven sequences, this was by far the most interesting. Define a(1)=1. The hint gave away most of the solution, that is, "i is in the sequence if and only if a(i) is odd." The only things left to say were to make clear the definition of the first term, and to say that the sequence is strictly increasing, that is to say, a(i+1)>a(i). E.g., a(2) is unquestionably the most fun to figure out why it is 4, so I'll leave that for the reader's pleasure. 3 is not in the sequence (since only 1 and 4 are, thus excluding 2 and 3), so a(3) must be even. The next lowest even number is 6. So a(3)=6. E.g., 4 is in the sequence so a(4) is odd. So we take the lowest odd number that greater than 6. Thus, a(4)=7.
   
7. The sequence of balanced primes. The sequence is formed by taking the mean average of each pair of primes (i.e., for all distinct pairs of primes p and q we find (p+q)/2) and if the value is prime it is kept in the sequence. Obviously the sequence is ordered least to greatest. E.g., the mean value of the primes 3 and 7 is 5 (i.e., (3+7)/2=5), and since 5 is prime, 5 is in the sequence, i.e., a(1)=5. As you can see, there aren't a lot of primes that are the mean of two other primes.
   

Proof of the exercise given for the sequence of Monday, April 14 (1, 2, 4, 6, 16, 12, 64, 24, 36, 48). I asked you to prove that for each positive integer i there existed a number with exactly i factors. It's fairly simple once you get the first step. The number 2^i-1 has exactly i distinct factors. So, there might be a number less than 2^i-1 with i factors (e.g., 48 is significantly less than 512, but they each have exactly 10 distinct factors), but there always is a number with i factors.

The following are the first ten terms of a sequence:

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

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 Wednesday, I'll give a hint. It's pretty easy, so you probably won't need 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.

Update: Hint: It's related to powers of 2.

I'll post the solution on Thursday. (Since I forgot to put the hint up for last week's sequence until today, I won't put the solution up for it until Wednesday of this week.)

Update: The sequence is the highest exponent for which 2 to the exponent of the entry divides the index. E.g., 2¹=2 divides 3 but 2²=4 does not, so a(3)=1. E.g., 2³=8 divides 8 but 2⁴=16 does not, so a(8)=3. E.g., 2⁰=1 divides 7 but 2 does not, so a(7)=0. E.g., 2¹=2 divides 10 but 2²=4 does not, so a(10)=1. It was not solved.

Update: Last week's second sequence (1, 2, 4, 6, 16, 12, 64, 24, 36, 48, 1024, . . .) was the list of smallest integers with exactly the index's number of proper divisors, that is, a(n) was the smallest positive integer with exactly n divisors. E.g., 1, 2, 3, 4, 6, 9, 12, 18, 36 all divide 36, and they are the only divisors of 36. Furthermore, no positive integer less than 36 has exactly nine divisors. So a(9)=36. It was not solved. As an extra exercise, prove that for each i=1, 2, 3, . . . there exists an integer with exactly i divisors.

The following is a list of sequences (of varying difficulty, where the difficulty is reported based on the number of terms listed, on my subjective assessment) for the following seven weeks, each with a varying number of terms listed:

1. 0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, . . .
   
2. 5, 7, 13, 19, 31, 43, 61, 73, 103, 109, 139, 151, 181, 193, 199, 229, 241, 271, 283, 313, 349, 421, 433, 463, 523, 571, 601, 619, 643, 661, 811, 823, 829, 859, 883, 1021, 1033, 1051, 1063, 1093, 1153, 1231, 1279, 1291, 1303, 1321, 1429, 1453, 1483, 1489, . . . (Update: Hint: Suppose p and q are primes. Which for which values of p and q is p + q in the sequence?)
   
3. 4, 8, 9, 12, 16, 18, 20, 24, 25, 27, . . . (Update: Hint: Look at the prime factors.)
   
4. 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, . . . (Update: Hint: (Upon further thinking, I should have given more terms to indicate that this sequence was tough.) It's something to do with 2^a(n).)
   
5. 1, 2, 4, 6, 3, 9, 12, 8, 10, 5, 15, 18, 14, 7, 21, 24, 16, 20, 22, 11, . . . (Update: Hint: First, notice that the greatest common divisor for successive terms beyond the first (i.e., gcd(a(i), a(i + 1))>1 for each i є {2, 3, 4, . . .}. Second, this sequence contains every positive integer.)
   
6. 1, 4, 6, 7, 8, 9, 11, 13, 15, 16, 17, 18, 19, 20, 21, 23, 25, 27, 29, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 70, 71, 72, 73, 74, . . . (Update: Hint: Notice that i is in the sequence if and only if a(i) is odd.)
   
7. 5, 53, 157, 173, 211, 257, 263, 373, 563, 593, 607, 653, 733, 947, 977, 1103, 1123, 1187, 1223, 1367, . . . (Update: Hint: This sequence is also a subset of the primes. It's somewhat similar to the sequence five above. For each positive integer i, a(i) is related to two primes, p and q, and more specifically the sum p + q. But, this sequence is dissimilar from the one above in that this one's terms, while all are directly related to p + q they're not necessarily of the form p + q. The terms are of the form p + q with something more done to them.)
   

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.

Within eight weeks from now, for any of the sequences that are still left unsolved I'll post a hint, and then on June 15^th, with that week's sequence, post the solutions.

I think that it's easy to think that the healings in the Bible are always related to physical ailments. For example, Jesus healed blindness (Jn. 9:1-7), a withered hand (Lk. 6:6-10), a leper (Mk. 1:40-42), paralysis (Mt. 9:2-7), and many other conditions. As a result, it's easy (at least for me) to think that prayers for healing should be limited to physical infirmities. But consider Psalm 107:17-20:

If I hadn't read it, I would have never guessed that the Bible had anything to say about anorexia. I'm happy that I read it, because it reminds me once again that God does care. Not only does God care when a person is poor, hungry, fatherless, physically broken, persecuted, etc., but He also cares when our minds aren't working properly. It gives me hope that God is willing to heal struggles with gluttony or depression or paranoia, or other psychological problems.

As a note of criticism of much of Christian counseling, this verse clearly says that it's sin that's responsible for this malady, not a deficient childhood where you didn't learn the lessons you needed to. (I'm very pro-biblical counseling, where Christian counseling seems semi-Pelagian at best.)

This week's was solved really quickly, so I'm posting another. The following are the first twenty terms of a sequence:

1, 2, 4, 6, 16, 12, 64, 24, 36, 48, 1024, 60, 4096, 192, 144, 120, 65536, 180, 262144, 240, . . .

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.

This afternoon's sequence (1, 4, 8, 9, 16, 25, 27, 32, 36, 49, . . .) was the sequence of Powerful Numbers. That is to say, the list of positive numbers where if the number has a prime divisor, the square of that prime divides it. E.g., 2 divides 8, so, since 8 is in the list it follows that 2²=4 divides 8, which is obviously true. T solved it.

Update: I've added another ten terms to the sequence so that there are now twenty.

Update: Hint: There's a relationship between n and the divisors of a(n), but probably not the category of relationship that first comes to mind. Since I put the hint up late, I'm not going to put the solution on next week's sequence (that of April 20^th) until Wednesday, April 22^nd.

I love John Piper's ministry. I've referred to it here before, and I have the sidebar on the right of my blog devoted to the resources of his that I've read or listened to lately. Yesterday I listened to a talk that he gave at Driscoll's pastors conference last year. It was the first time in a long time (a few months) that I listened to something from Piper. It filled me with conviction of sin, and a joy in the glory and holiness of God. As with most of the audio I link to in my entries, I highly recommend it.

The talk reminded me of his book The Supremacy of God in Preaching (2003). The book was probably one of the three most important books that I've read in my Christian walk (alongside Desiring God [Piper] and Evangelism and the Sovereignty of God [Packer]).

Here's a few paragraphs from the first chapter (pp. 26-27):

At 109 pages, it's a short read with fairly large print and fairly small pages. It's Piper at his best. Adam said that it's the most readable of Piper's books. I completely agree. Get it. Read it.

One of the blurbs on its back reads, "Here's a book that every preacher should read at least once a year. This book is a powerful antidote to the unbalance, self-centered preaching of today."

The following are the first twenty terms of a sequence:

1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 72, 81, 100, 108, 121, 125, 128, 144, 169, . . .

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 (1, 2, 3, 4, 5, 3, 7, 4, 6, 5, . . .) was the smallest number, say m, such that n divided m! (m-factorial). E.g., 10 divides 5!=120, but not 4!=24, so a(10)=5. E.g., 16 divides 6!=720, but not 5!=120, so a(16)=6. It was not solved.

The following are the first twenty terms of a sequence:

1, 2, 3, 4, 5, 3, 7, 4, 6, 5, 11, 4, 13, 7, 5, 6, 17, 6, 19, 5, 7, 11, 23, 4, 10, 13, 9, 7, 29, 5, 31, 8, 11, 17, 7, 6, 37, 19, 13, 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.

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, 1, 5, 6, 7, 2, 1, 10, . . .) was what's called the square-free part of n. That is to say, a(n) is the smallest positive (i.e., nonzero) divisor of n such that na(n) is a square. E.g., 18=2∙3² so (2)(18)= 2²∙3²=(2∙3)², yielding a(18)=2. KWTsui solved it.

Update: I've added another 20 terms to the sequence. Furthermore, here's a very strong hint: The sequence describes a certain relationship between n and a(n)! (i.e., a(n) factorial).

Blogger's note: The following contrast is extreme. I did not write it myself. I would like to give credit where it's due, but it was sent to me in an email. If you know to whom credit is due, let me know. Follows is the story of The Ant and the Grasshopper:

CLASSIC VERSION:

The ant works hard in the withering heat all summer long, building his house and laying up supplies for the winter. The grasshopper thinks he's a fool, and laughs and dances and plays the summer away. Come winter, the ant is warm and well fed. The shivering grasshopper has no food or shelter, so he dies out in the cold.

THE CANADIAN VERSION:

The ant works hard in the withering heat all summer long, building his house and laying up supplies for the winter. The grasshopper thinks he's a fool, and laughs and dances and plays the summer away. Come winter, the ant is warm and well fed.

So far, so good, eh?

The shivering grasshopper calls a press conference and demands to know why the ant should be allowed to be warm and well fed while others less fortunate, like him, are cold and starving. The CBC shows up to provide live coverage of the shivering grasshopper, with cuts to a video of the ant in his comfortable warm home with a table laden with food. Canadians are stunned that in a ountry of such wealth, this poor grasshopper is allowed to suffer so while others have plenty.

The NDP, the CAW and the Coalition Against Poverty demonstrate in front of the ant's house. The CBC, interrupting an Inuit cultural festival special from Nunavut with breaking news, broadcasts them singing "We Shall Overcome." Jack Layton grants in an interview with Mike Duffy that the ant has gotten rich off the backs of grasshoppers, and calls for an immediate tax hike on the ant to make him pay his "fair share".

In response to polls, the Liberal Government drafts the Economic Equity and Grasshopper Anti-Discrimination Act, retroactive to the beginning of the summer. The ant's taxes are reassessed, and he is also fined for failing to hire grasshoppers as helpers. Without enough money to pay both the fine and his newly imposed retroactive taxes, his home is confiscated by the government. The ant moves to the US and starts a successful agribiz company.

The CBC later shows the now fat grasshopper finishing up the last of the ant's food, though spring is still months away, while the government house he is in, which just happens to be the ant's old house, crumbles around him because he hasn't bothered to maintain it. Inadequate government funding is blamed, Bob Rae is appointed to head a commission of enquiry that will cost $10,000,000.

The grasshopper is soon dead of a drug overdose, the Toronto Star blames it on the obvious failure of government to address the root causes of despair arising from social inequity. The abandoned house is taken over by a gang of immigrant spiders, praised by the government for enriching Canada's multicultural diversity, who promptly set up a marijuana grow op and terrorize the community.

THE END

Blogger's note: I don't agree that laziness should be punished with death, but I think this parable does a good job of showing that circumstances are often self inflicted (though, entirely within the sovereign providence of God).

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.