Changing someone’s mind is incredibly difficult. We are seeing this problem writ large in the US election of 2016.

By the time you read this article, you may know the result of the US election of 2016, but at the time it is being written, the FBI has just announced that it has not changed its mind. FBI director, James Comey, said that after the FBI’s investigation of “all of the communications that were to or from Hillary Clinton while she was Secretary of State,” it had not changed its conclusions.

But this begs an interesting question. What difference will it make to the US election?

Ten days or so ago, Mrs Clinton had moved into a commanding lead in the opinion polls. Then the FBI revealed it had found more emails involving Hillary Clinton, and everything seemed to change. Her lead in the opinion polls fell sharply, and practically overnight – some had Mr Trump surging into the lead.

Now the FBI has revealed that its investigation has turned up nothing, one would assume that things would go back to what they were like before the FBI’s shock announcement.

But there are people involved in this, and it’s devilishly difficult to change minds.

Normally, it takes something pretty enormous and indeed dramatic to change someone’s mind. When it emerged that the FBI was re-opening its investigation into Hillary Clinton, many of her marginal supporters, the ones that were not sure but on balance were planning to vote Clinton, began to wonder if the Democrat candidate was in fact a criminal. ‘After-all’, they reasoned, ‘why would the FBI reopen its investigation days before the election, unless it knew something important’? Now that is big. That is important. The suspicion that the person you were thinking of voting more may be a criminal is enough to change minds.

And if that rationale goes away and Mrs Clinton is cleared, will that be enough to convert those marginal voters back again?

The reasons why we might hold a particular view are complex. Some psychologists argue that when we drill down and examine why we really think something, we find that our views are not based on the most solid of foundations.

David McRaney, author of "You Are Not So Smart" says in a podcast: "Most people don't have any idea why they think what they think or most people carry around a lot of opinions that they've never contemplated. They think they have, but they haven't.

“That's the biggest hurdle for trying to create a grassroots campaign or trying to get somebody to support a candidate or whatever you're doing in the political world, one of the biggest hurdles is to just simply get people to realise that they don't have informed opinions about stuff, but they have a meta belief that they do. I would imagine that's true for just about everything.”

Or, there are the ideas advanced by Daniel Kahneman in his famous book, Thinking Fast and Slow. We have two ways of thinking: a quick automatic way of thinking that requires little effort and a much slower more deliberate, more logical form of thinking.

Kahneman suggests that the fast way of thinking is much more important that we realise, or like to admit to. We react to give a stimulus, in a certain way, very rapidly, and employing a quick way of thinking. Then, after the event, we fit a narrative to explain our action, which assumes, wrongly, that we reacted the way we did through well thought out logical reasons.

Maybe when we form an opinion, we are thinking fast.

There is another way of looking at it. There are multiple reasons why we hold a certain view. For example, if we are an ardent Leave or Remain voter in the EU referendum, or we are a supporter of Clinton or Trump. These views can be represented by a network: interconnecting facts, evidence, and interpretations of facts, leading us to interpret other facts in a way that supports our first interpretation.

The study of network theory, whether it be for example the nodes in the brain, the computers that make up the internet, individuals who make up a social media network, or the spread of a disease, say that in the case of many networks, they are many nodes which connect to each other. But some nodes are highly connected, they are called hubs.

The distribution of nodes and hubs follows a so-called power rule. Most nodes may be connected to the network via just a small number of connections. A very small number of the hubs may have many hundreds of connections, while a very small proportion of super hubs may have thousands or even hundreds of thousands of connections. Networks that are configured in this way are called small world networks.

It is these hubs and super hubs that give a small world network structure.

But small world networks are very robust. To give another example, consider Al-Qaeda, this is a classic example of a small world network. Even when Osama Bin Baden was killed, a kind of super, super hub in the network, Al-Qaeda did not collapse. To destroy a small world network, you must destroy multiple hubs almost simultaneously.

When we try to change someone’s mind, we are battling with a network of views that form a whole. If we dismantle one of those views, the network simply forms new hubs to replace the ones that were lost.

This may explain such heuristics as confirmation bias.

Returning to the interview with David McRaney, he attended a Donald Trump rally and spoke to his supporters. He focused on the Trump claim that after 9/11, people in New Jersey celebrated the terrorist attack. No one seems to know where Mr Trump got this idea from – there is no evidence to back it up, whatsoever. When Mr McRaney confronted ardent Trump supporters with this point, he said the resulting reaction fell into three groups.

The first group reacted by saying words to the effect: “Well, all politicians lie, so if he's going to lie, at least it's for a greater good."

The second group reacted by saying: “Well, I think it really did happen. I think there's a cover-up. I think that what Donald Trump is uncovering here is that the media lies to its audience."

As for the third group, when they were told about the New Jersey anecdote, but without referencing it to Donald Trump, they were incredulous that anyone could promote such a ‘lie’. But when they were told that it was Donald Trump who made this claim, they changed their minds, and supported the New Jersey story.

For many people, if you remove the catalyst that led them to hold a certain view, they still hold that view. Indeed, if you do remove this catalyst, you end up with cognitive dissonance; in which conflicting views create a feeling of discomfort. To resolve cognitive dissonance, it may be easier to ignore the development that created it.

Returning to the Clinton emails.

It may all boil down to how rapidly the network of ideas that led someone to change their mind after the FBI first announced it was re-opening its inquiry, formed.

Or maybe, as all this happened so quickly, the revised network of ideas had not fully formed. If this is the case, then the final results of the election should be supportive of what the opinion polls were suggesting ten days ago.