An aside from the thread.
The thin column of our friend's standard lamp version, wobbled on the heavy base. Despite having tightened the 17 mm (A/F ) nut under the base, the wobble returned.
To stabilise it, I made up an Aluminium (Lacking any brass of sufficiently large diameter), sleeve, drilled and tapped M5 in four places before splitting it. The split sleeve was then clamped around the column to bear against the thin "gold" coloured steel cover over the base, after the 17 mm nut had been slackened sightly.
Since then, thankfully, the wobble has been absent.
Howard