Well, that’s because it’s possible to augment quantum mechanics with non-local hidden variables to achieve a deterministic theory. Quantum mechanics is deterministic, provided that one accepts the wave function itself as reality (rather than as probability of classical coordinates), which is philosophically similar to the “hidden variable” doctrine.*
This is interesting. Thanks.
*[Section 5.1]
When my school’s (competitive) academic team (which I was on) got our asses handed to us by pretty much every other academic team in the county–that pretty much disillusioned me that the best my school had to offer was anything special at all.
Something about not reflecting but shining with one’s own light? Not being obscured by reflected light?
It’s a good name for poetry.
I have always sucked at math. I expect it and I am prepared for it. In college I had to take a remedial math class. I studied incredibly hard and all I managed was a miserable C. That was not either unexpected or disappointing. Annoying as hell but not exactly a slap in the face.
What freaked me out was grad school and the day I realized that half the class could write better than I could. Listening to some of the really breathtaking essays one professor read aloud practically made me weep with jealousy.
I remain a good writer. But that was the first time I realized how much I will always have to learn about what it takes to be a better than good writer.
Huh. I actually just thought of that same angle…I was afraid it may be a stretch, but what the hell!
:o
Normally, they only weep when I do these explanations with math, or when they know there’s going to be a test on this…
For me, it was high school math and physics. I was in the bottom half of my class in algebra and calc, which pretty much meant I was fucked for AP physics. I tried to get my parents to let me take the remedial physics class just so I could have someplace to catch my breath and get back on my feet, but no dice. That was a humiliating year.
I took Calc I as an undergrad, and the twenty-something college prof finally told me he’d give me a straight B if I stopped bugging him during office hours and left him alone. I knew a bargain when I saw it.
The hell of it is that almost twenty years later in my mid-30’s, I bought an algebra textbook on a whim and began to work through the problems again, and BANG, this time I understood it. I even managed to teach myself some basic calculus.
But physics? That’s still a mystery. After teaching myself algebra, I borrowed a physics textbook from the library, and I couldn’t even get through basic force diagrams. I’m just not hardwired for the sciences I guess. I doubt I’ll ever be able to understand it even when I finish with more advanced calc.
High School, I go to an advanced high school (and ont eh enteence exam got 100th percentile, or maybe 99 can’t remember), but I knew from Middle School I would be completely screwed.
I can’t think on a test, and I knew I was going to a school with a lot of people as smart or smarter than me. I consistently am lower than everyone at everything. Don’t get me wrong I grasp the concepts, in fact the teachers often say i can grasp the concepts and applications better than anyone else but I
can’t
do
a
goddamn
test.
You see, I need to explain things to people to learn things. It sounds odd I know, but nothing becomes clearer to me than when I can talk freely it doesn’t matter if I’m explaining things to another classmate (more on this in a second) or a teacher, but the tests baffle me. When I retake physics tests and I can explain what I’m doing to the teacher (of course she doesn’t help me, just let’s me explain to her) I get grades over A’s (the test is graded so that if you answer all the questions correctly you get about two to three questions worth of extra credit), on a “silent run” I fail miserable. I could do it in middle school because the tests could’ve been passed while asleep and were basic regurgitation and not application.
As for my explaining things to other students. This also makes me feel stupid. In my AP Comp Sci Class we learn Java. The teacher all in one period teaches:
So you see, I was the kid that understood everything in my class the best so I basically ended up teaching the damn class (I’m not kidding if he didn’t quite have time for one of the people he’d tell them to ask me to help them with their lab/program). Leaving me unable to do labs or study the obscure points for the test and ended up dropping out becuase I had no class time to do notes or homework. Apparantly after I left he began teaching them. I’m too dumb to manage my time effectively or put my foot down and say no to another person. I can’t bring myself to hurt others, I’ll gladly give my lunch money and forego eating if someone I don’t even know forgot theirs (but no I do not hand out money to random hobos, I WILL bring them food though.). I’ll gladly sacrifice my grade to help someone study for antoher class.
I know I keep talking about how smart I am, but that’s the goddamn problem, that’s how the teachers percieve me and it gets in the way to a flaw. Do you know what I got in Trig last year? I passed with a D by one point. I aced (well, A-B’d) all my tests, and did all my homework, but I never turned in the homework because I didn’t think it was good enough for them. Same is happening with Physics, I do the labs but can’t seem to turn them in, they’re missing stuff and incomplete (even thought they’re mote thorough than my peers). I’m afraid I’m not going to pass this year due to my stupidity and inability to grasp when my work is good enough.
Same with Band I practice and practice until i’m wonderful at the piece and blow an audition horribly. My private instucter estimated my score to be 1500ish (out of 2000) I got a 643. Can’t audition, something’s wrong with me.
All of this points to me having no possible application in the business world. In other words I can’t do well on tests, I can’t do well in classes, what would make me think I can do well in the workplace? I’m thinking of just giving up and working at a low stress job like McDonalds, I obviously can’t perform well in anything that requires work. My boss isn’t going to sit there and listen to me explain what I’m doing on the project he’s just going to say “shut up and program” (or brainstorm ideas or whatever at the time).
I’m also a complete idiot when it comes to being social too. I haven’t done anything non-school related (meaning field trips, mandatory band section bonding time don’t count) with someone since 6th grade. I’ve enve rbeen to a school dance, and never had a girlfriend. I also have never had someone I could truly call a good friend since the first half of 6th grade.
So yeah, I realized I’m not as smart as I thought I was in highschool because I have an insane deficiency in the audition/testtaking/isolated process area. Nor can I manage time effectively, and i’m too nice of a person. And I can’t be a friend to anyone. Yeah there’s a lot that made me realize how stupid I am in high school.
I used to think I was pretty good at math, until I saw a thread here in which ultrafilter* and some other people were talking about stuff I never even heard of. Also, linear algebra beat me bloody several times in college before I passed it.
*Who, incidentally, is named after some sort of math concept I still don’t understand.
Oooh, ooh, can I explain this one? Though I’m afraid another thing that makes me realize I’m not as smart as I thought I was is my occasional difficulty in usefully explaining things to people who don’t already basically know them. Still, I’ll give it a shot:
Here’s one particular view of the ultrafilter concept which, if not necessarily the usual view, might at least be easy to wrap your head around: Take your basic Boolean operations “AND”, “OR”, and “NOT”. Let’s say that a set of variable names is called a “language”. A Boolean algebra is, in some sense, a language along with a bunch of equality statements between terms built up from the variables in the language using Boolean operations. For example, one Boolean algebra would be the one whose language had three variables named x, y, and z, and which came with two equalities: x OR y = x AND z, as well as NOT (x OR z) = z AND (NOT x). Of note, the language can be infinite, and there are also allowed to be infinitely many equality statements.
Now, an ultrafilter on a Boolean algebra is basically just a way of setting each variable in its language to either TRUE or FALSE in such a way that all the equality statements are satisfied. For example, on the Boolean algebra above, one ultrafilter would be the assignment where x is TRUE, y is TRUE, and z is TRUE. Another would be the assignment where x is TRUE, y is FALSE, and z is TRUE. However, the assignment where all three are FALSE, say, would fail to be an ultrafilter, since it wouldn’t satisfy the second equality statement.
Sometimes, instead of speaking of the whole assignment directly, we just talk about the set of things which get assigned to TRUE. When talking this way, the first ultrafilter above would be {x, y, z} and the second ultrafilter above would be {x, z}. But there’s no great need to talk this way if you don’t want to.
So far so good? Now, the notion of an ultrafilter can be generalized beyond that, but this is definitely the most common level at which it’s used; if you understand this, you understand the essence of ultrafilters. However, there’s also a slight specialization of this which is very common.
Specifically, one easy way to get a Boolean algebra is to start with some set X, make a language with one variable name for each subset of X, and then add equality statements as follows:
A) Add the equality “Y1 AND Y2 = Z” whenever Z is the intersection of Y1 and Y2
B) Add the equality “Y1 OR Y2 = Z” whenever Z is the union of Y1 and Y2
C) Add the equality “NOT Y = Z” whenever Z is X - Y (i.e., everything in X is in either Y or Z but not both).
We sometimes speak of an ultrafilter on a set X to mean an ultrafilter on the Boolean algebra you get in the above way. That is, an ultrafilter on X is an assignment of TRUE or FALSE to every subset of X in such a way as that intersection acts like AND, union acts like OR, and complement acts like NOT.
So, there you have it. You now (if I’ve done my job) know what an ultrafilter is (though, unfortunately, I’ve given only one toy example, little reason for why you should care about the concept, and absolutely no indication of the non-obvious properties and important questions relating to it. Well, it’s a start.)
Seventh grade, when I failed the first math test of the year. I had paid attention in class, did the homework, thought I understood, and was just shattered when I failed. I eventually discovered that if I did the same amount of work for a math test versus a history test, I would get an A on the history test and a C- on the math test. You’d think I’d resolve to study math harder, but no, I decided that math was stupid and and pointless and I Couldn’t Do It. I was so used to things being easy for me that I was incapable of actually setting to and studying my ass off. I figured that if I did poorly, there was nothing I could do to improve my grade.
I’m starting grad school in the fall and I have to take a couple math classes. I’m nervous, but at least I have now figured out that I CAN do math - I’m just not naturally good at it, so I have to actually, you know…work.
I had that experience going from elementary school to 7th grade, after entering a “gifted and talented” program; but rather than deflating, I found it liberating. I have no problems being, say, in the second quartile of an elite group: to me, it just means that that’s one damn elite group. I’d much prefer that to being the only standout, or one of two or three in a large group.
Now being in the last quartile of an elite group would probably bother me, because then I’d feel outclassed and out of place.
Plus, after reaching The Real World it became apparent that more than a few school-smart or test-smart peers of mine lacked the social or communication skills, the willpower or self-discipline to make something of themselves on their own. Or else lacked the ambition to do more than work a quotidian day job, being content being able to do it more effortlessly than another person might, to fund their passion for a hobby or interest on the side, so that in looking from the outside, there’s no obvious reason why this person was exceptional at all.
This is a big, big trap and why I so value my high school education. Nothing speaks more to me of wasted talent than to find extremely bright people underusing their talents, and not even realizing that they’re shorting themselves. Too often it’s because of a lack of opportunity, where their high school simply didn’t have the advanced courses or suitably expert instructors to match their potential, so they go through high school thinking “this is easy, this is my best/favorite subject, I’m a NATURAL baybee”. They declare their major on entering college, only to get demoralized when they find they’re underprepared both in terms of the material they’ve covered relative to others in the class, AND on how hard they’re expected to work to reach the next level.
My wife (a college math professor) sees this all the time, especially in the first “real” math courses like Calculus I or II. She would say that one one, maybe two out of every ten students like this react by gritting their teeth, getting a grim, determined look on their face, spending hours in the library and coming to her office hours sessions and running them into overtime to climb that hill. Most people try “coasting to the C” and ultimately change their major (in some cases, it takes a few courses before they figure out that coasting is no longer possible), even though they had “the spark”: ah, if they’d been pushed and challenged through their formative years, what they might have achieved!
Looking into my own soul, I don’t think I’d have been one of the “find that untapped reserve of will” type of people, especially not at the age of 18-20. Had I coasted through high school, and I don’t doubt I would have at my local school, I think I’d have been a Havey Wallslammer.
Ooh. Finally a thread I can respond to.
The dope is definitely one place I feel stupid. I love reading all the well thought out answers to difficult scientific, moral or philosophical questions but often realise I have no idea what people are talking about. Even if I have a coherent thought I mostly find it’s been said already.
That being said this place also sometimes makes me feel smart sometimes when I read some of the drivel that gets written.
I realized this a couple of seconds after I found out I was smart, and I’ve realized it anew every couple of hours since then. I think if I ever stop coming up against that realization, it will mean I’ve stopped learning.
Funny question.
I’ll say never.
But, that’s only because I’ve always had a pretty realistic grasp of how smart (or stupid) I am.
K-12, I was better at math than pretty much everyone in my class, but even back then, I’d been exposed to stories about mathematical prodigies who did amazing things at early ages, so I never thought that I was some genius.
When I got to graduate school, I finally met kids who were astounding, intuitive, and natural at math, but it didn’t surprise me; I knew they were out there, and I never thought I was that good in the first place.
There was a well-publicized study a few years back that said one characteristic of incompetent people is that they don’t realize the extent of their incompetence. They overestimated how well they did at things. I know people like that. I wonder if they’ll go to their graves like that or if it will dawn on them somewhere along the way.
If someone, exceptional or not, wants to live their life so that they can engage in a hobby or passion other than what they are paid to do, is willing to accept the downsides like a lower salary and a less prestigious job that go along with it, and is happy with that life, what’s wrong with that?
Not a damned thing, or at least I hope not. I have an anxiety problem that kept me from pursuing a high-stress, high-salary job. I do well for myself, don’t get me wrong, but I’m much happier in the job I’m in than I’d be as, say, an attorney or doctor.
Freshman calculus class. I was exploring several majors, but was undeclared at the time. I ruled Math out then and there. I found a better major 
It begins to make sense now. Maybe now there will be some small spark of understanding next time I’m looking around on Wolfram MathWorld.
I’m now starting grad school for Electrical Engineering, after a break from college for many years. My typical graded homework so far has been scoring in the mid-70s, and takes me a solid 12 hours or so to do each week’s problem set.
Last week I heard a girl chattering away behind me about her homework, and how it usually only takes her an hour or two, but she’s been getting 100s so she doesn’t mind spending the time :rolleyes: Oh yeah, and how it took her 3 years to double-major her undergrad :eek:
I realize that in grad school, my competition is no longer an accomodating bell-curve distribution where I can rest calmly on the assurance that there will be enough slackers, apathetic students, and strugglers to ensure that I will place high on the curve.
Grad school’s a bitch! And I can’t spell ‘acommodate’ to save my ass, (acomodate, accommadate) stupid spell-check, grumble grumble :mad: