Of course, knowledge isn’t very well-defined, but at least one reasonable definition of knowledge is pretty analogous to money. I am referring to the property of knowledge that allows you to make knowledge off of knowledge—knowledge-based interest. Even if you do not learn new things, you could philosophically toss around the knowledge in your mental bank and arrive at new conclusions from it that add to your knowledge—a rather small amount since only mental interpolation works to make new knowledge—but enough to be called “interest.” Notice that if you also use interest knowledge to produce more knowledge for yourself instead of just relying on your original amount, it is advantageous to your knowledge gain because you are compounding your knowledge interest rather than accepting simple interest.
Of course, just relying on this philosophical increase doesn’t really up your knowledge that much, so in your process of learning, you build up a mental annuity account, every once in a while depositing in an approximately equal amount of new material into your mental bank. (K is knowledge in the formula below.)
Since n is the compounding time, you can see that thinking more with your new deposits of money ends up earning you more in the long term, but the particular accumulation process of the knowledge annuity mental account is what helps you gain the most knowledge-based interest eventually.
The unfortunate result is that for knowledge, just as it is for money, the initial stage is the most difficult: once a knowledge account (or, a brain) has been going for quite a while, it builds momentum from the interest (notice, momentum is force times time, and that’s basically how interest works, the force proportional to the mass of money times the power of time the account has existed) and quickly makes you more knowledge (not to mention the morale and accessibility increases when you win competitions and earn stuff and fame). Thus, like dealing with money, the first stages of knowledge are the toughest. It is sadly drastically advantageous to start early, as the only instance of time in the knowledge annuity formula is in the exponent of the numerator, and the nation is horrendously inclined to celebrate prodigy. Fortunately, there are other things to pursue in life, like alternative definitions of knowledge.
Note one interesting question: it has doubtless been remarked that money corrupts. And knowledge, like money, is a general base from which a lot of connections happen. Does knowledge corrupt? It is well known that knowledge can be used for bad deeds, but does it happen at the degree that money does? Or does money not really corrupt that much? It would be interesting if one day people note an overwhelming parallel between knowledge and money and decide to refinance their moralistic views on the subjects. This is an interesting subject to explore (unfortunately, it would be done with knowledge, and possibly money; don’t you love recursion?).
One more thing: one mathematics teacher once gave the sarcastic joke that money is equal to work over knowledge, thus showing that money and knowledge are inversely related. Of course, he said it was sarcastic, as intuition confirms, but one must be rigorous in their proofs, and here we must somehow derive that it is actually not the case to be fully confident on the conclusion. What we have found is that money and knowledge are both quantities that accumulate via interest as well as deposit (let’s call it an “interesting” quantity), but work is most definitely just a deposit (let’s call it a “dull” quantity, since that word starts with the same letter as deposit). Thus, multiplying both sides by knowledge (and considering both the money times knowledge possibility and the knowledge times money possibility in case interesting multiplication is not commutative), we see that the product of two interesting quantities gives a dull quantity. We know this can’t happen, because interest can’t spontaneously generate in the highly oxidative academic atmosphere of modern day. Thus, such “dot products” are invalid, proving that money truly isn’t work over knowledge, and the fault in the original reasoning is that we are comparing quantities that are isomorphic to different fruits (say, scalars and vectors).