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Vladimir_M comments on Open Thread June 2010, Part 4 - Less Wrong
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I remember reading a post titled "Science as Attire," which struck me as making a very good point along these lines. It could be what you're looking for.
As a related point, it seems to me that people who do understand evolution (and generally have a strong background in math and natural sciences) are on average heavily biased in their treatment of creationism, in at least two important ways. First, as per the point made in the above linked post, they don't stop to think that the great majority of folks who do believe in evolution don't actually have any better understanding of it than creationists. (In fact, I would say that the best informed creationists I've read, despite the biases that lead them towards their ultimate conclusions, have a much better understanding of evolution than, say, a typical journalist who will attack them as ignorant.) Second, they tend to way overestimate the significance of the phenomenon. Honestly, if I were to write down a list of widespread delusions sorted by the practical dangers they pose, creationism probably wouldn't make the top fifty.
I'm extremely curious to hear both your list and JoshuaZ's list of the top 20 or so most harmful delusions. Feel free to sort by category (1-4, 5-10, 11-20, etc.) rather than rank in individual order.
I've separated some forms of alternative medicine out when one might arguably put them closer together. Also, I'm including Young Earth Creationism, but not creationism as a whole. Where that goes might be a bit more complicated. There's some overlap between some of these (such as young earth creationism and religion). The list also does not include any beliefs that have a fundamentally moral component. I've tried to not include beliefs which are stupid but hard to deal with empirically (say that there's something morally inferior about specific racial groups). Finally, when compiling this list I've tried to avoid thinking too much about the overall balance that the delusion provides. So for example, religion is listed where it is based on the harm it does, without taking into account the societal benefits that it also produces.
1-4: Religion, Ayurveda, Homeopathy, Traditional Chinese medicine (as standardized post 1950s)
5-10 The belief that intelligence differences have no strong genetic component. The belief that intelligence differences have no strong environmental component. The belief that there are no serious existential threats to humans. The belief that external cosmetic features or national allegiances are strong indicators of mental superiority or inferiority. That human females have fundamentally less mental capacity and that this difference is enough to be a useful data point when evaluating humans. The belief that the Chinese government can be trusted to benefit its people or decide what information they should or should not have access to. (The primary reason this gets on the list is the sheer size of China. There are other governments which are much, much worse and have similar delusions by the people. But the damage level done is frequently much smaller.)
11-20 Vaccines cause autism. Young Earth Creationism. Invisible Hand of the Market solves everything. Government solves everything. Providence. That there are not fundamental limits on certain natural resources. That nuclear power is intrinsically worse than other forms of energy. The belief that large segments of the population are fundamentally not good at math or science. Astrology. The belief that antibiotics can deal with viral infections.
There were a few that I wanted to stick on for essentially emotional reasons. So for example Holocaust Denial almost got on the list and when I tried to justify it I saw myself engaging in what was clearly motivated cognition.
This list is very preliminary. The grouping is also very tentative and could likely be easily subject to change.
Is it trust or fear that is the real problem in that case? What would you do as an average Chinese citizen who wanted to change the policy? (Then, the same question assuming you were an actual Chinese citizen who didn't have your philosophical mind, intelligence, idealism and resourcefulness.)
It seems like it is a mix. From people I've spoken to in China and the impression I get from what I've read about the Chinese censorship, the majority of people are generally ok with letting the government control things and think that that's really for the best. This seems to be changing slightly with the younger generation but it is hard to tell.
Good points certainly. I'm not sure any average Chinese citizen alone can do anything. If I were an actual Chinese citizen alone given my "philosophical mind, intelligence, idealism and resourcefulness," I'm not sure I'd do anything either, not because I can't, but because the risk would be high. It is easy to say "oh, people in X situation should do Y because that's morally better or better for everyone overall" when one isn't in that situation. When one's life, family, or livelihood is the one being threatened then it is obviously going to be a lot more difficult. It isn't that I'm a coward (although I might be) it is just that standing up to the government in that sort of situation takes a lot of courage that I'm pretty sure I (and most people) don't have. But if the general population took an attitude that was more willing to do minor things (spread things like TOR or other methods of getting around the Great Firewall for example), then things might be different. But even that might not have a large impact.
So yeah, I may need to take this off the list.
I get the impression that overall, the younger generation is more apathetic about politics than the older one.
(Though there is also the relatively recent phenomenon of "angry youths" (fenqing), who rant on forums and such.)
Lists like that are good !
I'm a bit surprised at that one - the current Chinese government seems pretty rational and efficient to me, and I'd be hard-pressed to say what I would do differently in it's place or rather - there are things I would do differently, but I'm not sure I'd get better results).
Control of information by the government should be seen mostly as a way of preserving it's own power. So I'm not really sure of how to interpret "The belief that the Chinese government can be trusted to [...] decide what information they should or should not have access to." - could you rephrase that belief so that it's irrationality becomes more apparent, maybe tabooing "can be trusted to" ? If you mean "Chinese people wrongly believe that the government is restricting information access for their own good", then I'm not sure that a lot of people actually believe that, and for those that do, that believing it does any harm.
Ok. My impression is that that is a common belief in China and is connected to the belief that the government doesn't actively lie. I don't have a very good citation for this other than general impressions so I'm going to point to a relevant blog entry by a friend who spent a few years in China where she discusses this with examples. There are of course even limits to how far that will go. This is also complicated by the fact that many of the really serious harm in China (detainment of citizens for questioning policies, beatings and torture, ignoring of basic environmental and safety issues) stem from the local governments rather than the central government, and the relationship between Beijing and the local governments is very complicated. See also my remarks above to wedrifid which touch on these issues also. So yeah, it may make sense to take this off the list given the lack of harm directly coming from this issue.
I don't interpret the story in that blog post that way at all. People repeating nationalist lies doesn't mean they've been fooled.
I highly recommend these posts about the psychology of mass lies. I don't recommend the third part.
Where would you put 'belief in free will' and 'belief in determinism'?
They probably wouldn't get anywhere on the list for the reason that a) I'm not convinced that either determinism or free will as often given are actually well-defined notions and b) I don't see either belief as causing much harm in practice.
This one caught my eye, I don't think I've seen this listed as an obvious delusion before. Can you maybe expand more on this? I guess the idea is that a much larger number of people could make use of math or science if they weren't predisposed to think that they belong in an incapable segment?
I'm thinking of something like picking the quarter of population that scores in the bottom at a standard IQ test or the local SAT-equivalent as the "large segment of population" though. A test for basic science and mathematics skills could be being able to successfully figure out solutions for some introductionary exercises from a freshman university course in mathematics or science, given the exercise, relevant textbooks and prerequisite materials, and, say, up to a week to work out things from the textbook.
It doesn't seem obvious to me that such a test would end up with results that would make the original assertion go straight into 'delusion' status. My suspicions are somewhat based on the article from a couple of years back, which claimed that many freshman computer science students seem to simple lack the basic mental model building ability needed to start comprehending programming.
Yes. And more people would go into math and science.
That's a very interesting article. I think that the level of, and type of abstraction necessary to program is already orders of magnitude beyond where most people stop being willing to do math. My own experience in regards to tutoring students who aren't doing well in math is that one of the primary issues is one of confidence: students of all types think they aren't good at math and thus freeze up when they see something that is slightly different from what they've done before. If they understand that they aren't bad at math or that they don't need to be bad at math, they are much more likely to be willing to try to play around with a problem a bit rather than just panic.
I was an undergraduate at Yale which is generally considered to be a decent school that admits people who are by and large not dumb. And one thing that struck me was that even in that sort of setting, many people minimized the amount of math and science they took. When asked about it the most common claim was that they weren't good at it. Some of those people are going to end up as future senators and congressman and have close to zero idea of how science works or how statistics work other than at the level they got from high school. If we're lucky, they know the difference between a median and a mean.
Does anybody actually claim to believe that ?
This view is surprisingly common. I don't want to move to much to a potentially mind-killing subject, but the idea isn't uncommon among certain groups in US politics. Indeed, they think it so strongly about some resources that they take it almost as an ideological point. This occurs when discussing oil most frequently. Emphasis is placed on things like the Eugene Island field and abiotic oil which they argue shows we won't run out of oil. The second is particularly galling because even if the abiotic oil hypotheses were correct the level of oil production would still be orders of magnitudes below the consumption rate. I'd point more generally to followers of Julian Simon (not Simon himself per se. His own arguments were generally more nuanced and subtle than what many people seem to get out of them).
I'll give you a big one: Dying a martyr's death gives you a one-way ticket to Paradise.
Mass_Driver:
I'm not sure if that would be a smart move, since it would mean an extremely high concentration of unsupported controversial claims in a single post. Many of my opinions on these matters would require non-obvious lengthy justifications, and just dumping them into a list would likely leave most readers scratching their heads. If you're really curious, you can read the comment threads I've participated in for a sample, in particular those in which I argue against beliefs that aren't specific to my interlocutors.
Also, it should be noted that the exact composition of the list would depend on the granularity of individual entries. If each entry covered a relatively wide class of beliefs, creationism might find itself among the top fifty (though probably nowhere near the top ten).
In this format that sounds like a good thing! At worst it would spark curiosity and provoke discussion. At best people would encounter a startling opinion that they had never seriously considered, think about for 60 seconds then form an understanding that either agrees with yours or disagrees, for a considered reason.
seconded, but a list of 20 seems too long/too much work, no?
I'd be thinking 5. :)
If I might jump in on the listing of delusions, I think that perhaps one of the most important things to understand about widespread delusions is who, in fact, holds them. A bunch of rednecks in Louisiana not believing in evolution isn't important, because even if they did, it wouldn't inform other parts of their worldview. In general, the specific delusions of ordinary people (IQ < 120) aren't important, because they aren't the ones who are actually affecting anything. Even improving the rationality and general problem awareness of smart people (120 < IQ < 135) doesn't really help, because then you get people who will expend enormous effort doing things like evangelizing atheism to the ordinary people and fighting global warming and the like. Raising the sanity waterline is important, but effort should be focused on people with the ability to actually use true beliefs.
I'm less sure. I would have thought that they affect things indirectly at least through social transmission of beliefs, what they choose to spend their money on, and the demands they make of politicians.
Arguably, one should expect it to help less than improving the rationality and awareness of people with IQ < 120, just because there are 11 times as many people with IQ < 120 than there are with 120 < IQ < 135.
I sincerely hope that you are using IQ as only the crudest shorthand for "ability to actually use true beliefs," but your point in general is very well taken. Please do jump in if you have a listing of the most harmful delusions. :-)
IQ >= 120 is a fairly low bar. IQ is also a strong indicator for the potential for someone's behavior to be influenced by delusions (rather than near mode thinking + social pressure being the dominant adaptation.)
Do you mean do say that people of ordinary intelligence, as a general rule, don't actually believe whatever it is they say they believe, but instead just parrot what those around them say? You might be right. I think I need to find a way to re-immerse myself in a crowd of people of average intelligence; it's been far too long, and my predictive/descriptive powers for such people are fraying.
Note that none of this is sarcasm; this comment is entirely sincere.
Wedrifid only said "potential"; most people, smart or not, behave as you say. And I would expand "delusion" to 'belief": being smart is correlated with being influenced by beliefs, true or false.
That people act on beliefs or have at all coherent world-views is the most dangerous widespread delusion. ("The world is mad.") Immersing yourself in a crowd of average intelligence might help you see this, but I rather doubt that your associates act on their beliefs.
Another thing that is dangerous is the people that actually act on their beliefs. They are much harder to control. People 'acting as if' pragmatically don't do things that we strongly socially penalize.
Not on their stated beliefs; surely, but don't most people have a set of actual beliefs? Can't these actual beliefs, at least in some contexts, be nudged so as to influence the level and direction of cognitive dissonance, which in turn can influence actions?
There's certainly evidence that intelligent people are more likely to have more coherent worldviews. For example, the GSS data shows that higher vocabulary is associated with more extreme political views to either end of the traditional political spectrum. There's similar research for IQ scores but I don't have a citation for that.
You really should watch your grammar, syntax, and spelling while commenting on intelligence. The irony is distracting, otherwise. Unless you were referring to the CIA and FBI?
It might be more generally a sign that I shouldn't comment when it is late at night in my timezone. Also, it should constitute evidence that we need better spellcheckers that don't just catch non-words but also words that are clearly wrong from minimal context (although in this particular case catching that that was the wrong word would almost seem to require solving the natural language problem unless one had very good statistical methods).
Are you saying more extreme political views are more coherent? I'm not following this.
Blueberry:
That seems like an almost self-evident observation to me. I have never seen anyone state clearly any political or ideological principles, of whatever sort and from whatever position, whose straightforward application wouldn't lead to positions that are utterly extremist by the standards of the present centrist opinion.
Getting people with regular respectable opinions to contradict themselves by asking a few Socratic questions is a trivial exercise (though not one that's likely to endear you to them!). The same is not necessarily true for certain extremist positions.
And it seems self-evidently false to me, so I'm very curious what exactly you mean.
If you take any one principle and apply it across the board, to everything, without limitation, you'll end up with an extremist position, basically by definition. So in that sense, extremist positions may be simpler than moderate ones. But that's more "extrapolation" and "exaggeration" than "straighforward application".
Moderate positions tend to carefully draw lines to balance out many different principles. I'm not sure how to discuss this without giving contemporary political examples, so I'll do so with the warning that I'm not necessarily for or against any of the following moderate positions, and I'm not intending to debate any of them; I'm just claiming that they're moderate and consistent.
The government should be able to impose a progressive tax on people's incomes, which it can then use for national defense, infrastructure, and social programs, while still allowing individuals to make profits (contrast communism and pure libertarianism)
Individuals over 18 who have not been convicted of a felony should be able to carry a handgun, but not an automatic weapon, after a brief background check, except in certain public places (contrast with complete banning of guns and with a free market on all weapons)
The government should regulate and approve the sale of some kinds of chemicals, completely banning some, allowing some with a doctor's prescription, and allowing some to be sold freely over the counter after careful review
People over a certain age X should be able to freely have consensual sex in private with each other without government interference; people under X-n should not be allowed to engage in sex; people in between should be allowed to have sex only with people close to their own age
The country should guard its borders and not let anyone in without approval, and deport anyone found to have entered illegally, but should grant entry to tourists and grant a visa to a small number of students and workers
You can feel free to add your own if you'd like. But I don't see how any of these are incoherent or contradictory. What Socratic questions would expose them?
Typically, yes. People with extreme views typically don't fail to make inferences from their beliefs along the lines of "X is good, so doing Y, which creates even more of X's goodness, would be even better!" Y might in fact be utterly stupid and evil and wrong, and a moderate with less extreme views might be against it, but the moderate and the extremist might both agree with X, even though the failure of logic that leads the extremist to endorse the evil Y is the belief that X is good.
Do more extreme political views signify more coherent worldviews?
I differentiate between 'actually believe' and 'act as if they are an agent with the belief that'. All people mostly do the latter but high IQ people are somewhat more likely to let 'actual beliefs' interfere with their lives.
I would say that people of ordinary intelligence don't actually have anything that I would identify as a non-trivial belief. They might say they believe in god, but they don't actually expect to get the pony they prayed for (even if they say that they do). However, they do have accurate beliefs regarding, say, how to cook food, or whether jumping off a building is a healthy idea, because they actually have to use such beliefs.
In a democracy, specific delusions of ordinary people are important.
In a representative democracy, the specific delusions of the elected and unelected officials are important.
Taking into account what I already said about needing to influence people who can actually use beliefs (thus controlling for things like atheism, evolution, etc.)...
What is the delusion here?
What is the delusion here? Do you mean people convincing themselves that they can't do math?
This seems too subjective to label a delusion.
What do you mean by best and by influence?
Inability to do math? Really? Are you talking 'disinclination to shut up and multiply' or actual ability to do math?
I love math but don't really think most people need it.
Dredging this up from deep nesting, because I think it's important: wedrifid says
Yes. Never tell anyone that what you're teaching them is hard. When you do that, you're telling them they'll fail, telling them to fail.
But if you tell them it's easy, then they will be embarrassed for failing at something easy, or can't be proud of succeeding at something easy.
Telling them it's easy is also a bad idea.
It strikes me that giving no information about the general difficulty of the subject is also a bad idea. (I imagined myself struggling with a topic where I had no information on how hard others found it, and my hypothetical self was ashamed, because clearly if it were something everyone found hard, they'd warn people and teach it more slowly, so it must be easy for everybody else but me.)
Ideally, you'd teach the student not to be concerned with how well or how quickly they learn compared to others, which is a general learning technique that can apply to any field.
Simply telling people not to worry about that doesn't... actually work, does it? That would genuinely surprise me.
When I teach, I don't say anything about "easy" or "difficult". I just teach the material. What is this "easy", this "difficult"? There is no "easy" or "difficult" for a Jedi -- there is only the work to be done and the effort it takes. "Difficult" means "I will fail". "Effort" means "I will succeed".
You are torturing yourself by inventing fictional evidence. You have an entire imaginary scenario there, shadows and fog conjured from thin air.
I don't think Alicorn's evidence is completely fictional. It's a simulation. It's not as much evidence as if she had experienced it in real life, but it's much better than, e.g. the evidence of Terminator on future AIs.
Right, and there's the issue of whose fault the difficulty is. Sure, the student might not really be trying. But also, the teacher may not be explaining in a way that speaks to the learner's natural fluency. A method that works for the geeky types won't work work for more neurotypical types.
For my part, I never have trouble explaining high school math to those who haven't completed it, even if they're told that trig, calculus, etc. is hard. It's because I first focus on finding out where exactly their knowledge deficit is and why the subject matter is useful. Of course, teachers don't have the luxury of one-on-one instruction, but yes, how you present the material matters greatly.
Most people don't need to understand evolution. Maybe we should distinguish between "harmful to self", "harmful to society", and "harmful to a democratic society".
If you can't do math at a fairly advanced level - at least having competence with information theory, probability, statistics, and calculus - you can't understand the world beyond what's visible on its (metaphorical) surface.
While as a mathematician I find that claim touching, I can't really agree with it. To use the example that was one of the starting points of this conversation, how much math do you need to understand evolution? Sure, if you want to really understand the modern synthesis in detail you need math. And if you want to make specific predictions about what will happen to allele frequencies you'll need math. But in those cases it is very basic probability and maybe a tiny bit of calculus (and even then, more often than not you can use the formulas without actually knowing why they work beyond a very rough idea).
Similar remarks apply to other areas. I don't need a deep understanding of any of those subjects to have a basic idea about atoms, although again I will need some of them if I want to actually make useful predictions (say for Brownian motion).
Similarly, I don't need any of those subjects to understand the Keplerian model of orbits, and I'll only need one of those four (calculus) if I want to make more precise estimations for orbits (using Newtonian laws).
The amount of actual math needed to understand the physical world is pretty minimal unless one is doing hard core physics or chemistry.
For example... trying to work out what happens when I shoot a neverending stream of electrons at a black hole. The related theories were more or less incomprehensible to me at first glance. Not being able to do off the wall theorizing on everything at the drop of the hat has to at least make 49!
The human-scale physical world is relatively easy to understand, and we may have evolved or learned to perform the trickier computations using specialized modules, such as perhaps recognizing parabolas to predict where a thrown object will land. You get far with linear models, for instance, assuming that the distance something will move is proportional to the force that you hit it with, or that the damage done is proportional to the size of the rock you hit something with. You rarely come across any trajectory where the second derivative changes sign.
The social world, the economic world, ecology, game theory, predicting the future, and politics are harder to understand. There are a lot of nonlinear and even non-differentiable interactions. To understanding a phenomenon qualitatively, it's helpful to perform a stability analysis, and recognize likely stable areas, and also unstable regions where you have phase transitions, period doublings, and other catastrophes, You usually can't do the math and solve one of these systems; but if you've worked with a lot of toy systems mathematically, you'll understand the kind of behaviors you might see, and know something about how the number of variables and the correlations between them affect the limits of linear extrapolation. So you won't assume that a global warming rate of .017C/year will lead to a temperature increase of 1.7C in 100 years.
I'm making this up as I go; I don't have any good evidence at hand. I have the impression that I use math a lot to understand the world (but not the "physical" world of kinematics). I haven't observed myself and counted how often it happens.
I've got a tangential question: what math, if learned by more people, would give the biggest improvement in understanding for the effort put into learning it?
Take calculus, for example. It's great stuff if you want to talk about rates of change, or understand anything involving physics. There's the benefit; how about the cost? Most people who learn it have a very hard time doing so, and they're already well above average in mathematical ability. So, the benefit mostly relates to understanding physics, and the cost is fairly high for most people.
Compare this with learning basic probability and statistical thinking. I'm not necessarily talking about learning anything in depth, but people should have at least some exposure to ideas like probability distributions, variance, normal distributions and how they arise, and basic design of experiments -- blinding, controlling for variables, and so on. This should be a lot easier to learn than calculus, and it would give insight into things that apply to more people.
I'll give a concrete example: racism. Typical racist statements, like "black people are lazy and untrustworthy," couldn't possibly be true in more than a statistical sense, and obviously a statistical statement about a large group doesn't apply to every member of that group -- there's plenty of variance to take into account. Basic statistical thinking makes racist bigotry sound preposterously silly, like someone claiming that the earth is flat. This also applies to every other form of irrational bigotry that I can think of off the top of my head.
Remember when Larry Summers suggested that maybe part of the reason for the underrepresentation of women in Harvard's science faculty was that women may have lower variance in intelligence than men, and so are underrepresented in the highest part of the intelligence bell curve? What almost everybody heard was "Women can't be scientists because they're stupid." People heard a statistical statement and had no idea how to understand it.
There are important, relevant subjects that people just can not understand without basic statistical thinking. I would like to see most people exposed to basic statistical thinking.
Are there any other kinds of math that offer high bang-for-the-buck, as far as learning difficulty goes? (I've always thought that the math behind computer programming was damn useful stuff, but the engineering students I've talked with usually find it harder than calculus, so maybe that's not the best idea.)
Tangential question to your tangential question: I'm puzzled, which math are you talking about here? The only math relevant to programming that I can think of that engineering students would also learn would be discrete math, but the extent needed for good programming competency is pretty small and easy to pick up.
Are we talking numerical computing instead, with optimization problems and approximating solutions to DE's? That's the only thing I can think of relevant to engineering for which the math background might be more difficult than calculus.
I was thinking more basic: induction, recursion, reasoning about trees. Understanding those things on an intuitive level is one of the main barriers that people face when they learn to program. It's one thing to be able to solve problems out of a textbook involving induction or recursion, but another thing to learn them so well that they become obvious -- and it's that higher level of understanding that's important if you want to actually use these concepts.
I'm not sure about all the details, but I believe that there was a small kerfuffle a few decades ago over a suggestion to change the apex of U.S. ``school mathematics'' from calculus to a sort of discrete math for programming course. I cannot remember what sort of topics were suggested though. I do remember having the impression that the debate was won by the pro-calculus camp fairly decisively -- of course, we all see that school mathematics hasn't changed much.
Probability theory as extended logic.
I think it can be presented in a manner accessible to many (Jaynes PT:LOS is not accessible to many).
Calculus might not be the best example of a skill with relatively low payoff, because you need some calculus to understand what a continuous probability distribution is.
I do? I thought I understood both calculus and continuous probability but I didn't know one relied on the other. You are probably right, sometimes things that are 'obvious' just don't get remembered.
For example, suppose you have a biased coin which lands heads up with probability p. A probability distribution that represents your belief about p is usually a non-negative real function f on the unit interval whose integral is 1. Your credence in the proposition that p lies between 1/3 and 1/2 is the integral of f from 1/3 to 1/2.
Yes, extremely obvious now that you mention it. :)
Well above average mathematical ability and cannot do calculus to the extent of understanding rates of change? For crying out loud. You multiply by the number up to the top right of the letter then reduce that number by 1. Or you do the reverse in the reverse order. You know, like you put on your socks then your shoes but have to take off your shoes then take off your socks.
Sometimes drawing a picture helps prime an intuitive understanding of the physics. You start with a graph of velocity vs time. That is the 'acceleration'. See... it is getting faster each second. Now, use a pencil and progressively color in under the line. that's the distance that is getting covered. See how later on more when it is going faster more distance is being traveled at one time and we have to shade in more area? Now, remember how we can find the area of a triangle? Well, will you look at that... the maths came out the same!
People get the simple concepts mixed together with a bunch of mathy-looking symbols and equations, and it all congeals into an undifferentiated mass of confusing math. Yes, I know calculus is actually pretty straightforward, but we're probably not a representative sample. Talk with random bewildered college freshmen to combat sample bias. I did this, and what I learned is that most people have serious trouble learning calculus.
Now, if you want to be able to partially understand a bunch of physics stuff but you don't necessarily need to be able to do the math, you could probably get away with a small subset of what people learn in calculus classes. If you learned about integration and differentiation (but not how to do them symbolically), as well as vectors, vector fields, and divergence and curl, then you could probably get more benefit-per-hour-of-study than if you went and learned calculus properly. It leaves a bad taste in my mouth, though.
When taught well the calculus required for the sort of applications you mentioned is not something that causes significant trouble, certainly not compared to vector fields, divergence or curl. By taught well, if you will excuse my lack of seemly modesty, is how I taught it in my (extremely brief - don't let me get started on what I think of western school systems) stint teaching high school physics. The biggest problem for people learning basic calculus is that people teaching it try to convey that it is hard.
I'm only talking here about the level of stuff required for everyday physics. Definitely not for the vast majority of calculus that we try to teach them.
Aw, please ? I'd be interested in hearing about the differences with other systems :)
I teach calculus often. Students don't get hung up on mechanical things like (x^3)' = 3x^2. They instead get hung up on what
has to do with the derivative as a rate of change or as a slope of a tangent line. And from the perspective of a calculus student who has gone through the standard run of American school math, I can understand. It does require a level up in mathematical sophistication.
That's the problem. See that bunch of symbols? That isn't the best way to teach stuff. It is like trying to teach them math while speaking a foreign language (even if technically we are saving the greek till next month). To teach that concept you start with the kind of picture I was previously describing, have them practice that till they get it then progress to diagrams that change once in the middle, etc.
Perhaps the students here were prepared differently but the average student started getting problems with calculus when it reached a point slightly beyond what you require for the basic physics we were talking about here. ie. they would be able to do 1. and but have no chance at all with 2:
I'm not claiming that working from the definition of derivative is the best way to present the topic. But it is certainly necessary to present the definition if the calculus is being taught in math course. Part of doing math is being rigorous. Doing derivatives without the definition is just calling on a black box.
On the other hand, once one has the intuition for the concept in hand through more tangible things like pictures, graphs, velociraptors, etc., the definition falls out so naturally that it ceases to be something which is memorized and is something that can be produced ``on the fly''.
(Actually, many would struggle with 1. due to difficulty with comprehension and abstract problem solving. They could handle the calculus but need someone to hold their hand with the actual thinking part. That's what we really fail to teach effectively.)
I'd like this to be true, as I want the time I spend learning math in the future to be as useful as you say, but I seem to have come rather far by knowing the superficial version of a lot of things. Knowing the actual math from something like PT:LOS would be great, and I plan on reaching at least that level in the Bayesian conspiracy, but I can currently talk about things like quantum physics and UDT and speed priors and turn this into changes in expected anticipation. I don't know what Kolmogorov complexity is, really, in a strictly formal from-the-axioms sense, nor Solomonoff induction, but I reference it or things related to it about 10 times a day in conversations at SIAI house, and people who know a lot more than I do mostly don't laugh at my postulations. Perhaps you mean a deeper level of understanding? I'd like to achieve that, but my current level seems to be doing me well. Perhaps I'm an outlier. (I flunked out of high school calculus and 'Algebra 2' and haven't learned any math since. I know the Wikipedia/Scholarpedia versions of a whole bunch of things, including information theory, computer science, algorithmic probability, set theory, etc., but I gloss over the fancy Greek letters and weird symbols and pretend I know the terms anyway.)
I have a belief that I can fix things like this, having spent time working with other students in high school. If I ever meet you in person, will you assist me in testing that belief? ;)
A public reminder to myself so as to make use of consistency pressure: I shouldn't write comments like the one I wrote above. It lingers too long on a specific argument that is not particularly strong and was probably subconsciously fueled by a desire to talk about myself and perhaps countersignal to someone whose writing I respect (Phil Goetz).
I'm pretty sure that most people around lesswrong have about the same level of familiarity with most subjects (outside whatever field they actually specialize). Although I do think that you are relatively weak in mathematics, but advanced math just really isn't that important, vis-a-vis being generally well educated and rational.
This one.
Are you then asserting that non-utilitarian views constitute a delusion?
I'm asserting that saying "We must do X, because it produces good effect Y", when there is option Z, which delivers the same Y for half the cost, is a delusion.
This seems more like a common cognitive error than a delusion. How are you defining delusion? It seems like I am using a more narrow definition of delusion. I'm using something like "statement or class of statements about the physical world that are demonstrably extremely unlikely to be true." What definition are you using?
Lucas's statement fits this definition. This may me be clearer if you consider just "we must do X", which is a claim about the physical world. The because part does not happen to change this.
If you don't agree that the truncated claim fits the criteria I infer that the most likely difference in definitions between you and Lucas is in not so much around 'delusion' but rather about what 'must' means in relation to the physical world. This would make what you say true even if it isn't grounded in my preferred ontology.
Ah, so the issue is that I see "must" as entangled with moral and ethical claims that aren't necessarily connected to the physical world in any useful fashion.
If you said that it wouldn't make the top 10, I'd find that not implausible. Claiming it wouldn't make the top 50 seems implausible. Actual dangers posed by creationism:1) It makes people have a general more anti-science attitude and makes children less likely to become scientists 2) it takes up large sets of resources that would be spent usefully otherwise 3) it actively includes the spreading of a lot of misinformation 4) it snags otherwise bright minds who might otherwise becomes productive individuals (Jonathan Sarfati for example is a chess master, unambiguously quite bright, and had multiple good scientific papers before getting roped into YECism. Michael Behe is in a similar situation although for ID rather than young earth creationism). 5) The young earth variants encourage a narrow time outlook which is not helpful for long-term planning about the world or appreciation of serious existential threats (although honestly so few people pay attention to existential risks this is probably a minor issue) 6) It causes actual scientists and teachers to lose their jobs or have their work restricted (admittedly this isn't common but that's partially because creationism doesn't have much ground). 7) It encourages general extremist religious attitudes.
So not in the top 10? I'd agree with that. But I have trouble seeing it not in the top 50 most dangerous widespread delusions.
Thanks, this is what I had in mind.