Author Topic: Studying Mathematics as a Way to Endure Time  (Read 3809 times)

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Nation of One

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Studying Mathematics as a Way to Endure Time
« on: March 24, 2016, 02:54:12 pm »
I have been trying to study several areas of mathematics simultaneously, areas which overlap, are interconnected, and sometimes rely on the others.

Now I want to allow myself to review fundamentals on top of all this.

I reminded myself today, that, basically, I study mathematics because I enjoy the process of learning and relearning.  Other than being a preliminary to other areas of study, such as physics, which mathematics is the language of, I have no goal to reach.   I study as an end in itself.  Unlike the career-oriented university student, it's not a means to an end for me, but simply a mental activity I engage in as a way to endure time.

This helps me keep things in perspective. 

If someone asks me, "What are you studying all that for, especially at your age?"

Much of it is an intense review while simultaneously investigating a little further along the path ahead.  This activity I have become obsessed with again clearly stimulates my brain enough to keep me fairly content, and this motivates me to continue to abstain from alcohol.  There it is.  That's got to be my main reason for allowing myself to indulge in this current obsession with mathematics, which has had previous incarnations in my lifetime.

This is what I do to endure time (as an alternative to drinking myself into oblivion) - an alternative to suicide.  I have made an unbreakable commitment to stick around for my mother's sake as she ages.  In the meantime, I have to stay out of trouble in order to actually "be around" and not just alive. 

So, it is rather simple and direct, not at all mystical or mysterious, although I do catch myself kneeling before the shelves of textbooks while deciding what to focus on next.

Heads up:  Library Genesis is back up at libgen.io

It's a good opportunity to track down some textbooks.  Be sure to choose your textbooks that also have solution manuals available.  I have found through experience that I am much more likely to become engrossed with exercises/problems in the text if I know I can check my results with a solution manual.

Does it feel strange to approach subjects I supposedly "aced" years ago as a "student"?  No, not at all, I enjoy returning to the fundamentals WHILE reviewing ... WHILE exploring a little further along ...

A few months ago I was exploring Abstract Algebra (so-called "modern algebra") and Number Theory, but now that I have invested in hard copy texts (sometimes just a couple of dollars each plus $4 shipping costs), I am fairly committed to this agenda.

The bottom line is that I am doing time in the universal mind.  I am not studying so as to build bridges or elevators or Volvos or Volkswagens.  I am studying math to endure time, to get through each day/month.

How is this working out?

Beautifully, actually.  At night, before collapsing, I place whatever texts I want to get into the following day on a little stand by my cot.  When I rise, I am usually enthusiastic about what it is I want to study that day.   When I feel overwhelmed and scattered, I shift gears.

Sure I will go through a chapter of a text that may be over my head, but then I let that sit while returning to other texts.

It takes a certain amount of humility to return to subjects one studied a decade ago, and then to review concepts one may have first been exposed to in high school, but this is the kind of intellectual honesty that makes this the perfect hobby for me.  I am able to enjoy my mental faculties in privacy, spending many hours enjoying these faculties.  This turns out to be the greatest revenge. 

It seems as though modern society places a great deal of importance on the monetary rewards of acquiring knowledge, and forget the instantaneous and daily reward of being able to turn inward and "do one's time" in solitude without getting jammed up chasing things outside oneself.


I never have to worry about "what are you going to do with yourself without a wife or job or children to care for?"

I am going to keep studying mathematics.  I could study every day for the rest of my life on fundamentals ... I'm just doing time while chained to biological necessity.  Really, it may all be some kind of mental mastur-bation in the end.  So, what.  Who cares what I do with my time anyway, as long as I'm not terrorizing the villagers and minding my own business?

Also, it makes my dreams very weird, and I like weird.

Maybe I am drawn to studying and continually reviewing  fundamental concepts in mathematics because I like "doing time" alone.   I wonder if mass extinction of our kind will occur in my lifetime.  I wonder if I will be flipping through old books studying mathematics while dying of starvation.  At least I won't have to become a cannibal just to feed offspring.  I might be able to die off with some grace.
« Last Edit: March 31, 2016, 10:46:40 pm by H »
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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It is over quickly.  Of course, sometimes I have to stock up on the fancy Sharpie pens or cool notebooks that will be there for me when there is nothing else.  Seriously, in hospitals or jails, I will write on scrap paper with whatever I can get my hands on.  When worse comes to worse, I just think ... like when wandering in the woods and fields ... one doesn't carry around a notebook ... It's a strange world, isn't it Holden?   Why do we write things down?


Your diary writing is fascinating.There is something there..let me think about it and I'd get back to you.
By the way,thanks a zillion for Library Genesis link.I was looking for a book and I found it there-for free! Thanks again.
La Tristesse Durera Toujours                                  (The Sadness Lasts Forever ...)
-van Gogh.

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Re: Studying Mathematics as a Way to Endure Time
« Reply #2 on: March 25, 2016, 11:55:05 am »
Library Genesis seemed to have been down for quite awhile, which is why I had been purchasing books like "Multivariable Calculus 6th edition by James Stewart" for 87 cents through amazon, along with the study guide ($3) and solution manual ($2).  I just had to pay the $4 shipping for each.  (New these would be close to $500 - prohibitively expensive!)

I have collected quite a few texts and solution manuals since then, and I was relieved to find Library Genesis again - with the new DOT io after libgen!  I stumbled upon it.  I had stopped looking for it.

As I have mentioned before, I had been interested in Husserl's early treatment of the Philosophy of Arithmetic, curious to see how the psychologizing of fundamental mathematical concepts led him to "invent" the branch of philosophy he called phenomenology.

Well, for twilight reading, it is kind of cool ...

You might want to check this out:  typing "Husserl and Mathematics" at libgen.io :

Husserl and Mathematics

It seems to be very close to the heart of what you talk about.  Uncanny, right?

I am a little aggravated with Frege for his harsh criticism of Husserl's Philosophy of Arithmetic, but, I guess some of our heroes could be a-s-s-holes at times, just like us, just like any social creature.

They even have Brouwer Meets Husserl which is heavy duty!

What a blessing to be able to have such a resource.  Grab what you need while you can, and then stay safe.  Maybe having a collection of texts to study will be enough to inspire you to stick around and endure our short little lifespans.
« Last Edit: March 29, 2016, 07:52:00 pm by H »
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 ~

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Re: Studying Mathematics as a Way to Endure Time
« Reply #3 on: March 29, 2016, 07:54:35 pm »
There is definitely something to this.  Sometimes I reach a very calm state of mind even while just working through exercises.  If a problem has many steps to it, if I reach this calm Zen-like state of mind, I am no longer in a rush to finish the problem set.  This calmness is then reflected in the way I write the symbols.

« Last Edit: March 30, 2016, 09:25:32 am by H »
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 ~

raul

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Señor Hentrich,
Just for curiosity, the mathematics that nuclear physicists study is much broader than the one you are studying? Raúl

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Studying Mathematics as a Way to Endure Time
« Reply #5 on: March 30, 2016, 01:05:23 pm »
I'm reviewing undergraduate level Linear Algebra and Multivariable Calculus in preparation for an in depth study of undergraduate level Differential Equations.  All this requires an in depth review of Algebra, Trigonometry, and Integral Calculus ... all of which physicists require to study whatever the hell they study.

I'm sure what I am studying is elementary to a nuclear physicist, but this makes it no less FUNDAMENTAL.

 ;)
« Last Edit: March 31, 2016, 10:47:06 pm by H »
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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Quote
There is definitely something to this.  Sometimes I reach a very calm state of mind even while just working through exercises.  If a problem has many steps to it, if I reach this calm Zen-like state of mind, I am no longer in a rush to finish the problem set.  This calmness is then reflected in the way I write the symbols.
I have experienced something similar.I long to experience that state of mind again.Let's see.

La Tristesse Durera Toujours                                  (The Sadness Lasts Forever ...)
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Studying Mathematics as a Way to Endure Time
« Reply #7 on: March 31, 2016, 08:23:24 pm »
I call "the study of mathematics" my hobby, but my engagement with it feels kind of spiritual, and now that it has become a daily obsession, I dare say it is taking on a religious feel to it as well.

I especially love when I am able to slow down long enough to appreciate even what I may discard as "elementary".

What a difference in one's state of mind, to compare one's heartbeat when stuck in stop and go traffic to one's heartbeat when content working through exercises in a textbook.

If only we could train our minds to cherish those moments when we reach that state of peace while studying, we may learn ways to return to it on a regular basis.
« Last Edit: March 31, 2016, 10:46:24 pm by H »
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: Studying Mathematics as a Way to Endure Time
« Reply #8 on: April 01, 2016, 10:34:08 am »
"If you want a safe compass to guide you through life, and to banish all doubt as to the right way of looking at it, you cannot do better than accustom yourself to regard this world as a penitentiary, a sort of penal colony.”-Schopenhauer

You may not believe it ,but I was chanting " Studying Mathematics as a Way to Endure Time"in my mind today at office.Yesterday,I was able to study math without any loss of concentration for many hours.This line emerged from your mind.A mind which cannot take anymore nonsense of this world anymore and which is also seeking a way out.And my mind was so receptive to this thought as perhaps it was thinking this subconsciously already but could not verbalise it.
La Tristesse Durera Toujours                                  (The Sadness Lasts Forever ...)
-van Gogh.

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Re: Studying Mathematics as a Way to Endure Time
« Reply #9 on: April 01, 2016, 11:36:02 am »
You are absolutely on point with this line of thinking, Holden Caulfield of India. 

In fact, I have found a text which would be perfect for a Jerimiah of the Jailhouse to teach interested inmates in a county lockup with at least a few months of time on their hands:  Sheldon Axler's Algebra and Trigonometry.   No hardcovers are permitted.  Unfortunately for this hypothetical math preacher and his hypothetical math disciples, books in the hypothetical jailhouse must be ordered new, and the cost of new books (textbooks containing mathematical knowledge, especially) are prohibitively expensive.

For instance, there is a unique text by the author of Linear Algebra Done Right, Sheldon Axler: Algebra and Trigonometry with Solution Manual.  I say it is unique because it is not at all dumbed down and is not at all boring ... a great exercise even if one feels it is "beneath one's level".  Anyway, the mathemaniac outside the jailhouse can get a used copy from Amazon for seven dollars, whereas the poor devil in the jailhouse who wishes to enrich his cellmates inner life would be forced to pay, what, $170  :o, were he so inclined to order one (must be from Barnes and Noble (new)) from the inside.

Now, that's just one example of how precious this fundamental knowledge can be.  I fantasize about being able to understand fundamental concepts so deeply that I would be able to enrich an enthusiastic student's inner life in a jailhouse scenario even if we could not access books.

Note that I have no fear of landing in a cage as long as I do not imbibe alcohol and can content myself to stay holed up in a room thinking.  This was Tolstoy's great observation about poor Raskolnikov, the former student in Dostoyevsky's Crime and Punishment:  if he would have stayed holed up in his apartment thinking, he would not have went wandering around axing down the pawn broker.

I mention this to point out two things: one, that studying mathematics is never a waste of time, and, two, that this activity really is a powerful way to endure time, even the kind of soul-destroying time one endures dodging basketballs out in a crammed yard of a county jail in Historic Downtown Freehold.

The released inmate may find that, when he is released, he has only entered the Open Air Prison of so-called freedom where he will find he is very much needed by his ageing mother to haul groceries, clean carpets, and help with computer problems.  The liquor store will be waiting for our newly released chimpanzee who can read, write, and do a little math.  He will experience that Ligottian realization that there is nowhere to go, no one to know, and nothing to do.

Ah, but the very thing that kept him sane in the jail cell, what that crazy old Steppenwolf was drumming into his head day after day and through the dismal nights crammed in the pitiful cell, would open up a mysterious realm where he could take refuge from the seemingly purposelessness of human existence.   Enrichment. 

At one point in our dialogue, you had mentioned that, no matter what level of mathematics you were contemplating, you could find yourself in a kind of rapture over it.

I have found that the areas of mathematics I enjoy studying the most require constant use of algebra and trigonometry.  I like the idea of studying Differential Equations because it requires me to use integration techniques that I otherwise would not ever put into practice.  Other concepts come up again and again: logarithms, the natural logarithm, the number e, exponentials, the trigonometric identities, geometric versus numeric interpretations ...

And why restrict this study of mathematics as a way of enduring time simply to actual inmates of a penitentiary? 

"If you want a safe compass to guide you through life, and to banish all doubt as to the right way of looking at it, you cannot do better than accustom yourself to regard this world as a penitentiary, a sort of penal colony.”-Schopenhauer

I am sure Kafka's "The Penal Colony" was inspired by this very sentence of Schopenhauer's.

I do not forget this for one moment!

This adds a spiritual dimension to daily existence that is the prisoner's greatest spiritual advantage over the "free men".  Everything has value to jailbirds: a plastic bowl, a dictionary, a sheet of paper, a pencil ... a special textbook (even something like basic electricity with diagrams ... a treasure!) ...

There used to be a library in the local county jail, but, as I may have mentioned, over a decade ago, school teachers on strike were placed in the jail, and they complained that there was too much subversive literature in the library.  The books were removed.  This is a truly ironic tragedy that it was professional educators who would instigate such a wicked act!

Quote from: Holden
Yesterday,I was able to study math without any loss of concentration for many hours.This line emerged from your mind.A mind which cannot take anymore nonsense of this world anymore and which is also seeking a way out.

Exactly. 
No more bullshiit. 
No more lies. 
No more "American Idol"
trying to mesmerize. 

And, no, teacher, I want to understand
- without the need to memorize!

It is like I noted in the post, What virtues does studying mathematics inculcate? from the How to Attain a Studious Life thread:

An appreciation for complexity and for the limits of our ability to understand things. I guess this is the same as humility above, but doing math makes you realize that most people, most of the time, probably don't know what they are talking about. Math, like programming, chess, or most complex pursuits, is an antidote to human BS because BS doesn't get you anywhere in trying to figure out something mathematical.

Bullshiit can get you a job, a car, or your own TV show, but bullshiit doesn't get you anywhere in trying to figure out something mathematical. 

Amen.
« Last Edit: April 01, 2016, 01:10:41 pm by H »
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: Studying Mathematics as a Way to Endure Time
« Reply #10 on: April 01, 2016, 12:56:53 pm »
Studying Mathematics as a way to Endure Time.Ramanujan was so intent on studying mathematics that he could not focus on any other subjects and failed most of them.Without a degree,he left college to pursue independent research in mathematics...
He died on his bed after scribbling down revolutionary mathematical formulas that bloomed in his mind like ethereal flowers -- gifts, he said, from a Hindu Goddess. Ramanujan told friends  Goddess Namagiri whispered equations into his ear:
"While asleep, I had an unusual experience. There was a red screen formed by flowing blood, as it were. I was observing it. Suddenly a hand began to write on the screen. I became all attention. That hand wrote a number of elliptic integrals. They stuck to my mind. As soon as I woke up, I committed them to writing.An equation for me has no meaning-unless it expresses a thought of God"

What some wrote off as the ravings of a mad-man, was actually a highly evolved vision of the cosmos.
La Tristesse Durera Toujours                                  (The Sadness Lasts Forever ...)
-van Gogh.

Holden

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Re: Studying Mathematics as a Way to Endure Time
« Reply #11 on: April 01, 2016, 03:38:29 pm »

Bullshiit can get you a job, a car, or your own TV show, but bullShit doesn't get you anywhere in trying to figure out something mathematical. 

GH Hardy said of Ramanujan's theorems -"They must be true because, if they  were not true, no one would have the imagination to invent them."
La Tristesse Durera Toujours                                  (The Sadness Lasts Forever ...)
-van Gogh.

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Re: Studying Mathematics as a Way to Endure Time
« Reply #12 on: April 03, 2016, 10:39:11 am »
You might also want to browse through e-booksdirectory.

Invest in some inexpensive notebooks and take notes like a monk, notes you may refer to again and again.

There is a limit to what one can focus on at any given moment, and over time, we definitely do forget ...

PS:  There is a beautiful extended version of a Physics text that covers a great deal of math.  The solution manual for an earlier edition is also available.  Get it while it's hot, and maybe sometime in the near future, it might make for a great guide ... where one can go through the text and supplement with other math texts when clarification is needed.
« Last Edit: April 03, 2016, 11:51:36 am by H »
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 ~

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Re: Studying Mathematics as a Way to Endure Time
« Reply #13 on: April 04, 2016, 07:13:18 pm »
If I were to invest in a bible, it would probably be the 12th edition of University Physics, since this one has used copies rotting away on a book dealer's shelf.

It is not much different than the current 14th edition.

Here's to taking our education into our own hands!

We are the self-ordained mathematical madmen.
« Last Edit: April 04, 2016, 08:55:43 pm by H »
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: Studying Mathematics as a Way to Endure Time
« Reply #14 on: April 04, 2016, 10:52:58 pm »
Mathematics is the science of patterns.Do you agree?
What is pattern:a regular and intelligible form or sequence discernible in the way in which something happens or is done.

And if it is indeed the study of patterns,then I think,the same mathematical concept should be studied in at least two different contexts to make sense of it.
La Tristesse Durera Toujours                                  (The Sadness Lasts Forever ...)
-van Gogh.