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

William Stein: Elementary Number Theory and SAGE

I stumbled across an awesome character in this plot:  William Stein. 

I was just getting into the very beginning of Elementary Number Theory: Primes, Congruences, and Secrets: A Computational Approach when I saw the reference to sagemath.org which I come to find out the author himself lead the project on to create.  He is devoted to Open Source, and with some determination, the user will have access to a free system which is as powerful as MatLab and Mathomatica (but not as streamlined).   It is native to UNIX, and therefor is easier to install on Linux.   With Windows, one would have to use a Virtual Machine.  VirtualBox is preferable to VMware.  Myself,  I just installed it on Linux since I want to get down to the details of using Sage, not spending time loading a Virtual UNIX machine into Windows operating system..

Anyway, I am indebted to this William Stein for reawakening my interest.  SageMath also uses Python constructs, so I can continue to learn as I go.   I am just far more interested in number Theory than in "pentesting" and "hacking".   I looked into Metaspoit and set it up and got a feel for the commands, but life is short, and I prefer to engage my brain by giving this Stein character some of my attention.  I think it will be a rewarding endeavor.

So, I have found a pattern.  Bertrand Russell proclaimed that he had been suicidal in his youth, and that the only thing that motivated him to continue with the redundancy of remaining alive was his interest in learning higher mathematics.  I am choosing Number Theory for now, and I want to start at an elementary level.

The pattern with me is that I become interested in an area of study ... enthusiastic even ... and then, when faced with an exercise such as "Prove that for any positive integer n, the set (Z/nZ)* under multiplication modulo n is a group."

I think two things:

• Why bother?
• Who cares?

Do I really care? 

So, since I am under no obligation to prove this, and since I don't really care, I move on to the next one.  Maybe I can handle it.  Maybe it won't fill me with the utter pointlessness of even trying to understand.

Compute the following gcd's using Algorithm 1.1.13.

gcd(15, 35)
gcd(247, 299)
gcd(51, 897)
gcd(136, 304)

The first one, of course, is trivial, but let's go through the motions ... to show ourselves we can handle the basic mechanics of the operation.  I prefer pencil and paper, so you will understand the lack of technical notes in these threads.

35 = 15*2 + 5
15 = 5*3 + 0
so, gcd(15, 35) = 5

299 = 247*1 + 52
247 = 52*4 + 39
52 = 39*1 + 13
39 = 13*3 + 0
so, gcd(247, 299) = 13

897 = 51*17 + 30
51 = 30*1 + 21
30 = 21*1 + 9
21 = 9*2 + 3
9 = 3*3 + 0
so, gcd(51, 897) = 3

You may be thinking, why bother with this exercise?  I enjoy observing what I call "the chimpanzee" in the act of computing.  There may not be a self, but the animal-creature that eats food, poops, sleeps, smokes tobacco, and is able to follow basic mechanical procedures, I call "the chimpanzee".

Why does this chimpanzee get a little frustrated and agitated or depressed when asked to "prove" a theorem?   Is it low frustration tolerance?  Do I lack the patience?  It doesn't matter.  I move along.

I could do these repeatedly and lose myself in the mechanics.

304 = 136*2 + 32
136 = 32*4 + 8
32 = 8*4 + 0
so, gcd(136, 304) = 8

I seem to enjoy watching the algorithm work itself through the numbers.

Now, the next one looks "fun" as well"  Find x, y of Z such that 2261x + 1275y = 17.

This one will require pencil and eraser.  I can use sage to check the answer.  We will use the Extended Euclidean Algorithm.  That's when you find the gcd and then use your work to substitute values until in the form of 2261(x) + 1275(y) = 17

I just got some fresh pencils and an eraser.

Now, of course I am thirsty, and I used to really enjoy pounding down beers ... but I have some carrot juice to guzzle ... and, as one of Ligotti's protagonists once said, "There is nothing to do, no one to know, and nowhere to go."

This chimpanzee is somehow pacified while becoming more familiar with some elementary number theory ... Maybe I will type it up after going through it in pencil.  There is no rush since there is no purpose to anything I do.  Really.

There is that German word, Bildung, which the translators obtusely define as "education."  It means more than that.  Bildung suggests true (inner) freedom through Zwecklosigkeit (non-purposeness), Innerlichkeit (Inwardness), and Wissenschaftlichkeit (scholarliness, enjoying one's mental faculties as an end in itself).

I'm content deepening my Bildung.

In our society, maybe there may be a reluctance to look into areas of interest since it involves the confession to oneself that one's understanding is inadequate.  It is far easier to just not look into the matter ...

Anyway, the pencils and eraser and paper with no lines are having a calming effect on this chimpanzee.  We'll keep you posted with our honest no "posturing" math diary.

So, we use the Euclidean Algorithm then the Extended Euclidean Algorithm with the Beginner's Mind:

2261x + 1275y = 17

2261 = 1275*1 + 986
1275 = 986*1 + 289
986 = 289*3 + 119
289 = 119*2 + 51
119 = 51*2 + 17
51 = 17*3 + 0

So, 17 is the GCD.  We use this to work our way to the solution using substitutions along the way.  Why am I typing this?  I already did the work in pencil.  I want to show the notation, how the numbers are kept in their form so as to get to the solutions x and y.  Notice how we're just substituting, using what we know from the work above.

17 = 119 + 51(-2)
17 = (986 + 289(-3)) + (289 + 119(-2))(-2)

17 = 986 + 289(-5) + 119(4)

17 = (2261 + 1275(-1)) + (1275 + 986(-1))(-5) + (986 + 289(-3))(4)

17 = 2261 + 1275(-6) + 986(9) + 289(-12)

17 = 2261 + 1275(-6) + (2261 + 1275(-1))(9) + (1275 + 986(-1))(-12)

17 = 2261(10) + 1275(-27) + 986(12)
17 = 2261(10) + 1275(-27) + (2261 + 1275(-1))(12)

17 = 2261(22) + 1275(-39)

x = 22
y = -39

sage: xgcd(2261, 1275)

(17, 22, -39)

 :)

And to answer your question-I love solitude, about the only thing that makes my life bearable.HELL IS OTHER PEOPLE,and never mind S.'s Ethics.

You wrote:
"I remember out in Seattle drinking with an elderly black dude, and he started getting very angry while he was shaking his Bible around, yelling at me about how he wrote the Bible. In a strange way, now I understand what he was saying. When I read Schopenhauer’s The World As Will and Representation or some of his essays, I find a part of me saying just that: I wrote this. I am this thing that wrote that. I am still that self-same thing writing this.

Damn it to Hell, I am still here … there is no way out, not even in death! How does this end?"

Well,it does not.

I keep pushing Husserl aside.  There is a book about him and Frege: Husserl or Frege.  Do you find yourself having to ignore so much just to remain focused, kind of like Husserl's phenomenological epoche?  How ironic that when I apply this epoche, the bracketing off of the whole so as to focus the laser beam of attention on something, our life-world I guess, that Husserl keeps getting bracketed out of my Lebenswelt! 

Husserl started out writing about Arithmetic.  My attention is limited.  I know he is an important thinker, and I always defer to him even as I have not read as much of him as I would like to.  I invested time in him rather than Heidegger.  I am not a very patient reader anymore.  I guess this is called "being jealous of one's own self" ... our attention is all we have ... what we choose to engage with ... it's everything, really. 

I am not surprised that you prefer solitude.  Like I have mentioned before, other people can really destroy one's love of learning.  It's as though "professionals" are trying to protect their "craft" so they try to make it as incomprehensible and as difficult as they possible can. 

Oh, what is that quote I had by Virginia Woolf?  It can be applied to all areas of study.

Literature is open to everybody. I refuse to allow you to turn me off the grass. Lock up your libraries if you like; but there is no gate, no lock, no bolt that you can set upon the freedom of my mind.

I am very frustrated at the moment.  I am following Stein's text and going through the exercises.  There is one that we can solve with the sage software, but, when trying to do it by hand (because I would like to be able to solve with pencil and paper, relying on Sage just to check my solutions), I am hitting a brick wall.  I am a little infuriated that Stein does not walk through the solutions even when the answer is in the back of the text ... apply CRT ... but does he mean just plug the numbers into a command?  I am currently going around in circles obsessively.

I feel like a "subgenius" --- by this I mean, things do not come easy for me and I am a very slow thinker who likes to go over constructions step by step.  I hate "whiz kids" who try to play like things are easy.

I feel like scanning my notes and sending them through email in pdf files, but I don't want to pull you into my "nightmare". 

I feel much more comfortable using the Internet to learn without the politics and posturing of an academic setting. 

I am not studying things way over my head, but I still get frustrated when things aren't crystal clear, or when problems are such that the trick is to know how to set it up for a computer to help us solve.  I so much want to do these by hand and see every step.  It makes me want to look at the code to see how the CRT(a, b, m, n) command comes up with its solution.   

Hmmmm .... that could be interesting.

How easy it is to become a madman! 

As for eating food, I find myself not inclined to eat in the morning in the summer, but in the winter I remember getting up very early to eat potatoes and eggs, sometime rice and eggs.

I eat a lot of chicken.  In the summer, melon like cantaloupe is very good.  Spinach ... salmon ... yellow rice ... I eat differently in the winter.  Then I eat more meat like meatloaf and meatballs ...

My sister is a vegetarian, but my mother and I are savage omnivores.

You know, peanut butter is good.  Like I said, my sister and even my nephew have much healthier vegetarian diets.  I even eat pork sausage and scrapple which is scraps of pig intestines and god knows what.

Maybe I am not the best one to ask.

Studying math and computer science again - full force - has put me in a self-deprecating mood.  This is a paradox:  those of us who try to learn may always be aware of how little we know, of how pathetic our grasp is, how we are inspecting the tip of an iceberg, whereas those who may only want to watch sports on TV or p-o-r-n-ography don't face their ignorance and may not be troubled in the least.

Anyway, I am paying for the Internet connection because I am using it as a university where I am able to move at my own pace and be spared the nasty politics of being made to feel inadequate simply because I am a slow thinker who wants to really gasp something before forging ahead.

It's no rush with drop box.  Even if I sent you all the notes I've scanned, I can't see how the bulk of it would do you any good.  It might distract you.  You have your own notes to keep, Holden.

While I will still be keeping a separate pad for math work in pencil, sketches, and details on algorithms behind specific code (modules), working in notebook() mode with Sage is like having an electronic math diary.   With an electronic text book open, I can follow along, type notes right in the command cell (commented out with # at the start of the line) and save the input and output in worksheets.  Hell, I can even cut and paste notes and lines of code directly from the pdf book when it's open with evince.  It's a very laid back scenario to say the least ... gives me a real breather.

I remember being in awe of Derive back in 1994 ("2000 years of mathematical knowledge on a floppy diskette"), but Sage is like a blessing by supernatural forces!  It's like, ah ... this is what computers are for.  This is it.  This is the tip of the iceberg ... and we are standing on the shoulders of giants.  The thing is, even Derive, over 20 years ago, was like $100.  I like Sage much more, mainly because it is so expandable via one's own spontaneous functions ... and it is Open Source.  I hope they remain committed to that spirit.

I am so in my Mojo when using it in between pencil and paper study sessions.  Even when working with pencil and paper, it's great to check my work with it.  I would go so far as to say it has renewed my interest in mathematics ... making it fun (for me) again.

And what's so great about the worksheets is that I don't feel as obsessed about writing important things down as I can type notes as I go along, right there with the live code, and save all I just went over right in the worksheet, giving the worksheets descriptive titles so as to accessed later if I want to review the session (or share it who I have no idea who).

Sage is native to the UNIX/Linux environment, and if you don't have access to Linux AND don't want to install it on Windows via a Virtual Machine (I wouldn't blame you), you can check it out and use it (with an internet connection) online.

You can type directly into a cell with an internet connection.

http://sagecell.sagemath.org/

or

http://sagenb.org

Sage Notebook - easy to remember.

It is software like this that makes a computer worth having and using.  Of course, I was using an old clunker for a few years and even lived without any computer at all for several years after one was stolen from my apartment while I was incarcerated after yet another "psychotic episode" ....

For now, while I can,  I like to run it on Linux.  If you get a notebook computer, even a small 11-inch model with 500GB hard-drive, you can shrink the Windows partition, put Linux on less than 100GB of it (much less if you want since Linux stays lean (installs less than 15GB), and then you create a fat32 partition that you can share between Linux and Windows, working in both environments, having access to the best of both worlds.  Windows is still more dependable when it comes to devices like scanners and getting printers to work with wireless routers.  It's great to have both.

Linux and Sage are just ideal together, and the fact that Sage is all intertwined with Python makes me that much more motivated to just incorporate Python into my brainwaves.  Sage just might turn me into a Python evangelist.   I read that the guy who created Python did so as a hobby.  Guido van Rossum from the Netherlands wanted to create a descendent of "ABC" that would appeal to UNIX/C hackers.

Anyway, all I know is that I had lost interest in everything, and when circumstances presented an opportunity for me to purchase a little computer (with more power than large desktops I've built in the past), even though the scanning of the diaries was it's first task, I have rediscovered an inner passion I have for mathematics and computing ...

While I agree with the Ligottian attitude that there is nothing to do, nowhere to go, no one to know, and nothing to be, the life of a Hikikomori exploring mathematics with Python and Sage is about as good as it gets, especially if you can learn at your own pace with no external pressures from corporate structure and business politics.

We can respect those who put so much thought and energy into these devices by using them in such an intellectually stimulating manner.  In the United States, you would not believe it, there are commercials on TV for "online gambling," like Poker on-line where people play for real money.   When I pass by a TV and see those advertisements, it's like being in a Philip K Dick science fiction story ... All that computing power ... to play poker and black-jack.  There's a gort born every day.

I am just thankful that I snapped out of the 10 year long drinking binge when I did, and I chose to purchase a computer before handing any more money to another slumlord.  It surely is a razor's edge, but I am appreciating this interlude of coherency.

I will eventually save all the Sage worksheets in a zip file ... in case you get around to checking it out.  I know you dig math, and there is not much to stick around for in this feeding frenzy ... some things are like diamonds in the midst of this swamp of misery.  Get the hardware.  Some of the best software is free ... starting with the Linux operating system itself.   And with Linux, you wouldn't even need Anaconda's Python Package since these are more easily installed in the UNIX/Linux environment.

It might lift your spirits.  You may be working with a smart phone as you are often on the raod for your employer.  I don't have a phone.  I never cared for them.   I don't think you will be too motivated working from a phone, but --- in the meantime, I think you could still check out at least a sage cell from even a retarded smart phone.   


The folks who are into Sage seem to be extremely Open Source oriented, so, in that same spirit, I am leaving a list of some guidebooks.

A Beginner's Guide To Sage

Sage for Linear Algebra

Linear Algebra Lab Manual with a good overview of Python and Sage.  It goes with this free Linear Algebra text I also found off the SageMath Books Link.

Sage For Undergraduates.


You can use Python constructions such as "list comprehension" right in Sage:

free = [index for index in range(7) if not index in dependent]

The ability to construct sets in Sage with notation so closely mirroring the mathematics is a powerful feature worth mastering. 

---- end of sermon -----   

I hope to use Python &take up all your suggestions,eventually.
By the way,do you know which part of Germany your family originated in &when did they come to the US?

I think you are in a much better state than you would have been if you'd have joined Corporate America.Who do you think came up with the "idea"
of Romans?Im becoming more like S. with each passing day.Im planning to buy an air gun.To get a real gun is very difficult here.Once I have the gun I guess I can shoot down all the rats &lizards which create trouble for me.And if any snake tried to enter my house I will shoot it all the way to hell.Some manifestation of the Will,eh

And if the social system broke down,I will just hide in a bush with my gun,a big box of pellets and WWR.
By the way, I have come across a very lucid book which explains the concepts in WWR.Will share it with you soon.

Do you own a gun?I know that its much easier to get one in the US.

Here's a serious question:  Do you want to be a saint or a philosopher or neither?

Schopenhauer knew that being a saint was not a requirement for being a philosopher. 

This must have relieved Schopenhauer of a great burden - understanding that he did not "have to live as a saint" in order to be a great thinker, which he was.   I think, if Schopenhauer was not a genius, I don't know what a genius is.  I know his high regard for saints and beggars represents a kind of contradiction to you.

For me, the great relief comes when I realize I don't even have to be a genius to LIVE as a philosophical deadbeat.  Nor do I have to be a saint.  Many people say they belong to certain political parties just to keep their positions in the social order (their cushy jobs).  Others claim to believe certain religious doctrines or to be in direct contact with divinities in order to be married or accepted in a group or tribe.  The world is full of s-h-i-t.

Maybe I myself have been full of s-h-i-t at times and not even been aware of it.  I may have even believed I was some kind of genius if I hadn't pursued my interests and met my limitations. 

You are right about me being better off outside corporate employment.  Robert Pirsig, author of ZEN AND THE ART OF MOTORCYCLE MAINTENANCE and LILA, who spent some time in a mental hospital, had written that some of his greatest failures turned out to be his best successes.  In other words, my not fitting into the corporate workaday world, my not attracting a mate, my not reproducing, my losing my job as a maintenance worker at a park, my not being able to afford to keep a car on the road ... and on and on - these may be seen as blessings rather than things I should feel ashamed of.

OK, so you are asking me, or maybe you are telling me that feelings of "love" and "compassion" and "sympathy" are not worth diddly-squat without campaigning for social justice.

This is a perplexing problem.

People don't seem to become "activists" until personal circumstances push them into the battle.

The longest nail gets the hammer and all that.
____________________________________________________

No ... I do not own a pea-shooter.

This isn't Switzerland. 



That's why I'm aiming for "philosophical comedian" --- I don't have to be a mathematical genius.  I just have to be "mathematically inclined" ... It's less pressure.   I don't even have to be very funny either ... a comical philosopher ...

Was Cioran a deadbeat because he didn't have a job or get married or have children?

No, silly ... he was a PHILOSOPHER!   

Although, you know, he would have denied that he was a philosopher.  He wanted nothing to do with THAT label. 

So, what are we to call ourselves, Holden?

I like your idea of being a Rejectionist.

It's got a nice ring to it.

And, who did come up with the idea of Romans anyway?  Were they chased out of Africa?  It was relatively close to Egypt, no?

We could start a religion disguised as a joke or start a joke disguised as a religion ...

Maybe we can only have compassion for ourselves.