It is no surprise that Scotland's police chief says coping with an £11m annual budget deficit is a struggle, but some of the reasons he cites are unexpected.

Police Scotland Chief Constable Phil Gormley's comments on the challenges ahead are timely.

We know the pressures on Police Scotland's budget and we know it has to adapt to new challenges. But they may not be the challenges many people would assume.

Take officer numbers: There is a public perception that fewer police men and women means recorded crimes will rise.

This is flawed.

Falling crime figures are a phenomenon across the western world, apparently regardless of regional differences in the number of police officers or the budgets invested in policing. Meanwhile there is reason to think that increasing the number of police can increase crime statistics in general terms.

More visible policing and pro-active campaigns - over recreational drugs, say, or sexual violence, or child exploitation - can lead more incidents to be recorded and investigated.

This is not to say more officers are desirable or otherwise. It merely shows the arguments cannot be viewed in simplistic terms.

Most policing, as Mr Gormley explains, is not even about crime. When we think of the rising elderly population, we think of overburdened hospitals and overstretched social care.

But the so-called demographic time bomb is a pressing issue for police forces, too. Around 80 per cent of police activity relates to no crime at all.

Demand on the police is rising partly because they field increasing numbers of calls related to people with dementia. Police forces are often engaged to track down dementia patients who have gone missing having simply walked off - a common symptom of their condition.

That might well be appropriate: The police are good at finding people, and have access to the tools to do so.

But there are question marks over whether the Police are the best people to deal with other calls: dementia sufferers may call the police themselves, often in a state of confusion. Others may call about them, out of concern, or about anti-social behaviour related to their illness.

Another significant drain on police time is dealing with members of the public with mental illnesses.

This is more clearly problematic: There are health professionals better placed and better trained to deal with such calls - or would be if our mental health services were not scandalously under-resourced and understaffed.

Former Detective Chief Superintendent and violence reduction expert John Carnochan has long argued that he would welcome fewer police and more health visitors. Perhaps he is right, perhaps, too, we could tolerate fewer police offset by more skilled mental health officers.

Having more civilians and fewer uniformed officers in Police Scotland may also help.

The Scottish Policing Authority is currently considering whether and how to redesign the national force to equip it for such demands today and ten years hence.

It should be allowed to do so free from simplistic interpretations and political short termism.

We do need a conversation about the future of policing in Scotland but we also have a duty to make sure we are asking the right questions.