Knowledge Quality

Some people read secondary sources or worse. Others read primary sources. And others read both.

Some people read one book on a topic and assume it is true. Others read ten and compare their stories.

Some people have high standards for what they will accept as scientific evidence, and others low. Some people read newspaper articles about studies. Some read the actual studies. Some just read the conclusions and say science has supported those conclusions. Others evaluate whether a coherent explanation has been presented, and whether the evidence is sufficient for the conclusion.

Some people look for authorities to get knowledge from. Others use their own judgment.

People who could be taken as authorities themselves have varying standards that they subject their own knowledge, and publications, to.

Some people are easily fooled (not that anyone is doing it on purpose). Some make it their mission in life to find truths and avoid being fooled.

Some people think mistakes and rare and don't worry about them very much. Others think mistakes and common and are always vigilant against them.

Some people select, say, a Burke biography based on the dust jackets. Others read 2 chapters from each candidate book to judge the quality for themselves, then read the one with the best author. And some other people insist on reading all the books, even the bad ones, in case they contain a useful tidbit or an astute argument.

Suppose Bob has the highest standards in every regard mentioned and many others, with regard to some topic he likes, say Xenophanes. All his knowledge has about Xenophanes gone through extensive criticism and vetting. He has never assumed that some author correctly read the primary sources; he always reads them himself to check. When he reads a statement saying, "On the issue of X, the best analysis was done by Sarah Parker. And she concluded Y." he is suspicious. That statement does not contain any arguments he can judge. He'll have to read Parker's book or disregard it. Bob is always wondering how an author knows what he claims to know, and whether anyone involved could have made a mistake (the author, a translator, Xenophanes' contemporaries who provided commentary and quotes about him, the editor who must have made at least a few edits the author wasn't pleased with, etc). Bob always compares quotes with the author's statement of what the quote means and decides if he thinks that's accurate. If he's not sure, he won't take the author's word for it. If the author doesn't give enough quotes to allow a comparison so Bob can judge if the author is interpreting the material correctly, then Bob becomes suspicious and guarded.

One day Bob meets Joe and they get into a discussion about Xenophanes. Joe is different than Bob. He only reads primary sources when they are quoted in secondary sources. When an author unequivocally states that X is true, Joe believes X to be true. When an author cites an authority as saying Y is true, Joe figures if it was good enough for the author it's good enough for him too. Joe knows he's not a world class expert. His knowledge is pretty good, and pretty reliable, but better is possible. But better isn't needed; it's good enough; it's reliable; it's accurate; it's genuine knowledge gleaned from serious study. He's looked into things in as much depth as he could, given the other things in his life, and it's a lot more than most people do. Joe knows not to trust everything he reads on the internet, but books are different and more reliable, especially the ones by PhDs. They do some of the work for Joe, and Joe can reasonably accept the help in his own truth seeking. That's what Joe believes.

Bob and Joe debate some issues about Xenophanes. Bob says what he knows on some subject, and Joe says what he knows. It contradicts. Both give their summaries of their recollection of some supporting evidence. Neither convinces the other. Both find the other says things they are quite sure are false based on their existing knowledge.

Bob sees what's going on. He remembers some of the books Joe refers to, and the flaws in them. He tries to say that he's read those books, as well as others. Joe says, "Don't ask me to accept your story on authority. Just because you read more books doesn't mean you're right." Bob pulls out a laptop and finds excerpts from one of the books. He shows Joe some internal contradictions, and then finds another source with a better take on the matter, shows Joe, and notes it does not have any internal contradictions that he can see. Joe says, "Look, I've read several books, and they back up this one. Maybe it made a mistake in this one area. Maybe you remember all the details better than me. That doesn't mean I'm wrong. It's not like you are a world class expert; these authors know more than you, and they sometimes contradict each other. I'm not just going to take your word for stuff. And you say this new source you offer doesn't have mistakes like mine does, but I haven't read it and checked it, and I'll bet I could find some criticisms of it if I googled around."

Bob starts to despair. Joe has no knowledge of sufficient quality for Bob to find it useful; Joe has nothing to offer. Joe doesn't have the appropriate attitudes to create knowledge of the same quality Bob is interested in discussing. And anyway, at low precision, who's to say which side is correct? If you simply ignore all the difficult details, and ignore whether theories can survive the harshest criticisms possible, you can make a perfectly good case for many different views. If you don't ask whether explanations solve the most hardest problems around, and accept ones that simply solve some subset of the easier problems, then you lose the power to differentiate between very good ideas and mediocre ones.

Bob has an idea. He tells Joe about standards of truth seeking and quality of knowledge. He tries to explain that Joe's method of approaching the subject isn't rigorous enough to find the truth. Joe says, "You're holding knowledge up to an impossible standard. No one lives up to this idealized version of truth seeking you speak of. You're giving a generic argument for rejecting the vast majority of existing human knowledge. You're finding tiny faults and then trashing whole enterprises."

Bob says, "It's not an impossible standard. I live up to it. And so do some of the authors I've read. Karl Popper's analysis of Xenophanes, for example, lives up to this standard. I can give you a list of the best authors if you'd like."

Joe says, "I've read about that Popper fellow. High standards? Hardly. His Plato scholarship is very questionable. Maybe he has his merits, but he's no perfect angel. And as to you, I'll overlook your arrogance, but I won't accept that you're some super genius authority without a bit more proof."

Bob says, "What sort of proof would you accept?"

Joe thinks for a while and says, "I guess I'll know it when I see it. Persuade me."

Bob says, "Yes, but how?"

Joe says, "Well, you're the genius. You tell me."

Bob says, "I've told you. You need to consider my statements, and everyone else's, according to this higher more rigorous standard. If you do that, you'll see that mine live up to it. Many of the things you think you know do not live up to it. Please drop your bias in favor of your existing knowledge and open your mind and try to learn. It's hard, but by an effort we can make progress."

Joe says, "Putting down all my existing efforts to learn things isn't friendly or persuasive. And I'm not going to make this huge effort to do as you ask before you've convinced me it's worth doing."

Bob says, "How can I convince you it's worth doing when your standard of judging ideas is wrong, so you can't tell what is worthwhile or not?"

Joe says, "Oh come on. I may not be perfect, but I'm not that bad."

Bob says, "It's not up to you to decide what is too bad, and what is an acceptable level of badness that won't hurt anything. It's not a human choice what is and isn't required to find the truth and correct errors."

Joe says, "Yes, I understand that. But my standards are pretty high. That aren't low. I accept truth finding is hard, and I make a serious effort."

Bob says, "Your standards are low enough you won't listen."

Joe says, "Disagreeing isn't failure to listen. I've been insulted for the last time. Goodbye."

Elliot Temple | Permalink | Messages (0)

Is it better to do or receive injustice?

Socrates said it is worse to commit an injustice than be the victim of one. A lot of people wonder how this could possibly be true.

Let's take an example. I live in communist Russia and am accused of a crime I didn't commit. Assume the only options available to me are to be wrongly convicted, or lie and have my friend wrongly convicted instead. This is not an entirely realistic scenario -- in real life one has more options; perhaps in real life my friend and I could both escape to America -- but the slant does not help my defense of Socrates, so it's fine.

Some people proceed to measure the result by years spent in the gulag, and conclude that betraying my friend is clearly better, so Socrates' view is not just wrong but blatantly ridiculous.

But Socrates is commenting on morality, and morality isn't measured in prison years. Prison years are relevant, but also an incomplete metric.

If I am wrongly convicted, I have nothing to feel bad about. I am guilty of no sin and I have nothing to be ashamed of. Just as if a meteor struck and killed me. Such things can happen, but they don't detract from one's life morally. They aren't your fault, they aren't preventable, and they have little bearing on the question, "How should I live?" or "What sort of lifestyle is effective and virtuous?" Because they are unpreventable and random, one can't factor them into any decision making.

Similarly, if I lie and my friend is wrongly convicted, he has nothing to feel bad about. He remains morally pristine. He lived his life as well as he could. No better was available to him.

But if I lie, my own situation is not like that. Now I stay up at nights pondering my guilt. I have a secret shame to hide from my friends and family. I sinned, and I know it; how can I live with that? How can I face another day when I've intentionally done something I consider very bad? It's harder to face myself in this situation than if I am in the gulag through no fault of my own.

One might object that only certain people would feel guilty; others wouldn't care; don't those people, in one way bad people, seem to have the advantage here? But being that kind of person has consequences for one's entire life. It may be convenient as it seems in a limited, artificial situation, but as a lifestyle that has to work in a wide variety of situations, it fairs poorly. Who would want to associate with a man with no conscience? Who would befriend a person who, as a general policy, will betray his friends? And this man of no conscious cannot be much of a philosopher, or he would learn better. He lives an unexamined life; Socrates tells us the unexamined life is not worth living, with good reason.

Which is the better option is still open to debate, but Socrates' position can't be lightly dismissed.

We can take this analysis further by considering the TCS idea of coercion, which is the only kind of suffering. This analysis is very simple. Lying to convict your friend, while wanting not to betray your friend, is coercion. You or your friend being jailed, through no fault of your own, need not be, though it may be. The just life is better because it has the possibility of being non-coercive, whereas the unjust life does not.

As a further issue, how to live a good life is not primarily about what to do in specific, extreme situations. It's primarily about creating a way of life to handle many situations. So a better question is: suppose I fear I may be arrested by the KGB? What are my general plans for how to handle that? Am I really going to plan that whenever I am arrested, for whatever reason, I'll betray my friends and get out of it? Will that even work? My friends might be arrested too, or the KGB might not want to make deals, or might not keep them. Natan Sharansky's way of dealing with it, as described in his book Fear No evil, was a better plan than betraying one's friends, not just for his friends but also for himself.

Elliot Temple | Permalink | Messages (0)

Herakleitos and Diogenes

Herakleitos and Diogenes by Guy Davenport is a book of fragments translated into English. Here are some I found interesting, Heraclitus first:
5 Our understanding of the greatest matters will never be complete.
Fallibilism :-)
13 Eyes and ears are poor informers to the barbarian mind.
Possibly a statement about fallibilism of the senses. But could also be racism against non-Greeks.
55 The stupid are deaf to the truth: they hear, but think that the wisdom of a perception always applies to someone else.
I run into that frequently.
57 Many people learn nothing from what they see and experience, nor do they understand what they hear explained, but imagine they have.
One meaning of this statement is that communication is fallible even when everyone involved believes the communication has been successful.
80 All men think.
I wonder why this has been preserved. Why did anyone find it worth quoting and saving? Was it controversial statement of equality (contrary to the possible racism above)?


6 It is absurd to bring back a runaway slave. If the slave can survive without a master, is it not awful to admit that the master cannot live without the slave?
An interesting perspective.
10 Of what use is a philosopher who doesn't hurt anybody's feelings?
A nice statement in favor of criticism.
23 It is luckier to be a Megarian's ram than his son.
From other fragments, I believe he means because the ram is fed and has an easy life, while the son is made to work hard. Though he could simply mean that parents are harsh.
42 There is no stick hard enough to drive me away from a man from whom I can learn something.
A good attitude which remains rare today. (Don't assume you are an exception. See Heraclitus 55.)
43 Eukleidos' lectures limp and sprawl, Plato's are tedious, tragedies are quarrels before an audience, and politicians are magnified butlers.
Plato gives bad lectures, Diogenes tells us.
48 Beg a cup of wine from Plato and he will send you a whole jar. He does not give as he is asked, nor answer as he is questioned.
To properly engage in reasoned debate with people who disagree, one must be willing to answer their questions clearly. Diogenes says Plato wouldn't do that.
49 Share a dish of dried figs with Plato and he will take them all.
I don't know ancient Greek etiquette, but I think this is saying Plato had bad character.
59 When some strangers to Athens asked me to show them Demosthenes, I gave them the finger, so that they would know what it felt like to meet him.
I wonder why Diogenes didn't like Demosthenes. Unlike with Plato, no specific grievance is given.
92 What lovers really enjoy are their spats and the disapproval of society.
This has some truth today as well. Without fights and controversy, some couples would grow bored. And don't forget Heraclitus 55.
99 Why not whip the teacher when the pupil misbehaves?
A wise comment. Why, indeed, are students blamed rather than teachers, or the pair together? The teacher is the responsible adult, and the leader, whereas the child's ideas are suppressed, so shouldn't the teacher bear primary responsibility for the outcome of a conventional education?
107 Make passes as you, do they? Why, then, don't you wear clothes that don't so accurately outline what they're interested in?
It's interesting that the same style of dressing sexually but denying having done so existed way back then.
109 I've seen Plato's cups and table, but not his cupness and tableness.
A criticism of Plato's Forms for their abstract nature and lack of evidence.

Elliot Temple | Permalink | Messages (2)

Democritus Book Quotes

Democritus by Paul Cartledge, p 6-7:
it is thanks chiefly to Plato that the scientists and philosophers known collectively as the Presocratics, of whom Democritus was the last, have almost without exception not survived to address us in their own right. For it was a major part of Plato's purpose, showing himself in this respect at any rate fully representative of the agonistic or competitive character of all ancient Greek intellection, to put out of court and drive from the market all earlier philosophers apart from Socrates — or at any rate his representation of 'Socrates'. This aim he achieved with near-total success.
That is very interesting. Some people assume we don't have more older books because they decayed. But which ones were preserved is not random and calls out for explanation.

This is quoting Democritus on page 24:
Nature and teaching are closely related; for teaching reforms a person, and by reforming remakes his nature.
The idea that nature can be changed is one of the major things missing from the current nature/nurture debate that assumes traits due to nature are permanent but traits due to nurture can be changed.

One more quote of Democritus from page 32:
Even when you are alone, neither say nor do anything bad: learn to feel shame before yourself rather than before others.
Here he anticipates Feynman's advice not to orient your life around what other people think, and connects it to morality.

Elliot Temple | Permalink | Messages (0)

Aristotle on Induction

How did induction get started? Where did it come from? What was it like, then? Here is the original argument that has, apparently, impressed the world. It's by Aristotle.
It is clear then how the terms are related in conversion, and in respect
of being in a higher degree objects of aversion or of desire. We must
now state that not only dialectical and demonstrative syllogisms are
formed by means of the aforesaid figures, but also rhetorical syllogisms
and in general any form of persuasion, however it may be presented.
For every belief comes either through syllogism or from induction.

Now induction, or rather the syllogism which springs out of induction,
consists in establishing syllogistically a relation between one extreme
and the middle by means of the other extreme, e.g. if B is the middle
term between A and C, it consists in proving through C that A belongs
to B. For this is the manner in which we make inductions. For example
let A stand for long-lived, B for bileless, and C for the particular
long-lived animals, e.g. man, horse, mule. A then belongs to the whole
of C: for whatever is bileless is long-lived. But B also ('not possessing
bile') belongs to all C. If then C is convertible with B, and the
middle term is not wider in extension, it is necessary that A should
belong to B. For it has already been proved that if two things belong
to the same thing, and the extreme is convertible with one of them,
then the other predicate will belong to the predicate that is converted.
But we must apprehend C as made up of all the particulars. For induction
proceeds through an enumeration of all the cases.

Such is the syllogism which establishes the first and immediate premiss:
for where there is a middle term the syllogism proceeds through the
middle term; when there is no middle term, through induction. And
in a way induction is opposed to syllogism: for the latter proves
the major term to belong to the third term by means of the middle,
the former proves the major to belong to the middle by means of the
third. In the order of nature, syllogism through the middle term is
prior and better known, but syllogism through induction is clearer
to us.

We have an 'example' when the major term is proved to belong to the
middle by means of a term which resembles the third. It ought to be
known both that the middle belongs to the third term, and that the
first belongs to that which resembles the third. For example let A
be evil, B making war against neighbours, C Athenians against Thebans,
D Thebans against Phocians. If then we wish to prove that to fight
with the Thebans is an evil, we must assume that to fight against
neighbours is an evil. Evidence of this is obtained from similar cases,
e.g. that the war against the Phocians was an evil to the Thebans.
Since then to fight against neighbours is an evil, and to fight against
the Thebans is to fight against neighbours, it is clear that to fight
against the Thebans is an evil. Now it is clear that B belongs to
C and to D (for both are cases of making war upon one's neighbours)
and that A belongs to D (for the war against the Phocians did not
turn out well for the Thebans): but that A belongs to B will be proved
through D. Similarly if the belief in the relation of the middle term
to the extreme should be produced by several similar cases. Clearly
then to argue by example is neither like reasoning from part to whole,
nor like reasoning from whole to part, but rather reasoning from part
to part, when both particulars are subordinate to the same term, and
one of them is known. It differs from induction, because induction
starting from all the particular cases proves (as we saw) that the
major term belongs to the middle, and does not apply the syllogistic
conclusion to the minor term, whereas argument by example does make
this application and does not draw its proof from all the particular
Notice how he says induction differs than argument by example because in induction one starts from every possible particular case, not just a limited set of examples. But when does anyone analyze every possible case? There are unlimited cases to consider. So no one performs induction up to the standard Aristotle sees is necessary for it to work.

Aristotle wasn't very consistent or clear about what induction is. He mentions in frequently. That passage was the closest thing I could find to an attempt to explain it.

Here's another mention:
Knowledge of the fact differs from knowledge of the reasoned fact.
To begin with, they differ within the same science and in two ways:
(1) when the premisses of the syllogism are not immediate (for then
the proximate cause is not contained in them-a necessary condition
of knowledge of the reasoned fact): (2) when the premisses are immediate,
but instead of the cause the better known of the two reciprocals is
taken as the middle; for of two reciprocally predicable terms the
one which is not the cause may quite easily be the better known and
so become the middle term of the demonstration. Thus (2, a) you might
prove as follows that the planets are near because they do not twinkle:
let C be the planets, B not twinkling, A proximity. Then B is predicable
of C; for the planets do not twinkle. But A is also predicable of
B, since that which does not twinkle is near--we must take this truth
as having been reached by induction or sense-perception.
What is he talking about? We know that things which are near don't twinkle via induction or sense perception? No we don't. Near things can twinkle. And even if we didn't have any modern flashing lights or paintings of Santa's eyes, there's no way to perceive that nothing that is near could ever twinkle. And if it could have been induced in Aristotle's time, as he seems to claim, that would prove that induction can reach false conclusions, since near things can and do twinkle sometimes.

Here's a relevant passage:
It is also clear that the loss of any one of the senses entails the
loss of a corresponding portion of knowledge, and that, since we learn
either by induction or by demonstration, this knowledge cannot be
acquired. Thus demonstration develops from universals, induction from
particulars; but since it is possible to familiarize the pupil with
even the so-called mathematical abstractions only through induction-i.e.
only because each subject genus possesses, in virtue of a determinate
mathematical character, certain properties which can be treated as
separate even though they do not exist in isolation-it is consequently
impossible to come to grasp universals except through induction. But
induction is impossible for those who have not sense-perception. For
it is sense-perception alone which is adequate for grasping the particulars:
they cannot be objects of scientific knowledge, because neither can
universals give us knowledge of them without induction, nor can we
get it through induction without sense-perception.
It tells us induction requires sense-perception for input, but that's about it.

In this next passage, as I read it, Aristotle says that induction is fallbile:
Nor, as was said in my formal logic, is the method of division a process
of inference at all, since at no point does the characterization of
the subject follow necessarily from the premising of certain other
facts: division demonstrates as little as does induction. For in a
genuine demonstration the conclusion must not be put as a question
nor depend on a concession, but must follow necessarily from its premisses,
even if the respondent deny it. The definer asks 'Is man animal or
inanimate?' and then assumes-he has not inferred-that man is animal.
Next, when presented with an exhaustive division of animal into terrestrial
and aquatic, he assumes that man is terrestrial. Moreover, that man
is the complete formula, terrestrial-animal, does not follow necessarily
from the premisses: this too is an assumption, and equally an assumption
whether the division comprises many differentiae or few. (Indeed as
this method of division is used by those who proceed by it, even truths
that can be inferred actually fail to appear as such.) For why should
not the whole of this formula be true of man, and yet not exhibit
his essential nature or definable form? Again, what guarantee is there
against an unessential addition, or against the omission of the final
or of an intermediate determinant of the substantial being?
Next, here's Aristotle commenting on a limit of induction. Aristotle says induction can only tell us whether a thing has some attribute or not.
may not proceed as by induction to establish a universal on the evidence
of groups of particulars which offer no exception, because induction
proves not what the essential nature of a thing is but that it has
or has not some attribute. Therefore, since presumably one cannot
prove essential nature by an appeal to sense perception or by pointing
with the finger, what other method remains?
Here's a final passage. In it Aristotle says that scientific knowledge is the truest type of knowledge, except for one superior type: intuition.
Thus it is clear that we must get to know the primary premisses by
induction; for the method by which even sense-perception implants
the universal is inductive. Now of the thinking states by which we
grasp truth, some are unfailingly true, others admit of error-opinion,
for instance, and calculation, whereas scientific knowing and intuition
are always true: further, no other kind of thought except intuition
is more accurate than scientific knowledge, whereas primary premisses
are more knowable than demonstrations, and all scientific knowledge
is discursive. From these considerations it follows that there will
be no scientific knowledge of the primary premisses, and since except
intuition nothing can be truer than scientific knowledge, it will
be intuition that apprehends the primary premisses
Perhaps I've searched the wrong books. If anyone knows another passage, let me know.

Elliot Temple | Permalink | Messages (0)

Example of Several Flaws in Courtship

In Hannah Montana: The Movie, Miley and a boy begin to date. He likes her; she likes him. He tries to confess his feelings on their first date, but circumstances intervene. She's busy; she leaves.

Soon he discovers why she left. It had to do with a momentous, life-changing secret of hers, which had nothing whatsoever to do with him. He, on the spot, dumps her for not being honest with him. She pleads with him, and says she can explain, but he says no and leaves. She accepts this as a reasonable reaction on his part, cries, and blames herself.

They get back together a few days later after she makes a large personal gesture and then also a huge change in her life in public as a method of apologizing and asking him for a second chance. The change was something he didn't know her well enough to ask for, there were no indications he actually wanted it and there was no reason for him to want it.

Notice anything wrong with this?

Confessing your feelings is a way of life involving independently creating feelings for each other, instead of gradually creating them together, and then having one conversation that instantly changes everything (possibly for the worse -- it's risky).

Dumping her amounted to giving up on their relationship when facing their very first problem, before trying to solve it. What sort of relationship can be conditional on no unexpected and unwanted problems ever occurring? Why doesn't he want to attempt problem solving?

One moment he's falling in love with her; the next he's ignoring her pleas and leaving her crying. What is his love worth if it's so fickle? What is he worth, if he's at any moment ready to hurt her if she does something he disapproves of too much? Why doesn't it occur to him to react by helping her improve?

They get back together without figuring out how to avoid any of their prior problems first. She doesn't seek any assurance he won't dump her again (without even trying to fix anything). He never apologizes. He doesn't seek any assurance she won't keep secrets again. She doesn't promise not to. She doesn't explain how she learned something new and has changed her mind. She simply concedes the one point he has made their relationship conditional on and he's satisfied; it's closer to extortion than persuasion.

She cries and considers that normal and doesn't seek a way of life without crying and pain, nor think seriously about how to prevent a recurrence.

When he dumps her, she considers it legitimate too. She agrees with the scheme of things where people callously dump their loved one and leave her crying without even giving her a chance to explain what happened.

Both of them blame the victim. She gets dumped and hurt, and she gets blamed for her own pain. He could have prevented it if only he wanted to, but no one blames him for choosing not to prevent her suffering.

Elliot Temple | Permalink | Message (1)

Why School Is Worthless

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.

Elliot Temple | Permalink | Messages (9)

Limits of Critical Discussion?

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?

Elliot Temple | Permalink | Messages (9)