It is funny how odd bits of relatively useless information that you learned in school sneak up on you. Somewhere in the back of our brains is a skip for stuff we crammed in at some stage. Every now and then some of it re-emerges. For example, last Friday night, Archimedes’ principle elbowed its way through the crowd to take an unwanted cameo role in my consciousness.

The image of Archimedes sitting in his bath trying to figure out how much water he displaced over the side every time he took the plunge is an affecting one. When he had finally understood that the weight of an object could be worked out by weighing the amount of water displaced from the bath he reportedly ran through the street of ancient Syracuse screaming “eureka” which means “I have found it”. Unfortunately, last Friday night’s Archimedes intrusion was not half as uplifting.

Looking down at the blocked, stinking toilet bowl on the overcrowded 7pm Iarnrod Eireann service from Dublin to Sligo, Archimedes’ principle suggests that it is only a matter of time before the entire fetid contents of the bowl spills over the lip, gushing in determined piss eddies all over the passengers who are sitting on their bags in the freezing corridor.

To get an impression of how poor some of our public services are, take the last train to Sligo on a Friday night. The loo is a place to start. Ten minutes into the journey, the bowl is clogged. Fag butts floated in the lilting urine and tobacco-coloured viscous slime. The door is jammed, so, quite apart from a lack of privacy, the trickling tributaries of commuters’ piss flow unimpeded into the carriage, soaking the rucksacks and coats of the people who sit on the floor. They only realise what’s happening when they felt unexpectedly damp. One sudden lurch or wobbly track and the piss levies would break. No one seems to care. There is no staff anywhere.

In America they refer to this wilful neglect of public property as “the broken windows theory”. If the State allows an area, an estate or a train to become so run down, this lack of respect for the property signalled by the owners seeps into the minds of the users. If the owners tolerate the deterioration of the service then the service will deteriorate further because the owners set the tone. If the owners have no pride in the conditions on the train, it sets the tone for everyone.

It’s difficult to say whether it’s the smell of urine or Kentucky Fried chicken or both which makes you retch. The overwhelming urge to vomit is unmistakable. Minister for Transport Noel Dempsey and the so-called, train-friendly Green ministers should get the last train to Sligo (leaving Dublin at 19.05) next Friday night. It might give them an idea of just how appalling our train service is. (In fairness to Irish Rail, the Dublin/Cork service has been upgraded substantially in recent years, but the point is why bother upgrading one line if you are going to treat your other customers with such contempt?)

We stand, as the tiny four-carriage “commuter” train (the average Dart train is considerably bigger), trundled through Maynooth, Kilcock, Enfield disgorging the victims of our property boom who have been forced — by the “land cabal” that runs this country — to buy ridiculously overpriced shoe-boxes miles away from work. These young workers are now picking up the tab for the faltering property market and will suffer negative equity for years to come. And as if that betrayal of a generation wasn’t bad enough, they are being given a large two fingers by the State every time they part with their cash to avail of the Sligo cattle train.

We finally get a seat an hour and 10 minutes into the journey after miles of jerry-built estates, replete with outside decking, trampolines and for some inexplicable reason — given the lashing rain outside — top-of-the-range barbecues! Past Longford and the train enters uncharted territory. The reason for saying this is that even the Irish Rail management advertise that the train is unsuited for the journey. It was never meant to go further than Longford, let alone two hours further. If you look up at the proud “network” map — Irish Rail’s equivalent of the bragging wall — you see the farthest extremity that this train is supposed to travel is Longford.

Yet, as we crossed the Shannon, this glorified Dart was bound for the north-west and Sligo when, even by the management’s own admission, the train isn’t up to it.

By now the smell from the loo is overwhelming, adding to the fragrance of dead sheep which steams off the wet coats and bags. It’s hardly a surprise that latest CSO figures reveal a 22pc increase in the number of people driving to work since 2002. Wouldn’t you?

Interestingly, as if this trend, and the Friday night ordeal, wasn’t capable of putting you off public transport on its own, the ads in the carriage suggest that Irish Rail’s management doesn’t believe in a future for trains either.

The most prominent ad is for a Bank of Ireland car loan, urging us to “get our skates on” and take out a car loan at “only 6.9pc APR for loans over €20,000”. This ad is complemented by the AXA insurance ad informing the long suffering train user about the joys of cheap, fully-comprehensive car insurance.

At 11 minutes past nine, over two hours after departure, Paul from the North of England finally arrives with the trolley. He is a member of Ireland largest ethnic minority, the English. Many of these “English” are members of the Irish Diaspora. They are the children of the 500,000 people who left this country in the 1950s and 1960s. These people are the demographic echo of Ireland when it was a failed economic entity. As we trundle into the West heading for Dromod, Carrick-on-Shannon, Boyle and Ballymote, it’s worth remembering how many people left these places in the bad old days.

Pulling into Sligo, the pretty young girl two seats in front is putting on mascara without smudging which, as the train lurches on ancient tracks, is quite an achievement.

She’s no more than 20, stretching her face in the tiny pink mirror. She pouts, flicks her hair and bounds off the train.

She is the next generation. It is her Ireland that we are supposed to be building. The three and a half hour ordeal on the Dublin/Sligo “Intercity”, suggests that we aren’t doing a great job.