Author Topic: Imitating Herr Hentrich's Mathematical Endeavors  (Read 242 times)

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Imitating Herr Hentrich's Mathematical Endeavors
« on: May 06, 2017, 05:15:55 am »
Your mathematical endeavors appear to as very similar to that of Damien among the lepers.
I know that my example is a religious one,but lets us not get bogged down with semantics,we are ,after all ,concerned with the heart of the matter,like Schopenhauer.

I think you study maths for the same reason Damien went among the lepers-ego-nullification.

Maths could be a great tool for ego-nullification,I'd love to use maths for ego nullification.
Studying high school maths takes a great deal of moral courage,I realise that. Thank you for your example.
« Last Edit: May 07, 2017, 08:55:39 am by Raskolnikov »
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Fundamentals as kindling and tinder
« Reply #1 on: May 06, 2017, 08:17:45 am »
Warning:  As of the 7th of May (about 10AM), the following post is nearly 2800 words.   It's turning into a god-dang'ed essay.

Filling in the gaps.   Imagine so many little questions in the unconscious mind scanning and looking for clarity.  The ego must be nullified in order to fill in the gaps.  Nullification is most likely the most accurate description.   You say this requires moral courage, and this is why I call it the Mortification of the Ego. 

While we associate mortification with the pain the flesh might feel, such as in going without food (fasting) to cleanse the body, this nullification requires that we smash our own egos, tear down the narrative of self, and even turn our backs on society, showing disdain for the values of industrialized academia of mass society, so that we might critically examine the subject matter of our student days.

Professional mathematicians have a busy schedule ensuring that few get around to critically examining the subject matter of their student days.

We must use our non-professional, non-academic status to our advantage.  As we have no status to uphold, no image to project, the nullification of our egos is in reach.  Whereas, there are those who, after having finally understood the infinite, have become psychologically attached to their pleasant sense of superiority; and hence, it is understandable that they may lack the humility required to relearn, or fill in the gaps, or even think carefully about problems that they might think are "beneath their level of sophistication".

I hate to use religious analogies, but, paraphrasing the Nazarene, it might be easier for an 18-wheel tractor trailer to get under a low bridge than for a fully grown adult (with a college diploma no less) to get around to critically examining the subject matter of their student days.

Again, I think we are fortunate that we do not have any public image to project, which may help us to break through the false consciousness and just immerse ourselves in thinking for the sake of thinking, rather than studying for the sake of a profession, an image, or a career.

There is another obstacle closely related to the threat to the ego, and this is the feeling that, if we take the time to revisit the fundamentals, we will fall further behind.   What has helped me is to think of the kindling and tinder necessary to get a fire going before dropping full logs into the fire pit, or, when the flames are suffocated by such logs, we then need to gather more kindling, and, more than likely, will remove the large logs altogether until we build the fire back up with suitable fuel by degrees.

I suppose the moral courage you speak of has to do with facing the fear that some of the more challenging exercises will require taxing our mental capacity, and for whatever reason, the necessity that one exert mental effort is somehow a threat to the ego.   The way I deal with the ego in these cases is to look upon the process as an opportunity to keep me grounded.

It's tricky territory, this conception we have that if we have to exert effort, then we become frustrated with ourselves.  We're the ones who have to get through this life, so we might as well become as intimate as possible with the quirks in our own mental apparatus.  I do believe that working in privacy in an almost secretive manner, minimizes the psychological difficulties caused by our overly sensitive egos.   Of course, rote drill computational exercises can often be scanned over since these kinds of computational skills are likely already second nature.  I am more concerned with going over the details of how to go about giving reasons why each step of the computation is valid.

One of the remarkable consequences of such humble aspirations is that it is harmonious with my place in the natural order of things.  I'm not attempting something radical like Wildberger and his Rational Trigonometry, although I find his project very interesting.  Nor am I trying to figure out how to "save the earth" or even find my own personal "salvation".  I'm just trying to get a better grasp of the fundamentals rather than diving into "computational physics".

Wildberger questions the reality of infinite sets, and even has reservations about the real numbers, especially irrational numbers such as pi, radicals like the square root of 2, and Euler's constant.  With this in mind, when I revisit the axioms and definitions of the real numbers, I will keep in mind that I am working with pure abstractions.

It's as though I feel I have never been more ready to revisit these subjects than I am now.  In the past, I was always in too much of a hurry to get to calculus and linear algebra, too anxious to learn C++ and then Python.  So what if the little programming exercises in some of the old books are in BASIC.  I'm not on an ego trip.  I can appreciate the texts more now that I am no longer that nervous and anxious teenager.   It's no longer about training to be a member of a future workforce.   Now it is just what I engage in to pass my time on earth while getting through the days.   I spent a good 15 years in a drunken stupor.   So, it really is no big deal to spend the next few years filling in some gaps.  Besides, I am not merely filling in the gaps, but actually learning how to "nullify the ego," as you put it, so that I might actually take some of the challenging exercises at the end of each section seriously.

One problem had me up until 3AM, and then on into the next day.  While at the grocery store, I had the problem on a piece of scrap paper.  I figured it out in the parking lot while smoking a cigarette.  I really had to think HARD about it!   The delight I felt at figuring out how to solve the problem was worth the price my ego had to pay.   I think you may have an inkling of what I mean as far as the ego being an obstacle in such an endeavor as this.   The ego thinks, "Isn't this remedial?  Surely I would never be required to go over this material.  I would test into the advanced courses."

And I answer to the ego, "No, this is not remedial.  These texts were designed for high school students who show mathematical aptitude.  Are you embarrassed that some of the exercises require you to wrack your brains?"

And so there is this humorous back and forth bickering between different parts of the brain or mind.  It's interesting to observe one's own quirks.  I see how you would say this requires moral courage.  One must be not only prepared to learn, but open to the learning experience.   If the ego thinks it already knows all it needs to know, or that some subject is "beneath" or "unworthy of care and attention," then this ego must me nullified or else it will keep us from becoming conscious of our ignorance.

Going through these texts will shine a light on questions I never knew existed, questions that may have gathered over a lifetime, such as just why, when we take the square root of a variable when solving an equation we must use absolute value.  I will never know just how many gaps there are until I go through these old books in a formal and systematic manner.  I will know which exercises are worth taking seriously.   In fact, when I get back to Modern Introductory Analysis (circa 1964/1986) and Introductory Analysis (circa 1987/1991), I am still committed to the idea of engaging with every single exercise.    Yes, the time factor can be daunting.  We're talking years, not months.  Maybe that is where the moral courage comes into play.

And I haven't even gotten into the thick of the geometry (which I did not care for at age 15).  So, sure, I agree that this takes moral courage.  I am venturing further and further into my own orbit, as an honest man who is not afraid to expose himself to his own deficiencies, for in the process I may learn a thing or two about things I considered "not worth my full attention" thirty-five years ago.  I have never had any inclination to revisit that material before.  Never.  Until now.

The eternal recurrence ... always going back around full circle to the start with a new perspective.

I also want to start over again to develop a different perspective on writing proofs.  I had never paid much attention to that formal aspect of mathematics, the Queen of Science.  I seemed only interested in Her computational power.  In a sense, I have used Her, but I think I may have deprived myself of the opportunity to understand Her.

I prefer doing this the hard way than to read a few books on "How to Write Proofs."    If there is time after this experiment to get to those books on "the keys to transitioning to advanced mathematics," then I will go through them as well.  It all seems so daunting, like there can't possibly be that much time, so I would rather proceed as though there will not be that much time, and be satisfied if I can develop a better appreciation for my grasp on fundamentals first and foremost.  Who knows?  I figure, despite all the tobacco I smoke, I might live to be a lonely old man.  Once one reaches a certain age, it is socially acceptable to be a little crazy; hence, I may come of age as a crazy old man-child.

I want to rebuild my house, so I have to first dig the hole where the basement will be.  The house which represents my understanding of mathematics needs some serious structural repairs, and so I wish to approach the fundamental areas with a different perspective, with more mediation, contemplation, reflection, and less blindness.

You see, when I attended the university and was able to hold my own in "Multivariable Calculus," Linear Algebra, and other "advanced mathematics" courses, even if I was feeling overwhelmed and wanted to jump off a bridge, since I received good grades, my ego was compensated, and I just figured that, while I hardly grasped what I was doing, I had a better grasp than many of my "peers".

All these years later, my approach to this experiment in self-education is from an entirely different angle.  Back then I had something to prove to myself after having lost my "secure" position with the State Parks Service.   I had a great deal of energy.  It was something I always wanted to do.  There is no way in hell I would have thought to revisit my old high school texts.  I didn't have that luxury, so I winged it.

Now that the smoke has cleared, I think I have a better chance of taming the ego and taking a look at some of the things that baffled me as a teenager.  I really want to understand and not just pass exams or graduate with a diploma.

I have a great deal of contempt for phonies, frauds, and fakes; and I want to be perfectly certain that I am not deceiving myself on some kind of ego-trip when I try to get a grip on advanced calculus, physics, and even linear algebra or differential equations.   I have this obsession with shoving my nose in shiit.  There is no one I need to impress.  There will not be any job interviews where I must display false confidence.   I am finally free to revisit the mathematics that is most likely at the root of many troubles undergraduates endure.

Have you ever considered how someone from ancient times might handle modern education?

Is there any time to reflect or to understand? 

Most people are only concerned with whether or not the mathematics they study will be used in their capacity as an employee.  Not everyone is going to be employed as a scientist, engineer, or educator.  Most of us will endure one disaster after another and be grateful just to be living indoors and have access to food and books and computers.

And so, what are we to do with our so-called "mathematical aptitude," all of us rejects, outcasts, psychotics, and deadbeats?

As our society judges our value by our job (or lack of), by our income, by our car (or lack of), by our teeth (or lack of), what better revenge is there but to refuse to pay deference to the academic hierarchy and revisit the algebra, geometry, trigonometry, and analysis that is apparently only needed by about 5% of the "careers" in industrial society.

I am not familiar with other cultures, but I have heard that in many parts of the world, there is a certain respect for education, even at the less advanced levels.   This is certainly not the case in North Amerika.   People tend to have more respect for the kind of car one drives.   

Like you, once the ego is tamed, I can find delight in studying what is considered less advanced mathematics.

Do you know why?   This is the kind of mathematics that the other branches are built upon.  And yet there is the dependency on transcendental functions like sine and cosine which ultimately depend on calculus which they sneak in before calculus, and then wonder why the more reflective students feel a sense of discomfort that they have to depend on tables or calculators to determine the sine or arctangent.

There is no turning back for me.  I am obsessed.  It is as though I were to transport myself back in time to study in a different order.  Maybe it will turn out one day that this is how to go about it.  I mean, maybe students should be encouraged to go back to start over once they have been through the systematic education process.

When you look around at the epidemics of madness that plague industrial societies, you will easily come to the conclusion that there are far worse things one could be wasting one's life doing.

When you find yourself in Limbo, why not make the best of it by doing what many others would not be inclined to do in a million years?  Why not take a trip down the rabbit hole of mathematics?  It's less expensive than drugs and booze as long as you don't invest any money in attending a university.  There is a good chance that I am addicted to studying mathematics.  It's my drug of choice.

So, just to be fair, I have to warn you that I have lived a rather uneventful life, and that it may not be in your best interests to "follow" this path as it surely leads nowhere.   :-[

On the other hand, if it is any consolation, I can also tell you that, once I nullify the ego (thanks for that word, by the way), that is, once I allow myself to "not know everything," when I do make some little breakthrough, and I am humble about it, it relieves many unnecessary worries.

I guess we will both have to accept these challenges to our egos as a kind of spiritual battle where our state of mind will determine whether our relationship with mathematics is one where we experience nightmare or one where we appreciate making little strides.

For me, the key may be to not be greedy for understanding.

There may be some parallels to those monks who are filled with desire for enlightenment, or even anxious to become detached.  Their desire for detachment is what prevents detachment.

If I do not overcome this greed for knowledge, then I will not be able to appreciate the little that I am able to learn.

At least I don't give a shiit about who won the game last night!

By the way, as my posts keep getting longer and longer, I have channeled my stream of consciousness back into the notebooks as, even with you, I am too embarrassed to write about what I consider to be the breakthroughs ... like using a ruler and protractor to estimate what I am used to calculating with formulas such as x = r*cos(t) and y = r*sin(t) ... or t = arctan(t).

It is cool to force myself to draw sketches large enough so that the measurements will give me a clue, write down my brute-force estimates, and then check with calculator or computer program.

Also, I have noticed many terms take on a different significance when seen through the eyes of Arthur Schopenhauer, even the most basic undefined concepts of point and line which are used to define the other terms.   The point is not an actual object, and the line has no breadth.   Now some of Schopenhauer has seeped into me by osmosis, and I do not take anything for granted.

If you do go in this direction, I would suggest you keep your studies very private.  From what I know about society, most people are vulgar and will only mock your sincere and noble efforts.

« Last Edit: May 07, 2017, 11:06:57 am by Raskolnikov »
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