The clock is ticking, and the hour approaching when we enter the polling booth and make our mark. Mine will be for staying in the EU and, if you trust the polls, two thirds of Scots will be joining me. Yet, while much has been said in these final hectic days of campaigning about the stronger allegiance we in the north feel with Europe, the scales are so finely balanced there is no room for certainty, let alone complacence.

It is not just Little Englanders who are keen to go solo. In recent weeks I have met more than a few Little Edinburgers and Little East Lothianers, who feel no affinity with this union, nor any sense of responsibility to hold it together. Pollsters’ assurances do not tally with conversations I and friends have had, in which you discover people you have known for years can take the same basic facts and come up with an entirely different conclusion. It reminds me of arithmetic lessons when, faced with a column of numbers, I could never make them add up to the same answer as everyone else.

As a potentially historic and devastating day draws near, it seems increasingly obvious that even if Remain wins the vote, what we need is not a looser connection with our neighbours across the North Sea, but one that is considerably closer. I am not talking about greater political integration, the very idea of which makes some nations go weak at the knees. I do think, however, we should have more to do with Europe rather than less, become more European rather than more British or Scottish, more outward looking than insular. In short, that we should think big rather than small.

Those belatedly waking up to an awareness of the first and most important purpose behind the original EU – to maintain peace across a newly war-torn continent – are talking about history as if it begins and ends with the two world wars. Our liaison with Europe, however, is almost as old as Scotland itself. The Auld Alliance is the best known of our ancient ties, dating back, allegedly, to the days of Charlemagne. Even if that’s hyperbole, there’s no doubt we and the French were hand in glove for centuries. At one point, in the 1400s, two per cent of the entire Scottish population was employed in its army. So long is the arm of our history with the land of burgundy and baguettes that anyone who was alive in 1906 still retains the right to become a naturalised French citizen should they wish.

We’ve made a great deal of our French connection, in part because it often involved bashing the English, who were its greatest enemy and, until 1603, often ours as well. But the bonds are much wider and more profound than that. In the middle ages our greatest thinkers were educated at universities from Paris and Bologna to the Low Countries. Some also went to Oxford, but after Edward I’s massacre of Scots at the Battle of Dunbar in 1296, we sent our cleverest sons, in the words of one historian, “anywhere other than England”.

As a small country with a backward economy, easy sea crossings to northern Europe facilitated strong trade, cultural and military links with Scandinavia, the Baltic and Poland. Since the times of Ivan the Terrible our soldiers earned medals and land for aiding their battles. One such, in the 17th century, was the ferocious General Tam Dalyell, described as “a Muscovia beast who has roasted men”. Perhaps to compensate for our murderous talents, our other great strength was in medicine, and it was Scottish doctors who revolutionised medical care in Russia.

While Scotland exported some of its ablest merchants and warriors and academics in a steady and much-lamented exodus, we imported the ideas that sparked the Reformation and the rise of Presbyterianism, and subsequent Counter-Reformation. Later, we absorbed Renaissance art and architecture, French novels and Italian opera, as well as sending Europe into ecstasies over the novels of Walter Scott and Lord Byron’s poems. Such was the wealth of intellectual exchange that in Kirkwall’s library in the 1680s there were books from Amsterdam, Cracow, Brussels, Rostock, Paris, Leipzig, amid dozens of others.

You could ask, of course, if history really matters. Sadly, not always. It is irrelevant unless it leaves a tangible mark on the way we think or behave today. Yet to look at our educational, legal, religious and cultural institutions, the influence of Europe on the Scottish way of thinking and living has been profound. It continues to shape us, in the cast of our mind and our points of reference. Why else would some of us feel more at home in Bordeaux or Hamburg than in London or Cardiff?

Europe feels like our extended family, a foreign but familiar cousin. Hence the number of my friends living there who dread a Brexit victory. One, who has lived in Italy for more than half her life, fears having to apply annually for a residential permit and standing in a queue alongside other immigrants, before being sent home by one of Italy’s famously contumacious bureaucrats “for another piece of paperwork to prove I exist”. Another, who lives in Paris with his Bulgarian wife, is breaking out in eczema with worry. Meanwhile, even among the expat community, dinosaurs still roam. In Crete recently, followers of Farage were overheard announcing that should they return to England, there would be no bungalows for them to buy, “because they’ve all been given to refugees”.

Henry James’s Europeans were exotic, and slightly suspect, viewed by their parochial American hosts as potentially disruptive and dishonest. How the compass has swivelled this past half century and more. These days we turn to America for inspiration and guidance, neglecting those closer to hand, with whom politically as well as culturally and historically we have much more in common. Once it was unthinkable for the educated not to have read the latest French or Russian bestseller.

Now our appetite for European culture has diminished. That it is there to be fed is obvious from the way we have leapt upon TV series from Scandinavia and France, such as The Killing and Spiral and their successors. But could you – or I – name the most prestigious Belgian novelists today, or the young German artists making waves, or Poland’s up and coming rock groups or architects? We are more au fait with what’s coming out of New Orleans than from Lisbon or Prague.

It is sobering to think that before the days of decent maps or roads, Scots confidently made Europe their own. Today, when it is only a few hours away, we are careless, or indeed heedless, of the role it has played in our lives. A vote for Leave would be a slap in the face for an alliance we have nurtured and deepened over centuries, to the incalculable benefit of each side. Breaking away would be less a divorce than an expulsion. Not from a Garden of Eden, but from what could be considered, without too much exaggeration, the cradle of our civilisation.