March 30, 2008, 10:17 pm
Filed under: Uncategorized

So commenting on the below post, I think some profs in some fields would be convinced (that it would be best for your own education) if you asked them for solution manuals for problems to do on your own as long as you kept them to yourself [in cases of perfect discernment when you can perfectly discern between when to do a problem and when you probably should look up the solution]

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Another thing: gaps in knowledge. A lot of people use a person’s ability to recollect a certain fact as representative of the person’s knowledge of other areas of the field. Recollections of some facts are sometimes sufficient enough to show that you understand something – for example – recollections of the theorems of vector calculus are usually sufficient to show that you have a basic understanding of vector calculus (unless you happened to be a “rare in this population” individual who happened to memorize without comprehension).  Sometimes they’re also necessary – an inability to do calculus betrays an inability to do a lot of fields (although there are some amazing counterexamples – for example – dyscalculia – a difficulty with arithmetic – doesn’t always come with diminished intelligence – the authors of “origins of mathematics” recollect a patient who was able to do physical chemistry without knowing how to add!)

When it comes to specific facts, the signal value of whether you know “fact” or not is often dependent on the percentage of the population who go through a particular educational system/curriculum (and also dependent on a small percentage of people who self-study out of non-traditional books).  Of course most facts are related to others and so an inability to recite one fact will usually betray an inability to recite other facts in the area (although this is just probability – there will be gaps in every person’s knowledge, and some people will have gaps totally different from those of others)

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