I've been lucky: I've had a half-dozen or so eureka moments in my career. I had one (or one and a half to be precise) not that long ago. For four years our group at Cardiff University has been working on some new experiments called Imitation Games. But somehow, we've never quite come up with the right way to understand them in a quantitative way. Writing a long summary paper on the whole passage of work forced me to think really hard about the problem and I worked out a long, convoluted set of excuses for why we were doing OK, along with a few complicated improvements that I struggled to "sell" to my colleagues.

Then at about 4.30am on a Monday, I woke up with the cold certainty that, in spite of all this, no referee who took statistics seriously could possibly find our analysis acceptable. After tossing and turning for half an hour, I suddenly "saw" how to do it right and knew I wasn't going to sleep until I'd tried it. I jumped out of bed, did a couple of lines of algebra on a scrap of paper and tried out the results on a spreadsheet - and it worked, with the complicated improvements I had been hacking away at popping out like magic! I slept soundly for the remaining hours. The next night, and this was the "half", I woke at 3.30am knowing how to polish up the final details. I had to get up all over again and go through the same antics with the spreadsheet. Mind you, we haven't had the referees' comments yet ...

The statistics solution was a pretty small eureka moment. One that was much more important to me happened when I was lecturing to a class on the argument of a book I was writing. As I spoke what was supposed to be one of my most convincing sentences, I realised I was talking nonsense. I was explaining that computers could not mimic human thinking because all human thinking was social and computers were not social. "Even arithmetic is social," I pointed out triumphantly, suddenly realising that what I ought to say next was "and that is why there is no such thing as a pocket calculator". In that case, the realisation that what I had been saying for years didn't make sense was the eureka moment, because it took months of thinking it out to get the basic solution and the writing of two books to work it out fully. I think the second book, The Shape of Actions: What Humans and Machines Can Do, written with philosopher Martin Kusch, is the best of my seven research monographs - but, sadly, it's the one that's least read.

The big daddy of my eureka moments was the first one, and it is why I had a career as a sociologist of science. It happened when I was driving an old Ford Galaxie through Nevada in 1972. Between 1970 and 1971 I studied for a taught masters at the University of Essex. For my final dissertation, I found myself trying to find out how scientists learnt to build a new kind of laser called a Transversely Excited Atmospheric Pressure CO2 laser, or TEA laser. What I did was drive around the UK visiting the half-dozen or so labs where researchers were trying to make this kind of laser work. I wasn't interested in who the scientists spoke to in general, but in what they did that made the difference between having a non-working laser - of which there were plenty - and a working laser.

ÖйúAƬ

To cut a long story short, the answer was that they needed to visit another laser laboratory with a working laser and pick up the relevant "tacit knowledge"; reading published papers just didn't do it for anyone. For my PhD I decided to complete this study by tracing this knowledge network back to North America, where it started, and to do some similar studies on more controversial sciences.

One of the controversial sciences was gravitational wave detection. Joseph Weber, a professor at the University of Maryland, was claiming that he had detected gravitational waves using two separated and very delicate apparatuses. But by 1972 other scientists had tried the same thing and failed to find the waves; there was an argument going on and I thought I would see if this affected the way knowledge travelled. So I bought a cheap airline ticket, landed on a friend of mine in Philadelphia, bought an old but massive Ford Galaxie and started driving around Canada and the US from one laboratory to another.

ÖйúAƬ

I went up to Quebec to interview the person who invented the TEA laser and traced the route to the successful American laser builders who eventually transferred the technique to the UK. At the same time, I was meeting all the scientists who were doing experiments on gravitational wave detection, as well as keeping up with what was going on in a couple of other fields. Without my being aware of it, a time bomb was ticking.

I had done most of my interviews and was on my way to do a last few in California. I was driving through Nevada when the bomb went off. I was thinking about how I was going to write up all the fascinating interview material using my successful masters dissertation as my template. Suddenly the hairs on the back of my neck stood up - I had made a mistake of monumental stupidity.

The key to the success of the TEA-laser study was the clear criterion of knowledge transfer - whether the laser actually worked. A number of scientists had something on their laboratory bench that looked like a TEA laser, and had been built following the published circuit diagram and well-understood concepts, even using supplied manufacturers' part numbers for their component purchases; but often these lookey-likey lasers would not actually "lase". It was easy to know if a TEA laser lased because the very powerful infrared beam made concrete smoke.

But what was the equivalent for a working gravitational wave detector? What should a working gravitational wave detector do? Should it detect gravitational waves or should it not detect gravitational waves because they weren't there with sufficient strength to be detected, as the critics argued? That was the whole crux of the argument that had attracted me to the field in the first place and it was what the detectors were supposed to settle. I realised I had no criterion of whether a gravitational wave detector was working or not, so I could not possibly write up the results following the TEA-laser template.

ÖйúAƬ

I had made just the sort of idiotic mistake that endless courses in sociological methodology tell you how to avoid: painstakingly prepare the ground, set out your hypothesis and how to test it, do everything carefully, and this kind of thing can't happen. I had proved to myself that I was an incompetent designer of sociological research, and my PhD, a small sum of taxpayers' money and I were all disappearing down the drain.

Half an hour seems to be a magical period, and that was about how long it took me as I drove on to have the eureka moment. If I didn't know whether a gravitational wave detector was working, the scientists couldn't know either! And if they didn't know, then they could not be sure about what the results of their experiments signified. When a scientist built a gravitational wave detector and failed to see the waves, was it because there were no waves to be seen or was it because the apparatus was not working properly? After all, TEA-laser builders frequently built what they thought were working lasers only to be flabbergasted when they could not make concrete smoke, so thinking you had done an experiment right when actually you had done it wrong was as familiar an experience for research-front scientists as it was for school students - except the school students had someone to tell them they'd got it wrong whereas the research-front scientists did not.

At the end of half an hour I knew that by turning my thesis "inside out" I was on to something far more interesting than the original laser study but that still followed from it in the nicest possible way. It was the very fact that knowledge of how to do experiments passed via the transfer of tacit knowledge rather than explicit knowledge that made it impossible to know if you had done an experiment right, unless everyone agreed what the experiment was supposed to do when it was working. In disputed areas, that is exactly what they could not agree about.

The foundational idea that science was the supreme form of knowledge because anyone could independently test a scientific claim experimentally could no longer stand! This formed the basis of my most well-known research paper, and eventually I described it as the "experimenter's regress" - my best-known contribution to the field. The experimenter's regress goes something like this: to know if there are "Xs" you have to have a working X-detector, and to know that an X-detector is working you have to know what it should do when it works and check that it is doing it, and to know what it should do when it works you have to know whether it should or should not detect Xs, and to know whether it should or should not detect Xs you have to know if Xs can be detected, and to know whether Xs can be detected you have to have a working X-detector, and so on.

ÖйúAƬ

I can think of at least two more eureka-ish moments that have happened to me. One that is a lot of fun again involved driving. Getting lost on the way to the Frascati Gravitational Wave laboratory, I stopped my car and conspicuously consulted a map, completely blocking one lane of an access to the Grande Raccordo Anulare - Rome's busy ring road. I noticed that no one hooted or gesticulated or exhibited any kind of road rage - they simply drove round me. The key to Italian driving suddenly struck me - expect the unexpected and cope with it. In Italy, safe driving is the responsibility of the whole driver "collective". In Britain or America, on the other hand, safe driving is the responsibility of the individual - you have to follow the rules in a pedantic and obvious way or people start screaming at you. The driving business was a perfect fit for a raging argument going on between an Italian group of gravitational wave scientists and most of the American groups. The Italian group was ready to publish tentative findings even if they were eventually found to be wrong - what I called "evidential collectivism" - whereas the Americans thought this was utterly irresponsible, exhibiting all the symptoms of "physics rage" - which I called "evidential individualism". The point, of course, is that both methods work. Once you get the hang of driving in Italy everything works fine, and the same went for the "irresponsibly" published Italian results - the collective would sort them out. It was just two different ways of doing the same science, one more private than the other. As a sociologist, I realised that I preferred the mistakes to be exposed in public rather than hidden, but that's another story.

The boundary between eureka moments and exciting passages of work is a fuzzy one. The only moment in my career when I have run out into the corridor whooping (fully clothed, I should add) was when I managed to construct a "toy" interferometer (these days the device of choice for detecting gravitational waves) out of a laser pointer, bits of broken shaving mirror and chipboard - but that was of no interest to anyone except me. The thing that helped to found the latest phase of my career was realising that the understanding of gravitational wave detection science I had built up over years and years of discussion with the physicists - what I call "interactional expertise" - was not unlike the knowledge of the high-energy physicists who managed the big gravitational wave projects, so that interactional expertise was much more powerful than implied by its usual description: "talking the talk not walking the walk". Interactional expertise was "walking the talk". And that turned into a whole theory about the nature of expertise and how it could be used instead of "access to truth" to evaluate scientific and technological claims. But I can't remember a specific moment when that happened, even though I can remember it as a new and important unitary insight.

ÖйúAƬ

In my experience, eureka moments are, in the old cliche, 1 per cent inspiration and 99 per cent perspiration. The perspiration is obsession. You have to be thinking about something nearly 100 per cent of the time, most often in a fruitless and frustrating way, if you are to create the conditions under which the brain can solve the problem on its own. It's the brain that does it, not you. That's why it feels so strange. It's something that happens to you, not something that you do.