The mathematician and Fields medalist Vladimir Voevodsky on using automated proof assistants in mathematics:
[Following the discovery of some errors in his earlier work:] I think it was at this moment that I largely stopped doing what is called “curiosity driven research” and started to think seriously about the future.
[...]
A technical argument by a trusted author, which is hard to check and looks similar to arguments known to be correct, is hardly ever checked in detail.
[...]
It soon became clear that the only real long-term solution to the problems that I encountered is to start using computers in the verification of mathematical reasoning.
[...]
Among mathematicians computer proof verification was almost a forbidden subject. A conversation started about the need for computer proof assistants would invariably drift to the Goedel Incompleteness Theorem (which has nothing to do with the actual problem) or to one or two cases of verification of already existing proofs, which were used only to demonstrate how impractical the whole idea was.
[...]
...I now do my mathematics with a proof assistant and do not have to worry all the time about mistakes in my arguments or about ho
"It is one thing for you to say, ‘Let the world burn.' It is another to say, ‘Let Molly burn.' The difference is all in the name."
-- Uriel, Ghost Story, Jim Butcher
It is easier to fight for one's principles than to live up to them.
-- Alfred Adler
ADDED: Source: http://en.wikiquote.org/wiki/Alfred_Adler
Quoted in: Phyllis Bottome, Alfred Adler: Apostle of Freedom (1939), ch. 5
Problems of Neurosis: A Book of Case Histories (1929)
Comedian Simon Munnery:
Many are willing to suffer for their art; few are willing to learn how to draw.
Philosophers often behave like little children who scribble some marks on a piece of paper at random and then ask the grown-up "What's that?"- It happened like this: the grown-up had drawn pictures for the child several times and said "this is a man," "this is a house," etc. And then the child makes some marks too and asks: what's this then?
Slartibartfast: Perhaps I'm old and tired, but I think that the chances of finding out what's actually going on are so absurdly remote that the only thing to do is to say, "Hang the sense of it," and keep yourself busy. I'd much rather be happy than right any day.
Arthur Dent: And are you?
Slartibartfast: Well... no. That's where it all falls down, of course.
Douglas Adams, Hitchhiker's Guide to the Galaxy
Now, one basic principle in all of science is GIGO: garbage in, garbage out. This principle is particularly important in statistical meta-analysis: because if you have a bunch of methodologically poor studies, each with small sample size, and then subject them to meta-analysis, what can happen is that the systematic biases in each study — if they mostly point in the same direction — can reach statistical significance when the studies are pooled. And this possibility is particularly relevant here, because meta-analyses of homeopathy invariably find an inverse correlation between the methodological quality of the study and the observed effectiveness of homeopathy: that is, the sloppiest studies find the strongest evidence in favor of homeopathy. When one restricts attention only to methodologically sound studies — those that include adequate randomization and double-blinding, predefined outcome measures, and clear accounting for drop-outs — the meta-analyses find no statistically significant effect (whether positive or negative) of homeopathy compared to placebo.
A bigger danger is publication bias. collect 10 well run trials without knowing that 20 similar well run ones exist but weren't published because their findings weren't convenient and your meta-analysis ends up distorted from the outset.
This principle is particularly important in statistical meta-analysis: because if you have a bunch of methodologically poor studies, each with small sample size, and then subject them to meta-analysis, what can happen is that the systematic biases in each study — if they mostly point in the same direction — can reach statistical significance when the studies are pooled.
Does anyone know how often this happens in statistical meta-analysis?
Fairly often. One strategy I've seen is to compare meta-analyses to a later very-large study (rare for obvious reasons when dealing with RCTs) and seeing how often the confidence interval is blown; usually much higher than it should be. (The idea is that the larger study will give a higher-precision result which is a 'ground truth' or oracle for the meta-analysis's estimate, and if it's later, it will not have been included in the meta-analysis and also cannot have led the meta-analysts into Milliken-style distorting their results to get the 'right' answer.)
For example: LeLorier J, Gregoire G, Benhaddad A, Lapierre J, Derderian F. "Discrepancies between meta-analyses and subsequent large randomized, controlled trials". N Engl J Med 1997;337:536e42
...Results: We identified 12 large randomized, controlled trials and 19 meta-analyses addressing the same questions. For a total of 40 primary and secondary outcomes, agreement between the meta-analyses and the large clinical trials was only fair (kappa ϭ 0.35; 95% confidence interval, 0.06-0.64). The positive predictive value of the meta-analyses was 68%, and the negative predictive value 67%. However, the difference in point est
As a percentage? No. But qualitatively speaking, "often."
The most recent book I read discusses this particularly with respect to medicine, where the problem is especially pronounced because a majority of studies are conducted or funded by an industry with a financial stake in the results, with considerable leeway to influence them even without committing formal violations of procedure. But even in fields where this is not the case, issues like non-publication of data (a large proportion of all studies conducted are not published, and those which are not published are much more likely to contain negative results) will tend to make the available literature statistically unrepresentative.
It is, in fact, a very good rule to be especially suspicious of work that says what you want to hear, precisely because the will to believe is a natural human tendency that must be fought.
"Throughout the day, Stargirl had been dropping money. She was the Johnny Appleseed of loose change: a penny here, a nickel there. Tossed to the sidewalk, laid on a shelf or bench. Even quarters.
"I hate change," she said. "It's so . . . jangly."
"Do you realize how much you must throw away in a year?" I said.
"Did you ever see a little kid's face when he spots a penny on a sidewalk?”
Jerry Spinelli, Stargirl
So as to keep the quote on its own, my commentary:
This passage (read at around age 10) may have been my first exposure to an EA mindset, and I think that "things you don't value much anymore can still provide great utility for other people" is a powerful lesson in general.
Specifically, [these recent books that deal with parallel universes] argue that if some scientific theory X has enough experimental support for us to take it seriously, then we must take seriously also all its predictions Y, even if these predictions are themselves untestable (involving parallel universes, for example).
As a warm-up example, let's consider Einstein's theory of General Relativity. It's widely considered a scientific theory worthy of taking seriously, because it has made countless correct predictions -- from the gravitational bending of light to the time dilation measured by our GPS phones. This means that we must also take seriously its prediction for what happens inside black holes, even though this is something we can never observe and report on in Scientific American. If someone doesn't like these black hole predictions, they can't simply opt out of them and dismiss them as unscientific: instead, they need to come up with a different mathematical theory that matches every single successful prediction that general relativity has made -- yet doesn't give the disagreeable black hole predictions.
-- Max Tegmark, Scientific American guest blog, 2014-02-04
How much of a disaster is this? Well, it’s never a disaster to learn that a statement you wanted to go one way in fact goes the other way. It may be disappointing, but it’s much better to know the truth than to waste time chasing a fantasy. Also, there can be far more to it than that. The effect of discovering that your hopes are dashed is often that you readjust your hopes. If you had a subgoal that you now realize is unachievable, but you still believe that the main goal might be achievable, then your options have been narrowed down in a potentially useful way.
-Timothy Gowers, on finding out a method he’d hoped would work, in fact would not.
Richard Feynmann claimed that he wasn't exceptionally intelligent, but that he focused all his energies on one thing. Of course he was exceptionally intelligent, but he makes a good point.
I think one way to improve your intelligence is to actually try to understand things in a very fundamental way. Rather than just accepting the kind of trite explanations that most people accept - for instance, that electricity is electrons moving along a wire - try to really find out and understand what is actually happening, and you'll begin to find that the world is very different from what you have been taught and you'll be able to make more intelligent observations about it.
reddit user jjbcn on trying to improve your intelligence
If you're not a student of physics, The Feynman Lectures on Physics is probably really useful for this purpose. It's free for download!
http://www.feynmanlectures.caltech.edu/
It seems like the Feynman lectures were a bit like the Sequences for those Caltech students:
...The intervening years might have glazed their memories with a euphoric tint, but about 80 perce
Trying to actually understand what equations describe is something I'm always trying to do in school, but I find my teachers positively trained in the art of superficiality and dark-side teaching. Allow me to share two actual conversations with my Maths and Physics teachers from school.:
(Teacher derives an equation, then suddenly makes it into an iterative formula, with no explanation of why)
Me: Woah, why has it suddenly become an iterative formula? What's that got to do with anything?
Teacher: Well, do you agree with the equation when it's not an iterative formula?
Me: Yes.
Teacher: And how about if I make it an iterative formula?
Me: But why do you do that?
Friend: Oh, I see.
Me: Do you see why it works?
Friend: Yes. Well, no. But I see it gets the right answer.
Me: But sir, can you explain why it gets the right answer?
Teacher: Ooh Ben, you're asking one of your tough questions again.
(Physics class)
Me: Can you explain that sir?
Teacher: Look, Ben, sometimesnot understanding things is a good thing.
And yet to most people, I can't even vent the ridiculousness of a teacher actually saying this; they just think it's the norm!
I will only say that when I was a physics major, there were negative course numbers in some copies of the course catalog. And the students who, it was rumored, attended those classes were... somewhat off, ever after.
And concerning how I got my math PhD, and the price I paid for it, and the reason I left the world of pure math research afterwards, I will say not one word.
A visit to wikipedia suggests that "secondary school" can refer to either what we in the U.S. call "middle school / junior high school", or what we call "high school". That's a fairly wide range of grade levels. In which year of pre-university education are you?
I suspect this is typical mind fallacy at work. There are many students who either can't, or don't want to, learn mathematical intuitions or explanations. They prefer to learn a few formulas and rules by rote, the same way they do in every other class.
There are many students who either can't, or don't want to, learn mathematical intuitions or explanations. They prefer to learn a few formulas and rules by rote, the same way they do in every other class.
Former teacher confirming this. Some students are willing to spend a lot of energy to avoid understanding a topic. They actively demand memorization without understanding... sometimes they even bring their parents as a support; and I have seen some of the parents complaining in the newspapers (where the complaints become very unspecific, that the education is "too difficult" and "inefficient", or something like this).
Which is completely puzzling for the first time you see this, as a teacher, because in every internet discussion about education, teachers are criticized for allegedly insisting on memorization without understanding, and every layman seems to propose new ideas about education with less facts and more "critical thinking". So, you get the impression that there is a popular demand for understanding instead of memorization... and you go to classroom believing you will fix the system... and there is almost a revolution against you, outraged ...
Speaking as a student: I sympathize with Benito, have myself had his sort of frustration, and far prefer understanding to memorization... yet I must speak up for the side of the students in your experience. Why?
Because the incentives in the education system encourage memorization, and discourage understanding.
Say I'm in a class, learning some difficult topic. I know there will be a test, and the test will make up a big chunk of my grade (maybe all the tests together are most of my grade). I know the test will be such that passing it is easiest if I memorize — because that's how tests are. What do I do?
True understanding in complex topics requires contemplation, experimentation, exploration; "playing around" with the material, trying things out for myself, taking time to think about it, going out and reading other things about the topic, discussing the topic with knowledgeable people. I'd love to do all of that...
... but I have three other classes, and they all expect me to read absurd amounts of material in time for next week's lecture, and work on a major project apiece, and I have no time for any of those wonderful things I listed, and I have had four hours of sleep (an...
Ah. I think this is why I'm finding physics and maths so difficult, even though my teachers said I'd find it easy. It's not just that the teachers have no incentive to make me understand, it's that because teachers aren't trained to teach understanding, when I keep asking for it, they don't know how to give it... This explains a lot of their behaviour.
Even when I've sat down one-on-one with a teacher and asked for the explanation of a piece of physics I totally haven't understood, they guy just spoke at me for five/ten minutes, without stopping to ask me if I followed that step, or even just to repeat what he'd said, and then considered the matter settled at the end without questions about how I'd followed it. The problem with my understanding was at the beginning as well, and when he stopped, he finished as if delivering the end of a speech, as though it were final. It would've been a little awkward for me to ask him to re-explain the first bit... I thought he was a bad teacher, but he's just never been incentivised to continually stop and check for understanding, after deriving the requisite equations.
And that's why my maths teacher can never answer questions that go under the s...
My first explanation was that understanding is the best way, but memorization can be more efficient in short term, especially if you expect to forget the stuff and never use it again after the exam. Some subjects probably are like this, but math famously is not. Which is why math is the most hated subject.
Another explanation was that the students probably never actually had an experience of understanding something, at least not in the school, so they literally don't understand what I was trying to do.
What do you think about these other possible explanations?
Some of these students really can't learn to prove mathematical theorems. If exams required real understanding of math, then no matter how much these students and their teachers tried, with all the pedagogical techniques we know today, they would fail the exams.
These students really have very unpleasant subjective experiences when they try to understand math, a kind of mental suffering. They are bad at math because people are generally bad at doing very unpleasant things: they only do the absolute minimum they can get away with, so they don't get enough practice to become better, and they also have trouble concentrating
if I was able to overcome this aversion and math was as fun as playing video games
Good video games are designed to be fun, that is their purpose. Math, um, not so much.
Math is a bit like liftening weights. Sitting in front of a heavy mathematical problem is challenging. The job of a good teacher isn't to remove the challenge. Math is about abstract thinking and a teacher who tries to spare his students from doing abstract thinking isn't doing it right.
Deliberate practice is mentally taxing.
The difficult thing as a teacher is to motivate the student to face the challenge whether the challenge is lifting weights or doing complicated math.
Being wrong about something feels exactly the same as being right about something.
-- many different people, most recently user chipaca on HN
He said:
When you play bridge with beginners—when you try to help them out—you give them some general rules to go by. Then they follow the rule and something goes wrong. But if you'd had their hand you wouldn't have played the thing you told them to play, because you'd have seen all the reasons the rule did not apply.
from The Last Samurai by Helen DeWitt
...“I propose we simply postpone the worrisome question of what really has a mind, about what the proper domain of the intentional stance is. Whatever the right answer to that question is—if it has a right answer—this will not jeopardize the plain fact that the intentional stance works remarkably well as a prediction method in these other areas, almost as well as it works in our daily lives as folk psychologists dealing with other people. This move of mine annoys and frustrates some philosophers, who want to blow the whistle and insist on properly settling the issue of what a mind, a belief, a desire is before taking another step. Define your terms, sir! No, I won’t. That would be premature. I want to explore first the power and the extent of application of this good trick, the intentional stance. Once we see what it is good for, and why, we can come back and ask ourselves if we still feel the need for formal, watertight definitions. My move is an instance of nibbling on a tough problem instead of trying to eat (and digest) the whole thing from the outset. “Many of the thinking tools I will be demonstrating are good at nibbling, at roughly locating a few “fixed” points that will help
Today is already the tomorrow which the bad economist yesterday urged us to ignore.
-- Henry Hazlitt, Economics in One Lesson
“If only there were irrational people somewhere, insidiously believing stupid things, and it were necessary only to separate them from the rest of us and mock them. But the line dividing rationality and irrationality cuts through the mind of every human being. And who is willing to mock a piece of his own mind?”
(With apologies to Solzhenitsyn).
– Said Achmiz, in a comment on Slate Star Codex’s post “The Cowpox of Doubt”
“Anything outside yourself, this you can see and apply your logic to it." She said. "But it’s a human trait that when we encounter personal problems, those things most deeply personal are the most difficult to bring out for our logic to scan. We tend to flounder around, blaming everything but the actual, deep-seated thing that’s really chewing on us.”
Jessica speaking to Thufir Hawat in Frank Herbert's Dune
There is an important difference between “We don’t know all the answers yet” and “Do what feels right, man.” These questions have answers, because humans have biochemistry, and we should do our best to find them and live by the results.
~J. Stanton, "The Paleo Identity Crisis: What Is The Paleo Diet, Anyway?"
Encoded in the large, highly evolved sensory and motor portions of the human brain is a billion years of experience about the nature of the world and how to survive in it. The deliberate process we call reasoning is, I believe, the thinnest veneer of human thought, effective only because it is supported by this much older and much more powerful, though usually unconscious, sensorimotor knowledge. We are all prodigious olympians in perceptual and motor areas, so good that we make the difficult look easy. Abstract thought, though, is a new trick, perhaps less than 100 thousand years old. We have not yet mastered it. It is not all that intrinsically difficult; it just seems so when we do it.
Hans Moravec, Wikipedia/Moravec's Paradox
The main lesson of thirty-five years of AI research is that the hard problems are easy and the easy problems are hard. The mental abilities of a four-year-old that we take for granted – recognizing a face, lifting a pencil, walking across a room, answering a question – in fact solve some of the hardest engineering problems ever conceived... As the new generation of intelligent devices appears, it will be the stock analysts and petrochemical engineers and parole board members who are in danger of being replaced by machines. The gardeners, receptionists, and cooks are secure in their jobs for decades to come.
Stephen Pinker, Wikipedia/Moravec's Paradox
I have long ceased to argue with people who prefer Thursday to Wednesday because it is Thursday.
On its own I can think of several things that these words might be uttered in order to express. A little search turns up a more extended form, with a claimed source:
My attitude toward progress has passed from antagonism to boredom. I have long ceased to argue with people who prefer Thursday to Wednesday because it is Thursday.
Said to be by G.K. Chesterton in the New York Times Magazine of February 11, 1923, which appears to be a real thing, but one which is not online. According to this version, he is jibing at progressivism, the adulation of the latest thing because it is newer than yesterday's latest thing.
ETA: Chesterton uses the same analogy, in rather more words, here.
If I advance the thesis that the weather on Monday was better than the weather on Tuesday (and there has not been much to choose between most Mondays and Tuesdays of late), it is no answer to tell me that the time at which I happen to say so is Tuesday evening, or possibly Wednesday morning.
It is vain for the most sanguine meteorologist to wave his arms about and cry: “Monday is past; Mondays will return no more; Tuesday and Wednesday are ours; you cannot put back the clock.” I am perfectly entitled to answer that the changing face of the clock does not alter the recorded facts of the barometer.
I think you could make a case for totalitarianism, too. During the interwar years, not only old-school aristocracy but also market democracy were in some sense seen as being doomed by history; fascism got a lot of its punch from being thought of as a viable alternative to state communism when the dominant ideologies of the pre-WWI scene were temporarily discredited. Now, of course, we tend to see fascism as right-wing, but I get the sense that that mostly has to do with the mainstream left's adoption of civil rights causes in the postwar era; at the time, it would have been seen (at least by its adherents) as a more syncretic position.
I don't think you can call WWII an unambiguous win for market democracy, but I do think that it ended up looking a lot more viable in 1946 than it did in, say, 1933.
Neoreactionaries doesn't like that sentiment that history decides what's morally right.
I am not a neoreactionary and I think the sentiment that history decides what's morally right is a remarkably silly idea.
Another month has passed and here is a new rationality quotes thread. The usual rules are:
And one new rule: