What is engineering to me?

I am used to see someone joking about the similarities and differences between the following three

• mathematicians
• physicists
• engineers

To me at this moment, one of the major contributions of the three people are, respectively,

• mathematicians give us legal generalization on any logic;
• physicists give us legal generalization on experiments/measurements;
• engineers use the above two kind of generalizations and transform one specific solution into another either analytically exact or statistically approximate.

And the quality of engineers is how far the transformation can be done as effortlessly as possible. The acronym of "transformation" is "engineering." So, it doesn't matter if someone couples "customer experience" with "engineering." What really matters to me are the following.

• Using 1000 staffs to serve 1000 customers and achieving supreme customer experience is not what "engineering" means to do in my own term, because there no generalization is done from serving customer A and no transformation is done from A to serving customer B;
• Using N*(N-1)/2 links to form a N-node network is not what "engineering" means to do in my own term, because there no generalization is done from a 2-node network (a link) to a N-node network and no transformation is done from connecting 2-node together into connecting N-node together. Nonetheless, such a network must provide the best customer experience with respective to any N-node networks whose number of links is smaller than N*(N-1)/2;
• The design of SIP protocol is definitive an beautiful engineering work as it generalizes the call setup signal flows into the single session initialization protocol and transforms the call setup solution into a videoconference session setup solution, white board session setup solution, instance messaging session setup solution, and any session setup solution;
• The design of IP is definitely a ground-breaking engineering work as it generalizes the different layer-2 networks into a single layer-3 networks and transforms among Ethernet/Frame-relay/radio-network/serial-link/etc connectivity solution;
• likewise.

I dream to work for a real engineering company.