As someone employed doing mid-level math (structural design), I’m much like most others you’ve talked to. The entirely non-verbal intuitive method is fast, and it tends to be highly correct if not accurate. The verbal method is a lot slower, but it lends itself nicely to being put to paper and great for getting highly accurate if not correct answers. So everything that matters gets done twice, for accurate correct results. Of course, because it is fast the intuitive method is prefered for brainstorming, then the verbal method verifies any promising brainstorms.
Correct and Precise may have been better terms. By correct I mean a result that I have very high confidence in, but that is not precise enough to be useable. By accurate I mean a result that is very precise but with far less confidence that it is correct.
As an example, consider a damped oscillation word problem from first year. You are very confident that as time approaches infinity that the displacement will approach a value just by looking at it, but you don’t know that value. Now when you crunch the numbers (the verbal process in the extreme) you get a very specific value that the function approaches, but have less confidence that that value is correct, you could have made any of a number of mistakes. In this example the classic wrong result is the displacement is in the opposite direction as the applied force.
This is a very simple example so it may be hard to separate the non-verbal process from the verbal, but there are many cases where you know what the result should look like but deriving the equations and relations can turn into a black box.
One of my current problems is that I don’t understand my brain well enough for nonverbal thinking not to turn into a black box. I think this might be a matter of inexperience, as I only recently managed intuitive, nonverbal understanding of math concepts, so I’m not always entirely sure what my brain is doing. (Anecdotally, my intuitive understanding of a problem produces good results more often than not, but any time my evidence is anecdotal there’s this voice in my head that yells “don’t update on that, it’s not statistically relevant!”)
Does experience in nonverbal reasoning on math lend actually itself to better understanding of said reasoning, or is that just a cached thought of mine?
Doing everything both ways, nonverbal and verbal, has lent itself to better understanding of the reasoning. Which touches on the anecdote problem, if you test every nonverbal result; you get something statistically relevant. If your odds are more often than not with nonverbal, testing every result and digging for the mistakes will increase your understanding (disclaimer: this is hard work).
So, essentially, there isn’t actually any way of getting around the hard work. (I think I already knew that and just decided to go on not acting on it for a while longer.) Oh well, the hard work part is also fun.
As someone employed doing mid-level math (structural design), I’m much like most others you’ve talked to. The entirely non-verbal intuitive method is fast, and it tends to be highly correct if not accurate. The verbal method is a lot slower, but it lends itself nicely to being put to paper and great for getting highly accurate if not correct answers. So everything that matters gets done twice, for accurate correct results. Of course, because it is fast the intuitive method is prefered for brainstorming, then the verbal method verifies any promising brainstorms.
Could you please explain what you mean by “correct” and “accurate” in this case? I have a general idea, but I’m not quite sure I get it.
Correct and Precise may have been better terms. By correct I mean a result that I have very high confidence in, but that is not precise enough to be useable. By accurate I mean a result that is very precise but with far less confidence that it is correct.
As an example, consider a damped oscillation word problem from first year. You are very confident that as time approaches infinity that the displacement will approach a value just by looking at it, but you don’t know that value. Now when you crunch the numbers (the verbal process in the extreme) you get a very specific value that the function approaches, but have less confidence that that value is correct, you could have made any of a number of mistakes. In this example the classic wrong result is the displacement is in the opposite direction as the applied force.
This is a very simple example so it may be hard to separate the non-verbal process from the verbal, but there are many cases where you know what the result should look like but deriving the equations and relations can turn into a black box.
Right, that makes much more sense now, thanks.
One of my current problems is that I don’t understand my brain well enough for nonverbal thinking not to turn into a black box. I think this might be a matter of inexperience, as I only recently managed intuitive, nonverbal understanding of math concepts, so I’m not always entirely sure what my brain is doing. (Anecdotally, my intuitive understanding of a problem produces good results more often than not, but any time my evidence is anecdotal there’s this voice in my head that yells “don’t update on that, it’s not statistically relevant!”)
Does experience in nonverbal reasoning on math lend actually itself to better understanding of said reasoning, or is that just a cached thought of mine?
Doing everything both ways, nonverbal and verbal, has lent itself to better understanding of the reasoning. Which touches on the anecdote problem, if you test every nonverbal result; you get something statistically relevant. If your odds are more often than not with nonverbal, testing every result and digging for the mistakes will increase your understanding (disclaimer: this is hard work).
So, essentially, there isn’t actually any way of getting around the hard work. (I think I already knew that and just decided to go on not acting on it for a while longer.) Oh well, the hard work part is also fun.