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Broken Brains

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How to Attain a Studious Life
« on: October 21, 2015, 12:54:35 pm »
I have found that rushing through material too fast or trying to cover too much leads to frustration and kills motivation.  When I find myself skipping the exercises, that is a sure sign that I am not genuinely interested in even trying to understand what I'm looking at.

So, I decided to slow down and do some of the exercises in pencil.  This has actually helped keep me calm. 

Oh, the reason for this thread:  I may have come up with an imaginative way to make autodidactic study a more enjoyable experience.   If one can "pretend" one is in some kind of futuristic prison complex, imagine how delighted one would be to be granted the privilege of holding onto a little notebook computer in one's cell (with mathematical software like Sage and SymPy/NumPy/SciPy [Python] and loaded with mathematics and programming texts), with blank sketchbooks and pencils and erasers ...

One would be quite content in that cell.   :D

It's a matter of using one's imagination so that what you are studying becomes like the Holy Grail.

« Last Edit: October 22, 2015, 08:26:49 pm by H »
Things They Will Never Tell YouArthur Schopenhauer has been the most radical and defiant of all troublemakers.

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Broken Brains

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To be a contently miserable weirdo
« Reply #1 on: October 22, 2015, 08:23:23 pm »
Maybe I have been approaching this the wrong way.  How about a different approach?  How about I get used to the fact that I am not always going to be enthusiastic about studying things that can often be difficult for me to understand.  How about I allow myself to be somewhat depressive and uninspired?

Is there a way to enjoy one's misery in a way so as to not really care too much one way or another?  I mean, if one expects to be inspired and enthusiastic and passionate about something, and then it turns out to be very dry, boring, and uninspiring, then one might be quick to give up ... totally.

Suppose one were to face the unpleasant truth that one is interested in something that is essentially boring and dispassionate.    One could be studying congruencies, and be like, "the inverse of 9 modulo 10 is 9 since 81 (mod 10) is 1" ... OK, I see ... it is what it is ... Do I care?   Well, it's a mathematical reality revealing some kind of inner nature or rules of modular arithmetic ... When a textbook includes too many exercises asking me to prove this or that, I find myself wondering why in the world I would need to do that.  I mean, proofs are a social activity, and I appear to be on my own with this.

In the book, Hitch-Hiker's Guide to the Galaxy, there was a depressed robot.  Tonight I find myself leaning in that direction.  With so much hype in the world over such meaningless things as World Series and Presidential Elections, I can at least have a private inner realm where there is no hype, where there is anti-hype.

I am not a professional justifying his existence or looking for validation of my craft.  I shamelessly depend on government relief.  I'm like a "social misfit" for whatever reasons ... too much intellect, not enough teeth, who knows?   It is what it is.

One of my favorite fiction writers when I was a teenager was Kurt Vonnegut.  He became a very bitter old man.  Good for him.  I commend his honesty and his bitterness ... at least it is genuine.

So, yes, I am interested in math and pessimistic philosophy. 

This may sound like a contradiction, but the way I am going about "enjoying the process of studying" is to become relatively depressed and at my own natural pace experience little moments (breakthroughs) where I can say, "well ... that's KIND OF INTERESTING ..."  but without passion, without hyped up enthusiasm.

If there is any invisible sentient intelligence observing us from another dimension, they will know me as the one "who does not blow smoke up the a-s-s of the <<<Creator>>>" ...

I am just a chimpanzee that can read, write, and do  little math.  So much for the miracle of birth.
« Last Edit: October 22, 2015, 08:59:45 pm by H »
Things They Will Never Tell YouArthur Schopenhauer has been the most radical and defiant of all troublemakers.

Gorticide @ Nothing that is so, is so DOT edu

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Broken Brains

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Re: How to Attain a Studious Life
« Reply #2 on: October 23, 2015, 10:55:53 pm »
I supposedly experienced a nervous breakdown when I was 18.  I wonder if it had something to do with my being torn between the realities of our world (Native American reservations and the nightmare world faced in inner cities) and higher mathematics.

I rebelled against "computers" when I was a teenager.

OK.  Fast-forward to 1998.  I left my job as a maintenance worker to formally study mathematics and computer science (at age 30).  While I did well academically, I never followed through and got a job in the industry.  Maybe I experienced yet another nervous breakdown at age 36 or so ... I seem to reach a point where I become frustrated and angry and depressed all at once, a prime candidate for the epidemic of alcoholism, right?

Now, for whatever reason I am meddling with math textbooks again, trying to focus on areas of math having to do with algorithms and data structures ... programming. 

I swear I still experience moments when I see how this material would make a youth just want to die.

I have a low frustration tolerance.  I understand why one would prefer to mop floors and clean toilets rather than study math or programming ... and yet there is another part of me that enjoys dabbling as long as it is at my own pace.

I am a very frustrated man.  I do not lash out at others over my frustrations but tend towards self-destruction.  I think this is why it is best I do not drink alcohol.  There is a great deal of repressed anger in me.  The authorities must know this about me.  I have to keep my cool.
« Last Edit: October 24, 2015, 12:28:53 am by H »
Things They Will Never Tell YouArthur Schopenhauer has been the most radical and defiant of all troublemakers.

Gorticide @ Nothing that is so, is so DOT edu

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Re: How to Attain a Studious Life
« Reply #3 on: October 24, 2015, 11:15:36 pm »
I will keep updating this thread.  Keep in mind that, while I may maintain a degree of enthusiasm throughout the day while studying, and while I have a great appreciation for having access to computers and even the Internet, I do reach a point where I lose interest.  This just means I have had enough for one day.  The thing is, that is usually when I post here.

In other words, when I am engrossed in study with a high level of interest, I most likely won't be typing about those feelings. 

It's like when someone once read my "poems" - which I don't seem to write any more (it was just a phase, I guess) - the person said my poems seemed very angry and negative.  That's when I would write them. 

So by the time I check in here to write on our little wall, I may have reached my limit as far as "enthusiasm" goes.

I just like to be honest.  What a revolutionary concept:  honesty.

The more honest I am, the more I have to admit how uncertain I am. 
« Last Edit: October 24, 2015, 11:52:49 pm by H »
Things They Will Never Tell YouArthur Schopenhauer has been the most radical and defiant of all troublemakers.

Gorticide @ Nothing that is so, is so DOT edu

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How to Attain a Studious Life: Slow Motion
« Reply #4 on: November 11, 2015, 09:56:31 pm »
If a professional psychiatrist were to see me in action while I was configuring, building, and installing the compilers last night, he/she might point out in a snide manner that I was "in a manic state".   And yet, I was very focused, and I was driven to get the environment right so that I could do what I am doing this evening ...

The demons that drive me in a state of hypomania are as valuable as the angels that calm me down to a slow-motion pace.

What makes actual compilers and debuggers so valuable while reading through a text such as Josuttis's The C++ Standard Library is that I can just place any given code into some text file, include the necessary header files, compile it, and then trace through the code with a debugger.

While reflecting upon the dynamics of a compiler can be overwhelming, once the environment is set up, the debugger itself can become our Teacher.

Suppose I am looking at an explanation of scope and lambda functions.  Reading it on a page is fine, but for whatever reason, tracing through the code in a debugger and inspecting the values of the expressions when inside and outside functions gives one an intuitive feel for the scope.

The GNU GCC debugger, gdb, has many useful commands that aid our understanding, such as displaying values and even inquiring "whatis x" - where it returns the type.

Perhaps the greatest advantage to autodidactic education is that a solitary student does not have to feel ashamed upon being delighted to learn something basic and fundamental, whereas in a classroom or formal setting, there may be discomfort and much posturing by others, which totally robs one of the pleasure of discovery.  Instead, one most likely becomes discouraged, feeling inadequate.

How does one embrace this beginner's mind and resist the irrational tendency to look down upon the little details as "simple", and romanticizing the complex?

You know, I don't have to be forever reading Schopenhauer in order to be living in a manner that Schopenhauer would smile upon ... Every time we hide in a cave-like dwelling to enjoy our mental faculties, we are implementing his philosophy. 

And yet this is not necessarily anti-social behavior.  Studying a book is not anti-social.  Other human beings organized knowledge in a presentable format to help seekers looking for a better understanding.  We may go on about how we despise the human condition, but there are moments when I am humbled by my dependence on other human beings.  The fact that we use these symbols to communicate ...

Perhaps I'm a bit mystified and hypnotized and even somewhat brainwashed.

I mean, I think I secretly worship computers and the scientists behind the scenes, and this most certainly conflicts with my youthful rebellion and glorification of living more harmoniously with the Natural World.  The cold rain does not love me. 

OK ... I will stop this flow of automatic writing and return to my quasi-religion - "programming and mathematics".   :-\

Afterthought:  When I use the term "worship" - adoration - I do not mean to imply awe, wonder, or extreme enthusiasm.  There is no mirth or fanatical praise.  The emotional connection has no passion whatsoever.  It's more like a curiosity or a seduction. 

There is surely an element of wizardry involved.  I remember my curiosity with mythological wizards when I was a child.  I used to have a poster of a wizard in his room filled with open books.   I tend to be especially attracted to books that may contain secret knowledge.

Hmmmm ... Just writing in a spontaneous manner here has made my interest in programming and its roots in the algorithmic methods of mathematical thinking clearer to me.  It is not so much religious worship as it is a love of knowledge, a lust for the acquisition of understanding something obscure and mysterious. 

I don't have to come to any profound conclusions about my reawakened interest.  To say I worship knowledge is a bit too much.  It is far too easy not to be impressed with anything and to curse the cosmic accident that brought forth life on this planet; and yet, as long as I do exist, and since I cannot reverse the event, as the manifestation of the organic consciousness of The Thing in Itself, I am drawn to some ideas and repelled by others.  It's how IT is wired.

When a "students and masters of a discipline or craft cherish the obscure nature of its core knowledge, it becomes like wizardry, but the elder wizards appear to be attempting to organize the unmanageable amounts of knowledge into usable and expandable libraries - to eliminate the necessity of "programmers" to have to start from scratch.   

Polish scientist, Alfred Korzybski, called this tendency "time-binding".  We are symbol using animals who time bind.

Unlike Korzorbski, I do not praise scientists or think scientists ought to rule society (although it might be better than a police-military rule or a corporate businessmen rule). 

I do not glorify humanity.

Writing always leads me to contradictory conclusions.

I appreciate technical tutorials and references, and much of my own notes are becoming more and more technical, more and more details about technical procedures or just keeping track of myself as if I were some kind of laboratory experiment ...

Here, though ... here I let my fingers just type as though I were kind of thinking while I am typing, rather than thinking before I type.  Long pauses between paragraphs ...

Maybe trying to learn to decipher more and more code is, for me, a way to occupy my mind lest I decipher the universe the way Schopenhauer and others did.
« Last Edit: September 10, 2017, 10:46:47 am by { { } } »
Things They Will Never Tell YouArthur Schopenhauer has been the most radical and defiant of all troublemakers.

Gorticide @ Nothing that is so, is so DOT edu

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Unbroken Spirit & Exploratory Studying
« Reply #5 on: November 15, 2015, 11:02:58 am »
All the effort I put into setting up a lab environment has not been a total waste of energy.  While I was able to set up the GiNaC library in Linux on my main notebook computer, and I can use the gdb-dashboard for stepping through the code, analyzing the data types and all that, I also have a smaller machine with an old VGA monitor and standard keyboard hooked into it that, for some buggy reason that I will not allow to drive me crazy, is just not compiling code with GiNaC libraries.

What I have decided to do is run Windows on that machine, using the free Visual Studio Community 2015 debugger, which I humbly submit is very cool, to step through code that it can compile.  The GiNaC libraries are a side interest, and I have a great deal to explore in the Standard Template Library as it is.

So, this is ultimately what I enjoy doing the most, learning through analysis with debuggers.  I refer to this as "exploratory studying".  I put much "work=energy" into setting up the compilers so as to have my own little real-time lab environment, and, "God willin' and the crick don't rise," I will continue to cherish it whenever possible (until the wheels fall off  :P).

I will take deep breaths realizing that every little breakthrough in understanding I experience during my "lab sessions" will certainly enhance my capacity to comprehend what I read in the hard copy texts that I plan to carry around in the spirit of the Unofficial School of the Weirdo-Rejectionist Scholar-Warrior.

As I foresee not having the leisure to take detailed notes from the Internet, the investment in actual texts has become necessary, and, wouldn't you know, it is a great feeling to have the actual texts in my hands.  I did not make compulsive purchases, but acquired the handful of texts that are "holy" to me at this point in my life.   Maybe some days I may even snatch Schopenhauer (or Cioran) or Husserl (or Merleau-Ponty) or even Lovecraft (or Ligotti) from the shelf in order to sneak in a couple pages throughout the day of mandatory psychiatric (behavioral) "treatment".

What I am exploring now is the Standard Template Library in C++.  Armed with compilers and debuggers, I compile the example code from a text, and run it in a debugger.  With a beginner's mind I explore the nature of the data structures and algorithms. 

For instance, with gdb-dashboard (in Linux) I can type "dashboard expressions watch t" and "whatis t"

type =  std::tuple<int, float>

With gdb, you set a breakpoint at main() with: b main, then run
Stepping through the code with s, and just calmly analyzing what you can.

In Visual Studio, there are also many ways to explore the code in debugger mode.  It is one of the things, like the Power Shell, where I throw all my anti-Microsoft prejudices aside, and just appreciate what the Visual debugger has to offer in Slow Motion Mode.

Can't we all just get along?  :-\

So, side by side, GNU GCC with the gdb-dashboard on one machine, and as a supplement, Visual Studio in debugger mode ... stopping the code and stepping through it as slowly as I need to.  This is Exploratory Studying.  What I see while "in" these debuggers, like I said before, will enhance my comprehension while going through texts.  The words may become more "alive".

This kind of studying has the****utic value in for the following reason:  a certain passion transforms the discipline from a boring technical interest to a rewarding and satisfying activity.

Why was I so particular in choosing who to invest energy in "following"?   It's not a game.  What we choose to focus our attention on is what becomes our life-world.

When we are restrained or constrained by forces more powerful than us, where the representatives of our society are in our face with intrusive and often denigrating questions, this is the illusion of CONTROL I think the character from Ishmeal was referring to.  We can choose to reflect upon the tenuous nature of our social status, or what Schopenahauer called the image we make in other people's heads.  It is secondary.   What goes on in our own heads?

I can be torn from my little programming laboratory, but the code is in my head.

I can't help but keep hearing those words of Virginia Woolf over and over again.

[Knowledge] "is open to everybody. I refuse to allow you to turn me off the grass. Lock up your libraries if you like; but there is no gate, no lock, no bolt that you can set upon the freedom of my mind."

dinosaur
« Last Edit: November 15, 2015, 05:52:31 pm by H »
Things They Will Never Tell YouArthur Schopenhauer has been the most radical and defiant of all troublemakers.

Gorticide @ Nothing that is so, is so DOT edu

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Continuously Sparking Imagination
« Reply #6 on: November 22, 2015, 11:38:11 am »
I want to have fun learning.  Does this lead to contradictions when I hit a wall?

I must keep repeating to myself, "My intellect has exhausted itself in order to demonstrate its own limitations."

Do I consider it fun to exhaust my intellect in order to demonstrate its own limitations?

I may bash academics and professionals, but most if not all my sources for learning are from the academic world or from industry.  I can't be a purist.  It is difficult enough to remain interested and not be overcome by a sense of futility without burdening myself with guilt and shame.

Am I still having fun learning?

I think so ... as long as I can handle the ego-squashing activity of deferring to the knowledge and experience of superior intellects. 

An analogy is called for.  There are cultures on this planet who teach their young how to make fire without flints or matches, or to build shelters from natural surroundings - to find food and water.  If I were dropped into such a society, I would have a great deal to learn from a 12 year old.  It would be humbling, but do I want to learn or not?

Likewise, technology is always changing.  Even C++ has transformed in the past 20 years since I was first exposed to it.  I was always terrified of Assembly Language, and I am curious about the low-level differences between 32-bit and 64-bit architectures.   I am just curious.  This is a spark I can refer to as "interest".

I am curious, therefore I am interested.  This has become very personal for me.

It seems as though I may be attempting to validate the 8 years of serious study.  After that I experienced about 13 years of psychopathic depression ... and I lost interest in what I had studied because I felt all the work was not worth it.

Why have I become interested again?  What has sparked my curiosity? 

Maybe it has to do with the fact that in 1993 or so I was drawn to material that only a post-graduate would be interested in, or there would be warnings about prerequisites.

Now, I at least can research material without the voice in my head telling me, "You are a janitor.  Maintenance workers cut grass, clean toilets, chop up fallen trees with chainsaws.  You are not qualified to study what you think you are drawn to."

In a sense, I have paid some dues.  I have been knocked around by the school of hard knocks.  I am just another strange character in this science-fiction reality ...

There are many different kinds of people in this world.  Whatever I have been drawn to over the past 6 months has a lot to do with having a computer before me.  How do I interact with the machine?   I make it dual boot so as to have access to Linux while not totally alienating myself from the Microsoft world.  I leave records here on this message board of the kinds of things I have been tinkering with.  Those are the things that have my interest ... not online poker.

In order to retain motivation and interest, it may help to see how the dots are connected in a causal chain of psychological events.  One thing leads to another. 

OK, so there are things I wish I would have known by now and never really got around to learning.  Like I said, this is very personal for me.  I can't allow the fact that I appear to have a kind of "unemployable personality" to prevent me from pausing to study the kinds of things I wish I would have understood better by the time I reached this age. 

I can't allow myself to be overcome by the sense that "I am too old to start over," for it is not even possible or desirable to start over.   I think I can blend my study of C++ STL (generic programming with templates) with some kind of disciplined study of 64-bit Assembly ... and continue to explore abstract algebra, group theory, and even the Scheinerman book, "C++ for mathematicians".

We go through these lives, and each of us has our own particular life-world.  The television portrays a global narrative, a national narrative, etc ... but is that how we really experience reality, as citizens and consumers and clients and inmates and employees?

Isn't there a personal inner life that trumps the meta-narratives?

One thing I do have in my favor is that I certainly can't help but value access to information.  I can honestly say that I treasure having access to texts and other mediums.
« Last Edit: November 22, 2015, 01:36:31 pm by H »
Things They Will Never Tell YouArthur Schopenhauer has been the most radical and defiant of all troublemakers.

Gorticide @ Nothing that is so, is so DOT edu

~ Tabak und Kaffee Süchtigen ~

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Mind Shift: Caring Enough To Think Slowly
« Reply #7 on: February 20, 2016, 11:47:04 am »
Since our local search engine is, let's face it, close to useless, I could not easily find the thread about slow thinking and repetitive learning styles, but this is as good a place as any to document an example from lived experience.

Suppose I am "working" through the exercises in a text I consider to be "elementary" just as a review, and I come to a problem that involves some thinking about trigonometric identities.  Now, let's assume I have a stack of textbooks I want to "get to," and one on top, say a Linear Algebra text, that I am most committed to, almost feeling as though I am just goofing off by working through Joyner's Differential Calculus and Sage.   I come to a problem where I have to prove that the limit (as h approaches pi/2) of cos(theta - h)/cos(2*theta - h) is -tan(theta).

Sage computes result as sin(theta)/sin(2*theta)

There is the temptation to skip this pesky little problem since I want to "get to" something else.

Aha, and this is an example of what I am referring to when I plead the case for SLOW THINKING in the spirit of bringing some "fun" into the learning process. 

This would involve what I am calling a mind shift.

This is the benefit of learning outside the confines of an academic or corporate setting: to have the inner (intellectual) freedom to respect one's own lack of clarity enough to CARE about the what and the why and the wherefore. 

[enter demon, Subscript One]: Now, it's getting late in the game, Herr Hallar ... do you have time to understand things in such a thorough manner?

[enter second demon, Subscript Two]: I'm afraid I'm going to have to INSIST we move slowly through this material, sir!  Do not piisss on trigonometric relations while calculating limits in an effort to go racing up the metaphorical mountain so as to get down to the serious business of trying to understand what differential equations mean!  Are you afraid you shall be suddenly ripped from your chamber and sent into the abyss before reaching your intended destination?  :o

[Subscript One]: There's no time to goof off and actually understand!!!! 

[Subscript Two]: No time?

[Steppenwolf]: I must face that which perplexes me with courage and show my disdain for those who act is if everything is trivial.  I have to agree with Subscript Two.  We can afford to go on a tangent if it promises a mind shifting experience.

master stroke

[enter third demon, Subscript Three]:  Hint:  sin(theta) == cos(2*theta), as in sin(pi/6) == cos(pi/3) = 1/2 

second hint:  tan(-theta) = -tan(theta)

tan(-pi/6) = -tan(pi/6)
_______________________________
cos(pi/6 - pi/2)/cos(pi/3 - pi/2) == cos(-pi/3)/cos(-pi/6) = -tan(pi/6)

A few more tid-bits:

cos(-2*theta) = cos(2*theta) = sin(theta)

cos(-theta) - cos(theta) = sin(2*theta)

tan(-theta) = -tan(theta)
________________________________________
Where I get jammed up is that sin(theta)/sin(2(theta) = tan(theta), not -tan(theta)

Note that cos(theta - pi/2) = cos(2*theta) = sin(theta)

Also, cos(2*theta - pi/2) = cos(-theta) = cos(theta)

so, as limit of h approaches pi/2,
cos(theta - h)/cos(2*theta - h) approaches cos(2*theta)/cos(theta) = sin(theta)/sin(2*theta) = tan(theta), not -tan(theta) !!!!

- and Sage agrees!   Those who publish textbooks sometimes make mistakes.

Another CAS computes result of limit as 1/(2*cos(theta)) which is the same.

Check:  1/(2*cos(pi/6)) = 1/(2 * (sqrt(3)/2)) = 1/sqrt(3) = sqrt(3)/3

And after spending the entire morning on "one easy little exercise," while my understanding isn't exactly intuitive, one thing is clearer to me, and that is the definite relationships existing between the trigonometric identities.

Do you think that the authors of such texts have that kind of time to consciously lead the attentive reader into specific conceptual arenas?  They must exist in eternity.  I mean, there has got to be some kind of transcendental realm where "time" no longer presses down on us.  That's the "place" where we can actually enjoy the thinking process and momentarily transcend drudgery.

Maybe ...  :-\
« Last Edit: February 20, 2016, 01:22:33 pm by H »
Things They Will Never Tell YouArthur Schopenhauer has been the most radical and defiant of all troublemakers.

Gorticide @ Nothing that is so, is so DOT edu

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Re: How to Attain a Studious Life
« Reply #8 on: February 20, 2016, 03:11:29 pm »
Quote
They must exist in eternity.  I mean, there has got to be some kind of transcendental realm where "time" no longer presses down on us.  That's the "place" where we can actually enjoy the thinking process and momentarily transcend drudgery.

Our minds are so alike that sometimes I find it extremely strange! Just today I have been reading about just such a "place".
Dog, dog, dog, dog, dog, dog, dog, dog, dog, dog, dog, dog, dog, dog, dog, dog, dog.

Wait, was that a word? Didn’t it mean something a minute ago?

This fascinating psychological phenomenon — when a word loses meaning after being repeated over and over without interruption — is called semantic satiation.Where it really gets interesting?

This leads to other curious phenomena, one in which you want to experience a type of semantic satiation, like during meditation when you sit down to meditate and employ a mantra word such as a mathematical formula to chant repeatedly.
https://youtu.be/yoYrLM5rGX8

I wonder if whats being done with "OM" in the video could also be done with mathematics.
From the "Dreams in the Witch-House":
Quote
Old Waldron, who had curtailed his activities before, would have made him take a rest - an impossible thing now that he was so close to great results in his equations. He was certainly near the boundary between the known universe and the fourth dimension, and who could say how much farther he might go?

But even as these thoughts came to him he wondered at the source of his strange confidence. Did all of this perilous sense of imminence come from the formulae on the sheets he covered day by day?

Can semantic satiation help me to cross the boundary between the known universe and the fourth dimension?
« Last Edit: February 20, 2016, 03:14:12 pm by Holden »
La Tristesse Durera Toujours                                  (The Sadness Lasts Forever ...)
-van Gogh.

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Re: How to Attain a Studious Life
« Reply #9 on: February 21, 2016, 01:54:09 pm »
I am not so sure I want to find the fourth dimension, but I suspect that we live in a 3-dimensional world simply because we are organisms equipped with apparatus for mental representation limited to 3 dimensions.   

I respect the limitations of the world-representing apparatus "I" (the thing in itself) am equipped with.

I do not think it is possible to OM myself into perceiving higher-order dimensions.  We handle 2-dimensions OK on paper, but even 3-dimensions gets a little tricky when trying to represent it on flat 2-dimensional space.  Something Cioran wrote that is very depressing but may be true in the end.  He wrote that there can be no "Instant India".   Ciroan wrote some depressing things, but I found this especially depressing.  It made me think that the only solution was a barbaric drowning in hard alcohol.  He wrote an attack against the "Instant India" that has been fashionable in the west for a couple of centuries now.  I mentioned it somewhere where Cioran seems to be promoting living as a beggar, that this would be authentically getting the gist of ancient teachings, quite the opposite of holding a position on the philosophy (of Asian Studies, perhaps) in some University, driving to a meditation temple in one's Volvo or Volkswagen.   


As for the trigonometric identities, I find them fascinating.

I love how circularly connected (pun intended) certain branches of mathematics are.  I mean, I want to understand how to solve differential equations, so this leads me back to Integral Calculus where there is use of trigonometric identities ...

Quote
These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.

I am tempted to take some time to transcribe such a list from wikipedia into a special high-quality art notebook and call it Techgnosis.

So, as you can see, I have my hands full just with 2-D and 3-D.  That's where my attention is focused.   :)

If I compare this intellectual journey to climbing a mountain, where the mathematics of classical and quantum physics is the mountain itself, then I see myself, personally, as spending many days at a time in a camp site off the beaten trail going on deep tangents.   (LIST OF INTEGRALS OF TRIGONOMETRIC FUNCTIONS

One thing leads to another.  I first loved Calculus because it forced me to use what I really enjoyed, Algebra.   Now that I want to learn about differential equations, I find I keep going further back to fundamental ideas ... Integrals .... and, as I said, this leads to an appreciation for trigonometry

Do you remember when Henry Fool tells Simon, "I'm gonna blow a hole this wide in this world's idea of itself!" ?

Well, I would like to embrace a feeling of indifference to the large egos of physicists working in N-dimensional space by realizing my cup is over-flowing in R^3.  I am serious about this.  My plate is full.  I am engaged in a spiritual battle with a mindset that spans many cultures, not merely the culture of Taker Prison, and that mind-set is based on "hierarchies". 

I hate to sound mystical, but the entire apparatus of the mathematics for physics would crumble without being grounded in the fundamentals.

For this reason, I will honor any text I approach by always pausing when necessary to review necessary grounds. 

Of course, at such a rate, one might not ever reach the top of the mountain.  I am not trying to reach that ... I am content just camping out somewhere on this mountain.   ;)

With this being said, please don't think I don't appreciate the passage you quoted.  Is that from Lovecraft?  I vaguely remember having read that.  Passages like that makes me suspect Lovecraft did a great deal of dabbling informally in higher mathematics.  He did not enter the university, but that did not banish him from a love of learning.

Quote
Did all of this perilous sense of imminence come from the formulae on the sheets he covered day by day?

Indeed ...  :o

It is kind of eerie that the words "qualitas occulta" - which we both admit to being somewhat obsessed with - were the very words that brought someone into our semi-private discussions.  That this has further motivated me to divert my attention from Number Theory and Abstract Algebra into more traditional branches of mathematics which are used in Physics, has forced me to adapt (psychologically) to the chaos of what we call "the mind".

I have no choice but to approach these subjects with humility.  I mean, fortunately I already have an interest in Linear Algebra and Multivariable Calculus ... so, preparing for this "disciplined self-study" of Differential Equations is pretty much where I peak out.   You see, I will be satisfied with this ... if I want to revisit physics with a "revived, revamped, and expanded" mathematical maturity, well ... if that's where it leads ... so be it.

I appreciated that one video about chaos theory, and how some are applying it to psychology.  I just want to spontaneously flow in the moment and not "minimize" what I am thinking about today.  I don't want to "glorify" theoretical physicists.   When push comes to shove, they must exert just as much mental concentration to visualize physical phenomena mathematically as anyone else.  I don't believe in "quantum gods" ...  ;)

Theoretical Physicists, Mathematicians, Engineers, and Scientists of all stripes have to eat food, sleep, poop, piisss, and the rest.  On an empty stomach, the brain does not function.  I mention this because I am constantly reminded of this when I have to put down the pencil and eat bread or drink carrot juice ... just because ... well, we are, as Kurt Vonnegut said, chimpanzees who can read and do a little math.  To be an organism is a humiliating experience.  hmmm ... I need water ...

You do understand that my goal is not to be a "great mathematician" who makes some kind of breakthrough discovery, but to humbly cherish gaining understanding of very basic and fundamental concepts.

It think it is vital to find enchantment in thinking about whatever we are able to grasp at the moment ... in a grain of sand, so to speak.  I do not want to try to appear to know more than I do.  You understand that it's all I can do to gain a tenuous grasp of the material.

Holden, I am the eternal student ... I am not attempting to master this craft, but merely able to demystify it a little for my own satisfaction.

If ever I sound like a "hater of professional scientists and engineers," it may simply be an underlying resentment against what I perceive to be a classist hierarchy of servile asslickers posturing for social status and ego-inflating positions ...

Studying this stuff is an ego-destroying activity for me, and I study it in defiance of the meritocracy.   I want to reach just beyond my intellectual capacity, and then come back around and focus on the level that I can comfortably comprehend.

It helps if I see myself as a chimpanzee, for then I will be patient with my frustrations when I face problems that incomprehensible. 

I do not ever want to be one of those who says, "Oh, that, I studied that, I know all about that.  It's boring."

Rather, I am more like, "Oh, that, yes, well I studied it formally but, ever since, I have felt as though I barely skimmed the surface ... and now I am left in a state of perpetual curiosity ..."

In the past I have used language such as "servile scientists" ... Both my grandfathers were scientists, a chemist and a mechanical engineer ... one helped build the atomic bomb.  My father studied refrigeration and continues to install walk-in freezers for semi-wealthy businessmen who own chains of liquor stores and what not.  Me?  Well, I am the skinny version of Ignatius Reilly.  I consider myself a misfit, an outsider ... I felt no shame cleaning toilets or collecting garbage cans.  Like Kafka, I may have been paying a kind of karmic penance ... you know, for grandpa's designing some little pressure relief valve component which may or may have helped with the construction of an atom bomb.

I am no space monkey.  I look at those who want to travel to Mars the way all the other animals on this planet would look at them ... as a pathetic joke to be mocked.

So, I am quite the frustrated chimpanzee, huh?

I can honestly say that I love mathematics, and I am fairly certain that I love computers ... This will not change the fact that I am a moody ape who seems most content when hiding away studying ... but I have contempt for anyone who would want me to compete or jump through hoops or act enthusiastic about "the space program" or the "arms race."

Just because I love mathematics and programming does not mean I want to get aboard the Starship Enterprise.

Hooooo Haaaaa

PEACE!
« Last Edit: February 21, 2016, 08:19:11 pm by H »
Things They Will Never Tell YouArthur Schopenhauer has been the most radical and defiant of all troublemakers.

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Holden

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Re: How to Attain a Studious Life
« Reply #10 on: February 22, 2016, 12:16:23 pm »
Quote
Both my grandfathers were scientists, a chemist and a mechanical engineer ... one helped build the atomic bomb.

That's interesting.You certainly come from a long line of German mathematicians.I cannot help thinking that its only with you that your lineage has reached its culmination & with it,its end. It made me think of The Kreutzer Sonata by Leo Tolstoy:

Quote
But," said I, with astonishment, "how would the human race continue?"

"But what is the use of its continuing?" he rejoined, vehemently.

"What! What is the use? But then we should not exist."

"And why is it necessary that we should exist?"

"Why, to live, to be sure."

"And why live? The Schopenhauers, the Hartmanns, and all the Buddhists,
say that the greatest happiness is Nirvana, Non-Life; and they are right
in this sense,--that human happiness is coincident with the annihilation
of 'Self.' Only they do not express themselves well. They say that
Humanity should annihilate itself to avoid its sufferings, that its
object should be to destroy itself. Now the object of Humanity cannot
be to avoid sufferings by annihilation, since suffering is the result
of activity. The object of activity cannot consist in suppressing its
consequences. The object of Man, as of Humanity, is happiness, and, to
attain it, Humanity has a law which it must carry out. This law consists
in the union of beings. This union is thwarted by the passions. And
that is why, if the passions disappear, the union will be accomplished.
Humanity then will have carried out the law, and will have no further
reason to exist."

"And before Humanity carries out the law?"

"In the meantime it will have the sign of the unfulfilled law, and
the existence of physical love. As long as this love shall exist, and
because of it, generations will be born, one of which will finally
fulfil the law. When at last the law shall be fulfilled, the Human Race
will be annihilated. At least it is impossible for us to conceive of
Life in the perfect union of people."


CHAPTER XII.

"Strange theory!" cried I.

"Strange in what? According to all the doctrines of the Church, the
world will have an end. Science teaches the same fatal conclusions.
Why, then, is it strange that the same thing should result from moral
Doctrine? 'Let those who can, contain,' said Christ.

Do you think its possible to have no interest in algebra,calculus,linear programming-no interest in any particular topic/branch of mathematics & yet be obsessed with mathematics,with mathematics- in- itself?
« Last Edit: February 22, 2016, 12:19:29 pm by Holden »
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-van Gogh.

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999: How to Attain a Studious Life
« Reply #11 on: February 22, 2016, 03:05:53 pm »
I am repeatedly astounded that we have been fortunate enough to have this medium for our correspondence.

As I am inclined to babble on and on, I will try to answer your question directly.

Yes, I do think it is possible to  be obsessed with mathematics while not committing oneself to any particular discipline (with no interest in algebra,calculus, or programming). 

Perhaps it all depends on how one is wired. 

Myself, I am comforted by some guidance and structure when approaching "mathematics" since it is so monstrously vast, where so many regions are incomprehensible to me.

You might be drawn to Chaos theory and fractals ... and, as you mentioned, Number theory ... It does seem a little grotesque to compartmentalize into so many branches, I know.

Some people are wired to zero in on what they feel is "the ultimate" area of study, almost the scientific version of Hegel's "Absolute".   Many theoretical physicist revere Quantum Mechanics as some kind of holy grail, presenting it to the lay public as a sort of streamlined modern day mysticism for an elite inner circle of "quantum gods".   ::)

Myself, when I venture into reading about Quantum Physics, I look at a few pages and back away from the text shaking my head - only because it appears to be utterly incomprehensible to me.

I am easily overwhelmed, you see, and, much like you, I don't want to feel as though my "appreciation of the realm of mathematics" is inadequate just because I have not mastered a particular branch.

However, speaking for just myself, I find that when I finally do find a source, such as a textbook, that is just a little beyond my comprehensibility, if I find myself respecting the effort the authors of the text have invested in trying to guide the reader/student to understand the subject (or branch or field), then, should I become engrossed in an exciting adventure, I tend to be less "nasty" and "mean-spirited" toward the "specialists" ... and attempt to put into words what I do and don't comprehend.

For example, since I have become curious about differential equations, I resisted the temptation to go diving into some incomprehensible physics or engineering text. I was very fortunate to find a book for five dollars on Amazon that really appears to be directed at my level of comprehension.

See Differential Equations & Linear Algebra

There are "exploratory laboratory" exercises in a supplemental Interactive Differential Equations ... I am curious about the authors' encouragement to learn how to "write in mathematics" where they promote "suggested journal entries" to practice writing about mathematics, which for me, has always been frustrating.

I suppose I am wired in such a way, where my mind can easily be overwhelmed by the chaos of it's own thinking, that I cherish some kind of "grounding" ... and, yes, guidance from experienced "mathematicians".

Remember how over the summer I was just exploring Number Theory, and I stumbled upon (purely by chance) William Stein's Elementary Number Theory: Primes, Congruences, and Secrets?  I was fascinated with the Chinese Remainder Theorem.  That text had a huge effect on my life, encouraging me to begin a special series of "Math Diaries" (which I now call Computational Sketchbooks).  It is also where I first learned about Sage - Stein is the founder, and, hence became intrigued with Python on whose libraries of modules much of Sage is built.


Quote from: Holden
    Both my grandfathers were scientists, a chemist and a mechanical engineer ... one helped build the atomic bomb.

That's interesting.You certainly come from a long line of German mathematicians.I cannot help thinking that its only with you that your lineage has reached its culmination & with it,its end.

It's end?  Yes, this appears to be the case unless the space monkeys lock me in a planet-of-the-apes cage (***blankets and bananas***) with a beautifully exotic specimen for the purpose of squirting in the last few drops of my evil seeds.    :P 

As you phrase it, I see "its end" more as a Schopenhauerian/Nirvanic culmination ...

As for a long line of mathematicians, no, no, and again, no.   It was just the fathers of both my parents.  My parents have absolutely no interest in mathematics.  As for great grandparents, I have heard stories about a Swedish great grandfather who was a heavy drinker and a hater of religion.  I feel a great connection with him.   Another great grandfather (of German lineage) committed suicide like Schopenhauer's dad, and I believe he was also a businessman like Heinrich Schopenhauer, but not quite as wealthy.   I think he owned a factory that crafted coffins.  Can that be true, or is that some kind of joke?   Well, I'm sure it wasn't a factory.  It wasn't a coffin boutique!  Maybe they were built on demand ... People are always dying.  :D

He committed suicide Mr. H?  And crafted coffins?   ??? ;D

How ironic!

In the tradition of Kurt Vonnegut Jr., I might as well spill the beans, since you alone display an interest in such hilarious details.

It was just Charlie Weber, the engineer who worked for RCA designing "pressure relief valves for water heaters" (and forced by the US government to help out on some minor detail with the Manhattan Project) ... and Carl Hentrich, the chemist who worked for DuPont (and tried to convince my father --- Mr. Bill, who constructs walk-in freezers for countless merchants from India who have set up shop [mostly liquor stores]  ;) on the East coast ---- to take a job at DuPont as a janitor).   When my father rejected this game plan, my grandfather suggested he study "Refrigeration" since it could not be "outsourced" ... it's hands on and expensive to ship the parts, unlike "information technology" which is zipped and zapped around the planet at the speed of 3×10^8 meters per second.

Too much information?

I am not ashamed of my grandfathers.  In fact, they appear to be the source of my mathematical inclinations.  I'm just more wired like my Swedish great grandfather as far as my insubmission goes, and a little like my father when it comes to disassociating myself with any class of people who seem pretentious or pompous, such as ... well, servile corporate scientists.   :-\

No offence to my grandfathers, I hope.

PS:

I suspect that I inherited my hand-writing directly from my great grandmother on the H side.

My "sober" hand-writing, that is. 
« Last Edit: February 22, 2016, 08:20:47 pm by H »
Things They Will Never Tell YouArthur Schopenhauer has been the most radical and defiant of all troublemakers.

Gorticide @ Nothing that is so, is so DOT edu

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Re: How to Attain a Studious Life (Why Mathematics?)
« Reply #12 on: March 14, 2016, 01:18:59 pm »
After reading this, I changed this forum's title from "Math Diary" to "Why Mathematics?" ...   

Quote from: Warren Henning
Recently I’ve been working my way through several lower-division undergraduate math textbooks. Why? Why spend your spare time learning math, which is challenging and sometimes dry?

Because math is too beautiful, too powerful, and too important to be reduced to mere mechanical calculation the way most of us experience it in school. That is not what math is really about. What matters in math, and what gives it its beauty, is reasoning and connections between ideas.

Reading books at my own pace lets me try a subject out without fully committing to it and making it a necessity that I find work based off of it. It confers the full lightness of being a beginner, exploring in a free, untutored fashion. A degree program may be a good choice for some people. If that’s you, fantastic. This article is for people who can’t or won’t commit to a conventional academic program.

The full article is: A Software Engineer’s Adventures In Learning Mathematics

I know we don't care for the title, "Software Engineer".  It sounds pretentious.  I prefer the term "code monkey."    8)

Regardless of what Warren classifies himself as professionally, as a fellow student of Mathematics, the Queen of Science (with Number Theory as the Queen of Mathematics), I like his suggestions.  I can tell that he must have a similar passion [LIFELONG OBSESSION ?].  I want to lift some of his tips here in our thread about How to Attain a Studious Life, giving him the credit, of course.  My own objective is to strip the requirement of usefulness from the subject, as if something needs to be useful or career-oriented in order to be worthy of our devotion.

We already know that most worthwhile pursuits are lonely paths ... but it's good to chronicle some advice by fellow math junkie, even if he pays homage to military training and anti-slack concepts such as "discipline".  Myself, I would like to transform the "difficult nature" of studying mathematics into "slacking off" ...  I will see if we can come to some consensus on just what it is that makes an activity mentally painful in one psychological setting, and mentally stimulating in another psychological setting.

Quote from: Warren Henning
Cultivating Disciplined Habits While Walking A Lonely Road

There’s something going on when attempting any challenging course of study. We’re striving to build within ourselves the discipline to achieve a worthwhile, ambitious long-term goal in small, manageable increments. We are training ourselves to become disciplined, effective learners. We are sculpting our minds and emotions to become used to working hard in our spare time.

This is challenging in an unusual way: for the most part, we are alone.

____________________________________________________________
Making time to study with work and family life can be very challenging. We live in a noisy, busy world, and math demands the deepest concentration, preferably in large, uninterrupted blocks of time. Just finding a quiet place free of distractions can seem impossible.

If possible, do not procreate ... and try to avoid living in apartments where you might be bombarded by intruders.  It might help if you drop out of the work-force altogether like a Japanese Hikikomori.  Yes, resign from the species, and find time to think and reflect.  The Establishment would like to have a monopoly on mathematics education.  They just can't stand not to be making money off some poor sucker who just wants to understand mathematics better, and is not particularly fond of how corporate drones and a-s-s lickers manage to destroy "the love of learning" with their pressure and stress.  If you inherit a little 4 cylinder vehicle and need to insure it just to gather groceries, stocking the shelves at the grocery store may be necessary to keep the car legal.  For now, let's bypass the complications of keeping your organism fed and dry.   :-[
_________________________________________________________________

I like this section on Facing YOUR Demons ... [the "Why Bother?" demons?]:

Quote from: Warren Henning
Facing Your Demons

I’ve had to contend with many self-defeating mental blocks I wasn’t initially even aware were impacting me. I’ve thought at various times that I didn’t even have the right to try teaching myself because math is somehow the exclusive domain of established experts. If you aren’t already a master by now, don’t even bother, part of me thought. That “don’t even bother” sentiment paralyzed me for years.

I hope you give yourself permission to pursue your own interests, even if you don’t have the traditional background of experts in your field of interest.

Fortunately, as an old gortbuster warrior, I do not defer to the authority of the gort establishment.  So, it looks like I am good to go on the pursuit of my own interests.   :D

Quote from: Warren
Average People Have Things To Add, Not Just Alpha Geeks

If you’re like me, the academic-industrial complex of research labs and paywalled research journals is a bit intimidating. There seems to be no room in such a place for mere mortals. And yet there are so many problems to solve in our world, and MIT-educated geniuses so few in number, that they will undoubtedly overlook things us average folk can be in a better position to actually do something about than they. Researchers often don’t focus on delivering complete solutions to problems their work may be useful in addressing; by necessity, they focus on the fundamental issues, and once those are figured out, they often move on to the next research problem. Valuable insights that could be useful to many languish in obscurity behind horrid paywalls. Let’s not make the established, traditional experts out to be more than they are, either; a lot of them are really only capable in their specific niche and lack a lot of valuable complementary skills you already possess.

It seems a great tragedy that many of our best and brightest in industry wind up working on better ways to sell ads online or allocate capital in financial markets. The amazing things they could do with their highly advanced skills go unrealized. Because of this, I think the wider group of intellectually curious amateurs have an opportunity to truly capitalize on the advances made in the sciences.
[italics added by H]

[This next segment is simply beautiful ... This Warren character is a true math preacher!  Great stuff!]   :'( [tears of enlightenment]

Advocation Of Autodidacticism In Math, Science And Engineering

To be honest, I feel nervous even publishing this. I left it sitting as a draft on Google Drive for well over a month after spending hours writing and editing it. What will the turbogeniuses who already know everything I aspire to learn and are also probably better software engineers to boot say? Many of them are several years younger than I am, already more accomplished in every way. I just have to learn to live with that.

The prize I have my eye on far overshadows any anxieties or reservations I have. A world of eternal truths and cold, subtle beauty awaits. We will fill whole notebooks with thoughts, scribbles, dead ends and epiphanies. We will construct a body of knowledge which we can truly claim for ourselves and which we can never be stripped of. Let us grant ourselves permission to be beginners, to be uncertain, to have more questions than answers, to be ignorant but motivated to learn. Let us dare to begin.

I’ve found searching Amazon and the wider Internet for books to be quite rewarding. You can be surprised by what you find.

Let us dare to begin!

More importantly, may we continually cultivate the Beginner's Mind by embracing our "not-knowing" state ...


« Last Edit: March 14, 2016, 01:24:18 pm by H »
Things They Will Never Tell YouArthur Schopenhauer has been the most radical and defiant of all troublemakers.

Gorticide @ Nothing that is so, is so DOT edu

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What virtues does studying mathematics inculcate?
« Reply #13 on: March 22, 2016, 10:52:44 am »
I was searching for articles related to "mathematics and humility" as I am hoping some kind of psychological transformations might make the endless lifelong encounter with mathematics less frustrating for me.

It is said that when mathematics is practiced with great devotion and humility, it involves the transformation of both mind and heart which leads to wisdom. 

What virtues does studying mathematics inculcate?

Patience. Math is hard. It takes time. Try to make progress today, but also know it will be there for you tomorrow.

Humility. Related to the above. Math will surpass your abilities on some days. That's fine. It does that to everyone sometimes.

This next one I just love:

Intellectual honesty. You won't get anywhere until you admit to yourself what you don't know.

In other words, sometimes our confusion may not stem from ideas in Calculus or Differential Equations, but in the Algebra and Trigonometry we are using to solve problems in "other subjects" that make heavy use of algebra, geometry, trigonometry, and even general number theory.  It is great to have to continually return to fundamental ideas.


Zenlike mental calm. It is impossible to do math if you are feeling overly emotional. To study math is thus in some sense to rehearse inner stillness.

An aesthetic appreciation for rationality.  You know that in some sense it will always be beyond you, but the slow, steady accretive work of understanding one piece at a time has its deep, life-long satisfactions.

Willingness to tolerate bad explanations.  Changing gears, a lot of pedagogy in math is terrible, perhaps because people generally don't understand math all that well, or just don't know how to talk about it clearly. By wading through bad explanations, you can learn how to mentally translate something complex into something that makes sense to you. This is a useful skill in other domains too.

An appreciation for complexity and for the limits of our ability to understand things.  I guess this is the same as humility above, but doing math makes you realize that most people, most of the time, probably don't know what they are talking about. Math, like programming, chess, or most complex pursuits, is an antidote to human BS because BS doesn't get you anywhere in trying to figure out something mathematical.

 ;D
« Last Edit: October 17, 2017, 06:18:14 pm by Non Serviam »
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Gorticide @ Nothing that is so, is so DOT edu

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Re: How to Attain a Studious Life
« Reply #14 on: March 26, 2016, 10:37:46 pm »
To motivate myself to forge ahead and continue studying ... I reflect upon those who are physically trapped in jail cells, frequently in pairs so as to NEVER have any true solitude and always be tormented by the presence of another human being in close quarters.

I reflect upon how precious is the access to paper, pencils, computer algebra systems, textbooks, coffee, tobacco, peanut butter, eggs, etc ... a blanket and pillow ...

Sometimes it helps to imagine oneself in some open air prison where you will spend your existence in your room, walking around outdoors (dodging automobiles) ... and you are studying to understand ... and you cherish being one who knows that there really is no one to know, nowhere to go, and no one to know. 

Study as though you are doing something forbidden rather than required, like a chattel slave sneaking a book of higher mathematics back into his quarters, then refusing to report to the master in the morning ... come what may.
« Last Edit: March 26, 2016, 11:56:27 pm by H »
Things They Will Never Tell YouArthur Schopenhauer has been the most radical and defiant of all troublemakers.

Gorticide @ Nothing that is so, is so DOT edu

~ Tabak und Kaffee Süchtigen ~