Chop a polearm with a sword is not feasible, in reality the idea was to push aside the pikes and not to cut them. Cut a movable piece of wood would be hard even with a chainsaw.
Another common myth, if pikes could deflected things thrown at them the scottish would have won Falkirk. I have already heard the same myth with Alexander and Spanish Tercios, but it is a myth.
A primary source, showing that pikes without langets were vulnerable to single handed infantry swords(!) from Lord Orrery in 1677:
The Pikes arm'd at the Points with Lozange heads, if the cheeks, or sides of the Pikes are not armed with thin Plates of Iron four Foot deep, are very apt to be broken off near the Heads, if the Push be vigorous, and the Resistance consi∣derable: Nor is this all; for unless the Pikes be armed with those thin Iron Plates, they are easily cut off with sharp Swords, for the Pike, especially toward the end, is carried ta∣pering, to poise it the better, and thereby renders it the more flippent for those who use it; so that the slenderer part of the Pike, if unarm'd, is the more liable to be cut off, it being there nearest the Enemy; whereas if the Pikes were armed with those thin Plates, and four Foot deep, no cutting Swords (which are alwayes of the shortest) could destroy the Pikes, since that part of the Staff of the Pike which is unarmed, would be out of the reach of the Horsemans sharp cutting Sword: I remember we once carried a Fort by storm, because the Enemies Pikes had not those Plates, whereby the Heads of them were cut off.