Actually he's right, and I don't think you're understanding what he's showing. Convexes will have a continuously decreasing angle the further back you get from the edge but at the apex will be identical in angle. The closer to the edge you get the greater the order of magnitude of influence specific geometry has on cutting performance. For equal edge angle, a convex will have superior cutting performance, but less lateral support to resist torque/side-loads. A 50° V edge would have to be compared to a convex with a 50° apex, but of the two the convex would overall be thinner. Convexes, not being limited to a linear geometry, can have more variation in them, though, and so some may be done thinner or thicker while retaining that same edge angle at the apex. When people convex their knives and make them tougher it's because they're not properly accounting for the deflection of their abrasive surface and so are inadvertently just thickening their edge angle. You could do a similar thing by just thickening the apex of a V grind. A straight V grind will thicken continuously, the angle is staying constant. That's kind of what makes it a V instead of a convex or hollow.
You and Marcinek are wrong for practical purposes, and here's why: What matters for cutting geometry is
blade thickness at the shoulder of the edge: You can put whatever angle you like below that, it is "within" the user's reach
in a way the blade thickness is absolutely not... You are using apex angle as a reference point because that leans your way, but apex angle is demonstrably meaningless in technical terms because it is not a
fixed and
unchangeable characteristic of the edge (for the user), and it is therefore not a solid reference point...
Why on earth would you use a
variable reference point when you could have instead a
fixed (edge thickness) reference point? Any scientist would laugh at this notion, especially since this is intended as a
comparable reference point for determining the
practical performance of a tool...
Predictable then as rain follows sunshine, Convex fans will say "but there is no edge shoulder to a full convex edge!": In this deft sleight of hand move, the fact that the corner has been "washed out" is used as an excuse to say the reference point is not visible, and from that it therefore follows that
something not clearly marked by a grind line does not exist!
Here on planet earth however, we have a strange high tech tool called "calipers", which we can slide along a convex edge until it gives us a figure equivalent to the desired figure measured at the
visible shoulders of the very V edge we wish to compare it to, giving us, as if by miracle, a comparable thickness to be used as a reference line...
A comparable edge thickness is what is the most important, and is the most legitimate comparison point, because it shows how hard material is
initially shoved aside... It is
doubly significant, on top of performance determination, because,
unlike apex angle, it cannot be easily altered by most users, so Convex fans are wrong
twice by avoiding it...
When you understand all of the above, you realize that, at comparable edge thicknesses, Convex edges do inevitably feature more metal just behind the apex, which does potentially help a metal deficient in apex stability for a given use (such as many Carbons or, in my experience, several CPM steels). For all other considerations, it is of course inferior in cutting performance (and sharpenability) to a V edge, because the theoretical "drag" of the V's side ridge only affects the dynamics of fluids, and fluids are not what knives cut...
In fact, by reducing the surface of friction to a single point, it is likely the V-edge also reduces friction in splitting tasks etc...
I am also beginning to wonder if today's emphasis on Convex edges is not derived from the inferior apex stability behaviour of today's fashionable steels, Carbons and CPMs, which, in the case of CPMs, have high abrasion resistance, but (from what I could observe) truly abyssal lateral stability at thinner V-edge angles: Stranger things do happen...
Gaston