Sigmund Freud once compared the human mind to the city of Rome. He was talking about its intriguing series of layers. Just as the human psyche has a build-up of memories, Rome has a history that goes down and down, deeper and deeper: every modern building is on top of a renaissance one, and under that you find the medieval buildings, and then ancient Rome itself. Freud might also have said that – just as with the mind – as you go deeper into the city you find the dirty bits (the mess, the slums and the filth) as well as the clean, official, splendidly "proper" façades.

Ancient Rome was home to a million people, the biggest city in Europe until Victorian London. Most of that million, from the dockers to the hairdressers, didn't live in spacious marble villas. They were packed into jerry-built tower blocks that lined narrow streets, with almost no public services (no refuse collection, no police, only a few amateur firefighters). It must have been a tough place to get along.

So where can you find the traces of these ordinary "high-rise Romans"? Amazingly, the answer is "all over the city". You only need to know where to look, and to keep your eyes open. Happily, it isn't all buried underground.

My favourite remnant of ordinary ancient Roman life is still standing – almost unnoticed – in the very heart of tourist Rome. It's part of a tower block, still surviving to five storeys in the modern Piazza Venezia – just underneath the vast Victor Emmanuel monument (the "Wedding Cake" or "Typewriter"). Most of these blocks have fallen down (in fact they were renowned for falling, or burning, down in ancient Rome itself). But this one was lucky: it survived because it was turned into a church, and because it was built right up against the slopes of the Capitoline Hill. All the same, hardly any of the thousands of locals and visitors who pass it every day give it a second glance.

It's easy enough to work out the basic organisation of the block. On street level, there are shops and workshops (a lot of the merchandise would have spilt out on to the street, chained up – we're told – to any convenient column, making it even harder to negotiate the narrow pavement). Above the shops, the principle was "the higher you went, the worse it got". There were no glamorous penthouses here. On the first floor you can see some spacious family flats; and above that, bedsits. The question is, how many people were crammed into these rooms? If they were single-occupancy, then this was "compact living". But suppose (as I guess) that these single rooms, with no obvious lavatory or cooking facilities, housed whole families, then this must have been the kind of slum that Roman satirists complained about – places where chamber pots (plus contents) were likely to land on your head if you walked past at night.

The Forum, used by rich and poor alike

And in Rome – as this particular high-rise block, right next to the grand temples of the Capitoline Hill, remin ds us – rich and poor lived and worked cheek by jowl. There weren't many "zoned" areas, given over exclusively either to the rich or the poor. In fact, if you look hard enough, you can find traces of real, ordinary people inside the most luxurious and ceremonial buildings of the city. Even in the Forum.

A visit to the ancient Roman Forum can be a disappointment. This was once the centre of Roman public life, where Cicero orated, where the senate met and where Julius Caesar's makeshift funeral pyre was set alight. It is now a rather baffling set of ruins, with just a few standing landmarks: two splendid triumphal arches and the three vast columns of the Temple of Castor (don't be misled by the Temple of Vesta, though: that was entirely reconstructed under Mussolini). The Forum becomes far more interesting if you also look for the evidence of the ordinary men and women who shared this space with the great and the good – and who had their own things to do there, from a bit of gambling to rudimentary dentistry.

Running along its south side are the now decidedly unimpressive ruins of what was once the splendid Basilica Julia (started by Caesar), home of one of Rome's law courts, plus some government offices. Not much survives beyond the floor and the steps running up to it. A barrier now prevents visitors from walking inside; but actually you don't need to. Peek over the barrier on to the steps, and you will see the clear traces cut into the stone of scores of "gaming boards" (various different arrangements of squares and circles). We haven't a clue about the exact rules of the games, but never mind. It's clear that the Basilica Julia wasn't just a place for busy lawyers; go back 2,000 years and you would find the place littered with men with time on their hands, betting a denarius or two on some ancient equivalent of backgammon.

The Colosseum

Next door to the basilica is the great Temple of Castor. Here you have to take your eyes off the columns, and look more carefully at the high platform on which they stand. Built into this, on each side, is what looks like a series of lock-ups. That is exactly what they are – little shops and storage units right underneath this grand monument. One of the corner units was none other than a primitive dentist's surgery. Among the most memorable moments for me in making Meet the Romans was going to see the almost 100 teeth discovered a few years ago in its drains, each one expertly extracted and rotten to the core. Each one a witness to human agony, I thought.

Of course, the Romans themselves knew exactly what a "mixed area" the Forum was. One Roman comic writer even provides a guide to "the types" you might find there: ranging from the "rich ne'er do wells and rather clapped out prostitutes" by the basilica, to the "butchers, bakers and fortune tellers" to the "rent boys" behind the Temple of Castor. There would be plenty of material for Professor Freud here.

Mary Beard is professor of classics at Cambridge University. Her series, Meet the Romans with Mary Beard, is currently being screened on BBC Two.

The marble Arch of Septimius Severus at one end of the Forum

Six places to meet the Romans

1. The remains of the ancient tower block in the Piazza Venezia are not usually open. But you can easily see down to the original street level from the pavement between the Victor Emmanuel monument and the steps that lead up to the Capitoline Hill.

2. The Forum and Colosseum are open seven days a week, and have a joint ticket (buy it online or at the Forum to avoid the queues at the Colosseum). The "dentist's surgery" in the platform of the Temple of Castor is the unit at the right-hand corner, as you look at the temple façade. There is a great museum inside the Colosseum. Look out there for the graffiti of the animals in the arena scratched on to the seats by eager spectators.

3. The Roman Houses (Case Romane) under the Church of SS Giovanni e Paolo are a short walk from the Colosseum (closed Tuesdays and Wednesdays). Underneath the existing church, you can go down first into the church of the fifth century AD, and beneath that into ancient Roman houses. It's hard to work out exactly what's what, but it is atmospheric, nicely evoking the rabbit-warren streets of ancient Rome.

4. The tomb of Eurysaces the Baker, next to the Porta Maggiore, is a wonderful memorial to a former slave who made it big in the baking industry. The site looks as if it is closed, but push the gate and you will usually find it's open.

5. Monte Testaccio ("Broken Pot Mountain"), near the Tiber, in what is now a great nightlife district of the city, by the Aventine Hill, shows another side of ordinary life – the remnants of feeding a million people. The "mountain" is actually a vast rubbish heap of millions of broken storage jars. It is not often open to the public, but you can look into the bowels of the pottery mountain at the back of the restaurants and bars around its base.

6. If you want to find some of the real personalities among the ordinary people of Rome, take a look at their sometimes wonderfully chatty tombstones. There are good galleries of these (with translations) in the Capitoline Museums (closed Mondays), and in the National Museum in the Baths of Diocletian (also closed on Mondays). Not many people spend any time there, but they're missing a treat. Two of my favourites are those of Allia Potestas, a former slave living in a ménage à trois with two men, and Geminia Mater, a five-year-old Roman tomboy.

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