This may seem an out-of-date question. Most of the Orthodox community is sufficiently “modern” to accept Rambam’s contention that magic is and always has been fraudulent. On this view, the difference between magic and science is that science works. if any form of incantation were convincingly demonstrated to have real-world effects, it would be considered science rather than magic.
If prayer “works”, should It be considered science rather than religion? Yes and no. Prayer that was predictably effective in the real world would either be science or else a theological monstrosity that turned G-d into a Newtonian machine. Any claim that prayer “works” must always be tempered by the acknowledgment that its effects are humanly unpredictable, and that it works only because G-d chooses to act in a certain way.
This recognition is particularly important over the Yamim Noraim, whose liturgy sometime creates the mistaken impression that reciting the 13 Attributes of G-d is an infallibly potent incantation. This impression may have as its source a powerful passage on Rosh HaShannah 17b.
“Hashem passed before h/His face, and h/He proclaimed”:
Were it not written in Scripture, it would be impossible to say this!
This teaches us that The Holy Blessed One wrapped Himself like a congregational prayer leader
and showed Mosheh the order of prayer.
He said to him:
Whenever Israel sins,
they should do before me just like this order, and I will forgive them.
Rabbi Yochanan seems shocked by his own theological audacity. But what is shocking here? It cannot be the anthropomorphism. Images of G-d as human appear all over Tanakh, and Rabbi Yochanan surely understood the concept of metaphor.
The declaration “Were it not written in Scripture, it would be impossible to say this!” appears seven times in the Talmud. The common denominator of all seven instances is their depiction of G-d as subject to the will of human beings. One clear example is on Bava Batra 10a, also said by Rabbi Yochanan.
Said Rabbi Yochanan:
What is the meaning of “Those who are gracious to the poor are Hashem’s creditors” (Proverbs 19:17)?
Were it not written in Scripture, it would be impossible to say this!
As if it were possible – the borrower (Hashem) is slave to the [human] creditor.
Another is on Berakhot 32a:
“Now you leave go of Me, and My anger will burn amidst them and consume them . . .”
Said Rabbi Abbahu:
Were it not written in Scripture, it would be impossible to say this!
This teaches that Mosheh seized The Holy Blessed One like a person seizing his fellow by the garment,
and said before Him:
Master of the Universe, I will not leave go of you until you absolve and forgive them!
In our case, Rabbi Yochanan knew that G-d was the One who proclaimed the 13 Attributes, and that He intended them to be recited efficaciously by Mosheh, because in Bamidbar 14:17-18 Moshe recites them after declaring that this is “as G-d had previously spoken”, and G-d then forgives them “in accordance with Moshe’s speech”. Rabbi Yochanan’s challenge was to make sense of this apparent theological absurdity in some way. His solution was the image of G-d as Shaliach Tzibbur.
How does presenting G-d in this way solve the underlying problem of G-d’s apparent manipulability? Why does this image help make the verse’s theology sayable, if only barely?
My very tentative answer is that Rabbi Yochanan’s goal was to connect the verses to the practice of communal fasts. Why? If reciting the 13 Attributes were simply a matter of magic, with forgiveness automatic, there would be no need to fast or repent. By limiting the efficacious recitation to the context of a communal effort at repentance, Rabbi Yochanan teachees that the 13 Attributes work only insofar as they help us change into the sort of people who can be at least plausibly worthy of Divine forgiveness.
At the same time, the depiction of G-d as shaliach tzibbur emphasizes that G-d very much wants us to make those changes, and that He Himself prays for His mercy to be revealed above His other attributes (see Berakhot 7a).