Strap the Roman visitor into the passenger seat of something like this. Start the engine. Explain to him that there's a box full of a special sort of oil that's burning in constant tiny explosions, making that thing in front that's like three sword blades fastened together spin around 2700 times per minute.
If he's not sure what a "minute" is, just shrug and say, "It's really fast, ok?"
Start taxiing towards the runway. You're moving at about walking pace, so while he'll be astonished by the lack of horses pulling this peculiar cart, he won't be too worried. He might wonder why you're talking to thin air when you start saying things like "Tower, Sierra Tango ready at runway 23," and even more shocked when a stranger's voice comes out of thin air to say "Sierra Tango, cleared for take-off." He might suspect ventriloquism, or possibly ghosts.
However, he won't be thinking about that for long when the noisy thing in front of you both suddenly gets much louder, and you're moving forward again. Faster. At walking speed. Faster. At running speed. Faster. At the speed of a ship under full sail. Faster. At the speed of a galloping race horse. Even faster. Faster still. Impossibly fast.
Brace yourself, as it's possible he may scream in terror as the ground suddenly drops away beneath you, and he's pressed back into his seat as you pull back the stick and soar into the air, like an arrow shot from a bow. Higher and higher, so the people and houses and odd-looking horseless chariots dwindle into small dots far below. If he turns to you in mute astonishment, confirm it to him: "Yes, we're flying. Like a bird. Except rather faster."
For maximum effect, I'm going to assume you're starting from Fiumicino, Rome's international airport, and you've got special permission for this flight to ignore the usual laws on restricted airspace. Bank out over the sea, then come in from the west, flying low so you can see all the landmarks. Point out Ostia to him -- in his day that was Rome's port at the mouth of the River Tiber, about 32km from the city itself.
The most impressive landmarks still visible today were built by Emperor Trajan round about AD 100 -- the artificial island now called Isola Sacra, and the huge hexagonal artificial lake called Portus (now Lago Traiano) that was used as an anchorage. If your visitor comes from that time, he'll recognise them - but so small below him, as if in a map or painting. (The Romans did have maps, so he'll be familiar with the concept.)
Now ask him how long it should take to get from Ostia to Rome. 32km is about a day's journey on horseback, or two days with an ox cart. In your aircraft? Six minutes. Demonstrate this to him.
Fly down low so he can see the landmarks he'll recognise -- the Colosseum, the Forum, the Circus Maximus, the Campus Martius. Then fly high so he can see how much larger the city has grown since his day. Casually remark that Rome now has a population of around three million people -- compared to just over one million at its height in ancient times -- and that it's no longer the largest city in the world. There are others far larger; some he'll have heard of like Londinium (London), Lutetia (Paris) and Byzantium (Istanbul), some in countries he may believe are only legendary, like India or Sinae (China); and still others in distant lands on the other side of the Atlantic Ocean that he's never dreamed of.
Then if he's feeling overwhelmed by everything he's seen and done, ask him if he'd like to relax and unwind by the seaside. Baiae near Naples was a favourite holiday resort for wealthy Romans: several Emperors built villas there, and it was noted for its hot springs. It's 240km south of Rome, about a week's travel by land or two days in a fast ship. In less than an hour you'll be landing at Naples airport, and get a taxi to a good hotel then find a restaurant. The lack of baked dormice and fermented fish sauce might be a disappointment to him, but the availability of fresh fruit and vegetables in the middle of winter should make up for it...
I chose 'flight' as the achievement because it's so dramatic. It's far beyond anything the Romans could dream possible, while still being immediately understandable to them.
A computer connected to the Internet containing all the world's knowledge might be more impressive in the abstract, but it's only a box with words and pictures in it.
A diabetic who would have died 20 years ago if not for insulin, a man who's kept alive by the pacemaker in his heart, the woman who's able to lead a normal life because of her kidney transplant, the child who's only alive because of antibiotics -- those changes might be far more significant for the human condition, but they're hard to appreciate simply by looking at a group of people walking down the street.
Telling him "We've landed on the Moon"? Yeah, sure. Prove it. And not just with pictures; the Romans had artists with vivid imaginations too.
But flying at hundreds of kilometres per hour, soaring thousands of metres above the ground, in a small aircraft where you can feel every shake and vibration of the wind? Now that is a visceral experience he won't ever forget.
About the author: Stephen Tempest
What modern achievement would most impress a random time traveller from the Roman Empire? originally appeared on Quora. You can follow Quora on Twitter, Facebook, and Google+.