Mathematical thinking

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exchemist said:
With maths, as it is so abstract, it is probably harder to sustain that approach all by yourself, I suspect. I at least would have found it difficult to do that.
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"All by myself" is actually a self-imposed delusion. It isn't and can't be true.
To learn you need instruction, but you can give this to yourself by looking at books, doing exercises that give you a clearer sense of what it does, what it's good for. Why anyone would bother trying.

So you and the books, written by your instructors whose directions you learn to follow, by yourself. You direct the course of your own learning. Yay, free at last. But yes it means effort, and it means adopting a somewhat monkish philosophy.

It is inevitable.
 
DaveC426913 said:
From what you are saying, it would not be too much of a stretch to wonder if - perhaps - you were one of those kids who thought (or had been told) they were so smart they could challenge the teacher on "dogma".
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Nope. I was told I was smart enough that they were going to get me to sit a test. I got a good, a high result. I was the smartest kid at my school when I went there.

When I stayed home, I was the smartest kid on the block. Sorry, I'm not bragging it was true. All the adults, all the teachers told me that. I had to accept what they said. I saw my test mark--it was 135. And I deliberately stopped doing the test 'cause my BS antenna was fully extended. I suspected another adult drama was about to unfold.

Much excitement and chatter. Yawn

So there it is. I deliberately dumbed down my smartness gene, because I suspected it would become the centre of a new production. My mother was after all, involved in a local theatre group. La de da.
 
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Kid Anymore said:
Nope. I was told I was smart enough that they were going to get me to sit a test. I got a good, a high result. I was the smartest kid at my school when I went there.

When I stayed home, I was the smartest kid on the block. Sorry, I'm not bragging it was true. All the adults, all the teachers told me that. I had to accept what they said. I saw my test mark--it was 135. And I deliberately stopped doing the test 'cause my BS antenna was fully extended. I suspected another adult drama was about to unfold.
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Yes, Not suggesting you weren't smart.

But that doesn't mean you're smart enough at that age to challenge "dogma". You cannot think outside the box until you have been taught what is inside the box. That's a common error smart kids make (basically, the Dunning-Krueger Effect). I was one too. I skipped grade four, being accelerated from 3 to 5.
 
DaveC426913 said:
But that doesn't mean you're smart enough at that age to challenge "dogma".
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You are absolutely correct. Challenge from a young human to an older one usually ends with something they once called disciplining a child who misbehaves.

Leather straps were often involved. Obey or else was the battle-cry. It seemed to work for them.
But as we know, violence is a well-known refuge for the incompetent. Score one for the monks.
 
Kid Anymore said:
You are absolutely correct. Challenge from a young human to an older one usually ends with something they once called disciplining a child who misbehaves.

Leather straps were often involved. Obey or else was the battle-cry. It seemed to work for them.
But as we know, violence is a well-known refuge for the incompetent. Score one for the monks.
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It is not clear whether you are saying this is what actually happened to you, or if you are merely alluding to others who were strapped by monks to the sound of their battle-cry.

I confess, between your first post about "some unnamed hypothetical people" and this post about "monks and belts" I am having difficulty getting my head around what your actual history is versus what is rhetoric, allusion and melodrama. You would would better to be less circumspect and more forthright.

Even if it's all experiential, there's a few discrete things going on in there:

That you were disciplined for misbehaving or challenging your teachers does not, in-and-of-itself, mean they were incompetent. Your teachers may have been perfectly competent and still needed to discipline you.
 
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DaveC426913 said:
I confess, between your first post about "some unnamed hypothetical people" and this post about "monks and belts" I am having difficulty getting my head around what your actual history is versus what is rhetoric, allusion and melodrama. You would would better to be less circumspect and more forthright.

Even if it's all experiential, there's a few discrete things going on in there:

That you were disciplined for misbehaving or challenging your teachers does not, in-and-of-itself, mean they were incompetent. Your teachers may have been perfectly competent and still needed to discipline you.
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Ok. I think that the evidence unfolding here is that, you're more interested in my history and my difficulties with early education than anthropology.

What you are displaying is something I've learned to negotiate with, and that started during that very same early education.
I call it how to keep the class interested in learning something, rather than their ideas of what learning is. I don't have to imagine I'm a teacher, or even a monk. I just have to remember I'm a student like everyone else is. Including the monks.

But, everyone wants to be the lead guitarist.

. . . which is one of the reasons it's a long way to the top
 
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Kid Anymore said:
"All by myself" is actually a self-imposed delusion. It isn't and can't be true.
To learn you need instruction, but you can give this to yourself by looking at books, doing exercises that give you a clearer sense of what it does, what it's good for. Why anyone would bother trying.

So you and the books, written by your instructors whose directions you learn to follow, by yourself. You direct the course of your own learning. Yay, free at last. But yes it means effort, and it means adopting a somewhat monkish philosophy.

It is inevitable.
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I always found I needed to talk to other people about what I was trying to learn, though. It helped me check whether I had understood clearly enough to put it into words and also to ask about what was unclear. I think it would be very hard just on my own.
 
Aha. News arrives that it's time for a break. Smoke 'em if ya got 'em, boys.

Sit back and relax. It's time to learn. I for instance, could elaborate on how playing a guitar is algebraic, there's a set of finite intervals, a covering space.
Some relations between elements of this set, etc. It's quite a musical construction, go figure. You can re-phrase as it were, some musical theory with a change of notation.
 
Kid Anymore said:
Aha. News arrives that it's time for a break. Smoke 'em if ya got 'em, boys.

Sit back and relax. It's time to learn. I for instance, could elaborate on how playing a guitar is algebraic, there's a set of finite intervals, a covering space.
Some relations between elements of this set, etc. It's quite a musical construction, go figure. You can re-phrase as it were, some musical theory with a change of notation.
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Yes music is mathematical, largely because octaves and consonant intervals and harmonies are determined by physics: the physics of the frequencies/wavelengths of the vibrating entity that produces the sound - the string, column of air, resonant circuit or whatever.

People like Bach enjoyed exploring what could be done within the constraints of counterpoint, in which the same or a closely related musical line has to fit with others, with an offset in time and pitch - a sort of mathematical puzzle. I used to enjoy listening to the Art of Fugue when I was at uni - strangely soothing to hear someone else working it all out so cleverly.
 
Kid Anymore said:
Aha. News arrives that it's time for a break. Smoke 'em if ya got 'em, boys.

Sit back and relax. It's time to learn. I for instance, could elaborate on how playing a guitar is algebraic, there's a set of finite intervals, a covering space.
Some relations between elements of this set, etc. It's quite a musical construction, go figure. You can re-phrase as it were, some musical theory with a change of notation.
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No.
Sounds are physical and empirical is physics. Our best models use nodes, wavelengths, harmony harmonics which we describe using mathematics.

Why is Cmaj7 so pretty? Er..
 
exchemist said:
Yes music is mathematical, largely because octaves and consonant intervals and harmonies are determined by physics: the physics of the frequencies/wavelengths of the vibrating entity that produces the sound - the string, column of air, resonant circuit or whatever.

People like Bach enjoyed exploring what could be done within the constraints of counterpoint, in which the same or a closely related musical line has to fit with others, with an offset in time and pitch - a sort of mathematical puzzle. I used to enjoy listening to the Art of Fugue when I was at uni - strangely soothing to hear someone else working it all out so cleverly.
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Damn it! Ten seconds dude you beat me to it!
 
Pinball1970 said:
No.
Sounds are physical and empirical is physics. Our best models use nodes, wavelengths, harmony harmonics which we describe using mathematics.
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I'm wondering why this starts with no, then says something about physics. I mentioned a set of intervals and a guitar.
Are you saying you can see some connection? What can we learn from it?

I'm using a poset algebra, I can develop or refine it how i like, subject to certain constraints or restrictions. There's Dilworth's theorem, do you know about it?

It's possible to elaborate a structure which shows you something about what music is. This won't really have much to say about the psychological effects. It won't be able to tell you what a note is, for instance, because it's strictly mathematical. That can be seen as intentional since you want to see structure, you want to know about invariants.

Trust me on this.
And I've considered what staring at a page of sheet music can tell you about what it sounds like. I can do this these days a bit.
Like, play it in my head by reading the music.
So replace sheet music with algebraic diagrams, a monoid etc. You can start with a category and all you need to worry about is that's what it is, much else can follow this simple decision.
 
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Kid Anymore said:
Ok. I think that the evidence unfolding here is that, you're more interested in my history and my difficulties with early education than anthropology.
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From the top your post is rooted in your history. It is what you have led off with as your preamble - your backstory. It is pretty apparent that's what you want us to know about how you've drawn your personal conclusions about life, which is what you go into next.

Which is fine, but you're not stating objective facts about the world, you're stating insinuations. And I still don't know which parts are true. So all we have to address is what you present, here. I didn't write all that; I'm only addressing what you wrote for us to read.

One example of a possible insinuation that raised a flag is in your very first post; Who are "these people" we're supposed to recognize? You've sketched some rough dots, and expect us to join them.

That flag was a herald to the next one: Is the picture you've painted about monks and straps a real recounting, or is it an allusion?

You don't have to answer; but it is very hard to discuss with you if it is apparent you are not being entirely forthright. It feels like manipulation.


Kid Anymore said:
What you are displaying is something ...
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What I am displaying is a thoughtful response to the message you are sending within the words you wrote. Is it possible your teachers noticed a similar sentiment in your communications?

For example:
Kid Anymore said:
Aha. News arrives that it's time for a break. Smoke 'em if ya got 'em, boys.

Sit back and relax. It's time to learn.
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Is this how you spoke to your teachers when you were a student?



I'm not trying to bust your balls here; I'm genuinely responding to the message I am receiving from you.
 
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I can't help it; I can't help the surprise I feel at some recent responses. It has to include that I'm reading what someone wrote, I didn't see them face-to-face and that makes it different. I have to imagine what the emotional part of it is. I should at least be charitable and, I should at least allow that I will involve how I feel at the time, I will inject this even if I try not to.

I'm an anthropologist too.

So perhaps that context--what is this group of humans really doing, which is us---in attempting a discussion. I didn't want it to be questions and answers about what I think my problems with the subject were, but here we are. Perhaps any perception of me being sarcastic--it might have been the cause of some of the troubles--is just that I want it to be about something else.
 
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