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@moth
Yes
no, i think, though i'm not quite clear what you mean by 'flex'.
Grasp a point on a straight, tensioned spoke. Either side of your fingers, the tension in the spoke is pulling on that point. As the spoke is straight, the two forces are equal and opposite so cancel out to nothing. You feel no force.
Now move the point a little to one side. The spoke is now bent at the point you are holding it. the tension forces are still equal, but not quite opposite. When you add the vectors, there is a small component forcing the spoke back towards straightness. You have to push against this force to keep the spoke bent. How big this force is depends on how bent the spoke is and how much tension is in it.
The tension in a bent spoke comes from two sources. There is the initial tension the straight spoke had to start with. Also, as a bent path from a to b is longer than a straight one, the bent spoke has been stretched longer, creating extra tension.
The initial tension doesn't depend on how thick the spoke is. It's just down to the geometry of the build and the total amount of tension that's been put in.
But the extra tension does. Specifically it depends on the spoke's spring constant, which is proportional to the square of its diameter.
So if 'flex' means 'bend under sideways loads' then a high tension spoke will flex less than a low tension spoke, and a thick spoke will flex less than a thin spoke of equal initial tension.
If initial tension is increased, spoke thickness becomes relatively less important.