{∅, {∅}, {∅, {∅}}} : Rage Against the Meat Grinder

Hey Holden,

I have a fairly good eye for books ... and I have been looking through many books on Linear Algebra.  In one semester at a state university, in January of 2000, I had taken three 4-credit math courses:  Mathematical Reasoning, Linear Algebra, and Multivariable Calculus (calc 3).  We used the Strang text, and I would take notes from his lectures on YouTube.  Still, even though I did well, the grades were "curved" and I still was confused about Null spaces and several other things ... even Eigenvalues are not very clear to me ... especially now fifteen years later with nothing to apply that knowledge to.

Anyway, I did well, but after graduating in 2002, after going on some interviews and realizing I just wasn't going to fit into the corporate world, I went on a long drinking binge ... real long ... it lasted until last March.

You know, I had been looking into Abstract Algebra, mostly motivated by the computer algebra software I was exploring - as well as by Alexander Stepanov's work (generic proramming, template libraries, etc).   Now I have been exploring Peter Gottschling's book, Discovering Modern C++.  He is also the creator of MTL4 (Matrix Template Library) [updated link 2020].  I am witnessing myself kind of switching gears.  It's when I have a few days away from the mandatory attendance at "treatment program" that I am able to settle back into my scholarly groove.

So, before I go galloping into C++ libraries for working with matrices and such, I had this impulse to return to Linear Algebra with the intention of "developing my understanding".  When I studied it formally at the university over 15 years ago, I had wished we did not go through it so quickly, and I was integrating it with what I was learning in Multivariable Calculus.  I was kind of stressed out.  Even though I did well, it was a blur ... and I lost all my academic notebooks in 2009 when I moved out to Seattle to drink myself to death.

So, I have this urge to start from scratch.  Certainly, at my age, this has nothing to do with looking for a career in Artificial Intelligence or anything like that.  I just think that mathematics, programming, and dark pessimistic literature may be a kind of drug for me in that it stimulates my intellect.  At this point, exploring the C++ linear algebra libraries would be like putting the cart before the horse.  I am in no rush.  I don't intend to master any of this before I croak.  In order to slow myself down, I want to get into a full-fledged return to a good textbook using pencil and paper, going through exercises from scratch.  I am sure to approach it from a different angle at this point in my life, when I don't give a damn about speed, grades, or employability.

I wanted to give you a heads up on the text I found and the difference in price between NEW and USED.  Also, the 4th edition of the text came out in 2014, so the 2011 3rd USED edition is even more of a steal now.

Note that such a textbook is most likely not very practical in ebook format.  This is why I haven't invested in a Kindle.  One day, if I ever find I have to abandon the precious little library I am once again accumulating, I may have no choice, but for the moment, I am seizing the opportunity (while my mind is clear) to see if I might not be able to discover that this is as good as it gets ... to study for the sake of understanding.

The text and solution manual, if purchased used, is in reach.  These are totally unaffordable if new.

I know that you motivated me to take a chance on the Schopenhauer biography, and I am enjoying the process of finding out the little details of Schopenhauer's life.   I know you are also interested in studying mathematics in your spare time.


1.  Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) 3rd Edition by David Poole

USED for around $50  [about $15 as of 2020.10]

It may seem like a lot, but considering the enormous amount it lists for ...

Compare this to what it sells for NEW ---> $317 !  (amazon) - out of reach ...    [only $50 or so in 2020]

prohibitively expensive – something which costs so much it would prevent most people from being able to do or purchase it.

At Barnes and Nobel: $ 321   

Here for less than $40.

There are some good and bad reviews of it.  I imagine if a student was forced to pay the full price and then had to rush through the material in a couple semesters, the said student might become very upset.  Trust me, I know that if one has to force interest, a textbook at that price could easily lead to suicidal depression or homicidal rage. 

It's a shame ... I mean, that structured learning in institutions of higher learning can often destroy the interest a student might have.  That's why I am fairly content to be an ageing deadbeat intellectual who doesn't give a damn about degrees or "certifications".   Last night I was reading about how Schopenhauer held back a great deal of his real feelings in the original edition of The Fourfold Root of the Principle of Sufficient Reason because he was going for his doctorate in philosophy, whereas, in the later edition, when he was older, he let the insults fly.

There is a certain amount of intellectual freedom in having nothing to gain. 

I can see how a disgruntled denizen of mass industrial society would take out his or her frustrations by lambasting the text.   Here is a level-headed description:  Gonit Sora.

I am going to order it, so, over the winter, I'll stay out of trouble, sharpen a bunch of pencils, and keep you posted.  It's not going to be an obsession - just one of the several areas I am interested in just to enjoy "the higher mental faculties".  As you know by now, Schopenhauer encourages us to stubbornly enjoy our mental faculties in solitude.  Hell, it could be the best revenge against those who would prefer to see us out of our heads with panic and anxiety.


2.
Student Solutions Manual with Study Guide for Poole's Linear Algebra: A Modern Introduction, 3rd 3rd Edition

Check this out.  NEW for $107 (amazon)

Barnes and Noble: for $50

USED at amazon for roughly $20 

So, if you had any inkling of an idea to look into Linear Algebra, or even if you already have and think you might want to develop a better understanding, you could justify buying this pair of texts used by telling yourself you will be saving $365 by spending around $60.

I did go over some mathematics with matrices back in July and August when I was exploring Python (sage, SymPy, NumPy, etc), and it is kind of "fun" on a symbolic and numerical level.

My motivation for returning to a good textbook, without so much focus on computer algebra systems, is to develop a more geometrical intuition for the ideas ... you know, like seeing the systems of equations geometrically ... copying diagrams from the text into my "computational math sketchbook" ...

... and then, slowly and spontaneously looking for libraries in C++ (Boost, MTL4) to implement the math ... but I don't want to proceed with too much code until I return to the roots, the math itself.

Of course, this time, unlike 15 years ago in the university, I am not going to be obsessively focused on just math, math, math and code, code, code, but will allow myself to read Celine, to enjoy Cartwright's biography on Schopenhauer, and even to check out authors who publish little books about Depressive Realism, birth and suicide, the spectacle of the void ...

In other words, I want to achieve some kind of balance, where literature and philosophy merge into one, where the demarcation between mathematics and programming gets fuzzy ... and I don't want to adhere to any schedules.

You know, as much as I agree that we all would have been better off never having been born, it is because I know how easily one can be put in a cage without access to books or computers, or even how difficult it is to lead the life of a scholar when homeless without a place to hide, store books and notebooks, I guess I am blessed to be so very content when I can just set up shop in some little room.   

I know from our discussions that you also appreciate just being able to lock yourself away in Hikikomori mode.  Does amazon deliver packages where you are at?  Or, are you on the road so much that you are forced to sneak around an electronic device to access your personal reading projects?

David Poole's innovative book prepares students to make the transition from the computational aspects of the course to the theoretical by emphasizing vectors and geometric intuition from the start. Designed for a one- or two-semester introductory course and written in simple, "mathematical English" the book presents interesting examples before abstraction. This immediately follows up theoretical discussion with further examples and a variety of applications drawn from a number of disciplines, which reinforces the practical utility of the math, and helps students from a variety of backgrounds and learning styles stay connected to the concepts they are learning. Poole's approach helps students succeed in this course by learning vectors and vector geometry first in order to visualize and understand the meaning of the calculations that they will encounter and develop mathematical maturity for thinking abstractly.

I can just hear a psychoanalyst referring to my mood swings as manic-depressive mental illness, but I don't give a damn what they call it.  I am generally depressed, but I am doing some personal research on depressive realism to encourage myself to validate these dreary moods I experience when reflecting on the problems of existence ... and when I get all "manic" with mathematics and programming, well, it is much less pathological to channel this energy into returning to studying mathematics than to chasing oblivion with vodka.  I can see in my mind's eye all those poor wretched bodies chasing a hit off a crack pipe, and I shudder at the horror of the human condition.

What is it do you think I am chasing when I seek to deepen my understanding of mathematics I was exposed to so many years ago?

When I visualize a vector in 3-dimensional space, for the moment at least, it doesn't seem to matter that existence itself is malignantly useless.

The Linear Algebra textbook arrived, and while I was tempted to skip the first set of exercises (1.1), I decided to go through the odd numbered ones in my math diary, Computational Sketchbook #3.  It was kind of cool the way I had to slow down for problem 13.  I actually had to make use of the fact that sin A = y coordinate and cos A = x coordinate.  In other words, I had to remember what Calculus instructor, Jay Dashabundo, taught me in 1994, constructing an equilateral triangle with sides of length 2, drawing a line down the center of length sqrt(3) ...

This leaves two triangles with sides 1, 2, and sqrt(3) ... angles 30, 60, 90.

This is something basic that I "remember remembering again in 1999" ... and now, once again, this little trick helps me right off the bat, fresh out of the gate as I reconstitute for a third time since my first psychotic break of 1985.

Now I am relaxed, deciding not to race through the text and just remembering what I needed to recall to solve this one problem.

30 degrees represents the real value pi/6
60 degrees represents the real value pi/3

One of the vectors was in the third quadrant, so I had to note that x and y values would be negative.

So, even though I am going back over Linear Algebra, I will not skip exercises thinking they might be a waste of time.  Each of the problems may require some thinking that is not covered in the text, so I will be rediscovering fundamental concepts that are somewhere in the recesses of my mind that I will be summoning to the threshold of consciousness.  It's like I am reconstituting ... It's a slow process.

I think I will even sneak the text into the day jail therapy/torture program as a symbolic attempt to claim my mental space.

I am trying to remain honest at all costs.  I feel like my brain's processing speed is slowing down.  As an honest thinker, I am quite aware if something is making sense to me or not.  It seems as though it is taking me longer to comprehend things.  It may be a combination of things. Even though, way back in the particular semester (in the year 2000), when I pulled a B+ in Linear Algebra, an A in Multivariable Calculus, and a B+ in Mathematical Reasoning, I felt as if I barely understood the material.  I would feel as though I had failed a test only to be shocked that I did so well.   I would study all the time.

Maybe this is why, 15 years later, now that there is no pressure to perform, and I am not deluded about being trained to be some kind of scientist or engineer, I am returning to this material, starting from scratch, so to speak ... with a beginner's mind, but somewhat familiar with the material.   I guess I am exercising my mental powers, even though it can be kind of depressing that I have to put more effort in concentrating than I had expected.

In one of the books I am reading, The Spectacle of the Void, David Peak writes that what we consider "horror" fiction arises from this inability to communicate and is exemplified through two distinct types of narrative: (1) the narrative of the person with something to say that cannot be said (an inarticulate lucidity); and (2) the narrative of the person who is able to articulate their thoughts and feelings but still unable to make sense of their reality (an articulate confusion).

I think what I am experiencing is the second type, an articulate confusion.  While I realize many may steer clear of mathematics because they may be intimidated by the prospect, but I am actually interested in the material.  The thing is, I am experiencing genuine depression while I am studying, perhaps because I am moving so very slowly.  You see, I am even able to articulate my reality.  I still can't make sense of it.  If I find myself in a deeply depressed mood while I am studying what I set out to deepen my understanding of, why do I continue?

That's just it.  Maybe this depressing feeling is my core reality.

Of course, since I want to be free to explore these moods without being coerced into taking psychiatric medication, while I do not hide the intensity of my moods, I make it clear that I really want to explore what I feel as I suspect it is inherent in reality itself.  I don't want my response to being-in-the-world to be medicalized as a chemical imbalance when I know it is just life itself. Life itself is my problem, our problem.   I mean, I prefer the truth to a fake and superficial happiness.

And now, after writing this I realize that I am just not in the right frame of mind to go through the math textbook tonight.  My mind is elsewhere ... I can't shake this feeling of pointlessness. I read something more depressing.  After all, that's why I am exploring Depressive Realism.  I want to get to the bottom of this ever present it.  Let's face it:  life is depressing as hell, and it only makes it worse when we blame ourselves for being so miserable.

I think there is something DEEPLY mathematical in my mind.
You know I really like patterns .Above all ,I like Repetition.

It's odd.  In the last chapter, the problems required thinking, and while they were difficult, the challenge made it interesting.  This next chapter, going over solving systems of linear equations is kind of trivial, so the solution manual isn't necessary.  Maybe I will appreciate the more difficult problems from now on instead of getting down on myself or thinking I am slow when I have to actually think.

This is a great distraction.  Sometimes I even feel calm ... something close to inner peace.

Some simple code for Gaussian elimination.  I have found that, along with using Sage or NumPy (Python) to check my work, it makes the process a little more fun building little bits of code from scratch in C++.  Eventually I will want to learn how to implement the Boost libraries (MTL4 by Peter Gottschling), but ... for now ... building as I go along using whatever guidance I can find on the Internet helps me slow down the process of going through the textbook.

As I did with the python code (storing *.py files as *.txt), I will do with *.cpp files.

Hence, I store gauss.txt.  When downloaded, rename to gauss.cpp

compile (with GNU g++):  g++ -g gauss.cpp -o gauss

to run:  ./gauss

enter number of equations
enter number of variables
Then enter elements separated by space <enter>

Are we having fun yet?

eldritch - weird, eerie, but with connotations of being unearthly and perhaps evil or mysteriously sinister

I had to look the word up.  You see, I have so much to learn.

Note:  Attached is rref.txt (I only change the extension because I can't upload rref.cpp).

This performs what gauss() does as well as showing the resulting matrix after each step.

It also prints out the row reduced echelon form.

It only works if the solution exists.

Still, I prefer going about it this way.

Actually, the only reason I am going over Linear Algebra from scratch is because of my interest in the extended libraries for C++.  I want a better understanding so as to have a better appreciation for the libraries.

There is a book which shows how to build many Linear Algebra tools with Python (without using numpy module), but I am going to wait on that for awhile.  Besides, the Kindle version is only $10 so I am going to wait until I get an ereader.  For now, I have plenty of hard copy material to keep me occupied.

In an exploratory manner ... Going through a bulky textbook (designed for a 2-semester course) in an exploratory manner, trying to see if I might experience any revelations along the way.  When I studied it formally 15 years ago, I might have been rushed and pressured.  I was also taking other math courses along with it.   I don't think I ever gave it my full attention, and there are some subtle points that I would like clarification on.   

I feel the only way to approach this is in an exploratory manner, where I take my time, where I pause to write code that can be used along with the problem solving done by hand, where I can look at code written in Python and see about how to do similar things using C++ ...

It is an exploration, not in the sense that I will be discovering things that others do not know (as in so-called "new" mathematics), but I hope to discover insights that are "new" to me personally, deeper insights than just what is necessary to do well on an exam.

Since I have no other goals than understanding what I am focusing on at the moment, and seeing how it all gels together with my interest in programming, I will be better able not to be overwhelmed with all the knowledge that I will never grasp, and be content to have whatever grasp I have of fundamental concepts.   

I specifically use the term "explore" to inject the spirit of "fun" into this process.  This is not work.

I study mathematics and programming for fun, and I think philosophically to endure the burden of consciousness.

I found that the time constraints in a university setting, along with a regimented format (labs, exams, etc) often destroys this exploratory spirit.  I am free to, well, explore.

Suppose I find it awkward to draw 3D objects, but I still want to develop a geometric understanding of a system of linear equations.  There is a great deal of free guidance floating around on the Internet --- when we have free time and access.  For instance:  How to draw planes from a set of linear equations in Python?

The explorations part is all about this carefree approach, where, I can go on these tangents along the way.  At the university 15 years ago we had to purchase MATLAB which is like Mathematica.  I would much rather be liberated from dependency on such (expensive) tools.  It's not just about money.  It's about being able to roll up one's sleeves and have an intimate connection to the tools one is building and using.  In this way, mathematical programming enhances one's study of mathematics ... and building mathematical tools becomes a motivation for "slowing down enough to get into the nitty-gritty details of the algorithms".

PS: Here is a pdf of a textbook I found online from ucdavis.edu

Another text from saylor.org


If one doe not have access to the GNU gcc/g++ compiler (Linux), one can always set up cygwin, or, alternatively, install Visual Studio Community (free version).  Then, to compile rref.cpp from the command line, launch Developer Command Prompt, navigate to the directory where rref.cpp is, and issue the "magic command":

cl /EHsc /Zi rref.cpp

This will create rref.exe

I have reached a point where, whether I create a routine with Python or C++, I can use it in Linux or Windows ... cross-platform.  Whereas Sage (CAS) does not run in Windows, one can use sympy and numpy (Python) in both Windows and Linux.

It's a cool feeling to be able to do this "off the cuff".

This is another reason I prefer a "desktop/notebook" computer over a smartphone or tablet.  I am into compilers and tinkering with homegrown command-line applications.

I would prefer an inexpensive 13" computer set up to boot into both Linux and Windows than to have an expensive smart phone with fancy GUI applications.

An inexpensive notebook computer is a great investment, especially if we configure it to dual-boot.  There is a great deal of "tinkering" one can get engrossed in ... and a keyboard is indispensable for spontaneous writing.

It's something to consider.