Sunday, March 31, 2013

Why curious children become scared adults


Monte Floyd Hancock Jr. said:
I like children; I find that I can be myself around them without having to worry about offending someone by "talking over their heads". Nothing is over a little kid's head! Heck, you can talk with little guys about Reimann surfaces, quotient topologies, simplicial homology, Stieltjes Integrals, Borel Fields, Banach spaces... and they will have something to say about every one of them. They aren't worried about what you think; they are telling you what they think, and you can do whatever you want with it... what's wrong with that?
 Sometimes at church I go into the 18-24 month classroom and sit down on the floor with my research notebook. The little guys come running over because they want to write in my book. I carry ink pens that "click"... it's a miracle! It "clicks", and then it makes marks! Or, I'll spin blocks on their corners, or balance things in unusual ways; they are amazed by everything, because everything is NEW...
...not at all like my grad students. When I walk into my classroom on the first day of a new term, I can see and smell the fear. Why? Because the students have been beaten down by years of small-minded "formal education", and the amazement has been replaced with FEAR. It's a lousy trade... a trade that I will not make, nor will I allow them to make. If we can't enjoy each other, then what's the point?
You know what I'd really like to do? I'd like to walk into class and gather everyone together on the floor. Then I would show them my research notebook, and hand each one a pen...

That raises the question: Why do curious children become scared adults?

Tests are bad. Homework is bad. Forcing kids to learn things they don't want to learn is bad. And most important of all, punishment is bad. And all of these things play a role in causing the change some people go through from curious child to scared adult. Without these things, a person would go from curious child to curious adult.


Why are these things bad for children? How do these things cause people to lose their curiosity? The answer requires an understanding of how people reason.


Reason is how people think. Children reason too, its not just adults. Children often notice contradictions in their parents arguments and point them out, 'na'ah yesterday you said X but today you're saying NOT X.' Being able to notice contradictions is the second most fundamental feature of how people think, the first being the ability to create concepts.


So what's the problem? What does this have to do with how people change from curious to fearful? Well the answer has to do with how parents react to their children when they disagree. If the parent uses reason, then things go well. But if the parent switches to anti-reason, e.g. punishing the child for not obeying, then things go badly. Repeatedly treating children this way causes them to learn anti-rational memes[1] -- these are the memes that cause people to stop thinking, to switch from reason to anti-reason. And by the time they are adults, they have lost their love of reason and its been replaced with a fear of confrontation/disagreement/criticism. And its these anti-rational memes that cause the fear emotion when they are presented with criticism, or when they think they might be mistaken, or when they know that learning something means that they might make mistakes.


Note that by punishment, I'm talking about a lot more things than just spanking. I'm talking about timeouts, facial expressions and tones intended to communicate that the child should feel shame, social outcasting at home and school, etc. All of these things share the same quality, anti-reason. And they all cause people to learn anti-rational memes because they all communicate that judgment should be evaluated by authority, rather than by reason -- by the authority of parents, teachers, principals, friends.


Thinking without reason means deferring to the authority of other people's judgment. But because the thinking is done without reason, its impossible for the person to know whether or not the other person's reasoning is flawed, or whether or not its void of reasoning altogether as in the case of people making unargued conclusions (i.e. unexplained assertions).


I just realized that I just described a first-hander and a second-hander[2]. The first-hander is the curious child that became the curious adult -- he judges ideas with reason. The second-hander is the curious child that became the scared adult -- he now judges ideas by the authority of other people's judgment.


So how should parents treat their children instead? Like this



[1] Anti-rational memes, and meme theory in general, are explained in _The Beginning of Infinity_, by David Deutsch. beginningofinfinity.com


[2] First-handed and second-handed thinking are explained in _Introduction to Objectivist Epistemology_, by Ayn Rand. You can also learn a lot about first-hand vs second-hand thinking from her novels _The Fountainhead_ and _Atlas Shrugged_.



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Wednesday, March 27, 2013

How does learning work?

-- Dated Jul/2011

How does learning work?
Most of them learn randomly. First a child experiences a problem: I touched the stove, and I got hurt. Very soon she learns a solution to prevent such problems: Don’t touch stoves. Then she experiences similar problems and begins to improve her solution: Don’t touch things that make fire or turn red. This new solution works for more than the just problems with stoves -- it helps her in dealing with far more problems than her first solution did. So with solutions, problems are easier to understand which means that with solutions, problems are more easily controlled, even if one has never experienced a specific problem before.
Then she learns a logic: Beware of electric and gas lines and machines because our flesh is conductive and not flame-retardant. Notice that a logic works for more than one solution; some logics apply to only a few solutions while others apply to billions or more. So with logic, solutions are easier to understand which means that problems are even more controllable, solutions are more easily understood, the task of determining which solutions to apply in certain problems is made much simpler, and finally solutions are more effortlessly applied in those problems.
But this process of learning is far too chaotic. There is far too much entropy, i.e. the amount of chaos, in this method of learning. More chaos means more possibilities for error. Consider language. The more possibilities that a statement could be interpreted into, the more ambiguous the statement is. More ambiguity equates to more error in understanding, which slows the learning process. So how do we make this less random? How do we reduce entropy in the learning process?
Figure 1
Let’s revisit the process of learning. First a newborn learns problems like, ‘When I touch the stove, I get hurt.’ Imagine these as points in the empty space of a newborn’s mind (see Figure 1). Then they learn more problems and they begin to learn some solutions like, ‘Don’t touch hot things.’ These are vectors in the space (see Figure 2).

A vector is a geometric entity that has both length and direction; think of it as an arrow. Note that when a solution 
Figure 2
changes from ‘Don’t touch the stove,’ to ‘Don’t touch things that
make fire or turn red,’ this change is represented as the 
lengthening and/or realigning of a vector.

Note that the more similar problems you learn, the more likely you are to realize that you should make a new solution, i.e. the more points you’ve learned that lie along a straight path in your 'knowledge network', the more likely you are to realize that you should put a vector along that path. If you make this realization,
Figure 3
then a new vector is installed along that line. Hence you’ve 
learned a new solution by projecting and more importantly, 
you’ll be able to tackle new similar problems that you’ve never experienced nor heard of previously. 

Then the newborn learns logic as in, ‘Beware of electric and gas lines and machines because our flesh is conductive and not flame-retardant.’ This is represented by the localized superstructure of vectors (see Figure 3).
Note that the more similar solutions you learn, the more likely you are to realize that you should make a new logic, i.e. the more vectors you’ve learned that are connected with each other, the more likely you are to realize that you should make a superstructure of the those vectors. If you make this realization, then a new superstructure of logic is installed along those vectors. Hence you’ve learned a new logic by projecting and more importantly, you’ll be able to  tackle new similar problems and solutions that you’ve never experienced nor heard of previously.
With a logic, solutions and problems are less necessary to be learned because they can now be projected instantaneously, i.e. on the fly. What does it mean to be able to project solutions and problems? Well most of this article is my mind's projections. I did not learn these things from a teacher, nor by reading. Instead, I learned them by projecting. The more logic one learns, the more accurately she will be able to project solutions and problems, i.e. learn solutions and problems without the help of teachers or even reading. So how does the mind learn logic? Or rather, how does the mind learn knowledge? First lets look at some examples of various terminology in various fields regarding knowledge.

What is knowledge?


Knowledge is all that can be learned by a mind. Therefore, knowledge is the entire set of problems, solutions, and logic in the Universe. So a person’s knowledge is the complete set of problems, solutions, and logic learned by their mind. Each mind has its own set of problems, solutions, and logic as its knowledge set. Think of knowledge as the untapped raw material from a mine; untapped only by newborns that is. Note that the mine occupies an N-dimensional space.
Figure 4
- Problems are points in this space; problems are 0th order knowledge.

- Solutions are the vectors that project points; solutions are 1st order knowledge.

- Logic is the superstructure of the vectors; logic is 2nd order knowledge.

- The Knowledge Network is the graphical representation of all the points and vectors representing all knowledge in the universe (see Figure 4).

- A person’s knowledge set is that person’s version of the knowledge network.

- Note that all knowledge is connected either directly or indirectly to all other knowledge, i.e. all knowledge is connected. What connects it? Logic.

- It stands to reason that all logic is at least partially the same since logic is pure, i.e. it is completely void of problems and solutions. Well, not all logic is void of field-specific terminology though. It seems we must define 2 types of logic.

- 2nd order knowledge containing field-specific terms is.......................    Field-specific Logic

- 2nd order knowledge void of field-specific terms is...................................    General Logic

- 0th, 1st, and 2nd order material of a specific field is..................    Field-specific Knowledge

- 0th, 1st, and 2nd order material irrespective of any field is................    General Knowledge

- It stands to reason that we could interchange 0th and 1st order general knowledge with 0th and 1st order field-specific knowledge in order to postulate new knowledge in other fields; that is to say that we could interchange solutions and problems from one field into those of another while keeping the logic constant.

- Every general logic should be applied to every problems and solution in a field before dubbing that general logic as unusable for said problems or solution in said field. This is the Socratic Method, a negative process of hypothesis elimination.

- More specifically, every field-specific logic should be converted into its general form, and then systematically attempted in other problems and solutions in all other fields.

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-- Dated Mar/2013

Note that problems, solutions, and logics are all ideas. Humans think with ideas. This means being able to notice contradictions between ideas. When someone notices a contradiction between ideas, he knows that one or both of them is wrong, and he continues by making a judgement call about which one that is. The way that we make judgment calls is by considering the contradicting ideas as rival theories -- only one of them can be right. Actually, since both of them might be wrong, we might need to brainstorm a new theory. And the way to adjudicate between the rival theories is to consider the reasons for each, and to criticize the reasons, and to criticize the criticisms. (Note that each criticism is an explanation of a flaw in an idea. Note also that noticing a flaw in an idea is a type of noticing a contradiction between two ideas.)



Learning is an iterative process of (1) noticing a problem, (2) solving that problem, and then possibly noticing another problem in the last solution, which brings the person back to step (1). And this continues step-by-step from birth until death, from problem to problem to problem.


Its important to note the difference between an abstract problem and a human problem. An abstract problem is like this: 2+2=?. A human problem is like this: I don't know the solution to the abstract problem, 2+2=?, and I want to know the solution. So for this example, the solution to the human problem is 'To acquire the knowledge that 2+2=4' and the solution to the abstract problem is '4'.

A problem is a conflict between two or more ideas. And its solution resolves the conflict. This is true for both abstract problems and human problems.

For example, Einstein noticed a conflict between Newton's laws and Maxwells laws. This is the abstract problem. And Einstein wanted to solve it, so this is his human problem. He solved it with his Special Theory of Relativity (it resolved the conflict between Newton's laws and Maxwells laws.)

A human problem means that a person is interested in solving an abstract problem. This raises the question: What happens to the learning process when a person is not interested in solving an abstract problem? It grinds to a halt because the person is not interested in thinking about the problem. Learning works best when the person is interested.

What are the implications on understanding each other? Answer here and here.


What are the implications on parenting and education? Answer here and here.


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While my article might not be very helpful to you, this will:

How do you think so that you come up with good ideas? What's the secret?


Choice theory.


Links to essays and dialogs about learning, parenting, education and related topics.


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Tuesday, March 26, 2013

What is ambiguity?

This essay is based on this theory.

What is ambiguity?

Or rather, how can one be conscious of ambiguity so as to prevent it from slowing down the educative process? Some dictionaries do not define ambiguity appropriately. They define it as ‘uncertainty in interpretation.’ The problem with this definition is that it does not express the quantitative nature of the term. A more appropriate definition which some dictionaries give is the ‘ability to express more than one interpretation.’ This definition is more accurate because it clearly expresses the quantitative aspect of the term with the phrase, ‘more than one.’ So lets further define the term ambiguity qualitatively so as to further reduce the ambiguity of the term ambiguity. Lets first employ philosophical logic then we’ll convert the philosophical statements into symbolic form.

Consider a situation in which a teacher teaches a subject matter to her student; this is a communication between two people, a transaction. A transaction has multiple events that occur against it. In this situation, the first event occurs when the teacher chooses an area in her knowledge network to teach. Note that some of the points and vectors in this area of her knowledge network are likely to be somewhat misaligned as compared to the Universe’s knowledge network; this difference is what Mathematicians call error. The next event occurs when the teacher translates her idea into words; and since no human is perfect, there is error here too and this is what we call ambiguity. Then the teacher speaks her idea to the student; and since no human is perfect, there is error here on the part of the teacher and on the student. This error is of many types; the teacher’s slurring of her words, the student’s lack of concentration, etc. Then the student attempts to make sense of the teacher’s statements and converts them to an idea; his version of her idea. There is error here too. At this point, the teacher must work towards decreasing this error. She asks the student a line of Socratic questions whose answers will provide the teacher with evidence as to what degree the student understood her idea. The questions serve to decrease the error in understanding by cyclically chipping away at the error through measurement. The students answers are the measurements while the teachers questions are the measuring devices. Lets now employ symbolic logic to define the objects in this transaction:

X = Teacher (female).
Y = Her student (male).
A = X’s idea. This is represented by a very small localized area of X’s knowledge network.
B = The Universe’s version of A.
C = X’s translation of A to English.
D = Y’s understanding of C.
∆E = The error between D and A, i.e. this is his misunderstanding of A. (∆ is pronounced delta and it means difference which in our case means error.)
Note that error can not be completely eliminated; it can only be minimized through the use of Numerical Methods. This is an axiom I learned from the field of Chaos Theory, a branch of Numerical Methods. This means that ∆E > 0.

Q = X’s questions to Y in order to determine D.
P = Y’s answers to Q

What is the object of the end goal of this transaction? It is D; the student’s understanding of A, the teacher’s idea. What is the end goal? We expect D to be as close to A as possible. So what is D’s relationship to A?

D = A +- ∆E. This means that the student’s understanding of the teacher’s idea is equal to the teachers idea plus or minus the error of the transaction.

D and A are trivial. That leaves only ∆E which is the error of the whole transaction. Since the transaction is composed of many events, the transaction error is the sum of the error from the events. Lets define the events and some attributes of the objects:

1. X thinks of A to teach to Y.
∆A = The error in X’s understanding of B. This is one of the terms that make up ∆E.

2. X converts A into its English language equivalent dubbed C.
∆C = The error in X’s translation of A to C. This is the ambiguity. This is a 2nd term that makes up ∆E.

3. X speaks C to Y.
∆S = The error in X’s speech to Y, as in the slurring of her words. This is a 3rd term that makes up ∆E.
∆H = The error in Y’s hearing of X, due to the lack of concentration. This is a 4th term that makes up ∆E.

4. Until ∆E ≃ 0, (The symbol ≃ means almost equal to.)

i. X asks Q to Y in order to determine D.
∆Q = The error in Y’s understanding of Q. Note that this is a sub-transaction in that it could contain more than one event and so each event comes with it another error term.

ii. Y answers X with A.
∆P = The error in X’s understanding of P.

So now lets use all the error terms we’ve just defined to determine ∆E.
∆E = ∆A + ∆C + ∆S + ∆H

Lets consider these error terms. Which of the 4 types of error do we as teachers have direct control over? Only ∆C and ∆S. But ∆S is trivial; the simple rule is to enunciate your words. This leaves us with only ∆C. Note that when the teacher translates her idea into words, she must realize the fact that the student’s knowledge network is quite different than hers. This means that any word in his vocabulary, which is part of his knowledge network, could have a slightly different meaning than the same word in her vocabulary, which is part of her knowledge network. Thus any one of her statements can be misunderstood by him. Lets dig deeper. Lets define some objects and their attributes of the event that results in ∆C:
Ci = A statement from C.
n = The number of statements in C.
As an example, if n = 3, then C = (C1, C2, C3).

Cij = one possibility that Ci can mean.
m = The number of possibilities that Ci could mean.
If m > 1, then Ci is dubbed ambiguous, meaning the statement could be interpreted in more than one way.
As an example, if n = 1 and m = 4, then C1 = (C11, C12, C13, C14).

Ui = Y’s version of Ci.

Lets assume, for simplicity, that the student only considered one of the many interpretations, i.e. he made an unconscious assumption, i.e. an assumption in which he was not aware that he was assuming because he could not imagine the other possibilities.

∆Ui = The error in Ui as compared to Ci. His misunderstanding of Ci due to the ambiguity of the teachers statement. To reiterate, this error is irrespective of the other types of error, ∆A, ∆S, and ∆H.

Therefore Ui = Ci - ∆Ui

So the total ambiguity error of the transaction, ∆C, is the sum of the ambiguity error of each event in the transaction, i.e. each statement in the communication:
∆C = ∆U1 + ∆U2 + ∆U3 … + ∆Un

So how do we decrease ∆C, the ambiguity error of her entire argument? It seems that we should decrease m, the number of possible interpretations of a Ci, the teacher’s statement. Or rather, we should decrease the average m across all the statements of a communication; lets dub this mAve. What happens if we decrease mAve to almost 1? Then we will have practically removed all error in ambiguity of the teachers’ argument, ∆C. But what if mAve is large enough to cause a large ∆C? Lets consider a statement in which m = 2. The teacher asks a Socratic question with the intention of revealing the difference between the 2 possibilities, i.e. the error, thereby removing all error in ambiguity of the teacher’s statement, ∆Ci. How far can this be taken? Or rather, how high can mAve reach while the teacher still retains the ability to use a Socratic line of questions in order to reduce the ambiguity to practically zero? Well that depends on how powerful the Socratic line of questions is.

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What is assumption?

Continuing with the same situation, can the student be trained such that he does not assume thereby causing him to ask questions himself rather than relying on the teacher to expose the misunderstanding? Remember that Ui is Y’s version of Ci and that we assumed for simplicity, that the student only considered one of the many interpretations, i.e. he made an unconscious assumption, one in which he was not aware that he was assuming because he did not imagine the other possibilities. Why doesn't a student imagine the other possibilities? It is because he has not yet learned the logic of assumption. Lets create a similar situation mimicking the previous one but with one change; the student does not assume and instead realizes the other possibilities. At this point, the student is to ask the questions while the teacher answers in such a way to reveal ∆E, the difference between D and A. Note that the teacher does not necessary need to answer the questions with answers. Instead she can use questions as the answers, thereby allowing the student to derive the answers himself, and since the student knows better than the teacher about what he understands, he is more likely to produce more appropriate questions to more accurately reveal the difference between D and A. Therefore the student’s line of Socratic questions to decrease ∆E would be a shorter list of questions as compared to the teacher’s line of Socratic questions. In other words, once the student learns the logic of assumption, then the entropy of the educative process is further decreased and thus learning occurs faster. So how does the teacher teach the child the logic of assumption? (flag till later)

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(later) This was my confusion as I defined it in my theory of knowledge. This confusion is the problem.

The problem: How do we learn to minimize assumptions?

The solution: Learn philosophy by reading and discussion.

I wrote this in another thread a few days ago:
Before coming to this site, I was a pretty good thinker, but not really. I used to make thinking mistakes like employing empiricism, reductionism, anthropomorphism, justificationism, etc. And while I was making these thinking mistakes I had no idea that I was doing this of course, so many [maybe most] of the conclusions that I would draw were wrong [and many of these were incorrect assumptions]. And since I've been on this [BoI] email list I've learned what these things are and so now I don't make these thinking mistakes as much. And I can also notice them in other people's arguments, although this is still very limited too. The other people on this site are still finding my thinking mistakes. And each time that they reveal one of my thinking errors, I learn that thing even more, and so my thinking skill improves.

So now I know what philosophy is. Its the practice of thinking without thinking mistakes in a way that tries to reduce mistakes.
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