Cyclists and motorists are like the Sunnis and Shi'ites in Iraq – they share the same territory but just can't get on. However, the schism twixt Australian cyclists and motorists is more baffling, because many of them are one and the same. Most cyclists also drive cars, many motorists also ride bikes, so just what happens mentally when a cycling motorist spits the dummy over a motoring cyclist is a challenge for any psychiatric conference.

Statistics released the other day showed that in the past five years 20 cyclists have been killed and 1818 seriously injured in Victoria, with most coming to grief in the Melbourne CBD, where 323 have tumbled out of the saddle into a hospital bed.

Dawn patrol: cyclists on Melbourne's Beach Road, which has a weekend clearway.

That is more than five a month and does not count the many who pick themselves up, dust themselves off and ride on, nursing bruises. Motorists would probably blame cyclists for their outrageous behaviour, pedalling blithely through red lights, passing on the blind side, riding at night without lights. Cyclists would probably blame bloody-minded motorists for their outrageous driving, safe in the knowledge that, while they keep finding other ways to kill themselves at the wheel, motorists always come off best in a car-bike collision.

Our psychiatric conference might examine the grudge factor at play here – cyclists and motorists share the same territory, yet cyclists pay no registration fees and they carry no visible ID like a car registration plate, so the errant cyclist can pedal off with impunity. This disparity is accentuated when the motorist is sitting in a traffic jam – say, in Alexandra Parade, waiting eternally for the East-West Link to be built – and sees cyclists breezily pedalling past. Grrr. Shades of someone elbowing in to a queue ahead of you. At times like these the more educated of these log-jammed petrol-heads might mutter unkindly about Karl Drais, the 19th-century German baron who, with his chief game-keeper Otto Shillinger, is credited with inventing the first two-wheeler, a device nicknamed the dandy-horse and patented in January 1818. This was at least 70 years before first car appeared, so the baron would never have envisaged the 21st-century conflict between horsepower and dandy-horse.

Back to our conference. While nutting out the nuttiness of bike-car relations, the shrinks should surely take note of the strange configurations that road authorities provide for the warring tribes. For example, drive your car down Macaulay Road, North Melbourne, past Arden Street oval, where half the road is perpetually empty. It was signed over to cyclists some years ago, even though a separated bike path is only a stone's throw away. So behold the daily sight of cars in a conga-line at the lights, alongside a huge expanse devoted to the odd cycling straggler. Consider also the city council brainwave of recent years, placing bike paths between parked cars and the kerb. An unwary passenger can be wiped out just trying to get to the footpath. In such situations, motorists naturally harbour dark thoughts about the baron and his brainwave of 196 years past.

In contrast, hop on a dandy-horse and pedal down William Street, past the Flagstaff Gardens, heading out of town towards the Dudley Street roundabout. It sure is a nice plump bike lane along there – you could almost ride two abreast – but not for much longer. See how it begins to narrow? See how the white line is angling in towards the gutter. In fact it is about to touch the kerb when it disappears. The cyclist is now jettisoned into the traffic, as cars and buses roar through the roundabout. Option A is to pedal on, praying the traffic behind is patient and considerate of your frail human form. Option B is probably more sensible – you cycle up on to the footpath, where a strange transformation takes place. From vulnerable weakling, you instantly become the chief gorilla. Any pedestrian who tangles with you is going to come off second-best. Here again, the same weird facts apply. All cyclists are also pedestrians, many pedestrians are also cyclists, but they still hate each other. Just what happens during that mental switch demands another paper to the conference. Maybe one for the afternoon session.

Fact is, any collection of shrinks would go nuts trying to fathom the leapfrogging mindsets as pedestrian switches to motorist to cyclist to pedestrian again. I twigged to the inherent paradox of bicycle safety in the 1980s, after interviewing cycling legend Sir Hubert Opperman at his home in Wantirna. I recall his wife, Lady Oppy, showing me the indoor cycle machine she had bought the knight after becoming concerned at his safety on the increasingly congested roads. A few years after we published that interview I read that Oppy had died. At 92, he had a heart attack while pedalling on his indoor cycling machine.