Thank you for the excellent advice. I’m going to have about a month and a half off this summer to work on the GRE, and have decided to get the Princeton Review book, but I’m also considering shelling out the money for a formal class. I’ve considered asking around on the Dope but the overwhelming response to GRE Threads is, ‘‘That? Oh, you’ll do fine. It was easier than the SAT.’’
That’s unhelpful because:
I never took the SAT; I took the ACT
I ALREADY KNOW THIS IS GOING TO BE HARD FOR ME.
Apparently for each problem in the GRE, there’s some kind of shortcut trick that’s supposed to make you able to find the answer instantly, without doing all the complex calculations. But I end up doing all the complex calculations. The ‘‘a-ha’’ moment never happens. If it looks complicated, I work it like it’s complicated. I have to find some way to change the way I look at math problems or I’m screwed.
First, a great big thanks to those dopers who explained, very clearly, what diphthongs and gerunds were. As English is my second language, my English grammatical education was kind of non-existent, and I never really understood these two concepts before. It felt lovely to finally understand.
Re. the definition of “noun”, it’s much easier in French, where “noun” and “name” are the same word. For us, a noun is, well, a name.
As for the bane of my educational life, does PE./Gym count? Being the fat asthmatic kid with glasses, I could never do a cartwheel, the parallel bars & pommel horse were instruments of humiliation, and I could never dribble a basketball AND run. I earned the contempt and scorn of most of my gym teachers, all except for the last one, who was kind, help me catch up, and introduced me to football and the javelin, where, amazingly enough, I did not suck. May he be richly rewarded.
If it does, I’m right there with you. I was neither fat nor asthmatic–just about as unathletic as it was possible for a kid to be. I couldn’t run a quarter of a mile without getting out of breath, was no good at sports, and just generally sucked at PE. I still remember my sadness when I couldn’t even manage to get the 50th percentile patch for the President’s Council athletics thingy (this was back in the 70s–they handed out patches for three levels–I forgot what the other two were, but I would have been happy with a mere 50).
The fact that my parents didn’t ever do anything athletic and didn’t place any value on it didn’t help either.
When I was in elementary school, we used a similar method for syllables. Put your hand under your chin and count the number of times your chin drops (you might have to say the word more slowly and carefully than usual). This is the number of syllables in a word. Very simple, and accurate. All you who are unsure about syllables, give it a try and see if that makes sense to you.
Significant digits. I haven’t had time to look at the rules, but they have never made sense. It’s been explained time and time again to me. And I’m not bad at math.
I didn’t really prepare for the GRE - got a book but didn’t look at it, that sort of thing. I got to the testing site half an hour early and sat in my car trying to relearn fractions. I mean, who uses fractions after the third grade? I hadn’t had any math in college because of my AP courses, and before that I don’t know the last math class I had that had, you know, numbers in it.
I did fine - not breathtakingly awesome, but good enough to get into grad school with no problem.
About 4 years ago, I took the practice tests without studying. On the verbal, I did pretty well.
On the math, I did not do well. Not good enough to get into grad school with no problem. I’m not assuming I’m going to suck at the math portion, I already know that I do. I am confident that if I study hard I will be able to meet that ‘‘good enough’’ marker, but I ain’t there yet.
Oh god, are you talking about significant figures from chem? Theose were the bane of my existence. My high school chem teacher would mark the entire problem wrong if your significant figures weren’t correct. Mine were not usually correct.
Finding something listed in alphabetical order, or worse, alphabetizing a list of words.
Sure, I get the concept just fine. Just that if you give me two randomly chosen letters. the only way I can tell you which comes first in the alphabet is to start with one, sing the ABC song (OK, I don’t have to actually sing it…I can recite the alphabet without the song) and see if I come to the second one before I get to Z.
I gather from seeing the ease which with other people do this that they can just look at “trust” in the page heading of the dictionary and know that they either need to go forward or back to get to “thrombosis”. Not me RSTUVWXYZ…nope, H must come before R.
Tell me to count backward from 2000 by 7s…no problem. Tell me recite the alphabet skipping every other letter…f**k me!
Oh, and those word search puzzles…I can only see the words if they are left to right, top to bottom, or diagonal top left to lower right. Finding any of the other words requires picking out the least common letter, looking for that, then looking around it for the letter that would come next. That’s for the version where you are given a list of words to find, and it will take me 5 times longer than anyone else. No list…f**k me.
I can read a page upside down fairly well, but I can’t see a word spelled backward in those damned puzzles. I remember teachers handing these things out as a reward, and other kids thinking it was fun…f**kers.
It is possible to be very precise, but not accurate. For example, let’s say I have a scale that says you weigh 3,456.789012 pounds. The scale I am using has a tremendous amount of precision (to six decimal places. For comparison, generally the most you’ll ever see in a chemistry lab on a scale is four.) However, there is no way that your weight is actually 3,000+ pounds. So what I have done is told you a very inaccurate number with very high precision.
It is also possible to be accurate but not precise. Let’s say you actually weigh 144 pounds. Now, if I have a scale that can only measure in ten pound increments, it won’t say that you weigh 144 pounds. Instead, it will say you weigh 140 pounds. Because it says you weigh 140 pounds it is accurate in the first two digits but is not very precise. Now, it may be that that level of accuracy with that amount of precision is good enough for you. But let’s say you’re trying to make the weigh-in for your wrestling match in the 145-pound class. You want to know exactly how much you weigh to at least three digits and quite possibly more.
As for significant figures, it’s a way to honestly report numbers in the sciences. Basically, you report numbers with the least amount of precision available. So, for example, let’s say I’m running a reaction. The only measures I have available to me is a scale that gives four decimal places and a syringe that can measure to 10 mL in 0.5 mL increments. I have one solid reactant that I weigh out on the scale and I measure out 7.1849 grams of solid. I also have one liquid reactant and I measure out 4.5 mL of liquid. The measurement of least precision is the liquid. So while I might have measured out 7.1849 g of solid, when I make any other calculations involving the liquid I have to round to the tenths place. So, if the liquid amount determines how much of a product I can get, I round the number I calculated to the tenths place, even though I have the solid to a precision of ten thousandths.
The rules and meanings get more complicated, but that’s generally good enough, at least for an understanding.
It might be more obvious what the concept of sig figs is about if you explicitly write uncertain quantities as intervals: between 7.12 and 7.13. Between 10 and 11. Between 2 and 6. And so on. And if I were to add (7.12, 7.13) to (10, 11), I’d end up with a new interval: something which could be as low as 17.12 or as high as 18.13.
That’s the main idea; instead of just giving a best estimate, one combines it with some indicator of the level of uncertainty. Significant figures are a (somewhat flawed) way of trying to squeeze such information into a single number. I’m not a scientist, but it seems to me that all those laborious, overformalized sig fig rules they stress so much in high school aren’t really used so strictly in the real world; when scientists are really paying attention to quantifying uncertainty, they use more sophisticated techniques than crude old sig figs, and when they’re just doing due diligence, they common-sense eyeball it. At least, that’s my impression. I’m fully prepared to be shot down.
I’d say common-sense eyeball it is common. I’m an organic chemist and have worked on very small scales (under 10 mg) and pretty large scales (up to about 500 g.) I could easily be working on multi-kilo scales. I’d say most people I know are happy with three or four significant digits in most cases. So if I’m working on a 400 g scale, say, I’d get as close to 400 g as possible without worrying if it’s actually 400.04 or 399.98. If I’m working on a 40 g scale, I’d get as close as possible to 40.0 g. A 4 g scale would be 4.00 g. 400 mg would be 0.400 g. Anything smaller than that and it’d depend on how precise the scale I’m using is. In all cases, it’s important to make sure that rounding gets to the number desired and I’d prefer to overshoot a tiny bit (40.04 g versus 39.98 g for instance, although they round to the same value) as a small amount of loss is expected in actually loading the material into the vessel. The smaller the amount, the more important the accuracy and precision of the measurement. Putting in an additional 0.04 g into a 400 g reaction is an error of 0.01%. By comparison, putting an additional 0.0004 g into a 0.400 g reaction is an error of 0.1%. In practice, there’s going to be at least that much loss during manipulation of the reaction anyway. You minimize it as much as possible, of course, but it’s just part of life. Heck, depending the analytical techniques you’re using, you might never see 0.01% or 0.1% anyway.
I haven’t used the real fancy methods since undergrad. Propagation of error was only ever done in physical chemistry lab and I haven’t done the types of analysis recently that requires statistical analysis and standard deviations. Synthetic organic is definitely not physical or analytical chemistry and it isn’t physical organic chemistry either.
Let’s say you’re converting temperatures: 37 degrees Celsius converts to 98.6 degrees Fahrenheit, as per the standard equation. Except if you say the material was 98.6°F when you measured 37°C on a thermometer only accurate to whole degrees C, you’re lying: The real temperature in Fahrenheit could be anywhere from 98.6°F to just below 100.4°F and you don’t know because your tools aren’t that good.
Significant figures are important because tools are inevitably limited but math assumes all numbers are perfect and absolute idealized forms.
Well, math only assumes that if you do. One could perfectly well use the mathematics of uncertain quantities rather than the mathematics of sharp ones. It’s just a question, in any particular situation, of whether one is prepared to bother.