Yeah, and two other egregious errors in that sentence, too.
Or maybe we just need to understand the true meaning of the sentence: "then right a new paper sighting the published one and submit to a more prestigious journal"
In other words, I take a new paper in the works and make it "right" by including research literally gleaned from the previous paper while staring at it ("sighting") and copying it.
Perhaps the GGP was actually talking about plagiarism and falsifying research to fit an agenda.
One thing I hate is when people tell me how I learn and force me to do repetitive assignments that test only for memorization and do nothing to bolster one's understanding of the material, which is the sort of thing I was talking about. I had to deal with that garbage too much in the past, and never bothered to do any of the assignments.
A few points:
(1) A well-structured set of problems in a basic math textbook is often intended to gradually allow students to work through various difficulties. The first few problems start with some new idea or skill, then a few more introduce some complications and special cases, then the next few combine it with previous knowledge and skills, and finally we arrive at greater fluency in using the new material. I, probably like you, never needed that many exercises to figure things out. I probably could have done 10% of the problems assigned, and I still would have absorbed the new material. But as someone who has actually taught high-school math, I can also tell you that you and I are NOT the norm. I tried not to assign too many repetitious problems, too. But many students need to work through at least some of this build-up of skills when incorporating a new idea into existing knowledge.
(2) Even for cases where there is more-or-less repetition to learn skills, it is sometimes useful to learn skills. This is different from memorizing facts (though with really basic arithmetic, there is a need for actual memorization too). Basic math is often about internalizing algorithms, to give you tools to be able to higher math. If you don't internalize these algorithms, higher math will become increasingly difficult to follow and understand.
(3) Also, sometimes the algorithm IS the goal. For >99% of people in the world, math is only useful as a tool, not some sort of higher-level "play in an abstract world and have cool insights" kind of thing. They need to be able to do basic manipulation of numbers and symbols to solve very particular types of problems -- with real-world applications. That should be the focus in math education for those not actually going on into higher math -- no need to do all sorts of wacky advanced algebra or memorize stupid facts about geometry in high school... let's teach students how to solve real world problems, and make sure they practice those skills to internalize them.
It sounds like abstract ideas came quickly to you. They came quickly to me as well. But that's not true for many students. Part of the problem is our curriculum structure, which seems to assume all students past middle-school math should be headed toward higher math, instead of focusing on applications and skills that could be useful. But part of the issue is that many students need significantly more repetition to get things, or they need a gradual build-up in difficulty when dealing with a new idea.
So my suggestion is that, if you really want to see a jump in math skills, start placing more emphasis on learning the concepts and less emphasis on how fast students can process problems. Allow students unlimited time on tests if they want it (maybe give them the option of taking tests after school instead of in class). It will give a lot of students like me a lot more confidence in themselves
As someone who has taught math at the high school level, I definitely agree with you up to a point. I usually tried to design tests so that an average student could complete it with plenty of time to spare -- those who needed a little more time could then take it.
However, there is a problem that gradually starts to accumulate with students who can't do math at a reasonable speed. My first year teaching (at a not-so-great school in a not-so-great location), I had seniors in high school who were enrolled in algebra II, but some of them couldn't do basic arithmetic. Sure -- if you gave them enough time, they could use their fingers or calculators to determine what 12 minus 7 is. (Don't ask how these students managed to get to algebra II -- it was years of terrible teachers and vacancies with substitute teachers passing students who shouldn't have been.)
These students were completely incapable of understanding most of the stuff going on in class on a regular basis. Even the students who could do some semblance of basic arithmetic hadn't internalized many of the basic rules of algebra, etc. So, while -- again -- they could work through these things at a very slow pace, they had no idea of what they were doing or why when it came to higher-level questions. Eventually, I realized the only way I could teach unprepared students algebra II according to the state-mandated curriculum was to teach basic algorithms for solving the minimum set of basic problems required. (Sending them back to algebra I was not an option, since officially they had "passed" it.) The students had no perspective for why they were doing anything, but they could do meaningless symbolic manipulation enough to satisfy requirements.
And that's what happens when most students aren't drilled enough to internalize basic skills at various levels. The point of taking speed tests at elementary levels is because if you can't immediately do arithmetic in your head, you'll have no clue what's going on when solving some 10-step equation in algebra. And, if you don't internalize the equation solving steps in basic algebra to the point that you can do them reasonably quickly, you'll have no idea what to make of your calculus teacher zooming through such a problem to get to the actual derivatives or integrals or whatever.
(Also, note that smarter students who are given unlimited time also can make use of unlimited methods to check their work -- even taking to guessing answers with trial-and-error, or doing the same problem 5 times until they come up with something that "checks." While there is a value in persevering until you can get an answer you're sure is "right," it doesn't necessarily tell a teacher whether you actually know what you're doing. The time to do trial-and-error is on homework assignments before a test until you can figure out the right way to do something -- by a test, you should have accumulated enough fluency to start on the right track.)
So, I agree that there needs to be a balance. Testing new skills should probably be done with plenty of time, so students have time to reason things out. But eventually they need to internalize the steps enough to do them reasonably quickly -- and subsequent tests using that material needs to evaluate that.
If not, you'll end up with students who can't do anything and can't understand any higher-level steps in math, because they're still stuck taking 30 seconds to figure out what 12 minus 7 is while trying to do a triple integral.
It actually bugs me more that RAM is referred to as "memory" which is and should be a very generic term.
If anything the harddisk is probably a better candidate for the term "memory" than RAM is. A harddisk is what ultimately must store the data permanently and recall it.
You make some really good points. But, interestingly, I think this is becoming less relevant today, where computers are left on for months at a time, and perhaps put into a low-powered "sleep" mode which preserves RAM contents.
For me, RAM now is more like human memory, in the sense of "what did you eat for breakfast yesterday" or "what projects were you working on last week"? It's the stuff that can be relatively actively recalled, because it's a current project or task. It's more than "short-term" memory, too. Hard drives are more like filing cabinets or photo albums or diaries -- a place I go to look up something I can't actually remember. RAM size is also large enough now that most common applications may almost have a continuous presence in RAM too... so it has really become a kind of repository like a "working brain."
Only assholes like you will celebrate as meat and dairy prices will skyrocket beyond the affordability of most poor families.
One could only hope. Then we might begin to lift the stranglehold of crappy food (including bad meats and fake processed "meats") and junk food producers. Cows are not meant to be fed corn -- but we do so because corn is cheap. Corn is cheap because it is subsidized. Cows get sick because they eat bad diets, so we feed them medicines and chemicals to keep them healthy enough to grow fast, live a short life, and satisfy meat demand. Any bad stuff that might get into bad food is concentrated that far up the food chain, which is probably one of the reasons red meat and fatty red meat seems "bad for us" -- it's not an inherent property of red meat, but of unhealthy badly produced red meat. And we don't have enough pasture land to satisfy meat demand at current levels, so there's no way to raise enough beef in a healthy way, even if we wanted to.
Americans eat way too much meat, and most of it is bad quality. A few generations ago, people ate less, but also spent a significantly higher percentage of monthly budgets on food. We've gotten cell phones and cable TV, while ruining our bodies by paying less for junk.
I'm NOT some "organic food" wacko -- but I recognize the benefits of having a food production system that keeps us and the animals healthy. For a few years, I could not afford to buy much quality meat, so rather than stocking up on junk meats from the average supermarket, I learned to eat beans, lentils, legumes and other things to substitute. Most Americans could eat something like 1/10th of the amount of meat that they do, and still get the major nutritional benefits from meat consumption.
Our system is really broken and unhealthy. Having less cheap meat to go around would be better for the environment, for the animals, and for us.
Philosophically, thought, it does seem quite silly, and I myself would never have regarded it as more than a mathematical curiosity,
Why? We currently accept a model where the universe spontaneously came into existence at one time with any explanation (at least none that we know of now). The steady state hypothesis postulates a continuous universe with spontaneous creation of stuff at a regular rate to remain a stable state. Exactly why is the latter more "philosophically" more problematic than the former? Both postulate events of creation out of nothingness.
Both creative people and cranks have lots of wild ideas. The difference is that a crank reflexively defends his ideas with irrational vehemence.
I've known cranks who were just obsessed with one thing and could never see beyond it, but I've also known many cranks who were very creative. I don't think the sets are as mutually exclusive as you claim.
A creative person usually discard his ideas, because he knows there's always more where that comes from.
I think this has more to do with ego than whether someone is creative or not. People hold fast to their ideas for all sorts of irrational reasons -- career, other people's praise of them, general acceptance within a peer group, politics, etc. Being a crank is more about personality type, in my view, than whether or not someone is "creative." The most effective cranks I have known are generally quite creative (and adaptive), enough so that it sometimes takes a long time for other people to realize they are simply wackos -- and they even attract followers to their irrational cause. (The shared characteristic in the crank and his audience in this case being a lack of specific knowledge or perspective to recognize how ludicrous the claims are.)
making $100,000/year and having $60,000 or $70,000 of that amount after taxes going to rent
That's way too high of a rent estimate. Even in San Francisco, you can get a decent place for 1 person for $3000/month.
Umm, re-read the GP - "after taxes." In CA, you're looking at about 10% income tax to the state. Add that to fed income tax bracket of about 25%, and you're looking at $60000 = $39000 or less after taxes. (Obviously a quick estimate.) You say you can get a decent place for $3000/month = $36000 after taxes. GP's estimate is not necessarily "way off": point is that it could easily require more than 50% of your after tax income in CA for rent. In TX, you not only have significantly cheaper rent, but no state income tax.
By the way, I have one final thought -- I actually have used the concept of this piece in teaching students about art. There are always factions. Some people immediately dismiss it, and no matter what we say in the discussion, they still think it is nonsense.
Other people listen to some arguments about it, converse with other students, and come to think there is something to be learned from the "principle" of the piece, if not the experience of the piece itself.
Others may find it actually changes the way they think about music and art in a real and permanent fashion.
My goal is not to get anyone to "like" it or even to accept it as intellectually interesting. It's just to propose it as a kind of experiment. Some people find it useful to think about, and they get something out of the exercise. If you don't, that's okay. I'm not judging you, nor am I insulted or offended that you don't appreciate it.
And I do apologize if I took the tone of your response to mean that you hadn't really thought about the piece. I did make assumptions. But I also replied to "you" as a reply to other people (e.g., people who modded your comment), because I know some of those people may fall into the categories I listed above -- they may be dismissive at first, but some may realize there's something else there.
Personally, I don't find it useful to insult other people. I try to respect other people's opinions, even when they differ from mine. When people don't agree, I like to engage and try to come to a mutual understanding; if the other party chooses to leave the discussion, that's fine.
You obviously find the need to declare other people to be "snobs" and to dismiss what they do as nonsense. That is indeed your opinion and your prerogative. I just rarely think that's a useful thing to do -- it's not very polite, it disrespects other people's opinions, and you often lose the chance to learn from a perspective other than your own. If you have some further thoughts from your experiences about why you view this piece as you do (and what else fits into your categories of "snobbish nonsense"), I'd be interested in hearing about it. But just to declare it to be such is more like an internet troll than having a discussion.
I made the error of assuming that you weren't informed about something, so I hoped to offer some knowledge to you. You appear to value calling people "snobs" and what they produce "garbage." To each his own, I suppose.
whether or not a person finds offense in a statement is on them, not the speaker.
Well, take a moment to re-read what you wrote:
pontificating on the topic as if they're the first person in history to ever do anything weird and/or stupid. You know, the kind of garbage that art snobs devour.
Look, I generally agree with you. I didn't actually take offense at your notion. I accused you of insulting other people, which, frankly, if you look at the text you wrote, you did. I don't think this is unclear in your writing: when you say people are doing something "weird and/or stupid" and are producing "garbage," I think there's some pretty clear implications. I don't think there's time for my own introspection -- your characterization was very clearly negative and, frankly, intended to devalue ("garbage") your target.
As I said, you don't like the stuff -- that's fine. And maybe you did know more about it, but still don't like it. That's great. It's your opinion. But you didn't give any details about why you think that way: you just declared, "This sucks, and the people who do it are doing something weird and/or stupid, and trying to impress pretentious snobs" (paraphrased, obviously).
You're more than welcome to your opinion. And if you engaged with the explanation of this, and you still think it's crap or nonsense, that's fine. But I think it's a more useful discussion to say why you think it's crap or nonsense, rather than just insult people and be dismissive.
It's all nice and all that you want to make up and be cheerful now, but that's not the way your original post sounded. Just letting you know. And, I have nothing invested in the opinions about this piece or my views on the piece. Did I say I actually LIKE it? No. I said it poses interesting philosophical questions. You want to think Cage is an idiot -- I don't really care.
I was trying to offer some context and perhaps some perspective for people who may not have thought about such things before. I thought some readers might find it more useful than a blanket dismissal and set of insults. But you apparently find it more useful to deny that you actually said anything negative and proceed to do exactly what you accuse me of, namely make assumptions and then insult me.
Namely because, to me, it represents that self-serving form of 'performance art,' that has absolutely no artistic value but rather is an expression of the "artists" narcissistic desire to be the center of attention by doing something remarkably weird and/or stupid, and subsequently pontificating on the topic as if they're the first person in history to ever do anything weird and/or stupid. You know, the kind of garbage that art snobs devour.
Okay, you don't like something. That's fine. But you might bother to learn something about it before insulting other people.
For one thing, this is actually the first time in history that a composer tried a particular kind of experiment. And yes, I mean "experiment" in the same sense that scientists do. In this case, it was an attempt by a composer to try to find out something about the nature of music (and art in general), and also to allow a group of willing listeners to participate in that experiment.
You are ABSOLUTELY RIGHT that there is a lot of nonsense "experimental art" out there which is just pretentious nonsense -- people trying to do something weird or "edgy" or offensive or "provocative" just to get attention. Most of these people -- and their audiences -- are something like what you describe.
But Cage's point was different.
The main problem with 4'33" is that you have to understand the context. Without context, it sounds ridiculous and like some sort of stunt. It would be like taking someone who doesn't know anything about physics and putting a 100-page paper full of mathematical proofs about string theory in front of them, and saying "Look! See how this explains everything about the universe!" And the reaction is, "Umm... how many dimensions?! What the heck is this talking about? This is just nonsense made up be pretentious snobs who like to play around with math for fun. Why should I care?"
And some people might have that reaction to string theory too. I've heard people say as much here. But maybe we should look a little deeper about what a theory or an experiment is trying to do before dismissing it with anti-intellectual rhetoric and ad hominem attacks on the people who value it.
Look -- here's an interesting question for you: what is music? Seriously. You may not care. You may say, "I just wanna go back and listen to my Top 40" or Alternative Death Metal or whatever random stuff you like. But some people have a career where they write music and think about how music is made. And some of those people might find that question interesting. So think about it for a minute or two: what is music?
Most people often say something like "organized sound." Okay, but what about birdsong or wind chimes? Can those be music? Some people say yes; others say no. Why? Most people will admit that something that sound "musical" can exist even if there is no human really "composing" or "performing" it -- whether it's actually "music" is a philosophical question, but many people say, "Well, it's a pleasant sound when I listen to birds, so it has some 'musical' quality about it."
Now, John Cage comes along, and he does other sorts of experiments. He himself spends some time in an anechoic chamber, in complete silence. Except it wasn't completely silent -- he became intensely conscious of hearing the rhythms of his own breathing, and a kind of sensation of his heart beating.
Now, if you think about issues like this -- how we heard "musical" elements in nature, and how our own bodies will always be influencing our perception of sound, eventually you realize that music is partly created by the listener. It's not just a composer or performer putting sounds out there -- it's also in the ability of a listener to find some sort of meaning in the sound world around him/her.
You may think all this talk is snobbish or pretentious or whatever, but it gets at the heart of why some people don't think rap is "music" or don't think jazz is
How about reading the Wikipedia article on the history of the SAT? And look up stats on the gradual decline in actual number of test scores above 600 particularly on verbal before the test was "fixed" in the 90s? The one error I made was mistaking the era of relative stability, which actually went from the late 50s through the 90s (with a few changes and reduced length along the way)... I wrote this without rereading anything else first.
This is the reason that education is *mandatory* in civilized countries - to take some part of the decision-making process away from uninformed parents.
Wow. Here I thought the reasoning behind mandatory schooling in "civilized" countries had to do with creating an informed electorate and a class with enough education to be productive in society (e.g. able to do jobs requiring basic skills).
Now you tell me the actual reason is to ensure state indoctrination. I've heard people murmur as much before, but I've rarely heard it said with such affirmation.
(Don't get me wrong -- I absolutely do NOT think religion has a place in a science class. I want the wacko religious nuts to stop interfering with schools for their own agendas. And I think the state has every right to intervene and protect kids from abuse, neglect, etc. But the primary purpose of school should be to make sure kids conform to officially sanctioned state beliefs, and to correct the bad ideas from parents? I'm sure that's what every benevolent dictatorship said as well when they started rewriting history books to make sure children get the one "true" story.)
The goal of the SAT used to be to predict performance in college. Now it is used to predict how much effort one is willing to put into it to game the system.
Well, it's always been about trying to predict college performance. Back in the late 60s through early 90s, it was a stable test format, normed rigorously through decades of testing, which was basically an IQ test and advanced reading comprehension test. Things like analogies and vocab testing both how well-read you were and your abstract ability to connect subtleties of meaning; things like quantitative comparisons tested logic and reasoning skills outside of normal basic math.
Then it was renormed in the mid 90s to make it about 100 points easier -- it no longer really could distinguish the top of the scale (which, if you look at the stats, appeared to be disappearing -- the actual number of perfect 1600s went down significantly in the 80s despite increases in number of test takers). The high-level critical reasoning was less stressed in many college programs too.
Gradually, over the past couple decades, the test has been further dumbed down, to service the increasing number of people who want to go to college and the decreasing number of people with high-level literacy and advanced critical reasoning. Analogies and quantitative comparisons disappeared. They added a writing test, but studies showed that the easiest way to get a high score was to write a longer essay, not actually have a stronger argument (at least not above some really basic level).
Increasingly, the test rewarded preparation instead of things harder to teach in some sort of crash prep course, like abstract reasoning.
The latest revisions just follow further in the efforts to service large number of unprepared people who want to attend college. Nobody reads at a high level anymore, so why bother with vocabulary beyond the basics? The test is aiming to be relevant for the average person, which is not where it started -- as an IQ test for the elite. At this point, it's not any better than high school grades for predicting college performance (and actually worse for people with high SAT scores but low GPAs, since it then basically is testing prep skills access to fancy crash courses, rather than higher-level reasoning). So they're basically turning it into a glorified set of midterm high school exams.
The article says explicitly that there are times when digging your heels in is necessary (for the more important stuff).
Yes, you're right. I was mostly responding to the quotation in the summary. But I still have a couple problems with this: (1) how exactly is a beginner to know what is "important"? And (2) the most insightful things that have happened to me were doing random exercises that interested me, rather than necessarily something "important."
I'd say his attitude is right that you needn't do every exercise or proof (and I actually already said this in my first post), but if you are interested and motivated to solve a problem, you often gain something by sticking with it, regardless of whether it takes more than 10 minutes or is "important."
Sorry -- accidentally hit submit before finishing my post.
A lot of early math courses are trying to teach the mechanics of established principles so that you can solve specific, common problems and situations.
If the only point is to teach someone how to apply some precise algorithm to a specific type of problem, why bother teaching math at all? Just say --if problem type X, type numbers into computer and run program A, if type Y, run program B, etc. There's no point teaching someone how to act like a glorified calculator anymore... this thinking is a couple decades out of date.
There is a lot of basic stat you can do if you don't know why the standard deviation formula is the way it is,
For frack's sake, no! If you don't know how standard deviation actually works, you are doing more harm than good by using it. There's more nonsense propagated by people using statistical measures without knowing what they are doing than just about anything else. I'd go so far to say it's the biggest problem in science today, aside from too much corporate influence in some areas. The derivation of statistical formulas often tells a lot about the assumptions each makes... which are essential to understand if the conclusion drawn are to be meaningful.
or a lot of practical calculus you can do without knowing how to do a delta-epsilon proof.
Those are only one way to derive basic calculus. And besides, there is a lot of room between deriving all of calculus from the fundamental axioms of the real number system rigorously, and not knowing anything other than some algorithmic symbolic manipulation without knowing what goes on "under the hood." I'm not saying everyone needs to do the former, but we should not assume the latter is fine either. I've seen a lot of crap done by people using basic math (or even educated folks using calculus or diff eqs) without realizing the assumptions of what they are doing.
A lot of early math courses are trying to teach the mechanics of established principles so that you can solve specific, common problems and situations.
If the only point is to teach someone how to apply some precise algorithm to a specific type of problem, why bother teaching math at all? Just say --if problem type X, type numbers into computer and run program A, if type Y, run program B, etc. There's no point teaching someone how to act like a glorified calculator anymore... this thinking is a couple decades out of date.
He then provides some advice for people learning college level math like calculus or linear algebra: 'I suggest you don't worry too much about verifying every claim and doing every exercise. If it takes you more than 5 or 10 minutes to verify a "trivial" claim in the text, then you can accept it and move on....
While I agree that one shouldn't waste time questioning every statement you encounter, there's a very ancient and useful tradition in math pedagogy that emphasizes these sorts of things. See, for example, gradually building up geometrical theorems from a few axioms, a la Euclid.
Often, the process of working out complex proofs for yourself is crucial to understanding why things work, not to mention developing and practicing logic skills that are essential in math and elsewhere.
I'm not saying one should waste time trying every exercise or redoing every proof, but some of my greatest insights into the inner workings on math have come from exercises that took me a couple hours to work out or textbook passages I went over a number of times and really dug into how the details worked. If I skipped everything I couldn't do in 5-10 minutes, I doubt I'd ever have developed the more advanced skills and intuitions that would be necessary to see why some results are "trivial."
I wonder what the company would say if an unscrupulous network admin steals the bank information from a bunch of employees and robs them?
Umm, the same thing they would say if a rogue janitor used a masterkey to enter the offices of a bunch of employees after hours and stole stuff? That is, "We're firing the guy, and reporting him to the police." I don't get your point. Lots of employees have access to sensitive information or actual physical items that belong to other employees. Those people can't steal stuff. The HR people can't take your personal info and go open fraudulent accounts in your name either.
I'm not sure "my system, my rules" would go very far in court.
You're using someone else's network to send sensitive financial information. Especially if the company explicitly discloses what they do and their network rules and practices, it's your choice to do personal transactions on someone else's network. Unless the company displays actual negligence in employing an admin with a criminal background or something, why should the company be liable for some rogue illegal actions?
Oh, and if you're willing to expand the term "device," we might include things like rings, necklaces, and other jewelry. Not so much little kids, but sometimes teenagers also some valuable jewelry; definitely grandmothers.
Even people without a lot of money often tend to wear wedding or engagement rings worth hundreds (often even thousands) of dollars around in public every day.
Can you think of a single other device that can cost several hundred dollars, most people want, and everyone from little kids to 60 year old grandmothers carries around in public?
Yes. Cars. Except they're generally worth thousands of dollars, instead of hundreds. (And though little kids generally want them, they generally don't own them.) Also, unlike watches and phones, we tend to leave these many-thousand-dollar devices laying around.
Cars are in some ways both more and less "portable" than watches or cell phones, so they pose somewhat different problems from a theft perspective. But it seems like we have developed a whole boatload of regulations and various technologies to try to prevent car theft.
Hell, it sounds like the most lucrative way to make money of bitcoins is to set up your own exchange, and then have one of your people steal all the money, and then say "oops, teh hax0rs, not our fault, too bad for you".
Yes, we've finally found something to fill in the "??????" blank before "PROFIT!!"
If you're not a bank, and not regulated like a bank, this is kinda like asking the kid with the lemonade stand to hold onto your life savings.
Well, to be fair, if your life savings is in Bitcoin, you're already basically asking the kid with the lemonade stand to hold onto your life savings. Bitcoin is still too volatile, and most of the "wealth" is still too concentrated among a relatively small group of users. There's simply no guarantee that these things will be worth ANYTHING next year or even next week.
A better comparison would be if you had a bunch of antique bottle caps that some weird salivating guys down the street would love to add to their bottle cap collection, and they've said they'll pay you lots and lots of money for them. So, you think you have a lot of value in these bottle caps, but you don't really know, and you don't really know if those guys down the street are serious. They might be investment bankers, or they might be crack addicts who are ready to dump their own bottle caps and run. (Maybe the two aren't that different?)
Anyhow, knowing all this, you entrust your bottle caps (of questionable value) to a kid with a lemonade stand. There -- that's a better analogy. (But no car... sorry.)
In the "STE" portion of STEM fields, if you are any good, there's no reason to take on debt at all for a post-graduate education.
I'd say there's little reason to take on debt at all for a post-graduate education -- regardless of field -- unless you're going to a professional school. Even if you want a Ph.D. in the humanities or something, you're looking at a much smaller number of potential jobs than STEM fields. The top-tier programs in the humanities generally also offer full fellowships with stipends. If you're not good enough to get admitted to one of those programs, chances are pretty good that you won't be able to find a job even if you get your Ph.D. from some random university.
Of course, some people want to do their "dream job," and they might need a master's or whatever in some field. If they can pay as little as possible (e.g., state university), that's reasonable. But spending more than that for graduate school, unless you're independently wealthy or someone else is paying, is probably not a good idea in the long run.
My theory: This "student loan bubble" is actually the bubble that caused the mortgage bubble. For the past 30 years, college loan professionals have been convincing 18 year olds that 5-digit debt is ok.
While I think there is probably some merit to your idea, I think you're overlooking the much larger problem -- the vast majority of Americans have absolutely no intuitive understanding of compound interest to begin with, and certainly no detailed knowledge of how to evaluate a complex set of loan terms in relation to that concept.
Let me tell you a little story: back in the early 2000s, I spent a few years teaching high school math and science. My first year of teaching, I taught algebra II to a class of mostly high-school seniors at a slightly below-average high school. (This wasn't some crazy terrible inner city school, but students there -- mostly minorities -- definitely had some more challenges than average.)
This algebra II class was likely the last math class many of these students would ever take in their lives. Very few of them were likely to go onto college -- those that were at that school were taking pre-calculus or calculus. But I didn't have the "bottom of the barrel" students either: these students elected to take algebra II, which was not required to graduate -- those less inclined to take academic subjects would have merely finished off with algebra I, geometry, and a year of some general math elective.
About halfway through the school year, when we were beginning to talk more about exponents in equations, I decided to pose some simple problems involving compound interest and loans, thinking that the general idea of these concepts might be familiar. They were not. Out of the 125-ish students I had in my sections of algebra II, only TWO students actually had even heard of compound interest, and only one of them would have actually been able to use that knowledge to make some informed judgments about loans or investments.
My digression on compound interest was not in the state-required algebra II curriculum. Unlike a bunch of useless topics that I was required to spend a lot of time on (e.g., putting conic section equations in normal form), practical math skills weren't part of algebra II... this is probably because many of these ideas were probably supposed to be introduced in middle school or something. But poor teachers along the way meant that it was likely that most students wouldn't have any knowledge of practical math.
So, at that point, I decided to carve a few weeks out of my school year to devote to teaching practical math that would actually get my students through their lives, even though the state curriculum told me I was supposed to do other things. Otherwise, these students would graduate that year, never have another math class again, and they would be clueless about basic financial math.
That's the reality we're facing for MOST students who graduate from high school in the U.S. It's not that they were lured away from their ideas about compound interest by loan sharks -- they never knew what compound interest meant to begin with.
These are the people who bought houses they couldn't afford. Even with my couple week tutorial to my students, I'm certain that many of them would probably still fail to be able to evaluate loan terms in a real-world mortgage situation without significant help.
That's what we're up against.
If you really want to prevent this crap from recurring as people continue to make stupid financial decisions, we should drop all of the crap standardized testing about wacky geometry and algebra and whatever to graduate high school, and instead have a simple test presenting real-world math scenarios, like evaluating investments and loan terms, choosing a credit card, and constructing a proper budget and realistic plans for saving for the future. Present students with scenarios designed to sound like loan sharks, bogus investment schemes, etc. If they can't spo
It is rather interesting they were using kefir for cheese making
Yes, this is actually the most interesting finding here, since what they discovered probably wouldn't be recognized as normal "cheese" by many people. It's not like they found a small wheel of cheddar placed lovingly on the chests of bodies. Rennet-based cheeses are what most people in the Western world think of when they hear the word "cheese," or perhaps artificially acidified cheeses, like mozzarella or paneer.
This "cheese" (if indeed that's what it was -- see below) was produced by a slower acidification from fermentation. Then presumably it was strained or dried to separate the solids. The closest approximation for people unfamiliar with kefir would be to take a bunch of yogurt, put it in some cloth, then hang it and let the liquid drain out for a couple days, going past the point of thick "Greek yogurt" to a drier texture. (Technically, this makes labneh, a Middle Eastern-style fresh cheese.) It's a different type of cheese from rennet-based cheeses, but one more common in traditional cultures around the world.
For those not familiar with traditional kefir, it's very different from the store-bought stuff. It depends on a starter composed of "kefir grains," which is essentially a small mass of colonies of many types of microorganisms, which look like a group of small pearl-like things with a rubbery texture. They are very stable and durable, able to be rejuvenated after drying out, freezing, or even being "starved" for months.
The reason this is relevant to the story is that these kefir grains, to my knowledge, have not been replicated using modern scientific methods, despite many attempts. (Most "starters" for things like sourdough bread, yeast for wine, or common fermentations for milk like yogurt, can be cultivated fresh with only minimal effort from the naturally occurring organisms on flour, grapes, or milk.) In kefir, there are too many bacteria in a symbiotic relationship, and scientists still haven't managed to figure out how to get them to create these grains by themselves. The only way to get traditional kefir is to get some grains from someone. (The store-bought stuff is produce, like yogurt, just by using a small number of bacterial strains for fermentation under controlled conditions.)
Because of the difficulty in reproducing traditional kefir grains, there are all sorts of origin myths about it -- stories about it coming from medieval Georgia or the armies of Genghis Khan or whatever.
Anyhow, what I wonder from reading the story is how exactly they know this is "cheese" and not merely a dried form of kefir grains? In the era before refrigeration, kefir grains were essential to preserve fresh milk for later consumption, and where highly prized. There are all sorts of traditional stories from these cultures about people stealing kefir grains, because you couldn't just make new ones easily. You had to get them somewhere.
So, the question that occurs to me is -- why do we assume this is food for the afterlife? Why not consider the possibility that these people were given a gift of kefir grains (in a concentrated dried form) to carry with them to the afterlife -- an essential food preserving and processing tool, which could not be simply "made." It was something you had to carry with you, something you had to get from a previous batch of kefir, so maybe this was the only way to get it to the afterlife.
That would be my first thought, if I found this stuff.
Slashdot Mirror
You missed "right a new paper".
Yeah, and two other egregious errors in that sentence, too.
Or maybe we just need to understand the true meaning of the sentence: "then right a new paper sighting the published one and submit to a more prestigious journal"
In other words, I take a new paper in the works and make it "right" by including research literally gleaned from the previous paper while staring at it ("sighting") and copying it.
Perhaps the GGP was actually talking about plagiarism and falsifying research to fit an agenda.
One thing I hate is when people tell me how I learn and force me to do repetitive assignments that test only for memorization and do nothing to bolster one's understanding of the material, which is the sort of thing I was talking about. I had to deal with that garbage too much in the past, and never bothered to do any of the assignments.
A few points: (1) A well-structured set of problems in a basic math textbook is often intended to gradually allow students to work through various difficulties. The first few problems start with some new idea or skill, then a few more introduce some complications and special cases, then the next few combine it with previous knowledge and skills, and finally we arrive at greater fluency in using the new material. I, probably like you, never needed that many exercises to figure things out. I probably could have done 10% of the problems assigned, and I still would have absorbed the new material. But as someone who has actually taught high-school math, I can also tell you that you and I are NOT the norm. I tried not to assign too many repetitious problems, too. But many students need to work through at least some of this build-up of skills when incorporating a new idea into existing knowledge.
(2) Even for cases where there is more-or-less repetition to learn skills, it is sometimes useful to learn skills. This is different from memorizing facts (though with really basic arithmetic, there is a need for actual memorization too). Basic math is often about internalizing algorithms, to give you tools to be able to higher math. If you don't internalize these algorithms, higher math will become increasingly difficult to follow and understand.
(3) Also, sometimes the algorithm IS the goal. For >99% of people in the world, math is only useful as a tool, not some sort of higher-level "play in an abstract world and have cool insights" kind of thing. They need to be able to do basic manipulation of numbers and symbols to solve very particular types of problems -- with real-world applications. That should be the focus in math education for those not actually going on into higher math -- no need to do all sorts of wacky advanced algebra or memorize stupid facts about geometry in high school... let's teach students how to solve real world problems, and make sure they practice those skills to internalize them.
It sounds like abstract ideas came quickly to you. They came quickly to me as well. But that's not true for many students. Part of the problem is our curriculum structure, which seems to assume all students past middle-school math should be headed toward higher math, instead of focusing on applications and skills that could be useful. But part of the issue is that many students need significantly more repetition to get things, or they need a gradual build-up in difficulty when dealing with a new idea.
It's not always "garbage."
So my suggestion is that, if you really want to see a jump in math skills, start placing more emphasis on learning the concepts and less emphasis on how fast students can process problems. Allow students unlimited time on tests if they want it (maybe give them the option of taking tests after school instead of in class). It will give a lot of students like me a lot more confidence in themselves
As someone who has taught math at the high school level, I definitely agree with you up to a point. I usually tried to design tests so that an average student could complete it with plenty of time to spare -- those who needed a little more time could then take it.
However, there is a problem that gradually starts to accumulate with students who can't do math at a reasonable speed. My first year teaching (at a not-so-great school in a not-so-great location), I had seniors in high school who were enrolled in algebra II, but some of them couldn't do basic arithmetic. Sure -- if you gave them enough time, they could use their fingers or calculators to determine what 12 minus 7 is. (Don't ask how these students managed to get to algebra II -- it was years of terrible teachers and vacancies with substitute teachers passing students who shouldn't have been.)
These students were completely incapable of understanding most of the stuff going on in class on a regular basis. Even the students who could do some semblance of basic arithmetic hadn't internalized many of the basic rules of algebra, etc. So, while -- again -- they could work through these things at a very slow pace, they had no idea of what they were doing or why when it came to higher-level questions. Eventually, I realized the only way I could teach unprepared students algebra II according to the state-mandated curriculum was to teach basic algorithms for solving the minimum set of basic problems required. (Sending them back to algebra I was not an option, since officially they had "passed" it.) The students had no perspective for why they were doing anything, but they could do meaningless symbolic manipulation enough to satisfy requirements.
And that's what happens when most students aren't drilled enough to internalize basic skills at various levels. The point of taking speed tests at elementary levels is because if you can't immediately do arithmetic in your head, you'll have no clue what's going on when solving some 10-step equation in algebra. And, if you don't internalize the equation solving steps in basic algebra to the point that you can do them reasonably quickly, you'll have no idea what to make of your calculus teacher zooming through such a problem to get to the actual derivatives or integrals or whatever.
(Also, note that smarter students who are given unlimited time also can make use of unlimited methods to check their work -- even taking to guessing answers with trial-and-error, or doing the same problem 5 times until they come up with something that "checks." While there is a value in persevering until you can get an answer you're sure is "right," it doesn't necessarily tell a teacher whether you actually know what you're doing. The time to do trial-and-error is on homework assignments before a test until you can figure out the right way to do something -- by a test, you should have accumulated enough fluency to start on the right track.)
So, I agree that there needs to be a balance. Testing new skills should probably be done with plenty of time, so students have time to reason things out. But eventually they need to internalize the steps enough to do them reasonably quickly -- and subsequent tests using that material needs to evaluate that.
If not, you'll end up with students who can't do anything and can't understand any higher-level steps in math, because they're still stuck taking 30 seconds to figure out what 12 minus 7 is while trying to do a triple integral.
It actually bugs me more that RAM is referred to as "memory" which is and should be a very generic term.
If anything the harddisk is probably a better candidate for the term "memory" than RAM is. A harddisk is what ultimately must store the data permanently and recall it.
You make some really good points. But, interestingly, I think this is becoming less relevant today, where computers are left on for months at a time, and perhaps put into a low-powered "sleep" mode which preserves RAM contents.
For me, RAM now is more like human memory, in the sense of "what did you eat for breakfast yesterday" or "what projects were you working on last week"? It's the stuff that can be relatively actively recalled, because it's a current project or task. It's more than "short-term" memory, too. Hard drives are more like filing cabinets or photo albums or diaries -- a place I go to look up something I can't actually remember. RAM size is also large enough now that most common applications may almost have a continuous presence in RAM too... so it has really become a kind of repository like a "working brain."
Only assholes like you will celebrate as meat and dairy prices will skyrocket beyond the affordability of most poor families.
One could only hope. Then we might begin to lift the stranglehold of crappy food (including bad meats and fake processed "meats") and junk food producers. Cows are not meant to be fed corn -- but we do so because corn is cheap. Corn is cheap because it is subsidized. Cows get sick because they eat bad diets, so we feed them medicines and chemicals to keep them healthy enough to grow fast, live a short life, and satisfy meat demand. Any bad stuff that might get into bad food is concentrated that far up the food chain, which is probably one of the reasons red meat and fatty red meat seems "bad for us" -- it's not an inherent property of red meat, but of unhealthy badly produced red meat. And we don't have enough pasture land to satisfy meat demand at current levels, so there's no way to raise enough beef in a healthy way, even if we wanted to.
Americans eat way too much meat, and most of it is bad quality. A few generations ago, people ate less, but also spent a significantly higher percentage of monthly budgets on food. We've gotten cell phones and cable TV, while ruining our bodies by paying less for junk.
I'm NOT some "organic food" wacko -- but I recognize the benefits of having a food production system that keeps us and the animals healthy. For a few years, I could not afford to buy much quality meat, so rather than stocking up on junk meats from the average supermarket, I learned to eat beans, lentils, legumes and other things to substitute. Most Americans could eat something like 1/10th of the amount of meat that they do, and still get the major nutritional benefits from meat consumption.
Our system is really broken and unhealthy. Having less cheap meat to go around would be better for the environment, for the animals, and for us.
Philosophically, thought, it does seem quite silly, and I myself would never have regarded it as more than a mathematical curiosity,
Why? We currently accept a model where the universe spontaneously came into existence at one time with any explanation (at least none that we know of now). The steady state hypothesis postulates a continuous universe with spontaneous creation of stuff at a regular rate to remain a stable state. Exactly why is the latter more "philosophically" more problematic than the former? Both postulate events of creation out of nothingness.
Both creative people and cranks have lots of wild ideas. The difference is that a crank reflexively defends his ideas with irrational vehemence.
I've known cranks who were just obsessed with one thing and could never see beyond it, but I've also known many cranks who were very creative. I don't think the sets are as mutually exclusive as you claim.
A creative person usually discard his ideas, because he knows there's always more where that comes from.
I think this has more to do with ego than whether someone is creative or not. People hold fast to their ideas for all sorts of irrational reasons -- career, other people's praise of them, general acceptance within a peer group, politics, etc. Being a crank is more about personality type, in my view, than whether or not someone is "creative." The most effective cranks I have known are generally quite creative (and adaptive), enough so that it sometimes takes a long time for other people to realize they are simply wackos -- and they even attract followers to their irrational cause. (The shared characteristic in the crank and his audience in this case being a lack of specific knowledge or perspective to recognize how ludicrous the claims are.)
making $100,000/year and having $60,000 or $70,000 of that amount after taxes going to rent
That's way too high of a rent estimate. Even in San Francisco, you can get a decent place for 1 person for $3000/month.
Umm, re-read the GP - "after taxes." In CA, you're looking at about 10% income tax to the state. Add that to fed income tax bracket of about 25%, and you're looking at $60000 = $39000 or less after taxes. (Obviously a quick estimate.) You say you can get a decent place for $3000/month = $36000 after taxes. GP's estimate is not necessarily "way off": point is that it could easily require more than 50% of your after tax income in CA for rent. In TX, you not only have significantly cheaper rent, but no state income tax.
By the way, I have one final thought -- I actually have used the concept of this piece in teaching students about art. There are always factions. Some people immediately dismiss it, and no matter what we say in the discussion, they still think it is nonsense.
Other people listen to some arguments about it, converse with other students, and come to think there is something to be learned from the "principle" of the piece, if not the experience of the piece itself.
Others may find it actually changes the way they think about music and art in a real and permanent fashion.
My goal is not to get anyone to "like" it or even to accept it as intellectually interesting. It's just to propose it as a kind of experiment. Some people find it useful to think about, and they get something out of the exercise. If you don't, that's okay. I'm not judging you, nor am I insulted or offended that you don't appreciate it.
And I do apologize if I took the tone of your response to mean that you hadn't really thought about the piece. I did make assumptions. But I also replied to "you" as a reply to other people (e.g., people who modded your comment), because I know some of those people may fall into the categories I listed above -- they may be dismissive at first, but some may realize there's something else there.
Personally, I don't find it useful to insult other people. I try to respect other people's opinions, even when they differ from mine. When people don't agree, I like to engage and try to come to a mutual understanding; if the other party chooses to leave the discussion, that's fine.
You obviously find the need to declare other people to be "snobs" and to dismiss what they do as nonsense. That is indeed your opinion and your prerogative. I just rarely think that's a useful thing to do -- it's not very polite, it disrespects other people's opinions, and you often lose the chance to learn from a perspective other than your own. If you have some further thoughts from your experiences about why you view this piece as you do (and what else fits into your categories of "snobbish nonsense"), I'd be interested in hearing about it. But just to declare it to be such is more like an internet troll than having a discussion.
I made the error of assuming that you weren't informed about something, so I hoped to offer some knowledge to you. You appear to value calling people "snobs" and what they produce "garbage." To each his own, I suppose.
whether or not a person finds offense in a statement is on them, not the speaker.
Well, take a moment to re-read what you wrote:
pontificating on the topic as if they're the first person in history to ever do anything weird and/or stupid. You know, the kind of garbage that art snobs devour.
Look, I generally agree with you. I didn't actually take offense at your notion. I accused you of insulting other people, which, frankly, if you look at the text you wrote, you did. I don't think this is unclear in your writing: when you say people are doing something "weird and/or stupid" and are producing "garbage," I think there's some pretty clear implications. I don't think there's time for my own introspection -- your characterization was very clearly negative and, frankly, intended to devalue ("garbage") your target.
As I said, you don't like the stuff -- that's fine. And maybe you did know more about it, but still don't like it. That's great. It's your opinion. But you didn't give any details about why you think that way: you just declared, "This sucks, and the people who do it are doing something weird and/or stupid, and trying to impress pretentious snobs" (paraphrased, obviously).
You're more than welcome to your opinion. And if you engaged with the explanation of this, and you still think it's crap or nonsense, that's fine. But I think it's a more useful discussion to say why you think it's crap or nonsense, rather than just insult people and be dismissive.
It's all nice and all that you want to make up and be cheerful now, but that's not the way your original post sounded. Just letting you know. And, I have nothing invested in the opinions about this piece or my views on the piece. Did I say I actually LIKE it? No. I said it poses interesting philosophical questions. You want to think Cage is an idiot -- I don't really care.
I was trying to offer some context and perhaps some perspective for people who may not have thought about such things before. I thought some readers might find it more useful than a blanket dismissal and set of insults. But you apparently find it more useful to deny that you actually said anything negative and proceed to do exactly what you accuse me of, namely make assumptions and then insult me.
Have a great day!
Namely because, to me, it represents that self-serving form of 'performance art,' that has absolutely no artistic value but rather is an expression of the "artists" narcissistic desire to be the center of attention by doing something remarkably weird and/or stupid, and subsequently pontificating on the topic as if they're the first person in history to ever do anything weird and/or stupid. You know, the kind of garbage that art snobs devour.
Okay, you don't like something. That's fine. But you might bother to learn something about it before insulting other people.
For one thing, this is actually the first time in history that a composer tried a particular kind of experiment. And yes, I mean "experiment" in the same sense that scientists do. In this case, it was an attempt by a composer to try to find out something about the nature of music (and art in general), and also to allow a group of willing listeners to participate in that experiment.
You are ABSOLUTELY RIGHT that there is a lot of nonsense "experimental art" out there which is just pretentious nonsense -- people trying to do something weird or "edgy" or offensive or "provocative" just to get attention. Most of these people -- and their audiences -- are something like what you describe.
But Cage's point was different.
The main problem with 4'33" is that you have to understand the context. Without context, it sounds ridiculous and like some sort of stunt. It would be like taking someone who doesn't know anything about physics and putting a 100-page paper full of mathematical proofs about string theory in front of them, and saying "Look! See how this explains everything about the universe!" And the reaction is, "Umm... how many dimensions?! What the heck is this talking about? This is just nonsense made up be pretentious snobs who like to play around with math for fun. Why should I care?"
And some people might have that reaction to string theory too. I've heard people say as much here. But maybe we should look a little deeper about what a theory or an experiment is trying to do before dismissing it with anti-intellectual rhetoric and ad hominem attacks on the people who value it.
Look -- here's an interesting question for you: what is music? Seriously. You may not care. You may say, "I just wanna go back and listen to my Top 40" or Alternative Death Metal or whatever random stuff you like. But some people have a career where they write music and think about how music is made. And some of those people might find that question interesting. So think about it for a minute or two: what is music?
Most people often say something like "organized sound." Okay, but what about birdsong or wind chimes? Can those be music? Some people say yes; others say no. Why? Most people will admit that something that sound "musical" can exist even if there is no human really "composing" or "performing" it -- whether it's actually "music" is a philosophical question, but many people say, "Well, it's a pleasant sound when I listen to birds, so it has some 'musical' quality about it."
Now, John Cage comes along, and he does other sorts of experiments. He himself spends some time in an anechoic chamber, in complete silence. Except it wasn't completely silent -- he became intensely conscious of hearing the rhythms of his own breathing, and a kind of sensation of his heart beating.
Now, if you think about issues like this -- how we heard "musical" elements in nature, and how our own bodies will always be influencing our perception of sound, eventually you realize that music is partly created by the listener. It's not just a composer or performer putting sounds out there -- it's also in the ability of a listener to find some sort of meaning in the sound world around him/her.
You may think all this talk is snobbish or pretentious or whatever, but it gets at the heart of why some people don't think rap is "music" or don't think jazz is
How about reading the Wikipedia article on the history of the SAT? And look up stats on the gradual decline in actual number of test scores above 600 particularly on verbal before the test was "fixed" in the 90s? The one error I made was mistaking the era of relative stability, which actually went from the late 50s through the 90s (with a few changes and reduced length along the way)... I wrote this without rereading anything else first.
This is the reason that education is *mandatory* in civilized countries - to take some part of the decision-making process away from uninformed parents.
Wow. Here I thought the reasoning behind mandatory schooling in "civilized" countries had to do with creating an informed electorate and a class with enough education to be productive in society (e.g. able to do jobs requiring basic skills).
Now you tell me the actual reason is to ensure state indoctrination. I've heard people murmur as much before, but I've rarely heard it said with such affirmation.
(Don't get me wrong -- I absolutely do NOT think religion has a place in a science class. I want the wacko religious nuts to stop interfering with schools for their own agendas. And I think the state has every right to intervene and protect kids from abuse, neglect, etc. But the primary purpose of school should be to make sure kids conform to officially sanctioned state beliefs, and to correct the bad ideas from parents? I'm sure that's what every benevolent dictatorship said as well when they started rewriting history books to make sure children get the one "true" story.)
The goal of the SAT used to be to predict performance in college. Now it is used to predict how much effort one is willing to put into it to game the system.
Well, it's always been about trying to predict college performance. Back in the late 60s through early 90s, it was a stable test format, normed rigorously through decades of testing, which was basically an IQ test and advanced reading comprehension test. Things like analogies and vocab testing both how well-read you were and your abstract ability to connect subtleties of meaning; things like quantitative comparisons tested logic and reasoning skills outside of normal basic math.
Then it was renormed in the mid 90s to make it about 100 points easier -- it no longer really could distinguish the top of the scale (which, if you look at the stats, appeared to be disappearing -- the actual number of perfect 1600s went down significantly in the 80s despite increases in number of test takers). The high-level critical reasoning was less stressed in many college programs too.
Gradually, over the past couple decades, the test has been further dumbed down, to service the increasing number of people who want to go to college and the decreasing number of people with high-level literacy and advanced critical reasoning. Analogies and quantitative comparisons disappeared. They added a writing test, but studies showed that the easiest way to get a high score was to write a longer essay, not actually have a stronger argument (at least not above some really basic level).
Increasingly, the test rewarded preparation instead of things harder to teach in some sort of crash prep course, like abstract reasoning.
The latest revisions just follow further in the efforts to service large number of unprepared people who want to attend college. Nobody reads at a high level anymore, so why bother with vocabulary beyond the basics? The test is aiming to be relevant for the average person, which is not where it started -- as an IQ test for the elite. At this point, it's not any better than high school grades for predicting college performance (and actually worse for people with high SAT scores but low GPAs, since it then basically is testing prep skills access to fancy crash courses, rather than higher-level reasoning). So they're basically turning it into a glorified set of midterm high school exams.
The article says explicitly that there are times when digging your heels in is necessary (for the more important stuff).
Yes, you're right. I was mostly responding to the quotation in the summary. But I still have a couple problems with this: (1) how exactly is a beginner to know what is "important"? And (2) the most insightful things that have happened to me were doing random exercises that interested me, rather than necessarily something "important."
I'd say his attitude is right that you needn't do every exercise or proof (and I actually already said this in my first post), but if you are interested and motivated to solve a problem, you often gain something by sticking with it, regardless of whether it takes more than 10 minutes or is "important."
A lot of early math courses are trying to teach the mechanics of established principles so that you can solve specific, common problems and situations.
If the only point is to teach someone how to apply some precise algorithm to a specific type of problem, why bother teaching math at all? Just say --if problem type X, type numbers into computer and run program A, if type Y, run program B, etc. There's no point teaching someone how to act like a glorified calculator anymore... this thinking is a couple decades out of date.
There is a lot of basic stat you can do if you don't know why the standard deviation formula is the way it is,
For frack's sake, no! If you don't know how standard deviation actually works, you are doing more harm than good by using it. There's more nonsense propagated by people using statistical measures without knowing what they are doing than just about anything else. I'd go so far to say it's the biggest problem in science today, aside from too much corporate influence in some areas. The derivation of statistical formulas often tells a lot about the assumptions each makes... which are essential to understand if the conclusion drawn are to be meaningful.
or a lot of practical calculus you can do without knowing how to do a delta-epsilon proof.
Those are only one way to derive basic calculus. And besides, there is a lot of room between deriving all of calculus from the fundamental axioms of the real number system rigorously, and not knowing anything other than some algorithmic symbolic manipulation without knowing what goes on "under the hood." I'm not saying everyone needs to do the former, but we should not assume the latter is fine either. I've seen a lot of crap done by people using basic math (or even educated folks using calculus or diff eqs) without realizing the assumptions of what they are doing.
A lot of early math courses are trying to teach the mechanics of established principles so that you can solve specific, common problems and situations.
If the only point is to teach someone how to apply some precise algorithm to a specific type of problem, why bother teaching math at all? Just say --if problem type X, type numbers into computer and run program A, if type Y, run program B, etc. There's no point teaching someone how to act like a glorified calculator anymore... this thinking is a couple decades out of date.
He then provides some advice for people learning college level math like calculus or linear algebra: 'I suggest you don't worry too much about verifying every claim and doing every exercise. If it takes you more than 5 or 10 minutes to verify a "trivial" claim in the text, then you can accept it and move on. ...
While I agree that one shouldn't waste time questioning every statement you encounter, there's a very ancient and useful tradition in math pedagogy that emphasizes these sorts of things. See, for example, gradually building up geometrical theorems from a few axioms, a la Euclid.
Often, the process of working out complex proofs for yourself is crucial to understanding why things work, not to mention developing and practicing logic skills that are essential in math and elsewhere.
I'm not saying one should waste time trying every exercise or redoing every proof, but some of my greatest insights into the inner workings on math have come from exercises that took me a couple hours to work out or textbook passages I went over a number of times and really dug into how the details worked. If I skipped everything I couldn't do in 5-10 minutes, I doubt I'd ever have developed the more advanced skills and intuitions that would be necessary to see why some results are "trivial."
I wonder what the company would say if an unscrupulous network admin steals the bank information from a bunch of employees and robs them?
Umm, the same thing they would say if a rogue janitor used a masterkey to enter the offices of a bunch of employees after hours and stole stuff? That is, "We're firing the guy, and reporting him to the police." I don't get your point. Lots of employees have access to sensitive information or actual physical items that belong to other employees. Those people can't steal stuff. The HR people can't take your personal info and go open fraudulent accounts in your name either.
I'm not sure "my system, my rules" would go very far in court.
You're using someone else's network to send sensitive financial information. Especially if the company explicitly discloses what they do and their network rules and practices, it's your choice to do personal transactions on someone else's network. Unless the company displays actual negligence in employing an admin with a criminal background or something, why should the company be liable for some rogue illegal actions?
Oh, and if you're willing to expand the term "device," we might include things like rings, necklaces, and other jewelry. Not so much little kids, but sometimes teenagers also some valuable jewelry; definitely grandmothers.
Even people without a lot of money often tend to wear wedding or engagement rings worth hundreds (often even thousands) of dollars around in public every day.
Can you think of a single other device that can cost several hundred dollars, most people want, and everyone from little kids to 60 year old grandmothers carries around in public?
Yes. Cars. Except they're generally worth thousands of dollars, instead of hundreds. (And though little kids generally want them, they generally don't own them.) Also, unlike watches and phones, we tend to leave these many-thousand-dollar devices laying around.
Cars are in some ways both more and less "portable" than watches or cell phones, so they pose somewhat different problems from a theft perspective. But it seems like we have developed a whole boatload of regulations and various technologies to try to prevent car theft.
Hell, it sounds like the most lucrative way to make money of bitcoins is to set up your own exchange, and then have one of your people steal all the money, and then say "oops, teh hax0rs, not our fault, too bad for you".
Yes, we've finally found something to fill in the "??????" blank before "PROFIT!!"
If you're not a bank, and not regulated like a bank, this is kinda like asking the kid with the lemonade stand to hold onto your life savings.
Well, to be fair, if your life savings is in Bitcoin, you're already basically asking the kid with the lemonade stand to hold onto your life savings. Bitcoin is still too volatile, and most of the "wealth" is still too concentrated among a relatively small group of users. There's simply no guarantee that these things will be worth ANYTHING next year or even next week.
A better comparison would be if you had a bunch of antique bottle caps that some weird salivating guys down the street would love to add to their bottle cap collection, and they've said they'll pay you lots and lots of money for them. So, you think you have a lot of value in these bottle caps, but you don't really know, and you don't really know if those guys down the street are serious. They might be investment bankers, or they might be crack addicts who are ready to dump their own bottle caps and run. (Maybe the two aren't that different?)
Anyhow, knowing all this, you entrust your bottle caps (of questionable value) to a kid with a lemonade stand. There -- that's a better analogy. (But no car... sorry.)
In the "STE" portion of STEM fields, if you are any good, there's no reason to take on debt at all for a post-graduate education.
I'd say there's little reason to take on debt at all for a post-graduate education -- regardless of field -- unless you're going to a professional school. Even if you want a Ph.D. in the humanities or something, you're looking at a much smaller number of potential jobs than STEM fields. The top-tier programs in the humanities generally also offer full fellowships with stipends. If you're not good enough to get admitted to one of those programs, chances are pretty good that you won't be able to find a job even if you get your Ph.D. from some random university.
Of course, some people want to do their "dream job," and they might need a master's or whatever in some field. If they can pay as little as possible (e.g., state university), that's reasonable. But spending more than that for graduate school, unless you're independently wealthy or someone else is paying, is probably not a good idea in the long run.
My theory: This "student loan bubble" is actually the bubble that caused the mortgage bubble. For the past 30 years, college loan professionals have been convincing 18 year olds that 5-digit debt is ok.
While I think there is probably some merit to your idea, I think you're overlooking the much larger problem -- the vast majority of Americans have absolutely no intuitive understanding of compound interest to begin with, and certainly no detailed knowledge of how to evaluate a complex set of loan terms in relation to that concept.
Let me tell you a little story: back in the early 2000s, I spent a few years teaching high school math and science. My first year of teaching, I taught algebra II to a class of mostly high-school seniors at a slightly below-average high school. (This wasn't some crazy terrible inner city school, but students there -- mostly minorities -- definitely had some more challenges than average.)
This algebra II class was likely the last math class many of these students would ever take in their lives. Very few of them were likely to go onto college -- those that were at that school were taking pre-calculus or calculus. But I didn't have the "bottom of the barrel" students either: these students elected to take algebra II, which was not required to graduate -- those less inclined to take academic subjects would have merely finished off with algebra I, geometry, and a year of some general math elective.
About halfway through the school year, when we were beginning to talk more about exponents in equations, I decided to pose some simple problems involving compound interest and loans, thinking that the general idea of these concepts might be familiar. They were not. Out of the 125-ish students I had in my sections of algebra II, only TWO students actually had even heard of compound interest, and only one of them would have actually been able to use that knowledge to make some informed judgments about loans or investments.
My digression on compound interest was not in the state-required algebra II curriculum. Unlike a bunch of useless topics that I was required to spend a lot of time on (e.g., putting conic section equations in normal form), practical math skills weren't part of algebra II... this is probably because many of these ideas were probably supposed to be introduced in middle school or something. But poor teachers along the way meant that it was likely that most students wouldn't have any knowledge of practical math.
So, at that point, I decided to carve a few weeks out of my school year to devote to teaching practical math that would actually get my students through their lives, even though the state curriculum told me I was supposed to do other things. Otherwise, these students would graduate that year, never have another math class again, and they would be clueless about basic financial math.
That's the reality we're facing for MOST students who graduate from high school in the U.S. It's not that they were lured away from their ideas about compound interest by loan sharks -- they never knew what compound interest meant to begin with.
These are the people who bought houses they couldn't afford. Even with my couple week tutorial to my students, I'm certain that many of them would probably still fail to be able to evaluate loan terms in a real-world mortgage situation without significant help.
That's what we're up against.
If you really want to prevent this crap from recurring as people continue to make stupid financial decisions, we should drop all of the crap standardized testing about wacky geometry and algebra and whatever to graduate high school, and instead have a simple test presenting real-world math scenarios, like evaluating investments and loan terms, choosing a credit card, and constructing a proper budget and realistic plans for saving for the future. Present students with scenarios designed to sound like loan sharks, bogus investment schemes, etc. If they can't spo
It is rather interesting they were using kefir for cheese making
Yes, this is actually the most interesting finding here, since what they discovered probably wouldn't be recognized as normal "cheese" by many people. It's not like they found a small wheel of cheddar placed lovingly on the chests of bodies. Rennet-based cheeses are what most people in the Western world think of when they hear the word "cheese," or perhaps artificially acidified cheeses, like mozzarella or paneer.
This "cheese" (if indeed that's what it was -- see below) was produced by a slower acidification from fermentation. Then presumably it was strained or dried to separate the solids. The closest approximation for people unfamiliar with kefir would be to take a bunch of yogurt, put it in some cloth, then hang it and let the liquid drain out for a couple days, going past the point of thick "Greek yogurt" to a drier texture. (Technically, this makes labneh, a Middle Eastern-style fresh cheese.) It's a different type of cheese from rennet-based cheeses, but one more common in traditional cultures around the world.
For those not familiar with traditional kefir, it's very different from the store-bought stuff. It depends on a starter composed of "kefir grains," which is essentially a small mass of colonies of many types of microorganisms, which look like a group of small pearl-like things with a rubbery texture. They are very stable and durable, able to be rejuvenated after drying out, freezing, or even being "starved" for months.
The reason this is relevant to the story is that these kefir grains, to my knowledge, have not been replicated using modern scientific methods, despite many attempts. (Most "starters" for things like sourdough bread, yeast for wine, or common fermentations for milk like yogurt, can be cultivated fresh with only minimal effort from the naturally occurring organisms on flour, grapes, or milk.) In kefir, there are too many bacteria in a symbiotic relationship, and scientists still haven't managed to figure out how to get them to create these grains by themselves. The only way to get traditional kefir is to get some grains from someone. (The store-bought stuff is produce, like yogurt, just by using a small number of bacterial strains for fermentation under controlled conditions.)
Because of the difficulty in reproducing traditional kefir grains, there are all sorts of origin myths about it -- stories about it coming from medieval Georgia or the armies of Genghis Khan or whatever.
Anyhow, what I wonder from reading the story is how exactly they know this is "cheese" and not merely a dried form of kefir grains? In the era before refrigeration, kefir grains were essential to preserve fresh milk for later consumption, and where highly prized. There are all sorts of traditional stories from these cultures about people stealing kefir grains, because you couldn't just make new ones easily. You had to get them somewhere.
So, the question that occurs to me is -- why do we assume this is food for the afterlife? Why not consider the possibility that these people were given a gift of kefir grains (in a concentrated dried form) to carry with them to the afterlife -- an essential food preserving and processing tool, which could not be simply "made." It was something you had to carry with you, something you had to get from a previous batch of kefir, so maybe this was the only way to get it to the afterlife.
That would be my first thought, if I found this stuff.