Sometimes, one plus one really can make three. Take the potential offered by Scotland’s two great cities, Edinburgh and Glasgow. Co-operation between the two has been suggested in the past and met with little enthusiasm. Traditionally the cities have seen themselves as competitors, not collaborators.

But the arguments in favour of them working together and projecting themselves as a single entity, as a Scottish metropolis, are now too compelling to ignore. For Edinburgh to compete globally it has to look west for help, and Glasgow has to look east.

Cities elsewhere in the world are seeing the sense of such relationships. The Swedish city of Malmo and the Danish city of Copenhagen are a fine example. A physical link between the two, the 10.5-mile-long Oresund bridge, was opened in 2000, and they are looking at a range of ways to work together.

In Holland, a project known as the Delta Metropolis has seen co-operation between Amsterdam, the Hague and Rotterdam to attract new business ventures.

In China, an initiative in the Pearl river delta area is linking Hong Kong, Shenzhen, Macau, Zhuhai and Guangzhou into a single entity that will one day be a supercity of 100m people, with enormous global economic power.

None of this should come as a surprise. One plus one equalling three is a common equation in corporate life. Companies realise that if they have synergies, they can make more of their assets and advantages.

I am not the first to suggest the benefits of closer ties between Scotland’s main cities. Professor Stuart Gulliver at the University of Glasgow has done much good work on the subject. But perhaps this is an idea whose time has come.

Glasgow and Edinburgh are in danger of being left behind. Other cities are looking at what can be gained by working together. Liverpool and Manchester see potential in linking up with Leeds, Hull and Sheffield in an initiative called the Northern Way. At a recent conference, Will Hutton of the Work Foundation — which campaigns to improve the quality of working life — pointed out that in Britain only Glasgow and Edinburgh had the same potential. He added: “And we all know they will never do it.”

Can he be proved wrong? The opportunity is there for Edinburgh and Glasgow to present themselves on the international stage as the Scottish metropolis and, in doing so, to project Scotland to the world. The cities already account for 90% of Scotland’s wealth and 90% of its top educational and cultural institutions.

To compete effectively on the UK stage, let alone the global stage, requires a critical mass of population, assets and economic output. The Forth-Clyde valley has a population of some 2.4m — not as large as the Northern Way’s 12m or the 20m of the Severn-Thames corridor in the south of England. But given the cities’ other advantages, it is enough to make a substantial impact.

In UK terms, Glasgow and Edinburgh have greater potential than Liverpool and Manchester. The Scottish cities are extremely complementary. They face different seas and waterfronts, one looking east and the other west. Glasgow is already a metropolis, a working city, still with a port of huge potential. Edinburgh is a surprisingly small city but has all the feel of a capital and it has a great financial centre, as well as a cultural focus.

There will be those who argue that too much civic pride needs to be swallowed for Edinburgh and Glasgow to collaborate. History suggests otherwise. Rival states came together to form both Germany and Italy. So it is possible. The Scots think it is more difficult than it need be and there is a hint of Celtic tribalism in some of the attitudes one encounters. In fact, the cities do not have to lose their identities at all — the answer is to create a third identity, that of the Scottish metropolis.

Another common objection is that co-operation would entail each city having to admit it was lacking in some way. This, I have to say, is a peculiarly Scottish way of thinking. How much better it would be to focus on what could be gained, rather what might be lacking.

Times Recommends

• Family cuts its waste to one binful a year
• Cameron can learn from Thatcher in 1979
• VAT is back ... and it's confusing