Thinking too deep into a problem? Do you think this exists? Support your answer.?
I think it most likely doesn't exist. All the smart people just use this as an excuse when they get a math problem wrong. A math problem is always still a math problem, the answer is always either right or wrong.
*I do not bear a grudge on anyone. I've just seen too many people think it's all a silly mistake or thinking too deep. It's sick man. Can you guys imagine yourself lying to yourself like that?*
What are your thoughts?
Update:Whitesox, it's even more funny that I don't know which question of mine you're talking about. Are you becoming paranoid or something? Get some rest and maybe you can feel more relieved.
Update 3:I think I've said the source pretty much, although not being specific. Too many of my classmates think it's something else when they get it wrong. "Oh, it's a silly mistake!", "Oh, I must be thinking too deep!". At least I'm being honest with myself by telling myself I can't do everything correctly.
Comments
I think that it's quite possible to think too deeply on a problem. Of course, that's not so much an excuse for not getting it, as it certainly isn't a good thing to be doing.
For example, earlier this semester I was tutoring calc2. A problem came up wanting the integral of tan(x). The only thing I could think of was doing integration by parts, and it didn't occur to me that a simple substitution on cos(x) would suffice. Actually, it was the guy I was tutoring that finally suggested it.
That sort of heavy-handed approach I think happens a lot. Like working a probability question that has a simple argument using, say the deja vu method (with infinite processes, notice that some subset of the process is the process itself and go from there), but only thinking about it in some ugly probability distribution method (say for instance using the moment generating function).
Perhaps you should let us know exactly what it is that set you onto this question. In general I would say that it's a perfectly acceptable statement, but doesn't really speak too well for your aptitude at problem solving.
Sorry, one more example springs to mind. In my number theory class, we came to the point of needing to solve some quadratic inequality, like perhaps p^2>9. My teacher, rather than simply finding that (p-3)(p+3)>0, went through a relatively long, tedious calculus approach, showing that for p=3 the equality holds, then showing that the derivative is increasing and positive after that, blah blah blah. Sometimes you just dive into a problem before thinking what the best path is.
Oh, and to "Can you guys imagine yourself lying to yourself like that," yes, I can. I sometimes find myself thinking that "perhaps I'm looking too deeply at this." I don't generally think that as a way of consoling myself for failing though, it just aggravates me more that I think there's some simple solution staring me in the face.
EDIT: Yes, I gathered that the source was a few classmates, but I wondered if there was a particular question that invited "too deep" of thought. I'll agree that for general classwork such remarks are likely to be excuses. As for silly mistakes, it all depends on whether they were actually small, silly mistakes. If they were, and they don't seem to occur on EVERY problem, then that's a satisfactory response IMO. If on the other hand, the "silly" mistake is something rather common (forgetting to distribute a negative across parentheses, as an algebraic example), they really ought not brush it off so calmly. That's something that needs to be worked on. An acceptable situation would be, say, multiplying incorrectly in a long differential equations solution. Presumably it's not something that happens in every problem, and if the person knows how they're actually supposed to solve the DE, that's really what the problem is about. It's still wrong, yes, but as for the learning process at least they've got the idea.
If your classmates are lying to themselves, then that's their problem. Sad indeed, since people infrequently work hard to find the source of such an excused mistake; leading inevitably to more of the same.
Sorry if I'm rambling a bit. I'm just throwing out ideas to see if any of them stick.
: ^ )
I'm not too sure what you're trying to say, or what you're thinking about. What you wrote was a bit ambiguous/obscure.
Well,....it has been proved that, in any axiomatic system, there exist statements or propositions which cannot be justified/proved. Actually, there are mathematical statements whose truth we cannot ever know. For example, look up the Continuum Hypothesis. It says that, generally speaking, there is no other magnitude of infinity that is strictly between that of the natural numbers and that of the real line. It has been proved that the Continuum hypothesis cannot be either proved or disproved under the usual ZFC system of logic.
So, your statement "the answer is always either right or wrong," is not necessarily true.
First, we want a fair definition of God. It is absolutely feasible to outline the time period in this type of method that the entity defined exists. But for so much, the time period refers to anything supernatural: actually above or past nature. But then if it exists, this can be a facet of nature, in view that that is what we imply through "nature." Certainly we will be able to suppose a supernatural entity, however that doesn't serve the reason for devout individuals.
Maybe they mean, like in the old saying:You can't see the forest from the trees...Sometimes the answer is right in front of your eyes and it takes a spark of intellect to see it...
Yes sometimes I find myself thinking too deep, then I say, "What the drat", and immediately I snap out of it.