At the beginning of the current decade I was often mistaken for the then North Korean dictator-in-waiting Kim Jong-un, which led to an embarrassing incident in a pet shop on Dalston High Road in February 2009. Needless to say, I was unable to convince the Polish lady behind the counter that I was merely looking for a canine companion for my elderly aunt, and did not in fact regard labradoodle puppies as a “superfood”.

But it was worse for Kim himself, who once ended up accidentally and uncomfortably appearing in my place on a December 2006 edition of Eight Out of 10 Cats alongside Sean Lock, Jason Manford, Liza Tarbuck and Nightcrawler from The X-Men. A comment Kim made about the production company, Endemol, was described during the recording by host Jimmy Carr as the single joke “least likely to make the final edit of the show in the programme’s history”. Needless to say, due to Kim’s poor performance I was not asked back.

Fans of unusual celebrity-dictator friendships with long memories will recall the physical comedian Norman Wisdom’s odd 1950s relationship with the totalitarian Albanian leader Enver Hoxha. In between mass executions of dissidents and incarcerations of anti-communists, Hoxha even found time, in 1951, to accompany Wisdom and his family on a week’s holiday to the Isle of Wight amusement park Blackgang Chine.

Beside the English Channel, the curious pair cavorted between the open legs of a giant fibreglass smuggler and frolicked in a fairy glade, all the while crying out “Mr Grimsdale! Mr Grimsdale!!” and “Have you, Albanian peasant brothers, ever sought the reason for the poverty, misery, hunger and gloom which have been your lot for centuries?“

In a modern echo of Hoxha-Wisdom, the American basketball player Dennis Rodman sees himself as the unofficial peacebroker between the US and North Korea. Having befriended Kim in 2013, and with whom he claims to go horse-riding, ski, sing karaoke and generally hang out, Rodman claims, “I just want to try to straighten things out for everyone to get along together.”

Since Kim took power in North Korea in 2011, the stress of the top job has relieved his friendly round face of much of its puppy fat, whereas I have slid into a porcine middle-aged spread of repellent aspect, meaning Kim and I are now rarely confused with each other.

That said, when one of my critically acclaimed standup specials from 2005 aired on Netflix in the US last year, I did notice a tweet from Dennis Rodman which read, “Yo! My bro Kim Jong-un on TV right now slaying the Scotch people at the Glasgow Stand! Tell it like it is! Braveheart was a fag!!”

At the risk of sounding arrogant, I do feel the many occasions upon which I am still addressed as chairman of the workers’ party of Korea, chairman of the central military commission, chairman of the state affairs commission, supreme commander of the Korean people’s army, and presidium member of the politburo standing committee of the workers’ party of Korea by shocked North Korean expats have given me some insight into the dictator’s mindset. Needless to say, Trump’s approach to dealing with Kim Jong-un is entirely the wrong-un.

I understand Kim, certainly more than Donald Trump, and perhaps even more than his hoop-bothering friend Dennis Rodman, who has all scribbles all on him. I am the most consistently critically acclaimed male British standup comedian of the century, while Kim is the most dictatorial dictator in the world today, and let me tell you, like little Kim, I know that it is lonely at the top.

I wonder if, like Kim, many of my life’s achievements (winning six Chortle awards and an edition of Celebrity Mastermind in my case, developing a nuclear arsenal in his) are simply attempts to gain the attention of an absent father figure. Instead of rattling his atomic sabre, and sticking his flaccid orange penis into the heart of the wasp’s nest of south-east Asian geopolitics, Trump could choose to be that father. What Kim needs is love from a big daddy, and Trump could be that big daddy, bear-hugging and play-wrestling us out of the impending apocalypse.

Donald Trump sees the world as a set of business deals. Business is not moral. It is about results. Trump is alleged to have done alleged financial or publicity deals with people allegedly worse than Kim – dodgy Russian oligarchs, Italian-American mafia families, and Michael Gove. All Kim wants is Trump’s attention, so why can’t Trump, in the interest of global security, simply invite Kim to the US for the holiday of a lifetime?

Kim and Trump in Long Beach, Washington, marvelling at the world’s largest chopsticks, laughing as they act out the futile attempts of normal-sized men to use them; Kim and Trump in Topeka, Kansas, at the Evel Knievel museum, bonding as they hold hands in silent humble admiration; Kim and Trump in San Luis Obispo, California, comparing notes at the Madonna Inn’s famous waterfall urinal, laughing as their twin torrents cross streams, Ghostbusters-style, in the soft subterranean lighting. You cannot make nuclear threats against a man whom you have urinated alongside in the beautiful waterfall urinal of the Madonna Inn, San Luis Obispo, California.

My friend the comedian and failed recluse Roger Mann recently befriended a goat near his Pyrenean hermitage in an experimental attempt to understand the nature of relationships. Were Trump to engage paternally with Kim, he himself may learn something, something that might cure the emptiness inside him that threatens to suck all human history into it like a black hole made of nameless need. For Trump, like Kim, is also lonely.

You can own New York, but you can’t make it love you; you can execute hundreds of North Koreans, but you can’t make North Korea love you. To be feared is not the same as to be respected. A father whose children obey him only through fear is a failed father. When we think of fathers they paint Airfix with us, and wrestle in the summer meadow of memory. They do not threaten us with warheads.

Kim Jong-un pleads to be disciplined. Donald Trump is desperate for love. If diplomatic channels could be opened to enable the gaping maws of these two desperate needs to meet, they would engulf each other with a flood of unrequited love, and we would all sleep easy again.

Stewart Lee is appearing with Jo Brand, Bridget Christie, Harry Hill, Athena Kugblenu, Shazia Mirza, Sue Perkins and Mark Thomas in a benefit for FGM charity the Dahlia Project at London’s Union Chapel on Monday 18 September. unionchapel.org.uk