Feynman explained differential calculus in 6.2 pages, half of which was more focussed on physics, and he had plenty of time for a lengthy real world example. It's in his physics lectures, 8th one in the first book.

His explanation was about 5000x better than anything I heard in school. I conclude school is worthless. One can learn more in an hour of Feynman's lectures than a semester or two of school. Note also: schools could, but do not, use Feynman's lectures. Improvement is easily available and rejected.

(Perhaps you can find a school somewhere that does use his physics or computer science lectures. I've never heard of one, and have heard that they are generally considered unsuitable for a school course. Complaints are made about both the difficulty and the style. But both are simply superior to standard textbooks...)

I am not exaggerating this factor of 5000, though it's hard to make it a number. I was never given any *explanation* of calculus in school, despite several calculus classes (as well as some physics classes). So a more accurate number would be infinity times better. Note that I refer to both high school and university classes, and that university was no better than high school in this regard.

In school, they give you formulas for doing differentiation, and problems which you can solve using about 5 formulas you memorize. They never explained where the formulas come from, why they were invented, what they mean outside a few set examples, or how to reinvent the formulas from scratch. They made a very poor attempt to state what dx and dy mean (it's the derivative of x with respect to y). Feynman addressed that same issue much, much better.

Without explanations, memorizing is the only choice. And if you forget, you can't work it out again with pen and paper, you have to look it up. That is awful.

If you ask a teacher why they never explain it, they probably won't know what you mean or have thought about it. But once you explain yourself more, they'd probably say either that it's too hard, long and complicated to do that, or that the kids wouldn't be interested and don't need to know it.

But Feynman did it in 6 non-dense pages, so it's not too long, hard, or complicated. (Admittedly 3 or so of those pages may be dense to some people. For those people, normal math textbooks would be dense too. And anyway, 6 dense pages would be far shorter and easier than the curriculum schools use.)

As to interest, it's certainly more interesting than memorizing formulas for no reason, which the large majority of students already consider boring.

How effective can critical discussion be as the primary mode of learning more in a field once you reach the very top of the field? Once you know all the common ideas and arguments, then people who only know those common ideas and arguments can be of little use.

Or perhaps not. If you have a new idea, then the reactions of those same people to the new idea will be new to you.

But what if you are so far ahead of others in the field that their reactions to new ideas consistently contain nothing you didn't already consider? Then critical discussion wouldn't be especially useful. Is such a scenario realistic? If one was in it, should they make progress by critical discussion within their own mind? Or should they find another field to work on? Or should they teach others and help them catch up? Or should they make progress in this field by some other method?

http://www.flu.cas.cz/rethinkingpopper/description.html

Preserving the authority of reason, Popper can...

The authority of reason is a contradiction.


http://www.flu.cas.cz/rethinkingpopper/papers.html

Jarvie:

Thus an author [like Popper] may be a privileged interpreter [of his own writing] but he is not necessarily reliable, infallible, the last word, or anything like that.

Why is a Popper conference paper claiming there exist privileged sources of knowledge (sometimes)?


Boyer:

Popper was essentially right about verification and passive induction : the former is inaccessible, outside formal sciences, and the latter is a myth

Why is a Popperian conference paper saying verification is possible (sometimes), and claiming further that that was Popper's view?

And we should certainly prefer the hypothesis that resists to our best criticisms better than the others do.

Why does he think we have a way to judge how good a theory is? And on a continuum, it sounds like. Popper offered no such technique.

What Popper offered is the idea that we can reject theories with even one false consequence. There's no continuum of falsity, they are just false, end of story. If criticism leaves us with exactly one remaining theory, then we should tentatively adopt it.

BTW that may sound implausible or unlikely to happen to have exactly one viable theory at some time. It isn't because there are techniques for ending up with exactly one theory, though I don't recall Popper ever explaining them.


Udell:

Moreover, it is Popper, not Rawls, who identifies and emphasizes the connection between justice and full employment.

I don't remember reading that and it has no citation. Can anyone provide a cite?

Rawls’s method reflects his recognition that a strong moral conviction about a particular action or institution—e.g., slavery, sexism—may override the appeal of an otherwise appealing moral principle

What does it mean for an idea to override an idea? Either it refutes it, or it doesn't. I think this concept is incoherent.

Popper the first anti-foundationalist philosopher in the analytic tradition

But Popper was not an analytic philosopher. He criticized analytic philosophy.


Verhofstadt:

This paper begins by explaining liberalism. However, it never mentions tradition (except negatively in passing). I would summarize the liberal attitude as about optimistic reform of existing knowledge (traditions), and contrast it with conservatism (keeping traditions unchanged) and radicalism or utopianism (which does not value tradition and try to reform it, but instead ignores it and is happy to start from scratch). When a supposed liberal has nothing good to say about tradition, I fear he is actually a radical. Popper himself certainly had good things to say about tradition, and a Popperian should know that.

The paper focusses more on liberalism as being about freedom, individualism, justice, and humanitarianism. But many conservatives and radicals are in favor of all of those things. So how can they be the defining characteristics of liberalism? Further, many liberals accept restrictions on freedom and the other things. This paper approvingly points out that Popper accepts restrictions on freedom later.

neoliberals and libertarians consider free market as a kind of scientific certainty

One can adopt fallibilism and be a free market libertarian, like me. The paper contains no argument that one cannot, just this alienating assertion.

The paper goes on to attack religion. I don't think it's a good idea for a Popper conference paper — and ironically one about liberalism, which is supposed to advocate tolerance — to be intolerant of views held by many Popperians. It'd be better to focus on things agreeable to Popperians.

A better, more Popperian way to criticize libertarianism or religion would be to consider what problem they are trying to solve, what they get right, what they get wrong, and how they can be improved, instead of being hostile to them. It is unliberal to be hostile to fellow liberals instead of trying to work together.


Swann:

Popperian Selectionism and Its Implications for Education, or ‘What to Do About the Myth of Learning by Instruction from Without?’

That's the title.

Although Popper was vehemently opposed to the discussion of words and their meaning (Popper, 1992[1974], § 7), my experience in talking about learning with educationists has led me to accompany any exposition of a Popperian view of learning with what I term an evolutionary definition. I propose that learning is best defined as

Swann acknowledges doing something Popper was "vehemently opposed to". She spends four consecutive paragraphs doing it. The only reason for opposing Popper that she provides is an appeal to experience which she claims "led" her. But experience does not lead people: that is the myth of instruction from without, the very myth her paper criticizes.

The process itself is not entirely conscious, so you will not be aware of more than a few aspects of it.

It does not follow from a claim that X is not entirely Y that little of X is Y.

A criticism, even if valid, may be inappropriate if ultimately it serves to stifle creativity and inhibit further trial and error-elimination

How does critically seeking the truth stifle truth seeking?

What is at issue here is a choice between two competing theories. One proposes that ‘No learning takes place by instruction from without’, the other that ‘Some learning takes place by instruction from without’. Although both theories are about events in the world, neither has the potential to be refuted by reference to empirical evidence.

Although we don't know how to test the theories today, surely we will in the future. They are theories about the mechanisms by which some physical objects function. Why would that be impossible to test by observing those physical objects?

The function of the brain is to select and create; it has no means of taking in information

The Popperian position is the brain cannot directly take in knowledge. Of course it does take in information through the senses. But that information is not useful until it is processed and interpreted. I am at a loss as to how someone can think the brain does not take in any information at all. The paper does not include any arguments for this proposition, though there is a cite.

Deutsch, Popper, and Feynman aren't inductivists. I could add more people to this list, like me. So here we see a clear pattern of people not being inductivists. There's a bunch of data points with a certain thing in common (a person not being inductivist). Let's apply induction to this pattern. So we extrapolate the general trend: induction leads us to conclude against induction. Oh no, a contradiction! I guess we'll have to throw out induction.

Q&A:

Q: Your data set is incomplete.
A: All data sets are incomplete.

Q: Your data set isn't random.
A: No data sets are entirely random.

Q: I have an explanation of why your method of selecting data points leads to a misleading result.
A: That's nice. I like explanations.

Q: Don't you care that I have a criticism of your argument?
A: I said we should throw out induction. As you may know, I think we should use an explanation-focussed approach. I took your claim to have an explanation, and lack of claim to have induced anything, as agreement.

Q: But how am I supposed to object to your argument using only induction? Induction isn't a tool for criticizing invalid uses of induction.
A: So you're saying induction cannot tell us which inductions are true or false. We need explanation to do that. So induction is useless without explanation, but explanation is not useless without induction.

Q: That doesn't prove induction is useless.
A: Have you ever thought about how much of the work, in a supposed induction, is done by induction, and how much by explanation?

Q: No.
A: Try it sometime.

http://footmenfrenzy.blogspot.com/2009/06/castle-fight-strategies-guide-to-rally.html

I wrote that guide. It looks like this blog has nothing but copied material.

These are my comments on The Comprachicos, an essay by Ayn Rand found in http://www.amazon.com/New-Left-Anti-Industrial-Revolution/dp/0452011256

This will make a lot more sense if you read it first. It is not a summary, and it leaves out a lot of good ieas from the essay.

I agree with Rand's pro-children attitude, as opposed to the usual more hateful one. Rand says young children should start learning abstract ideas, and I agree with her.

I agree with her criticisms of "the pack" and conformity and collectivism, and her view that the "problem children" often have the best chance to get through school with their reason in tact.

I agree with many of her specific examples about how some methods of teaching are nonsense, or contradict the educational philosophy the teachers claim to follow. I disagree with her apparent assumption that most of the effects and meaning of teaching methods can be discerned by looking at them and reasoning about them. I think that the bulk of what's done to kids is more subtle than that. And I think kids are resilient and such blatant methods, alone, are not enough to have the affects schools do have.

Rand only mentions parents briefly. She says mistakes of this size aren't made innocently. I don't agree with that logic. I do agree with her assessment that many parents want to get their kids out of their hair, and don't think carefully about what sort of place they are sending their kids, and also don't have thoughtful, rational discussions with their kids.

Rand takes a fairly nature oriented position on some aspects of the nature/nurture debate. She does talk a lot about how education matters, but she also seems to think being more or less intelligent is innate.

Rand sometimes appeals to "the evidence" or "scientific research" but fails to cite it or explain what research was done and how it is capable of reaching the conclusion it reaches. This is scientism, but it's mild and she provides arguments for all her conclusions.

Rand overestimates how much teachers hurt children *intentionally*. She thinks they somewhat plan for it. Alright, some do, but they don't actually know how to plan for things and then make them happen, so their planning hardly matters. Rand makes a comment that if they cared about the children they'd notice certain policies are harming children and stop or revise them, and concludes they don't care about children's well being. I disagree with that. I don't think they know how to evaluate what works and what doesn't. Doing that takes skill which they don't have. They have no idea if they are doing harm or not. I don't want to absolve them of all guilt, or even any guilt -- they do see crying children, and they definitely know that many children dislike much of what they do -- but let's not assume they know, plan, or intend more than they do. They are clueless and helpless, and have a mix of callous disregard; superficial, tender love and caring; some meanness; and for many teachers, especially the younger ones, only occasional hatred of the children. Many teachers have given up and don't think about what they are doing.

Rand says schools and culture used to be better and more rational, and the comprachicos only gained control quite recently, and the current educators had a better education themselves. I disagree. Rand doesn't go into detail here. It's true that schools have changed in some ways, and their explicit rhetoric has changed, but I see no reason to think their basic effect has changed. Perhaps Rand is going too much on the schools' explicit messages. If anything, school has gotten better. People are smarter now, and more capable; we can tell because they deal with more complex lives, have more possessions which are more complicated (like computers), there are more knowledge workers, and GDP per capita is much higher. And schools have had reforms, e.g. with corporal punishment. And we now have more and better sources of information (TV, internet, more books, etc).

Rand does a good job of emphasizing how much of a child's learning is inexplicit, and how much of what is taught is inexplicit (for example, she discusses the emotional vibe of the pack). And I agree with her comments on whim.

I agree with Rand's mentions of the *boredom* of school.

I agree with Rand that the primary way to do well in the pack is to learn to manipulate human beings, and this is disgusting, and not something an individualist would want to do. I agree that "socializing" and "fitting in" are wicked.

I liked Rand's comment that non-conformist children have *no one* on their side. Not even themselves, because they don't have much understanding of the nature of their battle. However, she's slightly mistaken: they have Rand on their side! She does indeed sympathize with them. Good for her. And I do too.

I don't agree with Rand's assumption about the developmental status of children being very strongly tied to age. She even mentions that is false at one point by saying children of the same age and intelligence can be at significantly different levels of development if one is educated well and the other isn't. Yet she still refers to what three year olds need, what five year olds need, and so on. (And it's not even clear if these age numbers refer to normal children or properly educated children.)

I generally agree with Rand's comments about how people automate large parts of their thinking. For example, Rand says you have to learn to focus your eyes, or to coordinate your muscles to walk. And this isn't obvious or trivial. Rand says we learn a huge amount in our first two years, and if any adult could learn as much, as quickly, or as well he'd be a genius. But adults have automated the process so much it seems easy.

I agree with Rand that fakers -- for example people who pretend to agree with the pack when they don't -- often become fakers by habit, and then live that way without thinking, and it becomes a major part of them, and the "real" self gets lost and forgotten.

Perhaps my favorite part is on page 197:

At the age of three, when his mind is almost as plastic as his bones, when his need and desire to know are more intense than they will ever be again, a child is delivered -- by a Progressive nursery school -- into the midst of a pack of children as helplessly ignorant as himself. He is not merely left without cognitive guidance -- he is actively discouraged and prevented from pursuing cognitive tasks. He wants to learn; he is told to play. Why? No answer is given. He is made to understand -- by the emotional vibrations permeating the atmosphere of the place, by every crude or subtle means available to the adults whom he cannot understand -- that the most important thing in this peculiar world is not to know, but to get along with the pack. Why? No answer is given.

He does not know what to do; he is told to do anything he feels like. He picks up a toy; it is snatched away from him by another child; he is told that he must learn to share. Why? No answer is given. He sits alone in a corner; he is told that he must join the others. Why? No answer is given. He approaches a group, reaches for their toys and is punched in the nose. He cries, in angry bewilderment; the teacher throws her arms around him and gushes that she loves him.

I like the "Why? No answer is given." theme.

I think Rand's comment that loneliness is only for people who have something of value to share, but can't find any equals to share it with, is insightful. She says the emotion that drives conformists to "belong" is fear. I'm not so sure about that. I think fear plays a role, but there are many other issues, such as not knowing what else to do, and thinking non-conformity is morally wrong.

Rand hates: Kant, John Dewey, Marcuse, Hegel, Logical Positivism, and Language Analysis.

Popper/Feynman/fallibilists/etc: Mistakes are very easy to make. In addition to imaginative conjectures, we need relentless criticism. If we don't have that criticism, we'll constantly be fooled by mistakes.

Others: Stop dismissing everything so easily. It's good enough. No one is going to be fooled unless they are an idiot. Imagination is more important than criticism. And anyway, the way to avoid mistakes is this: proven or supported ideas are not mistakes.

Here are some formulations of the "problem of consciousness" from Wikipedia with comments:

http://en.wikipedia.org/wiki/Hard_problem_of_consciousness

"Why should physical processing give rise to a rich inner life at all?"

What do you mean by a "rich inner life"? And why shouldn't it?

"How is it that some organisms are subjects of experience?"

Snails get to be subjects of experience by crawling near humans.

I think they meant to say something else. But it's not very clear what.

"Why does awareness of sensory information exist at all?"

This assumes there is "awareness of sensory information". That is a bad place to start for the problem of consciousness!

It doesn't make any sense to assume X exists and then get stuck on saying X is. If you can't say what X is, then you should reconsider whether it exists in the way you think it does.

This shouldn't be a *why* question. A *what* question would be better. But it shouldn't be "What is [some string of letters]?" It should give some specific facts or evidence or something and present some problem with them. Which this doesn't.

"Why do qualia exist?"

Assumes qualia exist and that we know what they are. Bad starting point.

"Why is there a subjective component to experience?"

Assumes there is a subjective component. Doesn't say what that is.

"Why aren't we philosophical zombies?"

Why aren't we rocks? Or snails?

Better question: how do we learn? How can we do philosophy?

"Phenomenal Natures are categorically different from behavior"

That's not a question, it's a very vague assertion.


I'm not saying there is no such thing as a legitimate problem that could be called "the problem of consciousness". But the people pursuing *these* questions A) don't know what the problem is and B) aren't doing anything to solve it.