I suppose this column grew out a confluence of things that made me realize yet another limitation of the computers in their gallant attempt to unseat the human race in its mastery of the planet.\u00a0 This limitation, unfortunately, also impacts the human being first learning a new skill.\u00a0 What is this limitation you may ask \u2013 it\u2019s the inability to distinguish technique from judgment.\u00a0 Fortunately humans can grow out of it, computers not so much (that is to say not at all).<\/p>\n
On the face of it, this limitation seems to be a mismatching of concepts bordering on a non sequitur.\u00a0 After all technique is how one does whereas judgment centers on the ability to decide or conclude.\u00a0 What do the two have to do with each other?<\/p>\n
To illustrate, let\u2019s consider the average student in one of the STEM programs at a university.\u00a0 The student spends large amounts of time in mathematical courses learning the techniques associated with Calculus, Linear Algebra, Differential Equations, Vector Analysis and the like.\u00a0 A good student earning good grades succeeds at tests with questions of the sort:<\/p>\n
A successful completion of this problem leads to the answer:<\/p>\n
demonstrating that the student knows how to compute a divergence.\u00a0 To be sure, this skill and the others listed above, are important skills to have and are nothing to sneeze at, but they don\u2019t take one far enough.\u00a0 Without the judgment of knowing what to do, the technique of how to do it becomes nearly useless.<\/p>\n
To illustrate this, our student, having gotten straight A\u2019s in all her subjects now moves onto an engineering class where she is asked to solve a problem in electricity and magnetism that says something like<\/p>\n
Suddenly there is no specification on what technique to use, no indication how to solve the problem. All that is being asked is a \u2018what\u2019 \u2013 what is the electric field.\u00a0 Prudent judgment is needed to figure out how to solve the problem.\u00a0 And here we find the biggest stumbling block for the human (and a nearly insurmountable obstacle for current computing).<\/p>\n
Lawvere and Schanuel, in their book Conceptual Mathematics: a first introduction to categories, summarize this distinction when they note<\/p>\n
Of course, any technique sufficiently refined, can be ‘taught’ to a computer. In the example from Vector Calculus discussed above, any number of computer algebra programs can be used to compute the divergence of the vector field $\\vec f(x,y,z)$. Almost nothing exists in the way of computing judgment to determine the best strategy to solve a ‘what’ type problem. Even the most sophisticated expert systems fail to compete with competent human judgment unless the application is heavily structured.<\/p>\n
The distinction between the \u2018what\u2019 and the \u2018how\u2019, between the judgment needed to determine what and when to do a thing and the technique needed to perform the thing is often complicated and subtle – even for the human.\u00a0 Much like the intricate interplay between language and thought the interaction between judgment and technique has no clean lines.\u00a0 In fact, viewed from a certain perspective, a technique can be thought of as the language of doing and judgment as the thought associated with what should be done.\u00a0 How we do a thing often affects what we think can be done. That’s what makes it fun being alive!<\/p>\n","protected":false},"excerpt":{"rendered":"