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)

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.

• Alan Sokal, What Is Science

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.

- Paul Krugman

"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

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.

http://www.reddit.com/r/askscience/comments/e3yjg/is_there_any_way_to_improve_intelligence_or_are/c153p8w

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

Being wrong about something feels exactly the same as being right about something.

-- many different people, most recently user chipaca on HN

“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

“Even if it's not your fault, it's your responsibility.”

• Terry Pratchett, A Hat Full of Sky

“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”

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?"