Author Topic: Arithmetic is Drudgery  (Read 3958 times)

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Nation of One

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Re: Arithmetic is Drudgery
« Reply #30 on: March 28, 2017, 08:47:20 pm »
Actually, even though I am determined to continue along this path, I am finding that I am still drawing a blank on the last few problems of some of the sections.

Maybe it is best I traverse this path alone. 

I have to consider all this work as goofing off even though it certainly doesn't feel like play.
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: Arithmetic is Drudgery
« Reply #31 on: March 31, 2017, 12:30:13 pm »
Herr Hentrich,

Thank you so very much for your offer of giving me the key to the difficult math text book. To tell you the truth,I do sincerely wish that someday,perhaps soon,I would be able to understand maths much better than can presently can.
Thank you very much again.

La Tristesse Durera Toujours                                  (The Sadness Lasts Forever ...)
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Arithmetic, like Life itself, is Drudgery
« Reply #32 on: March 31, 2017, 06:13:01 pm »
Take your time, Holden.  By the way, it is not so much that the text is extremely difficult as it is how formally and rigorously it presents the material.   It is very old school, very mathematically precise.

I am retraining my mind, forcing myself to consider familiar ideas in their purest form.

It helps me to keep my scratch work in order (and not to skip any problems) thinking that these notebooks might one day be scanned into pdf format and shipped to India on a flashdrive.

Even if this is just a trick I am implementing in order to psyche myself up to stick with this task, it does help me to write as legibly as possible.  I am using 50 cent notebooks so that I don't feel pressured to write smaller.  I tested a couple pages, and the pencil shows up fine on the scanned version.

I am actually relieved that you are not quite at the point you would want to get into this since this gives me plenty of time to work through it.  I invested in the solution manual for this old relic, so, even on the tough problems (especially these, actually), I make sure to erase my wrong solutions and replace them with the more elegant and precise solution from the manual.

I am taking my time.   I have so many texts I want to work through that I can't see getting through them in this lifetime.  I say this fully aware that I sped through much of this material at the university, "performed" above average, and feel I learned very little. 

I don't mind feeling "not so smart".  I guess facing that feeling is a necessary evil in really trying to learn something in the Now.

In the meantime, I allowed myself to go through one of the C programs from one of the computer-oriented numerical methods books I received from India.  It had a couple very subtle typos, and I was forced to place print statements all thoughout the code to trace where the logic errors were coming from. 

Something of interest to our most recent focus on the Unconscious:  I'm not sure if this is a consequence of all the reading I have been doing about the unconscious, but I found "myself" (my conscious awareness?) staying out of the way, allowing what I suppose is the subconscious mind go wild.  It was as though I were an observer watching another part of the brain do its thing without alot of conscious reflection or premeditation.   "It" was the one that littered the code with print statements so I could see what was going on.   When it was done, I did not want to remove the print statements.  You see, while I thought the unconscious was simply debugging the code, what it was actually doing was making the program explain itself.

This isn't the first time something like this has occurred.  I mean, if I spend time getting some code to run, I might as well keep whatever "educational" aspects it aquired while debugging.

I like "step by step" output.  It's the kind of code I end up with.   

This is similar to my engagement with math.  I like to gather documentation of solutions to exercises.   

So, keep that on the back burner for when you are tinkering with any programming.  You can be your own debugger simply by placing print statements in the places where the shiit is going down.  I call this using brute force, but it is essentially what coders are doing when they inspect variable values during the debugging process.


I do not miss reporting to a job.  Nor do I ever wish I were involved in some course for real-world programming with mobile devices, websites, and databases.   No, I remember what my aspirations were way back in 1994 or so.  Just getting programs to compile with GCC in Arch Linux, and then to load them into Visual Studio and compile them in WIndows 10, even though these are just "console" programs, this is all I ever aspired to be able to do.   I am content with my low level of skill and experience.   Do you see how similar my approach to programming is to my approach to mathematics?   I mean, when you really look at it closely, you can see that my involvement with these disciplines is highly personal, and that I do not seek approval from any so-called "professional authorities".  In other words, permission is not required.  We do not need permission to study, nor do we need anyone to evaluate the results of our investigations and explorations.   All those approval-seeking aspects of learning must be a consequence of social hierarchies.  I don't know.  Whatever it is, it makes me leary to engage in any dialogue in the regular "techie" forums.

Sure I am constantly hunting down information in the search engine and reading through technical threads.  I do not contribute.  To be blunt, I like to ramble on and on in a free-flowing manner.   I can count my posts on technical forums on the fingers of one hand.   Three or four posts over the years.  I don't have many "technical" things to say with any confidence.   All my technical notes are higly personal notes to a future self who has most likely lost his memory, frustratingly flipping through notes in a fog (and sipping on black coffee (or maybe even some brandy (Who knows?))) ...

I do not demand much from myself, and I am very pleased to discover I have become a little more familiar with certain things that were quite mysterious to me over 20 years ago.

That being said, the only way I can remain interested in this stuff is if I accept that I will only learn a very little bit over a lifetime.   The gorts will never rob me of my love for learning.
« Last Edit: March 31, 2017, 09:02:47 pm by Raskolnikov »
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Re: Arithmetic is Drudgery
« Reply #33 on: April 01, 2017, 12:03:28 pm »
The million dollar question goes around and around in my head constantly:  "Why bother?"

Indeed, this question is best considered while the body is in the horizontal position.

Do you know of any strategies for "tricking" one's own brain into thinking drudgery, toil, and agony is somehow "FUN"?

Oh, sure, we're having such a great deal of fun.  Loads of fun!

Sarcasm doesn't help.

How can we make arithmetic and algebraic manipulations more "fun"?

First of all, we do away with this ridiculous demand for fun.   Much like our attitude towards those who promote the pursuit of happiness, rather than looking to make computing and calculating "fun", a more honest approach might be to embrace the drudgery and mental toil of manipulating numbers and algebraic symbols simply as a brute fact.  In other words, this is what it feels like to stretch one's mind a bit.  To be blunt, we have to face the possibility that the act of thinking might actually be painful, and that the brain will resist being employed as some kind of calculating machine.

The brain may simply be protesting, and so it screams, "Why bother?   This is unnecessary!  Why are you abusing me in this manner?"

Maybe the brain is something like that character Maughan introduced me to, that Bartleby, the Scrivener.  Is it possible that the brain is telling us, "I prefer not to" ?

The brain just might prefer not to prove geometric theorems.

Maybe it would rather think about s-e-x, or it might prefer to think about death. 

Of course, this must be what it is.  The brain prefers not to think.  It is not naturally inclined to prove mathematical theorems.  It may not really care.

So how might we go about tricking our own brains into studying the language of mathematics as though there were some kind of purpose?

How do we make it more intellectually satisfying for ourselves?   (For ourselves, mind you.  We can worry about making it more satisfying for all the high school and college potential "maths suicides" only after we have discovered how to make it more satisfying for ourselves.)

Of course, I am not going to pretend to have the answer to this question ready-made.

Let's just say I'm working on it.  It is something that is of great interest to me.

I should stop here before I pretend to have an answer.  I realize I am certainly not the only person who has thought about this.   I just don't believe that trying to make it seem "fun" is the best approach.   Could a negative approach prove to be more effective?

What would a "Negative Path to Mathematics Training" look like, anyway?

Holden has mentioned a "Pessimistic Approach to Mathematics".

We are evidently on the same page.

The Negative Path would entail much rejoicing over finding the fundamentals challenging rather than racing into more and more complex and exotic areas (like "Abstract Geometry" or Quantum Mechanics).

The Negative Path would encourage delighting in the difficulty of the simplest things.

Those who embrace the Negative Path to Being Initiated into the Craft would see through the facade of those who claim something to be "easy".   Anyone who proclaimed something to be easy would be suspected of not really having given it too much thought.  Maybe they me the calculations don't require too much sophistication.

Nothing is easy except, of course, plugging in numbers into formulas.  That kind of drudgery is a breeze.  [Watch it, Hentrich!  Be careful.  OK, granted, the human brain is notorious for making erroneous arithmetic calculations.  Quick, 8 times 7 is ... see?  I always have to think "8*8 = 64" and "64 - 8 = 56", so "8*7=56".]  So, Holden is a very honest man who is up front about the drudgery of simple arithmetic.

Explaining why the formula spits out the correct result - now, that is an entirely different matter.    Certainly we cannot take any delight in something being difficult to explain in a precise manner, can we?  Surely there is a reason why so many are not inclined to pursue mathematical maturity as a hobby as an alternative to, say, uh ... well, as an alternative to suicide.   :-\

This could be where the Negativity plays a role.  Maybe we should not be looking for anything like delight, but, instead might behold the horrific detail involved. 

The Devil is in the details ... the details of why the formula works.   Once one has a formula, the calculations simply require attention and care, not too much "deep thinking".

It's in the derivation and proving of the theorems that the kind of thinking I consider painful comes into play.

How does one make this discipline more satisfying for oneself or for others who might be secretly drawn to this craft?   

I want to make it clear that I am not so much interested in generating interest in this so that each nation can produce more "techies" ... No, far from it.    I consider myself a representative of all the outcasts and outsiders who want to engage in this craft as a human rite of passage, and not as a way to be a more useful soldier or associate of some corporate entity.

Maybe "rite of passage" is going a bit overboard.  How about I represent all the outcasts and outsiders who wish to develop mathematical maturity as a way of enduring time ... as something one might wish to resort to even in a jail cell or mental asylum if the "staff" were sympathetic enough to supply you with materials: textbooks, solution manuals, calculators, pencils ...

Now, Johnny, pencils are for writing, not for stabbing! 

I refuse to work with crayons!  How they delight in humiliating me!   >:(

« Last Edit: April 01, 2017, 03:27:59 pm by Raskolnikov »
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Nation of One

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I was doing some research on Mary Dolciani and what was considered "New Math" in the 1960's and 1970's.   Evidently, she died in 1985, the year I was a senior in high school where Modern Introductory Analysis was the text we used. 

In 1987, the book called "Introductory Analysis" was published.  She is listed as a co-author even though she had already deceased.  Most of the material overlaps, but there is a some attention paid to Calculus.

I looked through some books on "Pure Mathematics" from Library Genesis, especially, Understanding Pure Mathematics (from England?)

From what I can tell, it presents the material in a similar fashion but with far less formality (rigorous proofs).

So, I suspect that what was considered "New Math" was how the material is presented, using set theory notation, rigorous proofs, definitions, etc

Maybe when they "reformed" the curriculum, they included some applied mathematics.

All I know is that I am looking upon my current study as the manifestation of a desire to become more familiar with pure mathematics.  For whatever reasons, I feel much more comfortable thinking of it as "pure mathematics" than as "pre-calculus".   I don't need to bone up on pre-calculus as I have a firm grasp on the algebra, geometry, and trigonometry used in "the Calculus". 

My entire reason for going through "Modern Introductory Analysis" [Mary P. Dolciani, Edwin F. Beckenbach, Alfred J. Donnelly, Ray C. Jurgensen, William Wooton] as well as "Introductory Analysis" [Mary P. Dolciani, David Myers, Robert Sorgenfrey, John Graham] is to, as I already stated, become more comfortable using formal notation, and to finally, over 30 years later, learn how to construct such proofs.  This is where I am still a little baffled.

Why do you think it makes such a difference to me what I call it (referring to this as pure mathematics as opposed to "precalculus")?   I think it is because the material is presented in such a different way than in texts that deal more with computational, mechanical drills.  It has to do with the presentation being formal as opposed to just mechanical computational drills.

The exercises actually force me to think, and I realize this is the kind of mathematics that I find so challenging, as opposed to the calculation-obsessed drills of differentiation and integration, which I have certainly had my fill of.

One might wonder why I can't just study everything at once.  Why do I feel I have to stop dead in my tracks, putting Multivariable Calculus, Vector Calculuc, and even Physics on the shelf?

This is just the way I am wired.  As this exploration will take 10 to 15 years, I figure it is best to rebuild my foundations, retrain my brain to be more comfortable with the more "pure" approach, before continuing with the "applied mathematics" one finds in Physics, Differential Equations, Computational Physics, etc ...

I really sympathize with the youth who aspire to become "mathematicians".  Do they yet realize how life can get in the way and totally mock their plans?

My main question is:  why do you think it matters to me what I call it?   I suspect that I would not be able to justify to myself studying "precalculus" as it might indicate something remedial - and it is not remedial, it is challenging to me to approach the material in such a formal manner.

Maybe clarifying that I am trying to better understand "pure mathematics" is a way to make it clear once and for all that I have no intentions of putting anything I learn to practical use.  Besides that, since the Physics and other "applied mathematics" texts are so intimadatingly fat, I figure I have the rest of my life to get into them, and I don't want to drown in that swamp of books until I face my uncertainties concerning pure mathematics.

As long as I am here on this earth for no particular reason, I think I owe it to myself to spend as much time as possible concentrating on the aspects of mathematical training that are mysteriously absent in university education. 

Even in courses such as Mathematical Reasoning, where the focus is on writing proofs, the foundations of the applied mathematics courses are never really explored.

In this world which rushes the youth from grade school to high school full steam ahead toward Calculus and Physics, there is not much "basic training" for those who need to be spoon fed "pure mathematics".

The reason I chose to major in Computer Science was because I was getting a grant from the goverment, and it was taken for granted that I would find some kind of job/career afterwards.

So I focused on applied mathematics.

Now I have the benefit of living without any hope of ever being employed as anything other than a janitor, so I am free of the delusions that I study so as to find a place in the so-called "modern day workforce".   I simply don't have the necessary servile temperament to be some kind of "professional scientist".

My failure to find any kind of vocation has liberated me to do nothing with my life.

That is why I have this opportunity to return to the text that was presented to us (at age 17) as "AP Calculus", and to approach it with my own personal intitiation into "Pure Mathematics".

There seems to be a psychological aspect to the mind set of the student.  If one approaches the text as an invitation to Pure Mathematics, then there is the potential for a quasi-religious encounter; but if one sees it as "precalculus" or a stepping stone to a career based in applied mathematics and science, well, it somehow gets contaminated by the student himself/herself with questions such as "what use is any of this?"

It doesn't have to have any use.

Student:  "When am I going to USE any of this?"

Teacher: "When you find yourself on welfare living off foodstamps, if you choose to continue to explore these areas of knowledge, you can lock yourself in a fortress of solitude and resist the conspiracy against you, the conspiracy that wants to see you crawling on the floor looking for a speck of crack co-caine."

"Should you find yourself in a similar predicament as H.P. Lovecraft and countless others like him, and if you have no particular talent for writing stories, you can spend many years apparently doing nothing whatsoever while developing what we call mathematical maturity."

Student:  "But, if I may be so bold to ask, oh wise teacher, what is the use of mathematical maturity?  Will it put food on the table?  Will it pay the landlord?"

Teacher: "Well, probably not; but you will develop an inner life of the mind in the process, and this might afford you enough detachment from practical concerns that you will be satisfied living on bean soup and sleeping on the floor."

"How's that for motivational encouragement?"
« Last Edit: September 09, 2020, 06:49:09 am by Sticks and Stones »
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 ~

Holden

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Re: Arithmetic is Drudgery
« Reply #35 on: April 04, 2017, 02:18:18 pm »
Well,I do greatly appreciate your pursuit of better mathematical understanding.I think studying mathematics certainly has a calming effect on you.As Schopenhauer says there are very few people who can focus on intellectual matters for long periods of time.
You are certainly one of them.

I guess the US government does not give grant to study philosophy & even if they did,& you majored in philosophy they would require you to study tons of stuff about Hegel & the like :(

Better to stay away from all sorts of school.Its a great honour for me to be able to witness you development as a thinker.

Keep well,Herr Hentrich.
La Tristesse Durera Toujours                                  (The Sadness Lasts Forever ...)
-van Gogh.

Holden

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Recently a long raging debate(19 pages long!) has been going on about how Non-Euclidean Geometry makes difference to Schopenhauer's philosophy,if any.

Now I could comprehend most of the arguments about Schopenhauer's philosophy but I was wondering if you would be kind enough to check out this thread & tell me what you think of it from the perspective of Non-Eulidean Geometry(which I know next to nothing to about,only what I have read in Lovecraft)/Mathematics.

Here is the link to the first page of the thread.
https://thephilosophyforum.com/discussion/1036/schopenhauers-transcendental-idealism/p1


Thank you in advance.


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Re: Arithmetic is Drudgery
« Reply #37 on: April 05, 2017, 10:24:24 pm »
I will have to take that in little parts at a time.

I am relieved that we do not argue about such matters.

Schopenhauer made his comments about Euclid's proofs being complicated when he felt just glancing at the two parallel lines gave the brain a kind of direct insight that all the axioms and propositions could never match.  Of course, he was talking about Euclidean Space before it was ever referred to as such, that is, before Einstein and the theory of relativity, which I suppose exposes the possibility that space itself is curved, so two lines are not actually parallel.

Eh, for all intents and purposes, Schopenhauer makes a valid point; but when people throw modern physics, quantum mechanics and the like around, I become discouraged.

It's like Gary from Mendham, New Jersey says, this Meat Grinder is not hard to figure out.  We don't need to know a great deal of complicated mathematics to be able to see what life and people and animals are all about.

Maybe Schopenhauer spoke mainly to our hearts.

"What the head makes cloudy, the heart makes very clear."

Does it matter who is right or wrong when it comes to such things as geometric proofs?

Look at the work that NJ Wildberger has done with Rational Trigonometry (Divine Proportions).   He want to reform Trigonometry and eliminate the need for transcendental functions like sine and cosine, making it possible to make everything in terms of algebra, thereby unifying algebra, geometry, and trigonometry.

Still, they would want to teach in the classical manner anyway.

One wonders about how much faith is required of us to put so much stock in what academic authorities tell us. 

Maybe Schopenhauer had a temperament that today would be classified by psychiatrists as a mood disorder.  Maybe when he made those statements about Euclid's proofs he was simply displaying animosity, causing some trouble.

I try not to get too involved in arguments.

Still, I will slowly but surely browse through the thread you linked to just to let it sink into my skull what they are arguing about.

In the meantime, I witness within my own brain all the disturbances associated with being a living organism, and it can feel a little inauthentic and contrived to sit here typing words as a "rational creature" with the whirlwind of irrational impulses swirling about like a storm.

It's probably best that we see our own moods as a kind of weather, and to observe our own thought processes in a detached manner. 
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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Holden

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Re: Arithmetic is Drudgery
« Reply #38 on: April 06, 2017, 11:22:29 am »
Please take as much time as you need.I am not interested in the arguments per se. I am firmly persuaded by Schopenhauer.I only wanted to understand some of the math related things they say on that thread & you are far more competent in that field than I am.

Again,please take you time.I am in no hurry-where one does need to go on a Penal Colony :)
La Tristesse Durera Toujours                                  (The Sadness Lasts Forever ...)
-van Gogh.

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Why is Geometry Especially Difficult?
« Reply #39 on: July 06, 2017, 06:30:16 pm »
I'm afraid it will be some time before I am able to give any clear input on Non-Euclidean Geometry, although I may have had some encounters with it in the past.

I am giving a great deal of attention to Euclidean Geometry at the moment and most likely will be engaged with this for the remainder of the summer and into the autumn, possibly extending into early winter.

You see, this was one of the first math subjects that I did not take to naturally.  No, far from it.  I remember how psychologically threatened I was by how difficult it was for me.  I would not be surprised to find out that this, along with the divorce of my parents a couple years earlier was what pushed me in the direction of teenage alcohol abuse.

Well, now I am studying with even college years behind me, and I have already told you that, while I am a far better student at 50 than I was at 15, I am a little stunned that it is so challenging for me - not the regular exercises, but the handful at the end of each section really get me stumped and take me a long time to understand and get a grip on.

I was wondering if you had any theories about exactly what makes geometry so challenging (for me) as compared to algebra or even calculus, which I found came more natural to me.

Oh well, I will stop complaining about my little ego troubles. 
« Last Edit: July 06, 2017, 07:47:01 pm by Raskolnikov »
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 ~

Holden

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Re: Arithmetic is Drudgery
« Reply #40 on: July 08, 2017, 12:08:30 am »
I have to say I do like pattern recognition.There is something in my brain that likes it very much.
It is only when some books claim that there are one-off problems which are without any patterns,which is much like saying that with the fall of the USSR the history has ended,that I lose all my interest.
I just don’t buy that-give me patterns no matter how abstract,but patterns-history has a habit of returning with vengeance to those who think they are exempt from it.
La Tristesse Durera Toujours                                  (The Sadness Lasts Forever ...)
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Embracing the Non-Mystical
« Reply #41 on: August 26, 2017, 07:28:58 pm »
I think I may be coming to realize just why I am so determined to investigate those aspects of "accelerated" high school mathematics that got me so depressed as a teenager now that I am older and kind of "out to pasture".

Now I am able to handle the depression that is bound to ensue.  In fact, I find myself embracing the depression which engulfs me.  It must be caused by the enormity of the subject in comparison to what can be held between the ears at any given moment.   As a teenager, it overwhelmed me, but now I think I am learning to rest in confusion, or I have simply become more comfortable with the limitations of OUR mental capacity.  I do not take it personally anymore. 

I want to understand, and I do understand - just a very small fraction of what I imagined what "understanding something" felt like.

I perservere.

I have come to expect feeling depressed, and so it no longer overwhelms me.

There is nothing mystical about it.  No supernatural visions. 

I feel as though I am the protagonist in an epic existential dystopian novel where I am such an honest man that I have tracked down some particularly challenging high school textbooks from the 1980's (which still were based on the "New Mathematics" of the 1960's), where, because I am so intellectually honest I exert the mental effort required to give my all to them.

Meanwhile, the not so honest students, those who did not suffer any nervous breakdowns since it did not bother them if they really grokked anything or not as long as they got the grades, got into and out of college, and into some decent paying job married with children ... season tickets to some arena, vacations to Europe and the Gulf of Mexico, they never looked back.  They never had any desire to revisit the material since they have to keep learning how to to navigate the ever-changing software in their office ... learning how to incorporate the latest app on their smartphone to manage their finances, secure their castle, and make reservations at their favorite restaurant (not to mention ordering their wine and having it delivered to their doors).

Do you see why I get this feeling I am the protagonist in an existential dystopian science-fiction novel about the present?   To be 50 years old and be struck with this obsession to really, really, most genuinely give those high school textbooks (and others) their due?  It's as though I expect to experience some kind of mental shift.   I have been through the university and I wondered about the gaps in the educational system, how each course can only cover so much as we race toward our inevidable suicides.

Are we expected not to understand?  And if so, are we expected to then devote ourselves to the pursuit of gathering "credentials" and "status symbols"?  If someone is driving a Mercedes-Benz or a Volvo or any kind of new car at all, they certainly don't need to be concerned about how to write a two column proof.  They have to practice their techniques for maximizing their number of orgasms, after all.

No, Holden.   I do not believe the great lies.

What I am up to these days is the last thing they would expect from me at this juncture.

They expect me to wallow in self-pity, contemplate suicide, walk around sexually frustrated and totally miserable, thinking myself such a loser, such a deadbeat, such a drain on the War Machine economy, contributing nothing to society.

They certainly never expected me to go looking through these old math textbooks and hunting down the solution manuals as though I have stumbled upon Secret Knowledge that we were never meant to be exposed to, or if so, we were meant to feel intimidated and to never want to look into these matters ever again.   

What's going on?   

I am looking where they never expected me to look.   I don't need any Zen Master or religious guru to guide me out of this illusory Matrix.  I just need to train my mind to work in a calm, even if somewhat depressed, manner.   Happiness and enthusiasm are unrealistic expectations since, after all, we are living organism with all that this entails.

(to be continued)

[Ah, finally something I can post at wordpress!]
« Last Edit: August 27, 2017, 01:20:37 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

~ Tabak und Kaffee Süchtigen ~

Holden

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Re: Arithmetic is Drudgery
« Reply #42 on: August 26, 2017, 07:42:55 pm »
Well,there are somethings which I have found about maths which I am not able to describe at present. But I can see them in my mind.In time I will tell you about them, if they prove out to be true and not mere mirages.
La Tristesse Durera Toujours                                  (The Sadness Lasts Forever ...)
-van Gogh.

Nation of One

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Unusually Difficult
« Reply #43 on: August 26, 2017, 10:38:33 pm »
Some of the problems in the Jurgensen text are marked as "unusually difficult", and, well, they are precisely that - and not just difficult for "high school students".  Just difficult.   I find I have to look at the solution manual, even slowly analyzing the steps of the solution, drawing diagrams, using different colored pencils to help me "see" the variaous relationships.

And so I enter a world within my own imagination, where the only place on earth I want to be is laying down with the solution manual with my sketch pad out, getting down to the business of explaining the problem to myself.

I recall trying to read the Three Pillars of Zen about blocking thoughts out of the mind, how the masters seem to be at war with abstract thought, and I feel compelled to start my own whacky religion based on forcing the brain to acknowledge the difficulty of making sense of certain mathematical concepts.  The concepts do not have to be all that sophisticated in order to become confusing.  I want to hold this feeling.  I sense that within this emotion of honest confusion, along with the humility and patience required to perservere, there lies the root of my contempt and disdain for professionals, especially professionals in the "psychiatric" and "behavioral health" industries - as well as public defenders, prosecutors, judges, social workers, landlords, apartment complex managers, court clerks, etc.

I sense that I am at a disadvantage in a society based on credentials and certificates, ass-licking, and one's willingness to pay deference to authority.

Why do I suspect that my preference for unusually difficult math exercises in certain high school textbooks hold some kind of key to explaining my contempt for the upholders of the status quo?

Nothing that is so, is so.  There are some problems in more advanced texts which will be less challenging than a handful of the more challenging problems in a less advanced, more elementary text.  This always fascinates me.  I love to discover one of these challenging problems, not only because it humbles me, but also because when this happens, I stand a good chance of learning something if I put some effort into understanding the solution.

And how is this related to my mistrust of the so-called "spiritually enlightened" who admonish their students to be leary of abstract thought?

I most certainly whole-heartedly defer to Schopenhauer since I recognize in his writings his devotion to writing as honestly as possible, and I applaud that he spent his life thinking about the problem of existence itself.  I am not Schopenhauer though.  I defer to his superior intelligence.

My own intelligence is not on par with his, but, following his council I have come to know a great deal about who I am.  I have also come to mistrust the judgements of others.

I suppose this is why I prefer spending my time with mathematics textbooks (especially one's which I have access to the details of the solutions to the exercises).  I can see for myself how to go about solving a difficult problem.

Late at night I try to read a little philosophy, and I often lose patience with all the verbiage.  It is as though the author is using a great deal of jargon to say almost nothing meaningful.

I am destined to be a miserable man, but I prefer this to being naive or duped.

« Last Edit: August 27, 2017, 04:34:48 pm by { { } } »
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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Kantian Apologetics
« Reply #44 on: August 27, 2017, 03:33:11 am »
Quote
Late at night I try to read a little philosophy, and I often lose patience with all the verbiage.  It is as though the author is using a great deal of jargon to say almost nothing meaningful.

 What philosophy book do you have in mind? Even Schopenhauer says that Kant wrote CPR,badly,however,there are good reasons for that.Kant says in the Prolegomena that if he had really tried he could have written it like Hume( I don't doubt him).But you see,he was very close to his 60th birthday & back in the day life expectantly was much shorter.He was genuinely afraid of dying & taking his thought with him to the grave.


While he thought about the book for close to 10 years he wrote it in a mad dash of a few months.Also,he wrote it in German & at that point of time he was one of the pioneers in the field of philosophical writings in German.Unlike the English one,there was no set tradition of German philosophical writings.

And then there is the subject matter itself-not exactly something Mills and Boon is ever likely to publish. His complex language ,to a large extent,reflects his complex thought.


I agree with you and Schopenhauer that Hegel and the like took full advantage of Kant's complicated language to ply their trade.
But I would not like to throw the baby with the bath water.
La Tristesse Durera Toujours                                  (The Sadness Lasts Forever ...)
-van Gogh.