what does without a shadow of a doubt mean

Trees, cows, goats, cats, frogs, insects, even wood and stones had shadows.

We set about it with the meticulous care of research scientists. You cannot deal with an adversary you don't know. Not sure who had tricked whom, we did not feel genuine triumph at the temporary success. Under a big tree or thicket, the bush shadow swallowed ours but as soon as we moved out, ours were back with us. Their disappearance in the darkness, however, gave us an idea on how to get rid of them. Sometimes they would multiplicate themselves, and continue mocking us in moves and waves that seemed choreographed to achieve maximum mockery. They played on the walls, on our faces, and depending on the flames, they would actually dance. Alas, it was not we who had escaped them, but rather they who had hidden in the darkness only to reappear suddenly and dramatically at storytelling time.

We escaped them only when it became dark, initially a matter of pride at our doing, but as soon as we sat by the fireside, they were back. On moonlight nights they were there, walking behind us, in front of us, besides us, mocking our failure to turn them into captives. Let us carry a load on our heads, in our hands, on our backs or drive a wheel, our shadows would come up with exact replica. They followed us, doing whatever we did, literally at the same time and speed that we did it. They would run away from us, but annoyingly kept the same speed as we did, accelerating when we did, slowing down when we did, and stopping when we did.

With the grim but eager determination of bounty hunters, we set out to capture our shadows. A rivalry of sorts grew into a sibling race to be the first to achieve the feat.

What does without a shadow of a doubt mean