To Edinburgh on Saturday to see Hamilton at the Festival Theatre. Had only been waiting nine years. Safe to say it did not disappoint. Wow. A thousand times wow.

Phenomenon is too small a word to sum up Lin-Manuel Miranda’s musical about Alexander Hamilton. Described in the opening song as “a bastard, orphan, son of a whore and a Scotsman”, Hamilton rose from nothing to become one of America’s founding fathers.

The stats tell their own incredible story. Tens of thousands of sold-out performances since its world premiere in New York in 2015; estimated earnings of a billion dollars (on a par with Taylor Swift’s Eras Tour); winner of 11 Tony awards; productions in Puerto Rico, LA, Australia, Hamburg, London west end, and now Edinburgh.

To appreciate Hamilton’s hurricane force you have to see it live in the theatre. Be in “the room where it happens”, as the song says.

Take Saturday. The audience of close to 2000 seemed mainly Scottish. (Judging by the packed train to Queen Street after there was a big contingent from Glasgow.)

On taking their seats in the theatre the audience was quietly excited, but still reserved in that oh-so-Scottish way. After two hours and 45 minutes, this shy lot had become a cheering, laughing, crying, multiple standing ovations-giving band of brothers and sisters who would happily sell their collective grannies for a chance to see it all again. Someone even whooped in my ear and I didn’t mind. This was art as a transformative experience. Miranda and his cast deserve every plaudit that comes their way.

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The Edinburgh show was a coming home of sorts for Hamilton. Scotland has been uncharacteristically cagey about its connections to America’s first Treasury Secretary. No wonder. Alexander’s father, James, was one of several sons of an Ayrshire laird. By all accounts, James was a spiteful, pathetic sort. After moving his family to the Caribbean island of St Croix he skedaddled, leaving them destitute. Two years later Alexander’s mother died in squalor.

James Hamilton you can keep, but Alexander is a different matter. If you hold Alexander Hamilton up to the light and squint a certain way, you can see a certain Scottishness in him. Ferociously hard-working, intelligent, ambitious, talented, passionate, what country would not want to claim him as a son? Plus, he could start a fight in an empty house and often did. You can’t get more Scottish than that.

Success does indeed have many fathers. People see what they want to see in the Alexander Hamilton portrayed in the musical. That is Miranda’s genius. Everyone wants a piece of Hamilton, one that reflects well on them, Americans most of all.

Hamilton plays to the enduring idea that anyone can come from nothing and be something in America, including president (not an honour afforded Hamilton but who knows what might have been). That may seem laughable given the cost of running for political office today, yet it can happen. It did happen. Remember that self-dubbed “skinny kid with a funny name”, born to an American mother and a Kenyan father, who became the 44th US president? Barack Obama might have been an outlier to the rich white men and dynasties that went before and after, but he made it to the top, as miraculous as that still seems.

That’s one “pinch me, I’m dreaming” moment in America’s history. The idea of writing a hit play about a relatively obscure figure in the grand sweep of history is another. Imagine 200 years from now a musical tribute to Gordon Brown, Alex Salmond, Nicola Sturgeon, or Humza Yousaf. Now there is a thought to make the blood run cold.

Many a politician would envy Hamilton’s skills as an operator and communicator. His achievements, including helping to write the Constitution and setting the ground rules for what became the world’s most successful economy, only become more remarkable the more you learn about them. Hamilton had vision; just as important, he got the job done.

Compare Hamilton and his times to what is happening in America today. The play has had its run-ins with politicians. In 2016, in a clip that went viral, vice-president elect Mike Pence was booed by sections of the audience, and a cast member made a statement praising the central role of immigrants in America’s success. That earned a rebuke from Donald Trump, who said on Twitter that the cast had been “very rude to a very good man” and should apologise.

Trump’s very good man is now his declared enemy. How times change. Consider the two men competing to lead America today. If Joe Biden and Donald Trump could borrow any aspect of Hamilton it would be his relative youth. Hamilton was 47 when he died. Trump would also like his war record and his financial skills, Biden the hard-scrabble backstory and original thinking. Neither man compares favourably to Hamilton as was. And what of the great but flawed man himself? It is natural to wonder how he would fare in today’s politics. His first major challenge, ironically enough, would be getting into America in the first place. No one stopped Hamilton at the border and deported him.

Ron Chernow, whose magisterial biography inspired the musical, believes the last place Hamilton would want to be in modern America was Washington DC. He would be temperamentally unsuited to the job of being a politician. For a start, he was an original thinker and fought for his ideas. The notion of moulding policy to please focus groups would have been anathema to him. If Hamilton was challenged he wrote a paper in response. He regarded politics as a serious, difficult business. No tweets or cheap slogans for him.

It is depressing to think a man of Hamilton’s calibre could not stand being in politics today. Chernow, by the way, thought a noughties Hamilton would be involved in leveraged buyouts and other complex financial transactions.

What happened to Hamilton the man was tragic. History has been kinder. Hamilton today, the man, the musical, the phenomenon, represents the best of America. Hamilton’s America is smart, talented, diverse, ambitious and united. It is a place where brilliance is recognised and nurtured. If countries were musical productions, America would win 11 Tonys too.

Who knows. Among the countless thousands who have seen or will see Hamilton on the stage or on film, there might just be another outsider, another kid with a funny name, who hears a call to action and wants to change the world for the better.