Exactly. Now, let me draw out the word "ambiguous" a bit more. Not that this is what you meant by the word, but to clarify how I understand it.
Ambiguous | Define Ambiguous at Dictionary.com
I mean it primarily in the sense of definition #3 in the link. Focusing even further on how the answer is difficult to
distinguish, I'm saying that the factors involved are confounded (definition #5 of the following link).
Confound | Define Confound at Dictionary.com
So, let's take a look at the analogy some more.
You've asked at least 2, if not more questions here, and the answers to them are not the same.
1. On average, would a control group of 1000 letter writers receive more money than a control group of 1000 who don't write letters (Matt 5:45)? I know you don't care about the Bible verses, but I think they're important in establishing exactly what it is I'm saying.
So, the answer is, probably not. The 1000 who don't write would receive extra money because of the 1000 who do write. IOW, you can't create the control group you're suggesting without the cooperation of the dictator ... which goes back to what I said about modelling "will."
I disagree. We're trying to see if letter-writing has any effect on who, if anyone, the dictator deigns to send money. We can control letter-writing - just observe 1000 letter-writers and 1000 non-letter-writiers - and measure their finances. The dictator doesn't even need to know about the experiment.
The result, if the dictator does indeed preferentially send more money to the writers, is that there should be a statistically significant increase in money received by letter-writers than non-letter-writiers. If the dictator gives out money purely by random, we shouldn't see anything statistically significant either way.
I don't see what you mean by the control group getting money from the test group - the money is given to them directly. Interest rates being driven down by the influx of cash from the dictator is too indirect for our purposes. The dictator gives them money on an individual basis, and God, if he answers 'yes' to a prayer request for someone's healing, does it on a personal basis as well.
2. Would the natives receive less money if all letter writing stopped (Matt 7:7-9, James 4:1-3)?
Yes. But, good luck getting every Christian in the world to stop praying for a controlled period of time. So, my yes is a statement of faith based on my belief in the Bible - not something I could prove. On the flip side, you wouldn't be able to conduct the test, either.
If I understand you correctly, you're saying that there will be less divine interventions if every Christian stops praying. That implies that there
is divine intervention
because Christians are praying - they ask, and, at least occasionally, they receive because of it.
3. Can we prove the dictator's special intervention for a specific native or group of natives? IOW, can we prove a miracle (1 Kings 18:16-39)?
Again, not without the cooperation of the dictator.
Why? We don't need to prove that a given instance is from the dictator or from their regular job - the money isn't traceable, and healing could be from medicine or from God. Rather, we look at the big picture. Even if we can't tell if a specific instance of healing is divine or not, I don't see why we can't deduce a correlation between prayer and healing. If God intervenes at least some of the time to grant a prayer for healing, no matter how stringent his criteria for a 'proper' prayer, there should be detectable increase in healing for those who are prayed for.
If there's a disease that kills exactly half of the time, 500 out of 1000 patients who are prayed for will die, while 500 out of another 1000 who aren't prayed for (they're homeless or alone or some such) will also die. If God intervenes based on prayer, if he grants prayerful requests for healing, then we should see slightly more than 500 people survive - even if it's just one, that's enough.
And notice that it doesn't matter
which one. Yes, I can't tell if you
his healing is from God or from luck, but we can still confidently say that
someone's healing was from God.
Special intervention is actually a very rare event in the Bible. If you were to consider everyone who has ever lived and the time span of the universe, the frequency of miracles as claimed by the Bible is very rare.
But that is not a problem specific to the Bible. It is a general problem for science. Can you give me a test that will establish the exact time when Betelgeuse will die (go supernova, explode, or whatever the correct term would be)? No. Can you give me a test that will establish the exact time and place when life began on earth? No.
No, but I can tell you that Betelgeuse
will die. The hows and the whys are interesting, but all I'm interested in is, "Does God ever heal because someone prayed for it?".
Your question, no matter how it is posed, is confounded. If you choose, then, to withhold belief about prayer ... shrug ... not much I can do about that. As I said earlier, belief in the efficacy of prayer comes after belief in Christ, not before.
I disagree. If praying for the divine healing of a sick person can occasionally change God's mind, and if God then heals that person, we should see a statistically significant increase in healing for those prayed for over those not prayed for. If not, then God doesn't heal the prayed-for any more than he heals the not-prayed-for, suggesting that praying for someone's healing is something of a futile gesture.