I'm in Thessaloniki, Greece's second city, which nestles on the coast next to Halkidiki's three peninsulas, snaking into the Aegean sea like tentacles. The peninsulas are an understandable tourist spot in Northern Greece, with their expansive beaches, street cafes and pine forests. Unfortunately, I can only visit two of them, Kassandra and Sithonia, because the third, Mount Athos, has banned all women for the past thousand years.

Athos is a monastic peninsula, but also a state within Greece, with carefully secured ports and borders, preventing all women, and men without the necessary permits, from entering. Women aren't banned purely because their natural charms are prone to distract the monks from their prayer and study. Hundreds of years ago after several monks reported visions of the Virgin Mary, it was decided that the Athos monks should devote themselves to her, and that no other woman should be allowed to outshine her.

All women were duly banished, from the peninsula, and with them all female animals. Sows, cows and ewes, even chickens were expelled. It was conceded that female songbirds and insects were allowed to remain, purely because it was impossible to keep them out. It's unclear exactly how plausible the danger of a chicken outshining the Virgin Mary is, but still. A rule's a rule.

Nonetheless, women have managed to make it to the peninsula: the Orthodox monks harboured women and female children during the Greek civil war, in addition to men and boys. In 2008, Ukrainian smugglers dropped four Moldovan women on the coast of Athos, who were quickly apprehended by monks and police. The women were apologetic, but must have been cursing their bad luck at being dropped at the spot least likely to permit surreptitious entry into Greece.

Not all interlopers were so innocent, though. Maryse Choisy, a French writer and patient of Freud, claimed to have undergone a double mastectomy in order to sneak into the monastic republic and pose as a servant boy. Suspicions grew, and Choisy was ejected after a month. A handful of women, including Syriza MP Litsa Ammanatidou-Paschalidou, scaled a fence and broke into Mount Athos in protest over a long-running land dispute with the monks. There's a long-running history in Greek political protest of hurling yoghurt at politicians to make them look ridiculous. Hurling women over the fence of a male community loth to pay their taxes is a fitting adjunct to this fine tradition.

Plotting to get on the peninsula doesn't get me very far. In order to enter Athos, you must apply for a pilgrim's pass, or "patriarchal privilege". I've spotted a fancy dress section in a shop at the top of Aristotelous Square, selling ostentatious fake beards and moustaches. Could this work? It seems not. I need to show my passport, and there is a very authoritative black "F" under the "Sex" section of mine, giving me away. I could parachute into Athos. But I lack the time or money to rent a helicopter and learn to parachute. Besides, I'm having horrific visions of landing chaotically, taking out a few monks and having to explain that I did it for feminism.

After boarding a bus, and trekking to Ouranoupouli, the departure point for ferries to Athos, I approach the harbour. Yiannis, who works in the harbour and is easily bribed with a takeaway frappé into speaking to me shakes his head when I ask him if it's possible to get to Athos. "Why would you want to?" I like a challenge. He laughs again. "The boats will take women no closer than half a kilometre to the beach. Some people say women have swum there, but I have never seen them". Swimming! Of course. Apparently there are men patrolling the shores of Athos, watching for this sort of stunt. Though if the EU parliament presses ahead with legislation that will force Athos to admit women, having declared in 2003 that the republic "violates the universally recognised principle of gender equality", they may need new jobs.

Just before Yiannis finishes his coffee and heads off, leaving me to ponder the distance and whether my front crawl is strong enough, he has one more question. "What would you do once you got there?" He has a good point. Probably revel in triumph for a few minutes before realising that I had to find a way back; then feel increasing guilt that my symbolic stunt had caused a considerable amount of distress for any monks I happened upon.

I decided to leave the monks in peace. Besides, their outfits are nearly as hot and uncomfortable as burqas. Why should a feminist punish them any more?