DISCLAIMER: I am sure our use of horror seems a little melodramatic, and the "horror story of mathematics" can't be compared with our more primal fears of suffering severe bodily harm (such as decapitation, having limbs chopped off, eyes gouged out, or eaten alive.)
___________________________________________________________________
I think I do see your point when you say,to paraphrase you,mathematics can be used as tool to unearth & bring to surface our unlimited ignorance or feebleness of the intellect/mind.
Great paraphrase! You articulate what I mean better than I can.
We are similar. The way you escape the horror of everyday life by reading horror-literature/philosophical-horror, I attempt to escape my fear of ignorance by bringing it to the surface so that I face the feebleness of the intellect less fearfully, that is, with courage and an almost calm, resigned demeanor.
I have done this by going back, and then further back still, until I reach a point where I can say, yes, even at this level, my ignorance is all too glaring (to myself, that is).
As I have said, such unlimited ignorance does not haunt those who never consider it.
Likewise, those who chant the mantra that "Life is good, God is good, or it gets better," well, they have solved the problem of horror by refusing to acknowledge it.
You take a more direct approach.
Now, as for mathematics, I escape the horror of my unlimited ignorance by taking myself back to school. The significance of privacy in this pursuit cannot be overstated, for it is only in such solitude that one can muster the greatest degree of shameless honesty when facing the root of one's confusion.
I'm afraid that, when it comes to formal (institutionalized) education, there is just too much ego that comes into play, and a general lack of humility mixed with false pride, which sets many barriers preventing individuals from seeking out the source of their confusion. Students in formal, structured settings, do not permit themselves to follow the trail of their doubts and confusion since there are time-restrictions, so there is a tendency not to go down into rabbit holes, but to instead, as I did at the university, study just enough to do well (relative to the herd) on the exams. I - or we - thereby forfeit opportunities to build our confidence. We forfeit confidence building in favor of acquiring credentials.
In solitude, there is no shame at confusion or ignorance, especially since one is actively trying to remedy the situation by "going back over things". We are able to close one book 3/4 of the way through so as to go down the rabbit hole ... and to rebuild.
I am glad that we are on the same page with this, for although we often jest about certain things, I doubt we would ever joke around about someone's private attempts to study mathematics. Who would suspect that so much psychology is involved? We would be accused of complicating matters.
The way I am dealing with this "horror of mathematics" is that I genuinely accept that I will never be a mathematician. This helps me keep things in perspective.
Now, having said that, I very much long to improve my mind by developing certain skills even at an elementary level. I would like to at least trust myself to begin jotting down some preliminary notes to constructing an elementary proof. This means I can not allow myself to be ashamed at taking baby steps.
People are wrong to call such obsessions a hobby, especially if the obsession keeps resurfacing throughout one's lifetime. Is it mathematics madness? Whatever it is, referring to it as a hobby seems to understate the facts.
I approach mathematics texts the way you approach horror ... Even, and perhaps especially, texts that I would have thought "beneath my level of interest" can be surprisingly challenging. BOOM: IGNORANCE UNEARTHED! - the horror and disillusionment in having to witness your own self-image destroyed.
I do not want to live a lie. As I have said, I suspect many students might deceive themselves about what they think they know. What goes on in other peoples' brains is none of my business. The thing is, no matter how much I have studied, in the present moment, in the Now, when thinking is required, that's it, the intellect is feeble. The brain is lazy.
And this is never a reason to stop, to choose a different path. No, and again no, I will move as slowly as necessary.
Such honesty requires social isolation. Do you know why?
Because the world is generally full of shiit.
The kind of honesty I demand of myself is not to be found out there ... in polite society ... maybe, just maybe, such honesty is found on psychiatric wards.
While there is an element of horror in this, there is also the treasure of being intimate with the degree of one's own ignorance. This treasure might be what is necessary for turning the horror of one's own ignorance upside down. I mean, rather than plunging ahead stubbornly into Computational Physics, where my horror might become amplified, I switch gears and return to elementary analysis so that I can show myself where my knowledge is weak.
Hence, if we go about this process with care, although we risk being mocked by the herd as some kind of useless dreamer, we just might defy reason and common sense, finding great calm and tranquility when we at long last learn how to THINK.
We might learn to think more clearly, more slowly, and never resist the compulsion to scribble notes on paper or draw diagrams or whatever ...
In this way, even though we are forever haunted by the enormity of our ignorance, we will have become intimate with our mental capacity, so we will not overtax it. We will have developed an intuitive grasp of the feebleness of the intellect, so our egos might not be so easily wounded when we make mistake after mistake.
We will learn to doubt ourselves and smash false confidence.
I still aim to develop humility, patience, and honesty in dealing with confusion.
So, when anyone questions the value of spending so many days and nights going over high school and undergraduate material while the world passes me by, I can say with dignity and self-respect that all this studying and thinking is helping to make me a more patient, humble, and honest man.
When I was a child, after the release of The Exorcist, some nights I would be very frightened that I was becoming possessed.
Do you know how I overcame the fear?
I became one with the Devil and the legion of demons.
They could not harm me if I merged with IT.
I am not demanding that I comprehend things far beyond my capacity. I just want to know where I stand, and to learn how to work with what I've got between my ears, as feeble as it may be at times.
_______________________________________________________________
related:
The epsilon-delta proof, the nemesis of many a calculus student, is an initiation rite into the mysteries of proof writing.How To Construct a Delta-Epsilon Proof* Note that my decision to devote myself to the text from high school that I had no recollection of doing any exercises in has to do with my anxiety in the face of writing proofs. I seem to really enjoy "doing calculus" or "doing algebra". I enjoy calculating and computing and mechanically deriving results via the "magic wizardry" of algebra, trigonometry, and calculus; and yet I would like to have more confidence in how to go about constructing proofs, even the simplest of proofs. For whatever reason, when I see the word "Prove", I draw a blank. I wonder if there was some kind of traumatic experience that is at the root of this mental block, or that I have encountered so many people who are getting through life without feeling compelled to learn how to read or write formal mathematical proofs.
I may never be officially initiated into this ancient craft, but it's something I just can't seem to shake. There is no law against trying to understand things that seem so obscure or even pointless.
There are those who might suggest I would be better off painting houses or digging ditches. And yet, I don't want to paint houses or dig ditches. I want to continue to unearth my unlimited ignorance.
Maybe there is a certain degree of horror involved. I suppose it has to do with the degree to which one is "haunted" by a sense of "lack" when it comes to their own understanding.
Maybe I have come to associate studying mathematics with goofing off. It's probably a reaction to how competitive our societies have become. I just want to fart around. It's not important to me to be doing anything useful. I do not live a "purpose-driven" life. I guess my only wish in all this studying is that I develop some latent math skills, to stretch my brain a little, to give me something to do with my life (other than writing a book - no, I do not want to write a book! I just want to complain to Holden on this message board).
One problem seems to be that if I am working on a series of problems that are too straightforward, that is, too "easy", I find that there is a voice inside my head that mocks me, accusing me of avoiding more challenging material. The thing is, though, in each section, the last several problems are real brain benders; but I don't want to just skip the easier problems either.
WTF, Holden, it's ok to say it. I'm pathetic. I don't mind admitting it. I'm down right ridiculous to the point of being comical. Maybe, after all is said and done, I'm the Germanic Woody Allen ... a neurotic Raskolnikov who would not know what to do if he found himself homeless except to hide in the bushes drinking himself into unconsciousness ... sobbing himself to sleep like an ill-tempered child.