She touched him playfully behind his ear, as she so often did, feeling an overwhelming tenderness. He had just been explaining his recent work to her, in response to her jibe that he was lost in his thoughts, today, on their pic-nic, of all days! It was a lovely day, sunny with a warm, caressing breeze. The lake in front of them rippled and reflected the sunlight into their faces.

Since they married, several years ago, Rose had begun to see his work as a part of him that she loved as much as his slow smile, his hesitant love for her and his thoughtful kindness.

“The problem is now so clear,” he said, “but I am walled-in with no obvious way out.”

For the last three years David Nielson and his team had been developing a theory to explain how the localized activity in the brain paralleled the conscious experience of the subject. They knew that the localized areas would switch on and off and pass the baton of activity to other areas as the subject’s thought progressed. They were attempting to predict the changing boundaries of this activity mathematically, using the latest deep-probe mapping of the brain, and relate them to the overall pattern of the brainwaves detected on the scalp along with the subjects’ verbal feedback. She had sensed that for months now he had been completely stuck.

“It’s damnable! We have all the data and the transitions are mapped, we just can’t express the dynamics in a way that keeps the time functions separate from the location functions. So the whole model is asleep and inert!”

“It’ll come,” she whispered, “with a bit more of your daydreaming!”

At the end of that long, sunny afternoon they had tea in the kitchen of the old Yorkshire farmhouse where they were spending their short holiday. Mary, the farmer’s wife, bustled about the stove, brewing tea and taking hot scones out of the oven. Mary’s ancient father sat, crumpled and mumbling, on one side of the hearth. While Rose helped Mary set the table, David went to the hearth and sat opposite the old man. Although it was a sunny day outside, Mary had lit a fire to take the chill out of the dark, stony kitchen. The firelight reflected in the rheumy eyes of the old man.

“There’s nowt wrong wi’ this country that a complete change of bloody government won’t fix!”, he mumbled, “Just look at the the state of them as is out of work. Gov’ment don’t care a damn!”

David glanced over at him in surprise and met his eyes. Immediately the old man sat up, leaned forward and focussed on David, his eyes clearing and his voice becoming distinct and urgent:

“Try the complex notation, lad, that’ll sort it for ye!”

David froze, all his attention suddenly inward, as the old man sank back into his chair, resuming his grumbling. Mary came over to her father and gently lifted him to his feet, saying:

“Now, Dad, don’t be bothering Dr Nielson with yer nonsense! Come out back and sit in sun for a bit. It’ll do your old bones good!”

David was silent all through the evening until they went to bed.

“I can’t believe it, Rose, but that old man seems to have given me the clue to solving our problem!”

“What, in all that mumbling and complaining?”

“Didn’t you hear him suggest using the complex notation?”

“I wasn’t really listening to him, just chatting with Mary…”

“But it’s exactly what we need! It’s a brilliant idea: the complex values will resolve into two components, always separate, no matter how we might insert them into the driving functions, so the time and position will compute together but remain distinct!”

“Surely it was your own thinking, David, just triggered by something in the old man’s mumblings?”

“But up to then I was completely stuck, and suddenly I heard him say it so clearly!”

“Well I’m glad you have a way forward. You’ll have a lot of work to do now. I shouldn’t worry about whether the old man provided the solution!”

Followed an intense time, David orchestrating the mathematicians and programmers, testing the emerging model and building the real-time display. First came the driver algorithms, this time with complex values, then the boundary matrix and finally the interface with the physiological map of the brain. It was in the third month that they loaded the subjects’ previous data and ran simulations which matched the clinical records second by second. The display came to life as the boundary matrix resolved repeatedly into zeroes on the leading diagonal and the parameters were passed to the physiological map. The display showed the diverging patterns of brain activity as a beautifully correlated dance of light.

The time came to repeat the tests on live subjects. Everything worked as planned. One day David returned home excitedly calling to Rose:

“She fell asleep seven seconds after the model predicted the transition!”

The cross checking and adjustments took a further four months and then David locked himself in his office and wrote up his paper. It was at the end of the summer of the year following their Yorkshire holiday that he contacted his old mentor and friend McDonald at Cambridge and sent him the final draft. The following day McDonald rang him up rather breathlessly:

“David, you’ve done it! I can see it closes the loop. It’ll run live! You must present it at the FENS Forum in Amsterdam. I’ll have a word with Richter without stealing too much of your thunder. He’ll keep mum and hold a slot for you. Publish after that. I’ll talk to Jameson of Nature, he’ll accept the paper for fast review. We can make the November issue. By the way, where did you get the idea of the complex functions? Chap called Bates used a similar trick in the forties, just after the war. Of course they didn’t have any real computing power then and the project just faded out. Broad Yorkshire the man was, apparently. Never heard of since. Came from a farming background, the bright son who left the plough to study medicine. I’ll dig out his later papers for you”.

David felt a pang of unease, but couldn’t identify the cause. The last few months work had exhausted him and he’d completely forgotten the few days holiday of the year before.

The preparations for the symposium were quickly completed now he had the model running reliably and the data logged securely. He flew over early with Rose and they spent a carefree couple of days in and out of the art galleries and cafés.

His slot was the following afternoon, and he woke that day with a strange tension in his body. His assistant set up the demonstration with the model projected onto the big screen at the rear of the podium. The laptop with the software running was placed on the lectern, and David took his stand there a few minutes after two with a raging headache.

Rose sat centre in the front row, with a slight worried frown, her face rather pale. She sensed something wrong, but couldn’t see what it was. Behind her sat the French team, muttering among themselves. At the back were the Germans, silent and a little aloof. The Norwegians were in a tight group in the middle seats. They had led the field for the last few years, and were leaning forward expectantly. Next to the Germans sat Nakamura’s US team, with a barely concealed video camera pointing at the screen.

McDonald walked over and gave a short introduction to the paper. David himself was well known to the audience. The hall fell silent and David cleared his throat.

His headache suddenly left him and the memory of the old man in the Yorkshire kitchen came back to him with paralyzing force. He was unable to speak, the speech centres of his brain disconnected from his voluntary control. He completely forgot who he was and what he was supposed to do next. Then the speech block dissolved and the words tumbled out by themselves:

“There’s nowt wrong wi’ this country that a complete change of bloody government won’t fix!”, he shouted, “Just look at the the state of them as is out of work. Gov’ment don’t care a damn!”