The trade solved the eyeballing problem a long time ago, by refusing to eyeball anything.
A carcass is the worst-case version of the problem: heavy, irregular, asymmetric, with dense bone in some places and air in others. Splitting one into two comparable sides by eye would be hopeless.
Butchers do not try. They follow structure.
Primal splitting runs the saw down the vertebral column. The spine is not chosen because it looks like the middle. It is chosen because it is a real anatomical midline that stays put regardless of how the animal is lying or how the muscle sits.
The lesson generalises. Where an object has a genuine structural axis, use it. Your perception of the middle drifts. A seam does not.
Even split down the spine, two sides are rarely identical in weight. Animals are not symmetric, and how the carcass hung changes how the muscle sets.
So the trade weighs. Sides are weighed, primals are weighed, and portions are cut to a target weight rather than a target look. A butcher aiming for 200-gram steaks does not eyeball 200 grams. They cut, weigh, and adjust the next cut.
Cut, weigh, correct. Nobody in a trade that depends on accuracy trusts their eye alone.
Find the seam before you find the middle. Muscles separate along connective tissue. Cutting along a seam takes less force, wastes less, and gives a repeatable line. On a melon, the ribs do the same job.
Cut to weight, not to appearance. If equal portions matter, put a scale on the counter. Two cuts and a correction beat five careful guesses.
Let the structure carry the accuracy. A visible landmark is worth more than a steady hand, because the landmark does not drift and your judgment does.
Most things you cut have no spine. A potato has no seam and no landmark, which is exactly why it is hard, and why the fat-side rule matters more the rounder the object gets.
Halfsies is the casual daily split-in-half cutting game, with the scale built in: three objects a day, one cut each, both halves weighed to the gram. Same loop the trade uses, minus the saw.