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Prayer is an activity that humans around the world engage in on a daily basis. It would make sense that the scientific community would be interested in prayer and try to analyze it.
The problem is that prayer goes beyond the realm of science and can not be complete explained by natural reasoning.
The Catechism of the Catholic Church points out this error in its section on prayer:
We must also face the fact that certain attitudes deriving from the mentality of “this present world” can penetrate our lives if we are not vigilant. For example, some would have it that only that is true which can be verified by reason and science; yet prayer is a mystery that overflows both our conscious and unconscious lives.
CCC 2727
Prayer does not fit the mold of modern scientific inquiry. It cannot be grasped at or examined under a microsocope.
It also cannot be subjected to medical tests or x-rays.
When prayer is seen as only a human activity, it does not allow for the presence of God.
Faith and science
St. John Paul II warned against such a view of this world in an address he gave to scientists in the year 2000:
In past centuries, science, whose discoveries are fascinating, has held a dominant place and at times was considered the only criterion of truth or way to happiness. A reflection based exclusively on scientific elements tried to accustom us to a culture of suspicion and doubt. It refused to consider the existence of God or to view man in the mystery of his origin and his end, as if this perspective might call science itself into question. It sometimes saw God merely as a mental construct which would not stand up to scientific knowledge. These attitudes have estranged science from man and from the service it is called to offer him.
He instead begged scientists to be open to God’s mysterious work in the universe:
Devote all your energies to developing a culture and a scientific approach which will always let God’s providential presence and intervention be disclosed.
If we were hoping that science could explain to us everything about prayer, we will be sorely dissappointed.
Prayer certainly involves the body, but it also involves the spirit, a part of the human person that science alone is not able to pin down to an exam table.
Prayer will always involve a mysterious aspect to it, and that is where faith comes into the picture. If we want to pray, we need to have faith in God that he is with us and calling us back to himself.