Absolutely, fasting is very powerful. That's why Christ said that some demons can only be cast out by prayer and fasting.
Which is also a good Scripture to reference when people start treating fasting as something strictly dietary - which of course it can be, but then it loses any religious significance. Fasting must be accompanied with prayer to accomplish its religious purposes - remembering of course all the different types of prayer that there are.
What I love about fasting is how it contextualizes things - provides clarity, as you say. By voluntarily denying yourself things that the flesh desires, you force yourself to remember what your nature desires, namely, God. As the Scriptures say, if a man lives to be 100, that is a long life - but like a drop of water in the ocean compared to eternity. The Church, in her wisdom, built penitential seasons like Lent into her liturgical calendar so that all the faithful would be encouraged - even commanded, insofar as the "minimum requirements" are concerned - to practice mortification, and thereby, accompanied with prayer, come closer to God. There are things I have given up this Lent that I hope to not pick up again at all; I see how much more fulfilling my life is without those distractions, and how much easier it is to pray about and work toward God's will without these things in my way. Obviously when it comes to not eating three meals a day, that's not something I would adopt year round - although I do certain minor weekly fasting throughout the year - since nutrition and bodily strength do have to be attended to. But other things can be given up permanently, and Lent is a good time to try to purge ourselves of the kinds of impurities we would have to be purified of in Purgatory, if we don't get around to it in this life.
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