Alex Clark, writer and literary critic:

We're both committed readers, so we should probably stick together rather than picking a fight. But this funny business of the Hawking Index, a lighthearted attempt to work out how far people persist in reading books, as indicated by the passages they highlight on their Kindles, has got me thinking. And it's made me realise that my view has changed. I used to believe that if you really weren't enjoying a book, you should toss it to one side and move on to something you might find more rewarding; essentially, it was born of an insurmountable fear of the sheer number of books I wouldn't get round to reading before I died.

But things have changed. Clearly, I've got older and realised that I was a fool to see world literature as a mountain I had to scale, but more to the point, I've seen the threat that endless distractions and a wussy, don't-like-it, bring-me-another attitude poses to our reading culture. I know I risk sounding po-faced, but the best books are a medium of thick description, painstakingly built word by word to produce strange and unexpected effects in the brain and heart; they deserve more than being treated like a passing bit of entertainment that hasn't quite lived up to the reader's exacting standards.

Tom Lamont, Observer writer

How do you expect to scale the world-literature mountain with a defeatist attitude like that? Look out for me, waving and popping a bottle of fizz, at the summit!

No: I'm not a clock-watching completist in too much of a hurry to give each book I start a fair chance. But of course you should stop reading when the fireworks aren't there. When you aren't impressed, lulled, entertained, lightened, depressed, remoulded, whatever you go to books for. Even if it means reshelving the thing with that telltale halt in the creases on the spine, or admitting to friends, spouses or book clubs that you've bunked a recommendation.

Alex, you speak as if the very fact of a book's publication, of it having adverts on the train, or chummy cover quotes, ensures quality. Like hell. All sorts of humdrum, one-draft, low-horizon filler gets released – gets pushed, gets bought, gets warmly reviewed, even. So be your own filter. A good time to abandon, I think, is when the peal from your in-built bullshit alarm gets too loud to ignore; if you want to do it by numbers, stop when you begin to groan at a rate of more than once per page. At that point do say: "I-don't-like-it, bring-me-another." Stop at once, mid-sentence if necessary, and throw that book into the sea.

AC Believe me, I am not defending every book that gets published, nor telling people to force themselves onwards when something is clearly a) dross or b) so completely antithetical to everything they as a reader hold dear that only misery awaits. That would be ludicrous, masochistic and likely to result in a more total disenchantment with reading. (By the way: do let's reconvene for a debate about the state of publishing and of the importance of high-quality review coverage another time.)

But I am saying that if you give up on a book the minute you don't like a character, twig a plot development, see quite where the author's going with it all, have a sudden yen for a game of Candy Crush – then you're going to miss out. I've nothing against reads that are quick and dirty fun, but seriously good books are immersive experiences, demanding of time and patience. Respect them.

TL But there is a masochistic sense out there – isn't there? – that it's somehow bad form or disrespectful or helpful to Hitler not to finish books. Very austere, very British. Very clear your plate.

Every time I go on holiday, I see first hand the futility of the soldier-on approach. My wife will push through a book she doesn't love (and soon doesn't like and soon palely loathes) making ever slower progress – and so the week vanishes. Meanwhile, I'm sprawled under a pile of discards, hurling about Updikes and Hazzards and le Carrés, all fine, all good, but not the novel I'm looking for, the one that climbs inside my head and eats out a hollow and uses the space to riverdance.

Humour me. I bet there are times, recently, when you wish you'd ditched.

AC Yes, of course there are and I've done it!

TL Name names.

AC Sorry, no names, no pack drill: given last week's reports about how little authors are earning, they don't need another kick in the teeth from me.

But the image of your holiday is exactly what I'm talking about: the idea of you like some Roman emperor, your thumb hovering over these peerless works of prose, poised for the downward jerk if your every whim isn't satisfied. Get over yourself! I'm slapping a literary restraining order on you: don't get within 50 feet of a Shirley Hazzard until you've had a long hard look at yourself.

Meanwhile, I simply produce my (admittedly subjective) experience of reading the final chapters of The Goldfinch. I had been gripped throughout, but nothing prepared me for the hallucinatory, mind-bending brilliance of its finale, truly one of the great moments of my reading life. Now, in a long and complex novel like that – or Don Quixote, or Roberto Bolaño's 2666, or, for example, in one of the twisty, red herring-strewn books by my beloved Nicola Barker – there are bound to be longueurs and bafflements, moments when you think, can I? You know what? You can. And you should.

TL It's art. It's personal. You're fully entitled to be a Roman emperor, condemning or championing, devouring or exiling. I'm still sore about a recent effort to get my friends to read a Penelope Fitzgerald, Human Voices. I loved this weird, scampering novella and brought it to them expecting to be credited with a major find. They hated it, all of them. Found the book irritating, tedious, twee, none getting beyond a dozen pages.

No work is "peerless" to everybody. And it's exactly the sense that we should find something peerless, because of a reputation, because of popular opinion, that tends to keep people death-marching through books that are wrong for them.

I know plenty of smart, literate people who couldn't get on with that widely ratified classic of our time, Wolf Hall, and binned it. Good for them. So Thomas Cromwell never got anywhere near Cardinal Wolsey, let alone Henry VIII, forever remaining a teenager getting beaten up on his father's shop floor. So they opted out of the deftness, the wit of Mantell in her prime. It didn't work for them, at bone level, at gut level, and they put back the book. Shouted: "Next!" They were right to.

It's beach time, and you've probably already scanned a hundred lists of summer reads. Sadly overlooked is that other crucial literary category: the summer non-read, the book that you pick up, all full of ambition, at the beginning of June and put away, the bookmark now and forever halfway through chapter 1, on Labor Day. The classic of this genre is Stephen Hawking's "A Brief History of Time," widely called "the most unread book of all time."

How can we find today's greatest non-reads? Amazon's "Popular Highlights" feature provides one quick and dirty measure. Every book's Kindle page lists the five passages most highlighted by readers. If every reader is getting to the end, those highlights could be scattered throughout the length of the book. If nobody has made it past the introduction, the popular highlights will be clustered at the beginning.

Thus, the Hawking Index (HI): Take the page numbers of a book's five top highlights, average them, and divide by the number of pages in the whole book. The higher the number, the more of the book we're guessing most people are likely to have read. (Disclaimer: This is not remotely scientific and is for entertainment purposes only!) Here's how some current best sellers and classics weigh in, from highest HI to lowest:

"The Goldfinch" by Donna Tartt : 98.5%
This seems like exactly the kind of long, impressive literary novel that people would carry around ostentatiously for a while and never finish. But it's just the opposite. All five top highlights come from the final 20 pages, where the narrative falls away and Ms. Tartt spells out her themes in a cascade of ringing, straight-out assertions.

"Catching Fire" by Suzanne Collins : 43.4%
Another novel that gets read all the way through. "Because sometimes things happen to people and they're not equipped to deal with them" is the most highlighted sentence in the seven-year history of Kindle, marked by 28,703 readers. Romantic heat in the late going also helps to produce a high score.

"The Great Gatsby" by F. Scott Fitzgerald : 28.3%
Like "Catching Fire," a love triangle set against a dystopian America deformed by vast inequalities of wealth and power. The most popular highlight isn't the boats against the current or the green light on the dock. In a nice piece of literary crowdsourcing, it's Nick Carraway's line, "Every one suspects himself of at least one of the cardinal virtues, and this is mine: I am one of the few honest people that I have ever known." It's the axis around which the novel spins.

"Fifty Shades of Grey" by E.L. James: 25.9%
Perhaps surprisingly, the top highlights here are family-friendly. You should apologize to the people you thought were reading this as pure smut, because they actually were just noting the names of the characters' favorite operas and marking, for further study, slogans like "The growth and development of people is the highest calling of leadership."

"Flash Boys" by Michael Lewis : 21.7%
Mr. Lewis's latest trip through the sewers of financial innovation reads like a novel and gets highlighted like one, too. It takes the crown in my sampling of nonfiction books.

"Lean In" by Sheryl Sandberg : 12.3%
The top highlight in this no-nonsense self-help book—"The most common way people give up their power is by thinking they don't have any"—is a sentence that Ms. Sandberg didn't even write: She attributes it to Alice Walker. Delegating and outsourcing are the keys to success for today's busy professional!

"Thinking Fast and Slow" by Daniel Kahneman : 6.8%
Apparently the reading was more slow than fast. To be fair, Prof. Kahneman's book, the summation of a life's work at the forefront of cognitive psychology, is more than twice as long as "Lean In," so his score probably represents just as much total reading as Ms. Sandberg's does.

"A Brief History of Time" by Stephen Hawking: 6.6%
The original avatar backs up its reputation pretty well. But it's outpaced by one more recent entrant—which brings us to our champion, the most unread book of this year (and perhaps any other). Ladies and gentlemen, I present:

"Capital in the Twenty-First Century" by Thomas Piketty : 2.4%
Yes, it came out just three months ago. But the contest isn't even close. Mr. Piketty's book is almost 700 pages long, and the last of the top five popular highlights appears on page 26. Stephen Hawking is off the hook; from now on, this measure should be known as the Piketty Index.

So take it easy on yourself, readers, if you don't finish whatever edifying tome you picked out for vacation. You're far from alone.

Which recent books have you left unfinished? What percentage of them did you read before you gave up? Tweet your responses with #unreadbooks.

—Dr. Ellenberg is a professor of mathematics at the University of Wisconsin, Madison, and the author of "How Not to Be Wrong: The Power of Mathematical Thinking."

No one owns a Kindle for very long without becoming obsessed by its social highlighting feature: unless you go into the preferences to turn it off, the glibbest and most epigrammatic sentences in any popular book begin to appear with dotted lines underneath them and the words ’19 [or however many] people highlighted this’. Our own Mark Mason has written brilliantly and sympathetically  about the consequences. But it is now necessary to admit that he may have missed a trick.

It turns out you may be able to use Kindle highlights to make a rough estimate of how many people are actually reading a book, as opposed to just buying it. The technique was described by Jordan Ellenburg in the Wall Street Journal; I saw it on the reliably interesting academic blog Crooked Timber. He calls it the Hawking Index, after that great unread classic A Brief History of Time:

‘Every book’s Kindle page lists the five passages most highlighted by readers. If every reader is getting to the end, those highlights could be scattered throughout the length of the book. If nobody has made it past the introduction, the popular highlights will be clustered at the beginning.

‘Thus, the Hawking Index (HI): Take the page numbers of a book’s five top highlights, average them, and divide by the number of pages in the whole book. The higher the number, the more of the book we’re guessing most people are likely to have read. (Disclaimer: This is not remotely scientific and is for entertainment purposes only!)’

On this measure, Donna Tartt’s The Goldfinch scores 98.5%, indicating compulsive readability and a highly quotable ending; and Thomas Piketty’s Inequality in the Twenty-first Century manages 2.4%, indicating either an exceptionally cogent and pithy introduction or a great many unread copies (or both). A Brief History of Time scores a relatively respectable 6.6%, but as Crooked Timber’s Harry Brighouse points out, this is probably a flattering result: the vast bulk of the unread copies will be in good, old-fashioned print.