We pressed him to try again—to scan the page and make sure he got every target. After staring intently, he said, “Oops,” and crossed out another two lines near the middle of the page. He still had missed every line on the left.

Then, as he watched, we rotated the page until the left was on the right. He gave a start, and laughed in astonishment. We had done a magic trick, as far as he was concerned. Suddenly he was aware of all the lines he had missed. They were on his good side now. He had no idea where they had come from, but he could finally cross them out.

We were pretty sure he didn’t have a problem with his eyes. If someone is blind in a part of the visual field, they know to move their eyes and head to scan the whole world. If someone presses you to point to every object in the room, you would remember to turn around and point to the objects behind your head even though they were originally out of your vision. But Mr. X was different. He suffered from a syndrome called hemispatial neglect. No matter how hard he was pressed to try, he had no concept of the left side of space.

I wish we had tried a few more experiments on Mr. X. The more you dig into the neglect syndrome, the more you see the seams in the mind. In many patients, if you give them the same kind of task such as cancelling lines on a page, but the lines are drawn on a wall a couple of yards away and the patient is given a laser pointer, the neglect goes away. The patient can process both sides of the wall perfectly, just not on a piece of paper in front of them.

Even more bizarre, if you give the same person a long stick instead of a laser pointer, the neglect comes back. They touch the distant targets on the wall with the stick, but they ignore the targets on the left side of the wall. Laser pointer, no problem. Stick, the left side of space disappears.

Results like this show that the brain breaks space into at least two parts: the space of things you can reach with your hands or a hand-held tool, and the space too far away to reach. In some patients, the reaching and tool-using space is damaged and the neglect is limited to it. In other patients, only the distant, unreachable space is affected. Some patients suffer both. Our Mr. X probably had a neglect limited to the near space, since he was able to navigate quite well walking around.

One of the most beautiful and revealing experiments on neglect showed that it is not just about the world around you, whether near or distant, but also about the world inside your imagination. The study involved patients whose far space was affected. If you ask one of those patients to close his eyes and imagine standing at the north end of a familiar city square, he can describe the square from memory. But he’ll list only the buildings on his right side, without noticing that he’s given an incomplete account. If you ask him to imagine standing on the South end of the same square, now he’ll suddenly remember the opposite set of buildings, on the right side of his new perspective, while forgetting the first set of buildings now on his left. This experiment doesn’t test lines on a page or on a wall, or any part of the world actually in front of the patient. The whole test lies in the patient’s memory and imagination. His brain simply can no longer handle the left side of space. Of course patients in these situations often notice that they’ve given contradictory answers. It distresses them, but they can’t understand what has gone wrong. The very concept of the left side of space has been erased.