New Yorkers call this week U.N. Week, the time every September when heads of state converge on Manhattan for the U.N. General Assembly. Which raises an obvious yet rarely asked question: In the digital age, why do they bother?

It’s so unnecessary. Everyone could stay home and participate in beautiful 4K video. All participants could know from moment to moment who is there and could communicate with any subset of the group by text in a messaging app set up for the occasion or by video. Meeting that way rather than in person would save hundreds of millions of dollars in direct costs. Heads of state don’t travel cheap; in addition, security costs are always huge, and in the wake of the Manhattan bombing over the weekend Gov. Andrew Cuomo announced that 1,000 additional law enforcement officers will be deployed for U.N. Week. Indirect costs are unknowable but massive. Much of Manhattan becomes virtually gridlocked for days – the U.N. has issued some 14,000 passes for dignitaries, aides, and press – and New Yorkers know that if they don’t have their own motorcade with police escort, walking is probably the fastest way to get where they’re going.

Why put everyone through this when we no longer have to? Turns out there’s a good reason quite beyond any symbolic value of the photo opps. Leaders know that meeting in person, face-to-face, creates a magic achievable in no other way. At least it feels like magic, though researchers have begun to explain it. When two people converse in person, eye-to-eye, their brains literally synchronize; the same parts of both persons’ brains light up at the same time. We’re not consciously aware of this happening, but we feel it. If those same people hold the same conversation back to back, the synchronization disappears.

When two people look into one another’s eyes, each one’s pupils dilate and contract in response to the other’s. Again, we aren’t aware it’s happening, but researchers have found that this unconscious interaction increases trust between the two people. In person, face to face, we unconsciously mimic each other’s posture and tone of voice, and this too builds relationships.

The physical act of shaking hands possesses a magic of its own. Researchers find that negotiators who shake hands first are more open and honest than those who don’t and reach better outcomes, even with all else held constant. Shaking hands is literally an electric experience: Brain imaging shows that we feel rewarded not only by shaking hands, but simply by seeing other people shake hands.

We persist in the antique ritual of U.N. Week for a very good reason. Humans accomplish things in person that are achievable in no other way. The best leaders know this even if they don’t understand the reasons, and they apply that knowledge in all parts of their lives. We’ll never give up communicating digitally – it’s far too valuable – but leaders know that when relationships count most, there’s only one best way to connect.

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Don’t miss the new episode of Aaron Task’s podcast, Fortune Unfiltered. His guest is Carol Roth, a jill of all trades as an author, investor, and entrepreneurship expert.

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