My wife and I recently took our children out of their local primary school to travel in the former Transkei for seven weeks. We thought that this would be a wonderful experience for them, experiencing life on the road in a completely different culture. Their school was programmed to see it differently. Its Ofsted rating could be adversely affected by the absence, and by the prospect of a six-year-old and four-year-old performing slightly less well in their assessments. The scientific culture of measurement risks so narrowing the concept of education that the system becomes unable to see any benefits (which cannot be directly measured) of such a trip.

Social or ‘impact’ investors, such as Panahpur with whom I work, try to achieve their purpose by blending the art of achieving their social goals with the science of managing their funds. They make financial investments for social, as well as financial returns.

The key challenge of doing this is understanding if, and how, the art of achieving social ‘returns’ can be measured in any scientifically robust way.

Successive governments have all but admitted defeat when it comes to the state’s ability to solve certain intractable social problems. There is a general recognition that charities, faith groups and other civil society organisations have an important role in reaching the parts that the statutory social services cannot reach. But to deliver their potential, they require access to capital. Contracting them to provide services has often led to a repeat of the problems of state provision, with a focus on inputs rather than outcomes. All this has led to the emerging world of social impact bonds and payment-by-results (PBR).

We invested in the first social impact bond at HMP Peterborough directly and have invested others subsequently indirectly. PPBR is a popular idea now, which might direct capital to those who can actually solve these problems. If charities and civil society organisations can do what the state cannot and help people to transform their lives, so the argument goes, then let’s pay them when they deliver.

But most charities lack the balance sheet strength to provide services at risk. Which means that PBR leaves private sector providers as the only realistic option. These private sector providers have fiduciary duty to extract all financial value they can from these contracts and return it to shareholders. So PBR contracts can become a proxy for privatisation. The extent of the privatisation of social services resulting from this and other trends is well documented in Social Enterprise UK’s report, ‘The shadow state’ and can be easily seen through the experience of the Work Programme.

All this is complex enough before one brings Einstein into it. But he would recognise that the intractable social problems that increasingly take the lions share of social service budgets can only be solved through the complex, time consuming and uncertain process of human transformation. Dysfunctional and deeply disadvantaged and distressed individuals need to turn their lives around, one by one. Graham Allen MP, through his work on early interventions, has demonstrated that the most cost-efficient interventions will occur during the first three years of an at-risk persons life.

The truth is that, in the context of gnarly social problems, building the link between inputs and outcomes is often impossible. What these social problems require are long term interventions, in the context of an uncertain rehabilitation journey and a chaotic client group. It needs persistence and, ultimately, love. Can one really measure the outcomes of particular interventions? Can a time-bound, tightly contracted and assessed financial confection achieve this deep change?

There is no question that the social impact bonds – for example, with offenders at HMP Peterborough or with children at risk of being taken into care in Essex – offer an exciting new opportunity to create significant positive social change by aligning the state, investors and the taxpayer.

But perhaps we need a deeper discussion, where we have the humility to accept that the relationship between inputs and outcomes of many things that society needs cannot be directly measured. And where we allow ourselves to make the philosophical leap that delivering and measuring social outcomes is not necessarily linear and regular.

Should we do this, we’d be led inexorably to a need to rediscover the notion of common values. Inevitably, in the context of the available evidence and budgets, we need to agree that some things should lead to taxpayer savings through better long term outcomes for the most distressed people in society because they are the right thing to do.

If we can do this, we might be able to direct capital with appropriate rigour to the best placed organisations to deliver long term change. If we cannot, we risk PBR just being the latest in a line of contracting methodologies that fail to address the root causes of our problems. Or, as Einstein might say, we may be doing what we can count but we may well not be doing what actually counts.