I've seen this now in two different articles on the subject of the border, and immigration policy, and I can't stand it any more: pictures of Hadrian's Wall, which the Romans built "to keep out the Scots."
Well, no, they didn't. They built Hadrian's Wall, and its northern neighbor the Antonine Wall, to keep out the Picts, who lived in Scotland in the first couple of centuries AD and didn't like the Romans very much. If you're interested, you'll find a good article on the Romans in Scotland here, see p. 4 of the article for the history of the walls. Or you can read Rosemary Sutcliff's classic novel, Eagle of the Ninth, which will be a lot more fun. It's classed as a "young adult" novel but I can read it still.
In fact, the "Scots" or Scoti as they're sometimes called, came to Scotland from Ireland, where they settled around the third or fourth century AD; they moved to Scotland and united with the Picts against the Saxons and Danes, around the 7th-8th century AD. You'll find a rather wordy history of the Scots at www.electricscotland.com. I'm not sure how much I trust their scholarship but it repeats stuff I've read elsewhere.
Getting back to borders with walls on them: we just don't learn, do we? Walls don't keep people out; they just make them mad. The people who smirk and quote Robert Frost, "Good fences make good neighbors", haven't read the whole poem. Frost was extremely dubious about fences.
This particular set of proposed walls is not just expensive, ineffectual, and stupid; it's expensive, ineffectual, stupid, and racist.I observe nobody's proposing a wall on the Canadian border, even though it's quite as porous as the Mexican border and a whole lot easier to walk across in the summer. And as I mentioned in my post on the Dubai Ports World mess, we're at a whole lot more risk from stuff smuggled into a seaport in a container, because only 5% of them are ever inspected. They could put a whole Al Qaeda strike unit inside, an Islamic Trojan horse, and who'd know?
And at least a third of the people who enter the country illegally each year don't come from Mexico at all, and if they do, don't sneak across the border: they come in legally on a visa, and they just never go home. We'd do far more for national security to spend the money on beefing up port security.