Author Topic: How to Attain a Studious Life  (Read 1675 times)

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Raskolnikov

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Patience, humility, and intellectual honesty.

What are the antitheses of these virtues?

Frustration, arrogance, and self-deception.

I tend to focus on more difficult material in the morning, but when my brain feels too stretched, later in the evening, I have been going over some more fundamental and elementary material.  During such "casual" study sessions, I am humbled by the fact that, regardless of the "level" of the exercises, I find that I still have to CONCENTRATE and THINK.

This requires patience and humility, true; but the most amazing virtue these sessions inculcate is intellectual honesty.  I have to accept that some problems are not quite as straight forward as they first appear.

Take equations involving absolute values.  These require a little more thought.

|x - 3| + |x - 4| = 1

It seems too "easy" to pay attention to ... what a pompous and arrogant professor might refer to as "baby math," but one should never be ashamed to stop and think.  That's why I enjoy going over more basic reviews later at night, giving my brain a little rest, and at the same time, developing a kind of humility in that I do not feel "above" having to think about more elementary material.

I remember hearing a story about how Einstein had difficulty counting his change.   He was prone to make arithmetic errors.   

Just think of how vulnerable all human beings are to miscalculating, where the error is arithmetical or algebraic. 

I really want to develop this kind of humility and patience and intellectual honesty.

Studying mathematics as an antidote to human bullshiit.

It is an antidote to human BULLSHIIT because BULLSHIIT doesn't get you anywhere when trying to figure out something mathematical.

Peace.

Holden

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Euclid: How to Attain a Studious Life
« Reply #16 on: April 03, 2016, 10:26:22 am »
Euclid alone has looked on Beauty bare.
Let all who prate of Beauty hold their peace,
And lay them prone upon the earth and cease
To ponder on themselves, the while they stare
At nothing, intricately drawn nowhere
In shapes of shifting lineage; let geese
Gabble and hiss, but heroes seek release
From dusty bondage into luminous air.

O blinding hour, O holy, terrible day,
When first the shaft into his vision shone
Of light anatomized! Euclid alone
Has looked on Beauty bare. Fortunate they
Who, though once only and then but far away,
Have heard her massive sandal set on stone.
You're on Earth. There's no cure for that.-Cioran.

Raskolnikov

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I think that there is an element of defiance in my renewed obsession with specific core subjects of mathematics and physics.  These subjects are associated with careers in science and engineering.  Maybe, when I finally reached the goal of graduating from the university back in 2002, already fairly "old" (35), when it began to dawn on me that I was not suited for corporate employment, I believed that all that education had been in vain.  So, I sunk into a depression and rebelled in self-destructive ways.

Now I approach those same subjects with an entirely different attitude.  I am still rebelling, but now in a fairly healthy manner.  I now study defiantly.  I do not use the word defiantly lightly.   Now, even if I feel, for whatever reason (for all I know it is my own fault just for being a cantankerous pessimist and anitcapitalist) that there is no place for me as a professional scientist, I want to study to develop as a thinking human being, a problem solving higher order primate.

I think Schopenhauer would encourage me to indulge in these studies.  For one, he had great respect for physics.  Another aspect has to do with experimentation.  Perhaps due to the pressure to prepare students for technical work in industry and business, the way these subjects are taught can be haphazard, where students do a great deal of cramming, graduating filled with doubt and very little confidence.

Maybe I wish I had this attitude back in 2003 when I first went on welfare for emergency assistance, but, I went on a downward spiral.  It is what it is.  Now, even though I have all the textbooks I will want to study, I found myself repeated the same scenario, trying to study 6 subjects at once.  Now, here is where the defiance comes in.  There is no need to proceed in this manner. 

I have going to stick to some kind of plan stretching from January 2016 into the summer throughout the autumn, and well into 2017, maybe even stretching into 2018.

Maybe my notes on this process will be more meaningful to some youth of the future than some kind of existential novel or collection of diatribes against being born.

The acquisition of the hard copy textbooks motivates me to remain stable and grounded.  To be blunt, the little library encourages me to "nest", to settle down for a good decade.  This will also serve my mother well, since she requires a companion at this time in her life. 

I lost the notes I kept from the university, so I am making these notes even better, hoping that I will have yet another opportunity to review this stuff, this time using notes which are more explicit than just haphazardly "searching the Internet".

In the past I have associated defiance with drunkenness, drums, and loud guitars ... Dionysus.

Now I suspect that studying math and science, when there is no motivation to become a working "scientist" may be a kind of stubborn defiance.  I will be developing skills that are useless for making money, acquiring security, automobile, et cetera.  I know that would sound like a false statement to the youth who associate scientific education with careers as nuclear physicists for the military.

In a world where professional athletes and TV celebrities are worshiped, studying for the purpose of filling one's head rather than one's bank account is a defiant way of life, all things considered.

In this way I am intend to flip the script.   Rather than be made to feel like an intellectual deadbeat non-breeding pariah of society, in my own mind, at least, I can live a somewhat heroic life ... where the hero happens to be an antihero in terms of not representing the wealth-warped values of his contemporaries.

There is one slight aspect of the autodidactic method:  when there is a mistake in the solution manual, a glaring fundamental inconsistency, this can cause unnecessary frustration.

It can be something very fundamental, such as a 2x3 matrix times a 3x1 vector yielding a result with dimensions 3x1 when you know the result should be 2x1.

The only good thing I have to say about such blunders is that encountering them can be a test of one's confidence.  What is one to do?  Complete the problem anyway, or move onto the next one?
« Last Edit: April 11, 2016, 09:51:01 pm by H »

Raskolnikov

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Re: How to Attain a Studious Life
« Reply #18 on: April 14, 2016, 11:40:38 am »
I cannot express strongly enough how worthwhile an endeavor it is to give Sheldon Axler's Algebra and Trigonometry its due.  While I initially presumed this would be a simple review of material, I have so far been pleasantly surprised by the density and diversity of the exercise sets.  If one is self-motivated, one will appreciate how many of the exercises really force one to think like an ancient scholar, like Euclid would.

This has altered my approach, and I will proceed with mindfulness ... seeing myself not so much as a former student living an uneventful life, but as one who aspires simply to be a learned citizen of the world. 

I know that you [Holden] are more attracted to Number Theory and the more esoteric branches of mathematics, but I have never seen an approach to Algebra and Trigonometry like Sheldon Axler's.  The exercises are a treasure trove, where one can momentarily put aside the realization that it would be better never to have been born, and get lost in analytic geometry, embracing this material as one of the ancient scholars would have, or even as an escaped slave who has come to lead a scholarly life outside of academia.  The Internet has made such scenarios possible.  (The intersection of the modern and ancient worlds?)  This technology is revolutionizing the way we educate ourselves. 

What is also cool about this particular textbook is that many of the solutions are worked out in detail at the end of each section, eliminating the need to track down a solution manual.

This book is all about the exercise sets, which would compel you to sharpen your pencil and stretch your mind.  I thought this book would be used just for reference, but it is turning out to demand my full attention.

For me, this is where patience and humility and intellectual honesty come into play. 

My goal is to stretch my mind and force myself to think carefully as opposed to racing through to get it over with.  Most of what I know of algebra, trigonometry, and analytic geometry I associate with calculus.  I have not allowed myself to approach these subjects as ends in themselves since 1993 when I was preparing to go to community college to take calculus in 1994, ten years after graduating high school.  I want to revisit the fundamentals to get a better appreciation for how much algebra (analytic geometry) and trigonometry is the foundation of the more advanced subjects.  Many things that I associate with calculus are really algebraic or trigonometric.  I can never consider my study of the fundamentals as complete.

Now I suddenly found myself grappling with problems in Differential Equations and Multivariable Calculus, thinking I would just pick up where I left off in 2002.

While I could work through the exercises, I was not calm, and even kind of frantic.  I want to redevelop strategies for problem solving.

I think that Sheldon Axler's textbook will help me rebuild my preliminary foundations.

Also, there is color pdf for Dale Hoffman's Contemporary Calculus, freely available on line.  That series of texts are sold in separate volumes, actually less expensive freshly printed at lulu DOT com than used from Amazon.  For instance, CC IV is $18 to print at lulu, but shockingly like $40 used through Amazon.  No, it's not reachable through Library Genesis (yet).  The author (Hoffman) encourages self-motivated students to make use of these online resources rather than investing in the texts. 

But, the font is small so you might be better off using the online pdf in color (also since you can't be lugging books around while traveling around for your employer).
« Last Edit: April 15, 2016, 09:20:48 am by H »

Holden

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Re: How to Attain a Studious Life
« Reply #19 on: April 14, 2016, 12:31:40 pm »
Thanks.Much appreciated!
You're on Earth. There's no cure for that.-Cioran.

Raskolnikov

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Re: How to Attain a Studious Life
« Reply #20 on: April 14, 2016, 01:49:27 pm »
Although it is not necessary, since we each march to our own drum, it would be interesting to see where our dialogue goes were we to suddenly find ourselves on the same page.

Some of the exercises in Axler's textbook, as I have said, are quite novel.

novel - new and not resembling something formerly known or used
         - original or striking especially in conception or style

Granted, there are a handful of exercises that can be "easy," but many others that one might expect to be easy end up requiring some thought, nothing too severe, but just enough make the text worthwhile.

I have a shelf filled with texts, and I figured that going through this one early on can only enhance what I get from the more advanced subjects.

From the investigations I have been making on the Internet, it appears that this itching to gain a better understanding of subjects one figured one was "finished with" years ago is not so rare at all.  I had read several comments by people doing something very similar to what I am engaged in now. 

No matter what level I am working at, whether advanced or elementary, I still find myself making errors, but fortunately they are careless errors, not really many logic errors.  I mean, I will copy the wrong equation initially and solve with the wrong initial equation or other values initially copied down differently than was in the text.  Then I am off and running, calculating correctly, but basically solving a different problem, so, of course, when I go to verify my answer with the solution manual, there is that WTF moment.

[Yes, I invested in a magnifying glass with LED light]

So, the main errors occur from "dumb errors" which are not as bad as totally not understanding what one is doing.
« Last Edit: April 19, 2016, 04:53:09 am by H »

Raskolnikov

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Re: How to Attain a Studious Life
« Reply #21 on: April 20, 2016, 03:31:33 pm »
Going through the Hoffman text, chapter 5, even though I am anxious to get into chapter 6 since I want to understand direction fields better, I am finding the core of Hoffman's approach is in the exercises, which is great.  When I need clarification, I have been looking for clarification in the Internet.  It has been money well spent paying for the internet connection and an almost required expense for any student (of whatever age) who wants to study in a non-traditional manner.

I am sure there are countless others studying in this manner.  Not everyone who enjoys learning is going to be looking for credentials or grovelling around tables on "Career Day" looking to be hired as an intern.  Some of us have given up on doing what we love for a living.  That doesn't mean we have to stop learning.

I'm going to ride this until the wheels fall off, this life of the lifelong student of mathematics.

I may have mentioned this before, but I feel as though I am a self-ordained monk of his own order.

I may start to point out those who offer helpful explanations without any monetary compensation for the time they take.  The least I can do is point out a few.

For instance, while researching how to go about deriving a formula for finding the volume of an ellipse rotated about an axis, I found a comment left by a Mr Harish Chandra Rajpoot.  There is a reason why it is the last comment on the page as he answered the question so succinctly.

Proving the Volume of an Ellipsoid

Do we need to justify our interest in mathematics?  The restrictions are imaginary social constructs.  The Kingdom of Mathematics is within us.   :D

Anyway, although I don't have to point it out, I will anyway:  For the time being I am spared from many of the horrors of existence.  I understand how fortunate I am to be able to do what I'm doing.  The world is filled with nightmarish suffering, especially when it comes to losing one's health or one's wits.

I don't want to come across as a spoiled brat who only cares about his own personal agenda.

I think I may post less about the details of my little world.
« Last Edit: April 20, 2016, 05:08:53 pm by H »

Raskolnikov

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Re: How to Attain a Studious Life
« Reply #22 on: April 22, 2016, 04:03:25 pm »
How Philosophical Pessimism and Depressive Realism might be conducive to attaining a studious life.

Question:  Do you think being slightly depressive puts one in a state of mind conducive to the kind of continuous daily effort involved with the commitment to studying specific subjects?

Put in a more crude manner, what else am I going to do?  I might as well be boning up on my problem solving skills.

When I become unenthusiastic, and the world seems to be passing me by, I quietly and slowly continue to take notes and prepare to tackle the next set of exercises.  This somehow makes it clear to me that living a boring uneventful life is precisely what is necessary.  It is a blessing I would not wish for, but a blessing just the same.

Raskolnikov

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Re: How to Attain a Studious Life
« Reply #23 on: July 27, 2016, 08:45:49 pm »
"If war is too important to be left to generals, then, for analogous reasons, mathematics education may be too important to be left to mathematicians."

 ~ Jerry King (author of The Art of Mathematics, c.1992)

Raskolnikov

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Re: How to Attain a Studious Life
« Reply #24 on: August 12, 2016, 07:55:42 pm »
In all honesty, I get much more from working through "novel" exercises in interesting textbooks than from taking notes from the examples.   

One great benefit of the Internet is that, rather than just skipping an exercise that is too confusing, unfamiliar, or otherwise taxing, access to the internet must give one more courage in tackling more of the exercises.

It is fun to learn when there is no pressure to "perform", when the attention you give something is motivated by genuine interest and curiosity, not by the demands or requirements of society (family).

I think I enjoy working through exercises in textbooks because it allows me to carry on a continuous written dialogue with myself ...
« Last Edit: August 13, 2016, 05:31:44 pm by {∅} »