15 July, 2008

From first principles

The following passage from a book struck me as insightful.

In every science, as you know, there are first principles, fundamental points that one must know at the very beginning because upon them rest all the later developments and the final conclusion. These primary elements need going into more deeply, and they demand more attention, in proportion as their consequences are more important and more extensive. Our minds, it is true, are so made as to be easily put off in the analysis or meditation of fundamental notions. Every initiation to a science, like mathematics; to an art, like music; […] calls for an attention that our mind readily shirks. In its natural impatience, it would like to run ahead at once to the developments so as to admire their ordered arrangement, to the applications so as to gather and taste their fruits. But it is much to be feared that if it does not fathom the principles with care, it will merely lack solidarity in the developments it can afterwards draw from them, however brilliant those developments may appear. The conclusions will often be unstable and the applications hazardous.
I deliberately omitted a few words from the passage, because I didn't want the reader to guess what the text was about. I reckon that anyone who read this would gather that it came from the pen of an individual possessing not only experience in education, but some insight into how the human mind develops certain knowledge, as opposed to mere conjectures that usually work.

One of the major obstacles that students have with learning mathematics is their haste to hurry past the first principles, which seem pointless, and rush into the final results, so as to gather and taste their fruits. The author describes the consequences of this habit of ours perfectly: unstable and… hazardous.

Where did I find such an insightful passage? In the book Christ, the Life of the Soul by Blessed Columba Marmion. The words I excised from the text might have given away the subject matter: to a doctrine, like that of the interior life. He wrote the book nearly a century ago.

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