Of course, at the end of the day, I have to realize that my notes are mainly the main medium for helping my mind focus on this particular discipline, and it is in no way, shape, or form dependent upon anyone else sharing an interest, whether in the future or not ever.
An audience is not required.
It is difficult to remain focused and to resist becoming overwhelmed with the Fear inherent in the human condition. We are not very efficient animals, perhaps even quite flawed by our very design.
People like to think "God" or "Nature" knows what it is doing.
I like to reflect on Kurt Vonnegut's assessment that it would appear that evolution doesn't know what it's doing.
Let us live in the moment, then, and face the possibility that the universe itself is a failure.
Let us doubt.
I will not assume anyone would be the least bit interested in my insignificant documentation of my study of mathematics, since, well, there are more pressing issues swirling around in peoples' heads.
I must learn to become more selfish, learn to not care too much at all about what happens to my notes should I die or become homeless.
After all, nothing really matters.
My nephew has become more difficult to reach and hardly responds to email. Hell, he could be dead for all I know.
So, I will stop kidding myself about "leaving a trail of notes" that someone might be interested in. If I get around to scanning them before I disappear from the grid via death or homelessness, then I suppose someone may eventually appreciate them, but whether that happens or not makes no difference, really. It makes no difference to me.
The main purpose of the notebooks is to help me remain focused, helping me to overcome daily anxieties enough to possibly be in some kind of control of what goes on in my own head.
I do not want to put any pressure on anyone to take an interest in these things. I am content to admit that what I do with my days is totally insignificant and of no consequence or importance.
Maybe the reason I am not fond of the "Made Simple" approach to mathematics is that, if you ever wish to engage with mathematics in a rigorous manner, then it is going to get complicated, and to many people, such complexity appears ugly. It all may seem so unnecessary.
It is difficult to discuss such things meaningfully since, unlike Holden, few are willing to admit ignorance on a subject, and they feel that if they have been exposed to something on even the most shallow level, that that "know about that."
I am used to working alone, and I understand that the only requirement for me to continue studying is that I maintain my personal interest in what it is I study.
Discussing things with others is not a requirement. Please note that I say this without any kind of resentment or anger or disappointment. I am not disappointed.
I am like Holden in that I am very accustomed to being alone, and very much accustomed to thinking about things few people are interested in.
I am not deluded into thinking I am somehow preserving the efforts of folks like Mary Dolciani and Frank B. Allen. My obsession with their books is simply a consequence of my estimation of the value these books have for me personally, that they do not sugar-coat things that are complicated. I would not expect others to share my excitement, enthusiasm, or passion; and I appreciate the encouragement Holden and Raul have given me.
It is difficult to speak to people about what I study as I may become angry if they were to misconstrue what it is I am actually up to.
I read too many comments on the Internet by those who call themselves "web developers" who find most mathematics quite unnecessary.
Sometimes I feel like a volcano about to erupt, but I am just a human animal destined to be eaten by the worms. This seems to be the only activity that helps me stay calm. I mean, it's something I never would have been able to do were I registered in some formal university "Physics" class. I suppose that, for whatever reason, proving trigonometric identities is more meaningful to me at this time than applying calculus to solve physics problems. My formal education seemed always to be geared to higher and higher levels, when I know from personal experience that I could benefit from a more rigorous treatment of trigonometry and analytic geometry before proceeding any further into an informal study of physics.
I am haunted by the fact that one can pull A's in physics and multivariable calculus, and then, years later, find proving trigonometric identities in a formal manner quite challenging.
The reason I take the liberty of describing the details of the kind of discipline and radical devotion it takes to face such challenges is because I sense that this will also be a lifelong issue in the background of Holden's life. The yearning to understand does not fade over time. If anything, you begin to realize that, if it is deeper, more intuitive understanding you are after, it really is your own responsibility to do what it takes to understand. Sometimes this amounts to forsaking any notions of formal education and tracking down the textbooks suitable to how you want to approach your personalized education.
I'm sure this is not a merely a Hentrich thing, but a human thing.
My math notes are really child like & if I were to get killed today in a motor vehicle accident then they would just be chucked away.
You may not think I understand what that feels like, but I do. In order for me to overcome that feeling of writing "child-like" math notes, I had to have some notebooks with a little heavier paper which would be used when neat diagrams were required. Now I mostly use the least expensive composition books I can find (50 cents for 100 sheets), but I would not hesitate to use a 10 dollar sketch pad were I to find an area I was going through required constant use of rulers and compasses, etc.
Yes, I understand how critical we can be of ourselves. That is one of the great hurdles, and why I encourage you to continue to pursue your interests in math privately.
Henry Fool was right about this. Do not give people an opportunity to poke you with a stick.
Try not to be too critical of your notes, however child-like they appear.
One thing I love about set-builder notation is writing the curly braces, and I like to use <----> symbol between corresponding statements which imply each other.
As pointed out in that video I linked to in
another thread,
Each individual learner has to discover mathematics for themselves.It is a private matter. Even more crucially, I see it as a sacred matter. After all, we are born alone, we die alone, and - for the most part - we learn alone.
Learning, like dying, is a solitary activity.
We don't need to be studying the same material. I would only like to keep encouraging you to continue
discovering mathematics for yourself.
That feeling that your notes are child-like, well, this is the sensitive ego chiming in. Ego was one of the things which prevented me from revisiting material from old high school textbooks, for you see, I saw myself as a "university graduate who pulled A's in Physics-II and Calculus-III"
I never allowed myself to experience the "humiliation?" or "ego-deflation" of realizing that there are very many gaps in my "mathematical training."
There is a reason I keep repeating myself over and over again about how important it is to nurture a Secret Private Inner Life of the Mind. I know, from being a maintenance worker wearing a monkey suit for the park for 10 years, or even when jobless, cleaning toilets at gas stations for beer and tobacco money, that a scholar is not really identifiable by garment or position in society.
I am fairly certain there are many scholars wearing State issued prison garb, or hospital gowns on psychiatric wards in hospitals.
I was thinking about this hole in the collective hypnosis of the early 21st century you credit me with tearing, thereby creating a wormhole of the imagination.
I am quite fond of this metaphor. While Hollywood and Sports Culture lay claim to the imaginations of the youth, my imagination is fertile ground for a New Math Revival. I don't need society's permission to honor these ignored or despised texts. Maybe they were too rigorous for high school students, but they are perfect for me at this stage of my life, when I am calm enough to take "mature" notes and really document my engagement with the exercises.
You may want to use scrap paper to work out what you call child-like notes, and then transcribe a more organized and detail version into a more permanent notebook.
I must encourage the use of notebooks and to learn always with pencil in hand, even if the marks you make on the paper appear child-like. You will witness maturity, but you have to be very patient and understand that it is a lifelong learning process.
I have found that it is also helpful to keep a few color pencils handy as well, for boxing, circling, pointing things out with arrows, topic headings, etc. [red, blue, green, black, or whatever you choose]. It helps to separate your work for each exercise with a colored line if you feel like it all looks like it is running together. You want to be able to refer to your work to see where you made any errors if your results are different from answer key or computer algebra system. Sometimes, I change an answer in a key if I am very confident, else I error on the side of caution and hunt down where I might be mistaken.
I would caution against the use of ink pens for "doing" math. There are those elite snobs who write their proofs in pen. I am certainly not one of them.