I believe that colinmhayes' point is that you dug the extra nine holes because there was a shovel, not because you got better at digging holes with your hands. The productivity gain was because a shovel was being used. It didn't matter who owned the shovel, it mattered that you were digging with one.

But that's not completely true, because a person who only knows how to dig with their hands still only digs one hole a day, even if there's a shovel just lying there. Knowing how to use the tools does in fact make you a more productive worker.

It seems to me, then, that part of the gain from the productivity from better tools should go to the worker who knows how to use the tools. And part should go to the person who bought the tools.

Well yeah. But the thing is, someone had to make the shovel to begin with. The gains in productivity of the shovel are just unrealized value of the original labour (and materials).

The shovel maker is paid handsomely. He's the equivalent of a tech worker.

Sure. And ultimately the gains in productively are due to his labour.

Not really sure what you're saying as this is an example of my point. The growth was caused mostly by the shovel, and partly by the worker learning to use the shovel. Wages have grown to show that.

The construction of the shovel itself is ultimately due to past labour and land, as well as by the invention of the shovel (labour). Capital is always ultimately a product of labour and land. In accordance, rises in productivity in the absence of discovery of new land is because of unrealized past labour. Therefore, this newfound productivity is to be attributed almost entirely to labour.

This is why Adam Smith, for example, cites labour as the primary factor of production, followed by land with capital as the last. In modern parlance you might hear that said as "human capital is the most important", but human capital really is a politically correct way of saying "labour potential".