After 25 years communicating science to different audiences, I finally put it all together in a talk delivered to staff and students at the University of Bristol’s physics department. It covers Stephen Hawking’s role, talking to politicians, dealing with the media, and of course my infamous Ig Nobel prize for using physics to work out the best way to dunk a biscuit.

Mostly, though, I focused on the way that mathematically-based thinking not only helps us to understand better how our increasingly interconnected world works, but is also becoming the basis of many decisions that affect us. Algorithms are now in regular use by decision makers (one Japanese firm even has an algorithm as a member of the board!), and mathematical modelling of social, economic and ecological networks can help us to make the right vital decisions for our future – so long as we can communicate what they are really about to decision makers and society at large. Here I suggest ways and means, with a measure of laughter.

Here is a link to the talk (start a couple of minutes in if you don’t want to see the bit with Sir Michael Berry introducing me to the audience):

and here is what it covered:

  • Why mathematically-base thinking is so important
  • What audiences are we trying to reach?
  • What is the best approach to reaching them?
  • My experience in communicating mathematically-based thinking to the public (including my Ig Nobel prize for producing the infamous biscuit-dunking equation)
  • My experience in communicating mathematically-based thinking to decision makers
  • Techniques that YOU can use to communicate science and scientific advice

For convenience, here are my ppt slides, followed by my talk notes. Enjoy!



There’s been a lot about Stephen Hawking in the media over the past few days, and especially about his role in communicating science. Quite a few questions have been raised, especially about how we can go about communicating mathematically-based thinking, and that’s what I want to talk about today. I believe that we as physicists have a very important role to play – in fact, a vital one.

So this is what I’m going to talk about:


So why is mathematically-based thinking so important? Obviously it’s important to us as physicists. But it’s increasingly important to the rest of the world as well. Our understanding of the world, and the processes of decision-making in that world, are becoming increasingly mathematically based.

Just to give one example, there is the increasing involvement of algorithms in decision-making – in the distribution of social benefits, for example. A Japanese investment company called Deep Knowledge Ventures even has an algorithm as a member of the board of directors, with full voting rights.





But to use algorithms effectively means understanding as a society just what they are and are not capable of. At a deeper level, social networks, ecological networks and economic networks are becoming ever more complex and interwoven, and the consequences of change in those networks are no longer predictable from simplistic views of the world. The complex adaptive networks of our societies, our economies and our ecosystems have emergent properties that are more than the sum of their parts, and behaviours that are all their own. One in particular is that complex adaptive networks are susceptible to sudden, dramatic, and largely irreversible change


and that’s something that I’ll come back to later.

So what audiences are we trying to reach? In my experience there are three main types:

6 SLIDES Audiences and examples

and there are three main approaches that we might use:

3 SLIDES Education; inspiration; consequences

Back when I was getting started, Carl Sagan had just written a book:

SLIDE Sagan cover and quote



That was the quote that inspired many of us, especially as Sagan implied that there was a seductively simple remedy. “Almost no one understands science and technology”. OK, let’s explain it to them in a non-technical, understandable way. Then we will have a scientifically literate public, and all will be well.

I know I’m not doing Sagan full justice, and he did understand many of the subtleties, but this was still the main point that came over to most readers. It has a technical name. It’s called the deficit model of science communication.   And it has landed us in all sorts of trouble because, despite its appeal, it only really works for audiences that are already interested in science and keen to learn about it.

The point is that science communication is not just a single homogeneous activity, with a single goal and a single audience. We have multiple goals, and multiple audiences, and it’s very important not to mix them up.

Another point is that these approaches to communicating science

SLIDE Approaches to communication

are not necessarily compatible.

So Stephen Hawking, for example was very successful at promoting the image of science as being worthwhile because it could be used to investigate the deepest mysteries of life. But at the same time he projected an image that you have to be incredibly smart to do science, and that understanding science is well beyond the reach of the average person.

I’m afraid that that image is reinforced by the history of A Brief History of Time. Whenever someone mentions it to me, I ask them to tell me what science they actually learned from it. Like C.P.Snow said in The Two Cultures “The response is usually cold. It is also negative.”

Just to drive one more nail in, investigating the deepest mysteries of life is not something that decision-makers are particularly concerned with.

But back when I got started in the mid-1990s, many of us were convinced that educating the general public was the way forward. In a sense it is, because what we are aiming for in the long term is a society where science is an integral part of our culture, and not seen as a separate ivory-tower activity.

The trouble with educating the public, though, is that it’s a two-step process. I pointed this out in an article in Nature

SLIDE Nature article

where I said that explaining science is not like explaining art, or literature, or even philosophy. There you can dive straight in, because those areas relate directly to human experience. With science, though, we have a whole set of hard-won, often counter-intuitive beliefs that we often have to explain before we can get on to talking about their consequences.



I know that my wife Wendy had trouble with this when she was suddenly confronted with learning advanced-level physics at school without having done physics before (she passed, incidentally). The general public have even more problems. By the time that you can get to the real point you’ve lost them, and if it’s a face-to-face talk they’ve usually wandered off in search of a drink or someone more interesting to talk to. When people at parties find out that I am a scientist, they usually turn to my wife and ask her what I do, because they think they’re more likely to get an answer that they’ll understand.

I hadn’t really thought all this through when I got started in the mid-1990s, but at least I was savvy enough to realize that the best way to hold your audience’s attention was to pick something that interested them, and then use that as a hook to hold their attention while you explained the science behind it.

Unfortunately the first topic that I chose was the physics of sex. I even got an article into Physics World about it.

SLIDE The physics of sex

But the idea rather backfired when the Institute of Physics invited me to give a pre-dinner talk on the subject. I noticed one man in the front row looking increasingly uncomfortable. It turned out that he was the one who had invited me, under the mistaken assumption that I was going to talk about the role of women in science.


I was also working with Pete Barham on various food-related projects. It’s something that Pete has done successfully over a long period of time. We had a column in the Guardian for a while, and we used to give joint lectures on things like the science of Christmas.

SLIDE Pete and Len

One day Pete he got a call from a publicity company working for McVities. They’d invented National Biscuit Dunking Day, and they wanted a scientist to make it sound reputable. For some reason Pete couldn’t do it, so he suggested me instead.

It turned out that they wanted an equation to describe biscuit dunking.

I thought this was a great opportunity, because by now I was on a different tack – instead of just explaining science, I thought that a better idea would be to share how scientists think. So how would a scientist think about the best way to dunk a biscuit? He or she would think in terms of equations, of course – in this case, the Washburn equation:

SLIDE Telegraph article with Washburn equation

(Describe equation and brief relevance)





I’m still not sure if the subsequent Ig Nobel Prize was an up-side or a down-side. The idea is to make people laugh, and then think, but I wonder how many of them get to the second step.

I’m still getting requests for interviews about biscuit dunking. The last one that I accepted was for the BBC “One Show”. It was fairly typical. I explained patiently why I had done the project, how I was trying to share how scientists think, how I was trying to open a door and make science more accessible. The response was something along the lines of “I see. So what is the best biscuit for dunking?”

You can’t win.

Well, you can, because one of the few positive outcomes was a letter that I received from a child at an inner-London comprehensive.

SLIDE Chao Quan letter

Note the last sentence.

I wrote back to him, explaining what the mathematics meant, and apologizing that I had eaten all the biscuits.

But the really touching bit came 12 years later, when I got an email from Chao, telling me that my response had changed his life. He had developed a strong interest in science as a result, and was now about to graduate as a doctor. The letter was from Oriel College, Oxford.

That’s when I learned a really valuable lesson:

SLIDE Trying to educate the public doesn’t work …

That’s where I think the second approach to communicating science has some merit. Remember?

SLIDE Promoting science as worthwhile

Stephen Hawking provided a model for this approach, while David Attenborough is one of the few who has successfully combined it with the educational approach.

But it usually has to be done through the media, and in general the media get in the way. They have their own agenda, and in most cases they couldn’t care less about yours. I learned that lesson the hard way when I had a stint as a British Association media fellow on a BBC television programme called Tomorrow’s World.

SLIDE TW logo and presenter

I had the bright idea to organize an indoor boomerang competition, and to use it to explain the physics involved in flying a boomerang.

SLIDE Len throwing boomerang

The producer liked the idea, and we had a breakfast meeting with the production team to discuss it further. At Simpson’s in the Strand, naturally. I gave them a quick, and I thought rather brilliant, explanation of how boomerangs fly.

The producer looked at me in utter disdain. “I don’t care about the science. I care about Tomorrow’s World”. And she gave the job of explaining to an actor

SLIDE Craig Charles (Lister in Red Dwarf)

who not only didn’t understand the science, but who actually held the boomerang the wrong way – as did Rolf Harris on the same show.

If you want more evidence on the mess that the media can make of things, have a look what they did to the Washburn equation.

This paper didn’t realize that the “2” meant “squared”

SLIDE Linear Washburn

and here

SLIDE Washburn with sigma

the publicity agent hit the wrong key on her keyboard when she was sending the story, and the journalist didn’t even notice.

So my strong advice is that, if you are trying to get a message across, don’t do it through a journalist unless you absolutely have to. If you do have to, have your (simple) message prepared in advance, and stick to it. Just one or two sentences; three at most. It sounds like really obvious advice, but it’s amazing how many scientists try to elaborate and leave it up to the journalist to summarize their ramblings.

So when I got clobbered with an Ig Nobel Prize, I handed them a quote that they could use “This is just scientists pulling each other’s legs. But it has a serious point. I’m trying to make science accessible by showing how a scientist might think about the ordinary things of life.” It got them onside. It also made their life easier.

Reuters picked it up first, so they all used it. And it saved me a lot of grief.

There is another way to deal with the media, and that’s to write or broadcast the material yourself. You could put it on your website and refer journalists to it, which I think is what Michael has done. Or you could submit manuscripts, but then you can still be at the mercy of journalistic principles.

This is what Michael Kenward said about it in a recent Facebook discussion:

SLIDE Kenward quote

Michael used to edit New Scientist, so he knows what he’s talking about.

I’ve managed to slip a fair bit past the gatekeepers in my time in my efforts to reach a general audience, but it’s a tricky job. I’ll come back later to some of the ways that you might be able to use, but in general it’s much better to pick the audience that you want to reach, and go straight for the jugular. Just make sure that you have the right set of teeth.

The audience that I have spent most time trying reach in recent years has been the decision-makers, and I’ll move on to my experiences with them now. This is also the audience that you are most likely to become involved with. They pose a different set of problems, with a very different set of barriers to overcome.

SLIDE Communicating with decision makers

They have different motivations, and a very different way of looking at the world. Forget about enthusing them. Forget about explaining the science. What you need to focus on is the consequences of the science – not just for the community or the world at large, but for the politicians and business leaders themselves, in terms of hanging on to power, gaining power, or maintaining profits.

I’m not just being cynical here. This is real stuff, even if it’s a bitter pill to swallow for those of us whose main goal is the pursuit of understanding, rather than power or profit. I wrote an article about it recently in Physics World; it even made the cover

SLIDE Physics World cover

I wrote it with John Tesh, who used to be a civil servant in the Cabinet Office, responsible for disaster planning (he was the one responsible for security at the London Olympics). So he was well aware of the practical issues involved in communicating with politicians. Together we came up with a series of twelve practical points. You’re all members of the Institute of Physics, so you can read them for yourselves (August 2015). They can be encapsulated:

SLIDE Give them a practical consequence, and persuade them to come to the experts rather than rely on their own intuition

There’s a sub-text to this:

2 SLIDES points from PW article


I met John at a meeting in Venice in 2011. It was sponsored by a Swiss-based organization called the International Risk Governance Council, and the brief was to introduce politicians, business leaders and senior civil servants to the problems of Slowly-Developing Catastrophic Risks, where a social, ecological or economic risk builds up imperceptibly until its too late to avoid a tipping point.

It was a pretty high-level audience, with people like the ambassador-at-large for Singapore and Michael Oborne, who used to be an adviser to Bill Clinton. So I was being thrown in at the deep end.

Luckily I’d written a couple of books about the problems involved with Slowly Developing Catastrophic Risks. They’ve been analyzed in detail by Marten Scheffer in Wageningen. In fact, I’m pretty sure that I was only there because Marten couldn’t make it, so I guess one lesson is to grab your opportunities.

Another lesson is that, if you have something important to say, get it down in concrete form. It needn’t be a book – it could be an article, or a blog, or maybe a podcast. Just anything you can point to when the time comes to act, because at that time you may have to act very quickly if you are going to have any impact.

Getting back to Marten, he did his analysis in terms of catastrophe theory. I wish I’d been here for Allan McRobie’s talk, but here’s Marten’s image of the appropriate fold catastrophe:

SLIDE Scheffer diagram

I’ll give you a minute to digest that.

But I couldn’t give the decision-makers in Venice the same sort of minute. In fact, I could see their eyes glazing over when I showed them this diagram. They just weren’t interested in this sort of understanding. What caught their attention was when I started to talk about real-life complex adaptive networks like banking networks, social networks and networks of influence, where the links and the strengths of the interactions between nodes are constantly changing and evolving.

Marten’s mathematics provided a really simple idea about such networks, and that’s what decision-makers want – simple, clear, practical ideas that they can get their hands on.

Marten’s idea was that all complex adaptive networks are liable to reach a critical transition at some point and “flip” suddenly to a different state.


And that’s the point that I have been pushing for the past few years. Sudden, unpredicted, and often unpredictable change is going to happen in our increasingly networked world. What, as decision makers, are you going to do about it?

That’s what you need to offer to decision makers – something that they can DO.



Incidentally, the person who kicked off much of the interest in the mathematics of complex networks was my old bridge partner, Lord May:


That’s his picture in the National Portrait Gallery of Australia, holding a thylacine (extinct carnivorous marsupial)

Bob was in the physics department at Sydney Uni at the time, and he was busy undermining the world of biology, which is something that physicists still delight in doing. The biologists believed that, the more complex an ecological network was, the more stable it would be. Bob pulled the rug from under them by showing mathematically that more complex networks ought to be less stable. It’s called the May paradox, because the biologists were right in practice, but it’s taken them a long time to realize that the source of the stability lies in the structure of the network. Bob was talking about random networks, and his conclusions were dead right, but most real-world networks (especially the complex adaptive ones) have emergent structures as well as emergent properties, and that makes a difference to their stability.

Bob must have been working some of this out while we were playing bridge, because occasionally he would dump me in some unlikely contract just so that he could be dummy and spend the time doing calculations while I sweated it out.



Getting back to Marten… here he is, you may as well meet him as well:

SLIDE Marten and guitar

he also analyzed the warning signs for upcoming critical transitions – in particular, that the system as a whole experiences increasing difficulty in recovering from small perturbations, so you get bigger and more frequent swings between extreme states. The trouble is that, by the time the warning signs become obvious, it’s usually too late to avoid the transition or to adapt to its consequences.

That was the take home message, and that was what many of the decision makers present were interested in, rather than the detailed mathematics. In fact, there was another scientist there who tried to instruct them on the statistics of risk. The basic idea with most real-life networks is that the risk of extreme events does not follow a normal curve. The distribution has a fat tail, so that the risk of extreme events is much higher that intuition suggests.

SLIDE Fat-tailed distribution

But my colleague kept talking about the mathematics of fat tails, rather than the risk and consequences of extreme events, and he just couldn’t get their interest, because he didn’t address their practical concerns.



I couldn’t get the interest of the politicians, either. They were principally concerned with justifying their own dogma, evidence notwithstanding. It’s important to remember that most politicians see scientists as just another pressure group – there was an article about this in Nature several years ago – and also there’s good evidence from psychology that the presentation of evidence that conflicts with strongly-held beliefs just results in those beliefs being held more strongly.

Singapore ambassador-at-large story

That’s a good example of how senior civil servants and others responsible for implementing policy are more interested than the actual politicians in understanding the science and its consequences.

I’m not the only person to have realized this. I talked with Paul Hoskisson from Strathclyde University. He was in the Royal Society scheme for pairing scientists with politicians last year, and said that if you could get the ear of a senior civil servant, then that was the very best way to get evidence-based policy implemented.

Incidentally, I raised this point with Bob May a while ago, and his answer was that he usually only spoke with Prime Ministers. But I suppose that if you regard the Chief Government Scientist as a senior civil servant, then it still works out. Don’t tell Bob that I said that, though.



So that’s my experience. I’ve continued on with pretty much the same message, and it’s had some interesting applications. Last year I was invited to address and audience of Reinsurance Industry CEOs at a conference called “Risk Re-imagined”. There were about 300 of them there, and I pointed out that, unless they re-imagined risk to take into account systemic risk (emergent risk to the system as a whole, not predictable from the behaviour of its individual components; cascading failure), they may not even have an industry in a few year’s time.

That’s because their risk assessment methods usually involve extrapolation and/or learning from the past, and you can’t do either of those things when you are looking at the behaviour of complex adaptive networks.

I said earlier that the trick with decision makers is to offer them something that they can DO. Just for your interest, this is what I offered to the insurance industry:

SLIDE Ideas for insurance industry

Bob May suggested a while ago that another way to tackle the problem is to change the structure of the network so as to make it less fluid, perhaps by cutting some links so as to make it more modular and less liable to cascading failure.

SLIDE May and Haldane



The trouble is that you run up against game theory and the tragedy of the commons, because highly interconnected financial networks are more profitable to their members – so who’s going to give up their individual profit to reduce the risk to the group as a whole?

There’s a very interesting history to this paper. Bob wrote it with Andy Haldane, who was the chief financial planner for the Bank of England (in fact, he was recently voted by Forbes magazine as being among the most influential 100 people in the world). But despite the pedigree, they couldn’t get it accepted by any of the top economics journals – it was too radical. So they published it in Nature instead.

The lesson here is that you can’t convince most politicians by mathematical arguments, and you can’t convince most economists either. They are both too concerned with maintaining their own dogmas. So stick to the audiences that you can reach and convince.

So this is what we’ve covered so far:


What I want to move on to now is some additional ideas that you might be interested in trying to get your own message over about the importance and relevance of mathematically-based thinking.


  • Pairing schemes

Mention Royal Society and AAAS (analysis of effectiveness in PNAS)

  • Websites

Michael’s is effective at many levels. I run one on Mini Stories from Science

  • Internet

Feed info and ideas to followers

  • Op-eds

The percentage success is low, but you can always then put the article on your website and refer to it on Twitter. Main thing is speed and relevance to news. My examples from Washington Post and San Francisco Chronicle.

  • Write your own article

As with the work from MIT on the spreading of fake news

  • Write a book

It hasn’t hurt me (shakes)

  • Find fresh descriptions

Robert-Jan Smits, civil servant who helped shape Europe’s science policy, thought that a major achievement was when he persuaded the EU’s statistical office the classify R&D as investment rather than expenditure.

  • Look out for quirky examples

Quirky stories e.g. netball shoaling (Aussie netball team used mathematics of shoal behaviour)

  • UseArt/Cartoons

Don’t overlook the value of pictures. It’s always worth checking for one on your subject. So Laszlo Barabasi, who is one of the founders of networks theory, recently came up with this one

SLIDE Picasso print

Here’s one for you astronomers

SLIDE Dracula cartoon


  • Narrative

When you can, tell a story, preferably about yourself. I have to admit that I found this terribly difficult when I started to write books – I had to force myself.

  • Establishing relationships

Once you’ve made contact with a decision-maker, keep it up. Trust is imperative. I gave a talk in Granada a couple of years ago at a conferences called “Physics meets the social sciences”. It was largely about the stability of networks. Luckily I was talking on the third day, because when I heard the earlier talks I could see how the stability problem could be resolved in every case if you introduced trust into the equation. So I threw my talk away, and when my turn came I just went through the previous talks one by one and made this point. If you can establish trust, you are a long way towards getting your scientific evidence accepted and used.

AND FINALLY (NO SLIDE) Public engagement

Many institutions, including our own, have excellent public engagement facilities, advice and contacts. So use them.

In conclusion, let me take you back to the beginning, where I said that communicating mathematically-based ways of thinking is an important key to the world’s future, and you are the ones to do it. If you don’t believe me, you might like to know what Charles Darwin had to say about it:

SLIDE Darwin quote

SO all you people with an extra sense, get out there and use it! The world needs you!

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