The meaning of technology, reprise

In a post from the Monday before last I defined technology as

"physical capital with a high level of education or knowledge required in use or maintenance."

The technology level might be defined as this education or knowledge, technological transfers as changes in technology by virtue of foreign influences, and technological gaps as the difference in technological levels between two countries.

These definitions sound like they might be OK, but encounter problems when one tries to use them in a production function. For example, with the famous (MRW) production function, we have

Output per person = A*capital per person^alpha*education per person ^beta

where A, alpha, and beta are constants. The technology level is a measure of education, so presumably education per person should be decomposed into something like

Output per person = A*capital per person^alpha
*(technology-relevant education per person) ^beta1
*(non-technology-relevant education per person)^beta2

where beta1 and beta2 are new constants. But then, how would the (non-technology relevant education per person) variable be defined? And if the technology changes, how should education be repartitioned? Furthermore, if we look at the original MRW production function, it is apparent that all education helps to increase the output of physical capital, so all education could be defined as the technology level, and our definition is weak.

Similar problems arose when I tried to define technology as the part of total factor productivity due to education. After playing around with various definitions, I think the following set works and captures the main content of the theory of scientific technology transfers:

"An economy’s technology level is defined non-uniquely as a measure of the scientific processes employed when using or maintaining aggregate physical capital. A technology gap is the difference in the technology levels between two economies. Technology transfer is defined to be an inflow to an economy from another economy, whether of knowledge or physical capital or another quantity, which change the scientific processes employed in use or maintenance of physical capital."

The definitions do not overlap with definitions of other variables, so the technology level can be entered into production functions without creating problems of determining the residual parts of variables which are not captured by technology levels. They allow for neat theoretical expressions of production functions including technology which embed many other production functions in them, whether they have included technology's effects or not.