The current races along at some points, and swells when it meets a blockage.
It may separate into streams but in the end it only has one direction.
From its origins along the Syrian border, it twists and turns but finally pools - largely in countries like Germany and Sweden, where those who travel the river finally find those who went before them.
But even as some arrive in what they hope will be their new home, others are only just emerging from the war-ravaged carcass of what was once Syria to cross into Turkey.
As some prepare to board over-filled inflatable dinghies and push out into the Aegean Sea in the dead of night headed for Greek tourist islands, others are pitching tents in dimly lit parks in Athens, Belgrade and Budapest, working out how to make the next step.
At this very moment through southern Europe and the Balkans, towns which few people would have ever heard of, are being circled on maps and tapped into apps by Syria`s refugees.
Idomeni in Greece; Preshevo in Serbia; Roszke in Hungary - these are just some of the names that are on thousands of lips.
People are heading towards or passing through each of them now.
The passage between the countries is without passport stamps and without any real guarantee of safety.
The crossings are not really crossings at all, simply natural points at which one state runs into another - railways and rivers, not border check points and kiosks staffed by immigration officials.
Along the train lines which thousands walk, rumours can spread in minutes.
Word of tents, food and water ahead can prompt some to break into a run.
But any suggestion authorities are waiting on the other side to take fingerprints can lead to a sudden halt, anxious discussions, and a search for different routes.
Attempts by some countries to deter this flow of Syrian refugees, and the migrants from other countries who are now joining them, have been predictably futile.
The erection of fences, or simply the absence of assistance, is nothing compared to what they have already overcome.
Too many are taking the path.
Too many of those on the road are babies being carried in nervous arms.
Too many are too desperate and too certain that they have no other option.
There are some indications that the inevitability of this flow is beginning to sink in.
Along the thousands of miles the refugees walk, the humanitarian infrastructure of volunteers, medical workers and shelter is now gradually beginning to take shape.
But so is the other industry that does business in suffering - the dark world of black markets, people traffickers and thieves.
They know many of the refugees are carrying cash. They do not care that it is all they have.
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