Whether calculation is more frequent than engineering: It is. While all engineering requires calculation, not all calculation leads to engineering. (Engineering as the application of mathematics with the physical sciences, purposed toward technological expression and advancement, and calculation as mathematical reckoning.) We should conclude then that calculation is more frequent than engineering.
Whether calculation is more potent than engineering: It is. Calculation guides the soul toward the truth through the science of numbers, and can do this on its own, prior to the other departments, especially without engineering. It would have done this pre-fall, and it does this post-fall. To be sure, engineering would have as well (pre-fall and post-fall), but an ordered soul precedes an ordered physical space. And because greater potency and authority belong first to the parent and not the child, so it belongs to mathematics over engineering. That is, there is no engineering with calculation. Furthermore, potency belongs first and last to the Lord, and mathematics, especially the “reckoning” at the essence of calculation, resides in the mind of God long before engineering resides on the hands of man. We should conclude then that calculation is more potent than engineering.
Whether mathematics is more than calculation: It is. Mathematics allows for calculation, but it is also arrangement, investigation, measurement, recognition, worship, spiritual enculturation, and in creation spatial enculturation. It is call and response with the science of numbers. To show this, and push against mathematical pragmatism and secular scientific humanism, was the purpose of the original piece on “Rescuing Mathematics from Troy.” That is to say, our classical Christian schools, above any, have the tools to rescue mathematics from inside Troy’s walls, precisely because we see mathematics with greater consideration. Hence, why this thread is happening in the "Geneva Dads FB page" and not over at the Louisiana Board of Regents meeting. We should conclude then that mathematics is more than calculation.
Whether building or designing requires calculation: Building and designing, either God’s or man’s, always requires mathematics (especially geometry), as Rhabanus Maurus states in his quote. And if we define arithmetic with Maurus as “the science of pure extension determinable by numbers” then designing and building, like music, also requires arithmetic. This is why I have called architecture, “concrete poetics,” or “visual music made with rocks.” And if we see the word calculation for what it is, then we should not forget that calculus is Latin for stone. By definition building is calculation and designing is "marking out." We should conclude then that building or designing requires arithmetic, geometry, and calculation.
Whether the purpose of learning can be known: It can be known. It is not only known, but it can be gained. The purpose of learning is to accomplish that which sums up all the law and the prophets: that we would love the Lord our God with all our heart, soul, mind, and strength, and that we would love our neighbors as ourselves. Learning for us exists, then, to repair, restrain, reconcile, rejoice, which all lead to the ultimate end, the education which God gives: “The education that God gives is the imparting of the truth that will guide us correctly to the contemplation of God, and a description of holy deeds that endure forever.” (Clement of Alexandria, “Christ the Educator”)
Whether that is also my purpose in learning: In my finest hours, yes. In my worst, no. In Christ, it will be so.
Whether pizza stirs the soul more than mathematics: “For just as a child cannot be born without a mother, so without the rudiments of geometry, pizza would have never come into existence. We must, therefore, forsake the pagan way of cutting circle pizzas into square pieces, and we must likewise do all we can to ensure mathematical order is respected by no crude or disproportionate slices.” – Basil of Little Caesarea, “De Pepperonicis”