"Not a good test taker..."- I don't understand.

Applying to College
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<p>Yes, if you have faith in humans’ ability to reason, math is inevitably true. That is, the if-then statements (if ZFC is true, this other thing is true, etc) are true. All math is based on axioms, chaoticorder- essentially, they are things you “suppose”, or “assume” for the sake of finding interesting results, and not things that are “necessarily true” or “accepted”. In fact, even rules of inference such as “you cannot have P and not P” are axioms in themselves. But this view is difficult to hold when you ask “how do you know that if-then statements can be ascribed a truth-value?” username- math is deductive, not inductive, so in principle, even if we were some dream, the theorems in math would still be valid.</p>

<p>One more thing that we can agree must be true is that we are observing something- that is, when I see something, I at least know that I saw something even if it does not correspond to some ultimate reality, though you can doubt the existence of something like that if you want. Hyperbolic doubt is not a consistent worldview though- if you take it too far, you must doubt doubt.</p>

<p>On topic though, I suppose that the people with anxiety problems would qualify as being “bad test takers,” under my own criteria. I don’t believe that the SAT is supposed to test cool-headedness, though that is probably a factor in your score.</p>

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But if it does, is that a bad thing? Surely being calm under pressure is a very valuable skill for almost anyone…</p>

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<p>Again, you wouldn’t be anxious if the material is 1st grade to you.</p>

<p>And all math is based on 1+1=2, a statement which was based on induction. There may be a rare case in the universe where 1+1 doesn’t equal 2.</p>

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<p>I haven’t been part of the philosophical sub-debate that’s been going on, but I am curious why you place such high value on induction. That basically confines you to your own experiences, which are by necessity very limited. I’m no rationalist, but induction has its problems as well.</p>

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<p>Let’s be careful. The fact that non-mathematical truths are more difficult to grasp does not mean that they are not out there. I imagine your statement wasn’t meant to deny that, but I want to clarify because it can be taken that way.</p>

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<p>to mcgoogly post 107#
Your comparison to the Nazis is false. The jews were not the “bad test takers”, as they outperformed the average german. The Nazis hated them because they were successful.</p>

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<p>112, i don’t… I’m saying that mathematics CAN be flawed because it is based on induction…</p>

<p>And I think he means there are no non-mathematical truths that we are aware of, for example, science is just a series of induction, language is just completely made up, and history is… what you make of it.</p>

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<p>I answer more questions wrong as the test goes on because I can’t concentrate. That’s probably a fault, and I am working on it – but in the end, I can still do math and read and write. </p>

<p>20 years from now, it will matter how well I do these things, not for how long I can do them at a stretch.</p>

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<p>I was referring to some of your earlier posts, where you talked about how you favor empiricism over rationalism.</p>

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<p>Scientific and historical knowledge can indeed be flawed or just plain wrong, but that does not mean that there is no objective truth regarding such subjects, even if we fail to grasp it with absolute certainty.</p>

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<p>Yes, exactly. there is “truth”, and there is what we know. What I meant was the only knowledge that we “know” is math. Other subjects like science or history has a “truth”, but we just don’t know it.</p>

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How exactly do you know that? Nobody is impervious to time pressure.</p>

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Mathematical induction is deductive and is not flawed if done correctly (wow, you don’t see a contradiction and a tautology in the same sentence every day).</p>

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<p>Not exactly. In the end, neither induction nor deduction can be proven to be perfect, because just because we can’t find any other possible alternative doesn’t mean there isn’t one.</p>

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<p>Is the fact that one and one make two really based on induction? I’ve always considered it a self-evident proposition. Our minds can’t conceive of it being otherwise, so we automatically accept it as truth. It’s not like we can really see it happen in the world, anyway – if I put two identical objects side by side they are still separate; they don’t suddenly become “two” – numbers are mental concepts.</p>

<p>As a side note, one other source of knowledge we haven’t even brought into the discussion is knowledge based on authority… the vast majority of the things we accept as fact are based on our belief in the authority of the person telling us. I really can’t prove to you that China exists; I just accept it because people I trust have told me. Of course, their knowledge is based on either induction or deduction, but it is important to realize how much of what we know comes from the authority of others.</p>

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<p>I’m not sure what this means, but it’s hilarious.</p>

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<p>Mathematical induction (proofs) is deductive reasoning, not inductive.</p>

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<p>Just a little insight from a “bad test taker.” I’m a good student because I can process information I learn in class easily and understand it easily, but put me in front of a collegeboard test that I know contains information I haven’t seen for years causes my mind to race, speed through things, lose all concept of time, my face gets extremely red, and I get incredibly anxious. Perhaps I could spend more time preparing like you said, but still knowing how important the test is would be enough to give me the same side effects.</p>

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ah, so it’s because you forgot what you’ve learned. So in the end, it’s still because you don’t know the material.</p>

<p>lockn, we’re not talking about mathematical induction</p>

<p>112, you don’t think of it as induction, but really, the only reason we believe so is because we can’t find any counter examples.</p>

<p>A philosopher once tried to prove 1+1=2, and went crazy.</p>

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<p>“And all math is based on 1+1=2, a statement which was based on induction. There may be a rare case in the universe where 1+1 doesn’t equal 2.”</p>

<p>No. That is completely false. Most of math is based on ZFC (or more informally, set theory):</p>

<p>[Zermelo?Fraenkel</a> set theory - Wikipedia, the free encyclopedia](<a href=“http://en.wikipedia.org/wiki/ZFC]Zermelo?Fraenkel”>Zermelo–Fraenkel set theory - Wikipedia)</p>

<p>And even then, you can create a new system if you want, with different axioms. It does not matter whether these axioms are “true.” In fact, I believe most mathematicians will tell you that it is pointless to discuss the “truth” of these axioms. They are only supposed. THe truth comes in the form on if-then statements.</p>

<p>In fact, it took (sorry I forgot the names) a couple of people interested in the foundations of mathematics (something interesting to wiki) something like 400 pages before they proved that 1+1=2. But, for all intents and purposes, you may consider 2 to be defined as 1+1. That is, if you start with some axioms for reals (or, for torture, start with axioms for integers and construct the reals), one of them is that there is a multiplicative identity, denoted by “1”. 2 may be defined to be the addition of the multiplicative identity to itself.
And math is not based on induction. It is based on deduction using valid rules of inference, which are themselves assumed for the sake of whatever you are doing.</p>

<p>EDIT: Honestly, if you want to talk about foundations of math, the only people who really know what they are talking about most of the time are people who do research in the field.</p>

<p>If you want to talk about knowing things about reality… I’d say that feynman would be a good author to read on the subject. If you want to torture yourself, you could read certain parts of Hume where he talks about empiricism. But maybe I’ll leave one thing: It is not certain that there is an “objective reality” out there. As someone hoping to go into physics though, I sure hope that there is.</p>

<p>To clear something up, I think that what the above two posters meant by mathematical induction is different from what username meant. The former were talking about a particular method of proof while the latter I believe, was talking about the basis for 1+1=2</p>

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<p>Crazy how a discussion of bad test-takers turns into a philosophical debate…</p>

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<p>Just another note from a “not so good” test taker…I was in the top 10% of my high school class (private school). I was the top student in my department when I got my BS degree. I had the highest GPA in the graduate business school when I got my masters. I worked hard, studied hard, and did well.</p>

<p>My PSAT, SAT, ACT, GMAT scores were well above average but by no means stellar. I was nowhere close to getting National Merit recognition (altho my brother did).</p>

<p>Why? I hate those types of tests - I freak. My mother and brother find them fun and amusing - that is why they test off the charts. </p>

<p>When I took the GMAT - I spent weeks reviewing and studying. I used 3 different review books and completed each one. I went in as well prepared as anyone could be. I felt confident and ready - but I still choked. Again, my score was fine by average standards - but definitely not a match for my school grades.</p>

<p>So, to me, the OP’s comments - “I mean, I could be wrong. But I think being a “bad test taker” just means you aren’t prepared. … I’m just saying- if someone wasn’t prepared, it’s no fault of the test. He didn’t know the information. Period.” - is just bogus and rather arrogant.</p>

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<p>Feynman is excellent. i have a couple of his books: Surely You’re Joking Mr. Feynman, and what do you care what other people think.
112- Yeah, it’s pretty funny how a few remarks can turn a thread around.</p>