Politics is so much more complicated than science. For every action there isn’t an equal and opposite reaction and nor are there equations that predict how the system will respond to changes in the input conditions. So how do we work out what to do when it comes to the referendum on whether or not Britain should stay in the European Union?

The impact of Brexit on UK science is unlikely to loom large in most people’s decision on how to vote, but the EU is an important matter for many scientists. As professional investigators, you would expect us to deal in facts, to sift through the evidence to figure out the principal components of the debate.

The trouble is that such sifting is unlikely to yield a clear solution because the problem has too many dimensions. For a start there are so many facts – and quite a few “facts” – that just keeping track of them all is difficult, never mind the effort required to verify which ones have real weight. It would help if much of the opinionated noise could be filtered out of the discourse, but that’s not likely. We have to recognise the fact that this is an emotional matter, calling on beliefs and allegiances that are informed from our earliest days. However hard the head may try, the heart will have its sway.

Scientists are no less susceptible to human and political passions but we should at least keep reminding ourselves to check back with the evidence. That’s easier said than done, particularly on social media where political exchanges are often too testy and too fleeting to permit examination of the data. In the past week or so I have found myself embroiled in more than one unedifying ‘debate’.

But the experience has at least galvanised my determination to be better informed, on both sides of the argument. So let me tell you where I’ve got to so far. In the interests of open discussion, I should at the outset declare that my instincts have long been that UK science (and the UK generally) is better off within the EU. Naturally, that colours my analysis and yours may very well differ – but none of us is free from bias.

I turned first to the opposing cases made by Scientists for EU and Scientists for Britain in their submissions to the recent House of Lords Science and Technology Committee inquiry into the “Relationship between EU membership and the effectiveness of UK science”. The case made by Scientists for EU is measured in tone and, though it could be clearer on some points, is supported by extensive citation of primary sources of information. In contrast, Scientists for Britain’s argument is highly rhetorical. It opens with the declaration that their Noble Lords’ inquiry is based on a ‘fallacy’ and, although it frequently asserts that UK science will be immune to any ill-effects following exit from the EU, offers not a single link to external sources in support.

I recommend both documents for anyone wanting to get up to speed on the scientific debate about EU membership. Unfortunately, they’re both quite long, though each has a summary or overview and you can get a taste of their differences just by reading the opening remarks.

I do not have space here to do justice to the contents in detail but wanted to pick up on a couple of important points. As far as I understand it the case made by Scientists for Britain is that the UK could achieve all the scientific benefits of EU membership from outside the organisation. It points to nations like Switzerland and Israel, which are associated states rather than full members and yet have good access to EU research schemes. Both countries perform well: they have higher or comparable success rates in applications for grants and win more funding per head of population than UK researchers. On the basis of such figures Jamie Martin, one of Science for Britain’s core activists, claims with “100% certainty” that associated nations can extract the same benefits as EU members.

But I don’t know how he knows that for sure. It is important to dig beneath the headline figures to understand why Switzerland and Israel do so well.

A first point worth noting is that the success of the Swiss and Israeli researchers in winning EU research funds is probably due in part to the fact that these countries spend much higher proportions of their GDP (2.8 and 4.4% respectively) on public and private R&D than either the average for EU nations (1.9%) or the UK (1.7%). Science for Britain contends that quitting the EU would release a dividend that could easily be used to boost UK spending levels. In theory, that would mitigate some of the ill-effects of exit but it’s uncertain that such a fillip to the UK science budget is in the offing. Notwithstanding the economic downturn predicted in the immediate wake of an exit, the UK government has steadfastly resisted calls to increase public spending on R&D to match our international competitors. Public investment in the UK research base is currently flat-lining in real terms (and declining as a percentage of GDP), while EU spending has trebled since 2002. Of course that trebling has been done with the agreement of our government, but the comparison suggests that, if anything, the EU has a positive effect on the UK commitment to research.

There are also important qualitative and quantitative differences between the UK and the current crop of associate states. For one thing, they do not have the same rights that full members enjoy; associate members attend meetings of the European Research Area Committee only as observers and therefore have restricted input into the key body that advises the EU on research and innovation policy. For another, the participation of associated states in EU research schemes has so far been confined to nations that do not command a large share of the resources available. But Britain is a major player within EU research.

Just look at the figures. Switzerland and Israel might perform well in relative terms, but the UK ranks alongside Germany as one of the dominant nations on the European scene. Detailed comparisons are complicated because the big picture is made up of various schemes to fund research, infrastructure, and capacity building, but a useful sense of the numbers can be gleaned from the Royal Society’s analysis. In the last full funding period, which ran from 2007-2013 (Framework 7), the UK won the lion’s share of the most prestigious grants awarded by the European Research Council, valued at €1.7bn. By contrast, Germany won €1.1bn, Switzerland €0.6bn and Israel €0.4bn. This pattern has broadly continued in the present funding period (2013-2020) – the Horizon 2020 programme. More tellingly perhaps, UK-based researchers are the lead coordinators in far more projects in Horizon 2020 than any other nation: 892 compared to 532, 90 and 15 for German, Israeli and Swiss researchers. This is one of the critical intangible benefits of membership – the EU provides rich opportunities for UK researchers to demonstrate and develop leadership in multi-state projects.

As a full member, the UK enjoys a leading role in shaping and executing the EU research agenda, one that contributes substantially to its research productivity in a scientific landscape that has grown ever more international in the last 30 years. It is hard to envisage how this position would be strengthened by downgrading to associate status.

Of course it would be ludicrous for the EU to shun a nation with the evident research prowess of the UK in the event of a vote to quit the organisation, and it would certainly be in our interests to negotiate hard for associate status. But such negotiations would be unprecedented.

Politically, a UK exit would be a seismic shift for the EU. The immediate concern of the organisation would probably be to seek stability and part of that agenda would be to re-enforce the advantages of membership among the remaining nations. At the very least, such a political climate is going to make things difficult for the UK to seek a favourable settlement.

An exit would also be politically unsettling for the UK. Setting aside the impetus given to the efforts of the pro-EU SNP to take Scotland out of the UK, leaving the EU would be a boost to UKIP, the party that pressured David Cameron into promising a referendum. This could further harden government policy on immigration and may make it difficult to win political support in the UK for the freedom of movement terms required to secure associate status for access to EU research networks.

Political predictions are necessarily speculative but the damaging effects of this kind of turbulence have recently impaired Switzerland’s relationship with the EU. After the Swiss voted narrowly to limit mass migration in 2014, it was reduced partial associate status, and may be relegated to ‘third country status’ in 2017 unless efforts to ratify the Croatia protocol on freedom of movement are successful. As a result, the country has seen its share of Horizon 2020 funding fall dramatically and also reported a loss of confidence in the ability of its researchers to commit to EU projects (see p53 of this official Swiss government report).

The tribulations of the Swiss underscore the importance of adhering to EU rules on immigration, an issue that has been one of the driving factors behind political discontent in the UK with the European project. Science for Britain supporters like to point instead to Israel, which enjoys full associate status without having to conform to EU rules on freedom of movement. But Israel’s position is anomalous since it cut its deal before freedom of movement was incorporated into EU law in 1999. A similar exemption has evidently not been extended to the Swiss and is hardly likely to be offered to a post-exit UK.

Inevitably much of this is arguable: we have not been down this road before so all bets are off. Even if we restrict ourselves to consideration of the implications for UK science, the facts remain gelatinous, and intermingled with opinion and gut-feeling. And of course the impact on UK research cannot – and should not – be isolated from other weighty matters in the referendum debate such as sovereignty, democratic accountability, regulation, and differing perceptions of the long-term goals of the EU. I said it was complicated. The best that any of us can do is attempt a reasonable assessment while keeping our biases in mind. To do that you have to get mired in the detail, no easy task given the institutional complexity of the EU. Just look at the length of this article, which only deals with one portion of the necessary deliberations.

I don’t share the view, expressed by some, that leaving the EU would be a disaster for UK science – I’ve been around long enough to know that politicians will usually find a fudge to limit the damage. But I cannot discern a convincing case that abandoning the added value of membership in favour of associate status will improve our research base. That’s not to say that we should see ourselves as tied to the EU in perpetuity, or that it is an organisation without flaws. But I am not alone in believing that we stand a far better chance of enriching our evidently productive relationship with our European friends by working within the EU.

12 June 2016: This article was amended to clarify that the percentage GDP spending figures given for Switzerland, Israel and the UK are total (public and private) investments, not just government spending.

@Stephen_Curry is a professor of structural biology at Imperial College. Whatever you think about Britain’s membership of the EU, please make sure that you are registered to vote.