Living in a culture of distraction: Are we capable of "deep work"?

We live in a culture of distraction. This was expressed by T.S. Eliot nearly 100 years ago: Neither plenitude nor vacancy. Only a flicker Over the strained time-ridden faces Distracted from distraction by distraction Filled with fancies and empty of meaning Tumid apathy with no concentration Men and bits of paper, whirled by the cold wind That blows before and after time, Wind in and out of unwholesome lungs Time before and time after ("Burnt Norton," Four Quartets)

How capable are we of "deep work"? The contemporary author, Cal Newport, who has a book by that name (Deep Work: Rules for Focused Success in a Distracted World), defines "deep work" as "distraction-free concentration that pushes your cognitive capabilities to their limit, creating new value and improving your abilities." Citing the likes of Mark Twain, Bill Gates and J.K. Rowling, he notes that deep work was necessary for their creativity. We live in challenging times, Newport points to a number of studies that suggest that, with all of the networking which we feel compelled to do, we are losing our ability to do deep work. One recent study (Brain Drain: The Mere Presence of One's Own Smartphone Reduces Available Cognitive Capacity) speaks of the "brain drain," or reduced cognitive capacity, that is caused by the mere presence of one's cell phone.
Your child's homework time should be a period of independent study so that they can engage in and grow in their capacity for this "deep work." In addition to math and science, they are reading the greatest books ever written--- those which have nourished western civilization. Working deeply with these subjects and texts will enable them likewise to be fed by the truth, beauty and goodness therein and "to push their cognitive capabilities to their limit." What would our classes and seminars be like if each student prepared for class by engaging in this "deep work"?