The Beatles asked, do you believe in love at first sight, and answered, “Yes, I’m certain that it happens all the time.” Do you believe in the idea of the soul mate, that there is someone out there somewhere who represents a perfect fit for your own cluster of values, principles, habits, perspectives, and desires?

That idea goes all the way back to Plato’s Symposium, written around 380 BCE. One of the characters at the philosophical dinner party argues that humans were originally doubles — four arms, four legs, four eyes, two mouths, etc. Zeus became angry with humans and split each of them with a bolt of lightning.

So, we spend our whole lives looking for the other lost half that, if we ever found her or him, makes us whole again. That’s the basis of love — seeking the lost other half and making all sorts of mistakes in choosing too quickly with too little evidence or picking any other merely because we are lonely.

I wonder what Jefferson believed. He surely knew Plato’s Symposium, and probably he read in the original Greek, which, by the way, I did, more or less badly, when I was a student at Oxford.

Here’s what we know, and it is not much, for he was a very private man about his romantic life. His first big crush was on a beautiful young woman named Rebecca Burwell. Jefferson was about as shy and awkward as it is possible to be in pursuing her. He finally worked up the courage to propose to her at a dance in the Apollo Room of the Raleigh Tavern in Williamsburg, Va., but he was so pathetic, so tongue-tied and inhibited, that he left the dance not knowing if he had even managed to make her understand his ardent attraction and desire to marry her. She soon married someone else and made fun of Jefferson for the rest of her life.

Then he married Martha Wayles Skelton, a widow with an infant child. That was Jan. 1, 1772. Jefferson later said they had experienced 10 years of uncheckered happiness before she died Sept. 6, 1782, at the age of 33. They had six children together in that decade, and several miscarriages, so it is clear that there was plenty of sex. She was beautiful, shy, amiable and talented in music. Whether they were quite soul mates is difficult to determine. Probably Jefferson would have scoffed at that notion. But the first bond that brought them together, beyond her availability and her beauty, was a shared love of music. Whether Martha was enough for Jefferson, who was a Renaissance Man and a genius, is unclear, and whether he would have been enough for her —we just don’t know what her deepest life aspirations were — is unknowable. We do know that he suffered something like a nervous breakdown when she died and committed never to remarry, and never did.

Then came Maria Cosway, whom he met in August 1786 at the Halle aux Bleds in Paris. Cosway was an Anglo-Italian painter and musician, petit, blonde, lavender-eyed and apparently profoundly alluring. She is said to have made a game of getting men to fall in love with her, and scores of men did, including poor Jefferson, a self-proclaimed savage from the woods of America. It is fair to say he had never met a woman who had such powers of attraction and was not even slightly afraid to use them to full advantage. You get the sense that he just surrendered to it — her charm, her European sophistication, her talents, her flirtation, her open sexuality. It’s as if he said, “I have been a man of duty and self-discipline all of my life. For more than 20 years I read 10 to 1 hours a day, mastered seven languages, performed every public function asked of me, and married a highly respectable woman who pleased me in many important ways. But she was cruelly taken from me in our prime, and now I am in Paris, which is 3,927 miles from Monticello” — yes, he would have calculated it — “and there is no Madison or Patrick Henry or George Washington to raise an eyebrow here, so I am going to invent the phrase, what happens in Paris stays in Paris and just surrender to this, probably my only chance to have one towering romantic and erotic romance in life, and you only get one, after all.”

Whether Jefferson and Mrs. Cosway consummated their intense romance is unclear — I suppose it hardly matters — but it was certainly an out-of-character moment in Jefferson’s life, and he clearly later blushed to think how completely his mighty head had lost control for a few glorious months.

But when he came back to the United States in 1789, Jefferson pulled away from Mrs. Cosway and held her at arm’s length for the rest of his life, though she proposed to come to the United States per his repeated declarations to her that it is worth a trip across the Atlantic to see the Natural Bridge and the confluence of the Potomac and the Shenandoah, and what he called “our own dear Monticello.”

After that, after 1789, there is no evidence that Jefferson ever bonded with a white woman again. Yes, Margaret Bayard Smith, the wife of Samuel Harrison Smith of the National Intelligencer, had a wonderful crush on Jefferson during the White House years, and he gave her a favorite geranium when he left the presidency in March 1809. She cherished that flower, of course, because it was all of Thomas Jefferson that she was ever going to possess. She and her husband visited Monticello during Jefferson’s retirement years. This was an agreeable light and socially acceptable flirtation, but there is no evidence that Jefferson had romantic interest in Mrs. Smith or she, probably, with him.

And then there is Sally Hemings. He was 30 years older than she was and if their liaison began in 1788 in Paris, she was just 15 when she became the lover of the future president of the United States.

We have no reliable idea of what their relationship amounted to. If you place rape and predatory sexual exploitation on one end of the spectrum, and a 34-year star-crossed love affair defying race and a huge differential in age at the other, the truth probably belongs somewhere in the middle. But here’s what we do know. There were no demands that Sally Hemings could make on Jefferson — take me with you to the White House, introduce me to polite society, publicly acknowledge your mulatto children — that he was bound to grant. She was his slave, his property. She had no rights that any white person was bound to respect. Perhaps they developed a serious common law marriage based on love and mutual respect. We’d like to think so. But we have absolutely no way of knowing that. Her son, Madison, decades later said Jefferson was cordial to his black children, his slave children, but not affectionate.

In Shakespeare’s “Othello,” the cynical Iago says love is “merely a lust of the blood and a permission of the will.” That could characterize Jefferson’s relations with Sally Hemings. I do not think so because he was a man of exquisite sensitivity and delicacy, but we simply don’t know what transpired behind those closed doors, and that’s the way Jefferson wanted it.

Do you believe in love at first sight? I do, but there are so many barriers between that moment and human felicity that it makes sense to take a much wider, wiser, more sober view. I do not agree with Jefferson’s Head, from the famous Head and Heart letter he wrote to Mrs. Cosway, that we should never snatch at the bait of pleasure until we know there is no hook beneath it, but I do think it never hurts to work a little calculus before jumping off the cliff of the heart.