Schopenhauer's Cosmic Miserablists

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.

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. 

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  ).

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

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? 

[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 ... 

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 ...

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.

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

Indeed ... 

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!

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.

    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.     

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. 

He committed suicide Mr. H?  And crafted coffins?   

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. 

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.