Thank you, honorable Rabbi, for the response.
A. He does not say that prayer is not answered. Exactly the opposite. He only says that we do not see its results *right now*.
For example, he said that the establishment of the State is the result of an answer to an accumulation of prayers that built up over hundreds of years.
B. Assuming the Rabbi can accept that "no prayer goes unanswered" as presented by Rabbi Lundin, can the Rabbi consider changing his mind and say that prayer does have significance?

Best regards, Ehud

A. He certainly does say that. He says that one does not see that it is answered, but insists in his example that it is answered. That is exactly what I was talking about.
B. Strange question. If I become convinced that prayer is answered, then I will certainly think that prayer is answered.

The answer is not necessarily that we asked for X and X happened. Rather, it lies in the fact that we expanded our vessels to receive the divine abundance (which in the end will come down at some point). Rabbi Lundin's claim is that if one prays (for example for healing), then by wanting there to be more healing in the world (or for oneself), that itself is already considered an "answer to prayer," because we expanded the vessels, and once the vessels are broader (there is more desire), then more abundance can be absorbed from the infinite good (the divine light) that exists in the world. For example, once one prays properly for healing, there is more motivation to eat healthily in order to prevent disease (for example), or to find cures for terrible diseases that have already spread.

When the Rabbi (and the whole State of Israel) prayed for the welfare of the soldier Nachshon Wachsman, of blessed memory, we expanded our vessels in love and concern for our soldiers, and perhaps because of that we became more careful about the safety of our soldiers, and even more caring toward one another.

So I have two additional questions for the honorable Rabbi.
The first, and may the honorable Rabbi forgive me for the spiritual nosiness, is whether the Rabbi feels that he expands his vessels when he prays to the Creator of the universe.
The second: assuming one experiences an expansion of the vessels, and then necessarily one's mental state is better, and I am fuller, happier, and more motivated, can the Rabbi accept that this is an "answer to prayer"?

*Although the effect of prayer is usually apparently only internal, the address is external, toward the Creator of the universe.
**Most likely there is divine attentiveness to prayer; I just do not know exactly how it works, or what its meaning is.

Best regards, Ehud.

Hello Ehud.
I understood his argument and responded to it. I understand that he argues that the answer is not on the objective plane but in personal change. To that I say that one can define an answer in other ways too, like a warm feeling in the belly or eating a sandwich in the morning. The answer on the plane of the request actually being fulfilled does not happen.
An answer in other senses can of course occur. That is what is called psychosomatics. Meditation too is answered in the same way: it affects the person doing it, and then good things happen to him. This is the kind of excuse I have been hearing for a long time, and I did not understand what novelty you saw here.

I do not feel an expansion of vessels, especially because I mostly read during prayer. I am not in the habit of engaging in meditations.

The expansion of vessels happens in prayer, in meditation, and in all sorts of ways (some of them negative). But the difference is that as a result of prayer, at some point the "divine indwellings" clothe themselves in the vessels that are more ready to receive them—the most positive ones there are. Maybe the Rabbi is right in his claim that usually one does not see the light clothed in the vessels, at least not in the empirical sense (in the end, a dying cancer patient dies whether people pray for him or not), but there is no doubt that the light is indeed absorbed in the vessels that were created—in this incarnation or another, in that person or another.

The Rabbi notes in his book that he does not accept this explanation. But our inability to check whether prayers were answered in some way does not mean that they do not have an effect at some point. It reminds me of how creationists say that the theory of evolution is incorrect because we will never fully know how the immune system or the nursing system in mammals developed. The fact that we probably will never merit to understand it at a sufficiently high level does not mean that it did not happen (evolutionarily); it just means we lack the perspective. Here too, regarding prayer, at least on the individual level, we probably do not have the perspective. And therefore perhaps it is not such a good idea to give up on the idea of praying, even for someone who finds it difficult.

As for general providence, here one actually can assume it on the basis of rational observation:[1]
– Prayer for the welfare of the State: it seems to be working quite well, when a state surrounded by enemies that are not weak qualitatively, and many times stronger quantitatively, survives for decades and several wars (in some of which the enemy had a qualitative advantage too, not only a quantitative one).
– The return of the Jewish people to its land, after many prayers.
– The Land of Israel was relatively desolate for almost 2,000 years, even though it is not a bad region, is holy also to other religions, and was full of conquerors who had the opportunity to plant a serious stake here.[2]

[1] I note that I read the Rabbi's words that just as in the case of "individual providence" the matter is not possible technically/physically, so too with general providence; and still, the evidence for general providence for this people cries out so loudly that it is very hard to ignore.
[2] In the trilogy the Rabbi writes that everything described above does not, in his opinion, indicate divine intervention in history, but only that the planner of history knew about the high qualities that exist in the people, and therefore foresaw from the outset that it would return to its land. So perhaps (according to the Rabbi's view alone), the fact that the Jewish people returned to its land and survived almost 2,000 years in an exile that was mostly hostile does not indicate general providence over the Jewish people, but merely that this is a high-quality people. But how can one explain the fact that this land remained fairly empty for almost 2,000 years, while around it huge cities arose (Alexandria, Cairo, Aleppo, Damascus, Hama, etc.), and if such huge cities had arisen in the area of the Land of Israel, the Return to Zion would not have been possible…
What "quality of the Jewish people" explains that?
Can the Rabbi think of something?

*Sorry for the length. If the Rabbi nevertheless finds it appropriate to read/respond, I would be grateful.

Regarding prayer, it seems to me that everything has been explained.
The issue of the people's return to its land has already been discussed here on the site several times at length. None of these events proves involvement. What remains is the starting assumption.