Tying Up Loose Ends

Tying up loose ends = To take care of, finish, or resolve some issues or pieces of business that are not critical but have remained outstanding.

Discussion Board and The Wayback Machine

For posterity:



Interests in Computer Programming archived at: https://github.com/Gorticide


Mental Health Experiment

The private study of mathematics as a spiritual exercise in developing patience, courage, and humility :

– patience with learning how to work through one’s confusion

– courage to devote many years, if not an entire lifetime, to work alone at one’s own pace with no expectations of any financial returns, no payoff but for the satisfaction of becoming a little more familiar with a vast mental discipline; courage is also required to face down the materialistic society of philistines, that is, the middle-class with its warped values and narrow definitions of success

– humility in taking some delight just for understanding what you work towards understanding, and not wasting too much energy moping about how little you can learn in a lifetime, or how mediocre you feel in comparison to some mathematical geniuses

It is possible that my continued devotion to my private encounter with mathematics is at once neurotic and potentially damaging to my mental health in that I block out the rest of the world and society; but it is equally likely that that the rest of the world is so psychologically damaged that my devotion to my studies and the isolation it requires serves as a kind of Fortress of Solitude shielding me against the harmful semantic reactions experienced from exposure to “the sick society”.

When others accuse you of wasting your life or not contributing to society, you can explain that you are just waiting to die, and since the study of mathematics is so very time consuming where the progress made, if any at all, is slow, this is surely an interesting way to get through this life not worth living in the first place.

And so I see, I recognize, that I am involved in a mental health experiment. Will this obsession lead me into a deeper state of detachment, and, if so, will such detachment exacerbate the anxiety inherent in Being, or will it, paradoxically, decrease this anxiety?

Remember that such an obsession may be a form of escapism, where I do not do anything constructive to alleviate any concerns about “the future”. In fact, the kind of discipline I require of myself does not allow me to rush along through the texts. I go through about 6 texts from the same subject, trying to do all the worthwhile exercises. I am in no rush to get through them since, unlike the high school student, I have already taken the courses the material is a preliminary to.

There is not so much mystery. What I am exposing myself to is what Schopenhauer referred to as “drudgery”. Also, I sense that Schopenhauer may have felt that too much calculating and computation would somehow damage the brain. It certainly can’t damage it as much as hard liquor!

Have I bitten off more than I can chew in the sheer amount of texts I have been going through, and the ones I intend to follow through with? It’s all an experiment, the experiment of a man who feels he has already lived his life, a man who has sobered up mostly to assist his aging mother and to contribute his government relief funds toward paying her bills and providing shared groceries. In return, living like a monk in a cell, the Creature is no longer roaming around and getting into trouble, handcuffs, psychiatric wards.

I felt the only way I would be able to keep the Creature occupied and enthusiastic about waking up in the morning is to do something it had never had a chance to do before, which is return to the mathematics which troubled him so as a young adult. Sure, the Creature was granted the opportunity to enter university from age 31 to 35, and he did graduate; but as he returned to his “studies” years later, after making the commitment to reside with The Mother, he/it realized that, he may have an opportunity to do something which he will never have an opportunity to do again. I mean, once I committed to physics texts, differential equations, linear algebra, number theory, abstract algebra, etc, there would be an endless procession through difficult material, and I would wonder if the difficulty was rooted in confusions at more fundamental levels.

When integration got hairy, was it not with reference to trigonometric identities or parametric equations? When a problem required detailed sketches and breaking down into parts, I would become a little frustrated.

So, I thought, maybe I can start over, bringing to the beginning all I have learned up to this point in my life, and tracking down texts from the 1960’s [with rigor, proofs, and set-builder notation] along with texts from the 1980’s and more recent ones that incorporate graphing utilities and computer algebra systems.

At this point in my life, with the trouble I have been in, not to mention the official diagnosis of bipolar disorder, my chances of ever being employed in some kind of “Institution of Higher Education” are null. And so, if I was to become a Teacher of Preliminary Mathematics, the Bridge to Advanced Mathematics, I was to become my one and only Student.

Student and Teacher in One Creature. Often the Creature complains that maybe some of the material is redundant or not challenging enough; but then, no, moving along the exercises become challenging enough, and it realizes that it has made a wise decision, that it is involved in a kind of remarkable process, defying the myths, facing the brute fact that this discipline requires endless devotion. It helps to have no social life whatsoever.

Do you see how I have flipped the script on the psychiatrists and their Mental Health Industry?

Isolation is frowned upon. Structure and social interaction is encouraged.

What if it is precisely structure and social interaction which drives the Creature to seek oblivion via drugs and alcohol?

So this is my “mental health experiment”.

I figure that seeing my devoted study in this light, as opposed to the “career-oriented” mindset contaminating the discipline of mathematics world-wide, would enable me to define my own peculiar approach and relationship to mathematics.

You see, there are those of us who study math, and then there are those who are professional mathematicians. I study math. This is how I deal with consciousness. What are we but meat that defecates and will one day rot in the earth? It’s as though we were organic machines which eat and emit waste.

There is no “soul” that religions speak of; and there is no “self” that psychoanalysis speaks of.

There is this Creature, and anything it has learned from books it has had to work it out alone in its head. There were a few important tips from a calculus instructor from India, Jay Deshubundi, in 1994 while attending community college on Saturdays when working for the park service, but mostly this has been a solitary intellectual adventure, which includes the evolution of the computer algebra systems and my tinkering with programming.

The point is that I am now a man obsessed, and, from the outside, I may even appear to be mentally ill, the way I isolate, the way I do not look for employment or put away for the future. Yes, I may not be right in the head, as they say. Maybe I’ve always been a little weird, to say the least.

So be it. I would challenge the professors in the universities to return to some of the “high school” mathematics being presented in the 1960’s. I would challenge them to engage with some of the more challenging exercises, to work through them, if they can muster up the courage to stoop so low as to allow themselves to be challenged by what some of them sneer at as “baby math.”

It is not “baby math,” not the way it was presented by Mary Dolciani or Frank Allen.

Some of your university students might do well to drop out of college for a good five years and check them out!

Maybe there exist throughout the world certain psychiatric patients who might benefit from “Math Therapy.”

(originally posted at How To Get Through A Life Not Worth Living)

Embracing the Non-Mystical

I think I may be coming to realize just why I am so determined to investigate those aspects of “accelerated” high school mathematics that got me so depressed as a teenager now that I am older and kind of “out to pasture”.

Now I am able to handle the depression that is bound to ensue. In fact, I find myself embracing the depression which engulfs me. It must be caused by the enormity of the subject in comparison to what can be held between the ears at any given moment. As a teenager, it overwhelmed me, but now I think I am learning to rest in confusion, or I have simply become more comfortable with the limitations of OUR mental capacity. I do not take it personally anymore.

I want to understand, and I do understand – just a very small fraction of what I imagined what “understanding something” felt like.

I perservere.

I have come to expect feeling depressed, and so it no longer overwhelms me.

There is nothing mystical about it. No supernatural visions.

I feel as though I am the protagonist in an epic existential dystopian novel where I am such an honest man that I have tracked down some particularly challenging high school textbooks from the 1980’s (which still were based on the “New Mathematics” of the 1960’s), where, because I am so intellectually honest I exert the mental effort required to give my all to them.

Meanwhile, the not so honest students, those who did not suffer any nervous breakdowns since it did not bother them if they really grokked anything or not as long as they got the grades, got into and out of college, and into some decent paying job married with children … season tickets to some arena, vacations to Europe and the Gulf of Mexico, they never looked back. They never had any desire to revisit the material since they have to keep learning how to to navigate the ever-changing software in their office … learning how to incorporate the latest app on their smartphone to manage their finances, secure their castle, and make reservations at their favorite restaurant (not to mention ordering their wine and having it delivered to their doors).

Do you see why I get this feeling I am the protagonist in an existential dystopian science-fiction novel about the present? To be 50 years old and be struck with this obsession to really, really, most genuinely give those high school textbooks (and others) their due? It’s as though I expect to experience some kind of mental shift. I have been through the university and I wondered about the gaps in the educational system, how each course can only cover so much as we race toward our inevidable suicides.

Are we expected not to understand? And if so, are we expected to then devote ourselves to the pursuit of gathering “credentials” and “status symbols”? If someone is driving a Mercedes-Benz or a Volvo or any kind of new car at all, they certainly don’t need to be concerned about how to write a two column proof. They have to practice their techniques for maximizing their number of orgasms, after all.

I do not believe the great lies.

What I am up to these days is the last thing they would expect from me at this juncture.

They expect me to wallow in self-pity, contemplate suicide, walk around sexually frustrated and totally miserable, thinking myself such a loser, such a deadbeat, such a drain on the War Machine economy, contributing nothing to society.

They certainly never expected me to go looking through these old math textbooks and hunting down the solution manuals as though I have stumbled upon Secret Knowledge that we were never meant to be exposed to, or if so, we were meant to feel intimidated and to never want to look into these matters ever again.

What’s going on?

I am looking where they never expected me to look. I don’t need any Zen Master or religious guru to guide me out of this illusory Matrix. I just need to train my mind to work in a calm, even if somewhat depressed, manner. Happiness and enthusiasm are unrealistic expectations since, after all, we are living organisms with all that this entails.

(to be continued)

The Lifelong Student: A Good Reason to Isolate

It’s been so long since I posted here that I forgot my password for wordpress.com

My attitude has been “Why Bother?” – as in http://whybother.freeboards.org

I’ve been corresponding to only one, sometimes two, individuals, both from different continents. One thing we most certainly have in common is our NEED to isolate from most of society.

I am always writing about mathematics and the study of the fundamentals.

The thing is, I am a 50 year old deadbeat layabout. Sure, I spend morning into late at night working through problems in textbooks.

I understand that I will never be a “mathematician”.

This is a good reason to isolate, to pursue something that interests me without needing the permission or approval of society.

I have read that “real” mathematicians do their best work when they are young.

So I guess I have never been a mathematician or a computer programmer, and that I am just a human animal who studies mathematics and reads/compiles/tweaks the code.

I am fascinated with Open Source computer algebra systems and the online calculators, like this one: http://www.integral-calculator.com/

SO this is how it ends … so be it. One must isolate from the “Big Bad Real World” in order to get down to the business of studying mathematics and programming and, yes, even physics.

Nothing that is so, is so. What do you call someone who studies mathematics all day, day after day? A student of mathematics? Is there such a thing as a lifelong student of mathematics? Is this possible without becoming bitter and self-deprecating?

Nothing Need Be Done

I am trying out a new strategy in my approach to working through texts. I am allowing myself to move slowly, to write larger, to work in a manner that could be called “taking baby steps”.

I even go out of my way to remove any kind of pretentious attitudes concerning mathematics. For example, I refer to what I study as “basic advanced mathematics” since I don’t care for the sound of advanced. What I study is basic, even though it is advanced.

Sometimes the print is small and the explanations not clear. I intend to make my notes intelligible, forcing myself to write larger.

Yes, the time has come to be kind to myself and to cease playing a role in my own oppression.

When something is totally incomprehensible, I can put it back on the shelf. When I am covering something which is not as clear as I would like, I will slow down and take baby steps.

I will leave this world with 25 unfinished notebooks where I went only just so far … and then moved on to something else. I will not hold myself prisoner, not even to my own plans or agenda.

Also, I think I want to embrace the depression that makes itself felt when I consider the futility of my mental exertion. All the books, all the helpful tools on the Internet, all the advanced calculators with computer algebra systems … all the time in the world … and still sometimes all I can do is bow my head into the palms of my hands … my empty head that suddenly cannot make sense of anything.

Some days and nights I feel sharp, and I don’t want to go to sleep. Maybe I am afraid that the sense of finally mastering some technique or concept will have vanished come morning time, when I groggily grind the coffee beans for my morning shot of enthusiasm …

No wonder some people just doodle on paper and stare off into space …

The Mediocre Faust (not a PhD)

I think I will see myself as someone with mediocre intelligence attempting to grasp ideas invented and discovered by eggheads and madmen.

I am determined to spend the rest of my days exploring the math.  I do not feel any pressure to master anything, and yet I secretly do want to master some things.

I don’t want to compare mathematics to playing the drums, but I can’t resist using this as an example to help me clarify (to myself, mostly) what is driving me to study math so obsessively again.

When I was around 27, after asking my live-in girlfriend to leave, I purchased a drum set.  It was during the period of my life I lived in an historic house next to the maintenance shop where I was a state employee/slave … a privileged slave, actually.  It was the same time in my life when I started attending community college, starting with Calculus.  I have never been a musician, but I loved to keep a beat on a drum kit, and I loved to beat on the drums like a madman when alone with Ozzy Osbourne’s Mr. Crowley cranked to the hilt.

Yes, I also loved beer and herb.

Well, I sense a real similarity in my relationship with drumming and my relationship with mathematics.  I love them both.  I am a master at neither.   If I approached a drum kit, I would want to be alone … it would be a mystical encounter.

Now, enter mathematics.  There is a very similar dynamic here.  When I work with mathematics, I like to be alone, just as I would like to be alone if I were ever to sit at a drum kit.  Math, like the drum, is one of the things in this life that has touched me ever since I was a child.   I think this is why, for now at least, I am focusing on undergraduate level “higher mathematics” and not concerned too much with the pure branches of mathematics, the things Bertrand Russell was grappling with.  I am not too concerned about the foundations of mathematics; nor am I concerned about being able to “read music” or “keep time” the way a “professional musician” would require a drummer to keep time.

This is the spirit of how I am using the word “mediocre”.  I do not want to use it in a self-deprecating manner.

I once heard that some cultures consider playing music as belonging to humanity,where it is not reserved for a class of professional musicians.  I would like to create this kind of culture for myself as far as mathematics is concerned.  I mean, as a religion of one, like insanity itself, I want my own private relationship with mathematics (as with drumming) that transcends any kind of metric.  No competition, no rating, no grading, no bullshiit.

I want to pay respect to Riemann when I use his methods …

If I can reach the point where going through some exercises in a mathematics textbook, at a level I am quite comfortable with, is like playing the drums alone with a 12-pack of Molson Ice and a bag of herb … then I will have found my mojo.


What Has Driven Me To Drink: Frustration

I think I am seeing what has driven me to drink, from my teenage years to my downfall as a maintenance worker at the park, and after graduating from the university in 2002 … well, around 2003 I experienced another “downward spiral into oblivion”.

Recognizing this general pattern may help me to prevent myself from reaching that point of total frustration again.

Now the problem is not lack of access to the resources for self-education, but quite the opposite.  Now I have access to the PDF files of more textbooks in just a handful of subjects than I could possibly devote attention to over several lifetimes.  This may be why I chose to collect used books rather than invest in an eReader.  This has to do with choosing which textbooks, which areas I find most necessary to master, and to focus on those, using the other books (PDF) as reference.

In the meantime, if my life were to fall apart where I was looking for a residence where I had nowhere to store books, then a small computer would have to serve as my lifeline to the textbooks I stored in PDF format.

In making this commitment to return to those subjects I found to be most essential, I also have, in an indirect manner, made a commitment to stay out of trouble, to abstain from inebriation, to forget about chasing women.

So, unlike those who are promoting a certain way of life for others to follow, I am simply doing what I have to do to get through my life, hopefully becoming a wise old scholar whom the teenage version of myself would honor.

I will just embrace this calm period of my life and try to forget the tyranny of public opinion.  If I am viewed by society as a deadbeat layabout who contributes nothing to society, then this is just the way it is.  I will not add unnecessary unhappiness to my daily life by concerning myself with public opinion.  As Jimi Hendrix sang, “Ain’t nobody know what I’m talkin’ about.  I’ve got my own life to live.  I’m the one whose got to die when it’s time for me to die, so let me live my life the way I want to.”

“Go ahead on, Mr. Business Man, you can’t dress like me.”

Each of us has to get through this life as best we can.

There are worse ways to waste one’s life than studying mathematics.   :-\

The point is, this daily study of mathematics, which is heavy in working through exercises, forces me to come face to face with my “low frustration tolerance”.

It is similar to “sensitivity”, where I become frustrated – not so much by confusion over higher levels of complexity, since I generally stick to a level that I stand a chance of understanding.  The frustration is with myself in computational errors, some of which are from basic carelessness.  For example, I will not copy a negative sign from the original problem, and so even when I verify that my calculations are correct (with computer algebra system), my results are wrong.  That’s not a big deal. It just forces me to track down the error, and I don’t feel so bad seeing that it was some “stupid” mistake and not a mathematical error.

It’s ok for me to have to work through these frustrations.

I predict that I will develop a calmer, less frantic, mindset simply by devoting so much time to this kind of problem solving.

So, as it turns out, I may be using mathematics to enhance “psychological and emotional” coping mechanisms.

Do you think this is an accurate assessment?

The Role of Psychology in the Quest for Mathematical Maturity

Do you think privacy may encourage intellectual honesty in one’s pursuit of mathematical maturity?   Could a delicious secrecy about where one is at concerning one’s own understanding eliminate the unnecessary psychological anguish that many associate with “higher mathematics”?

I remember, in 1994, how much I would appreciate when the calculus professor (from India) would share with us his “algebraic and trigonometric” insights.  To me, these were even more valuable than the teaching of the actual “calculus”.

Why?  Well, because these were fundamental mind tools we were working with.  It is similar to the way Integral Calculus is a fundamental mind tool for solving differential equations.

When I say, studying mathematics is NEVER a waste of time, I am attempting to transcend a tendency (in me?) to berate myself should I find myself still experiencing AHA moments of catharsis when considering something like function transformations, how the domain and range relate to the graph.

This is why someone my age may prefer solitary study.  There is a certain psychological liberation when one nurtures intellectual honesty in the learning process, since one can let their own confusion become their best guide.  As soon as something seems “counter-intuitive”, that is an internal recognition where the root of the confusion might exist.

When the graph shifts left or right, the domain changes, so in order for the outputs to remain consistent, the INVERSE of the transformation of the domain must be performed on the function.

The reason I mention this is because after getting through the first chapter of a textbook on differential equations, filling an entire notebook working through exercises, I decided to make a commitment to myself to relearn some fundamentals again, to slow the process down, and to devote several months to reviewing algebra, trigonometry, and integral calculus.

The thing is, this morning I suddenly suspected that this might be very boring for me.  Wasn’t this a waste of time?

But then, while begrudgingly working through some exercises, I found that certain transformations on functions felt counter-intuitive to me.  I was kind of amazed by this fact, so, after clearing up the confusion, I realized that returning to some fundamentals as a kind of strengthening my foundations may be seen as a “time/energy investment” that will surely enhance each phase as I forge ahead.

What role does one’s personal psychology play in one’s quest for mathematical maturity?  First of all, I think the metric of maturity is defined on an individual basis and should not involve society as a whole.  This is where privacy and that delicious sense of secrecy I mentioned comes into play.

Maybe students just getting out of high school should be encouraged to loaf around and study at their own pace for 10 years before committing themselves to a major course of study.  This way they can take their education into their own hands and brush up on things that may not have been explained well … or maybe they were just too distracted to pay any attention.

I am interested in the role my own psychology plays.  While I do intend to challenge myself, I also want to be able to appreciate reality, and not to berate myself for constantly reviewing preliminaries.

Can this “secretly studying” scenario be compared to other private pursuits involving inner growth?   Learning and maturity are things that happen “inside the skin”.

Is it possible that exams, tests, grades, diplomas, job-titles, i.e. “systematic education” is a case of Nothing that is so, is so?

Maybe some things can’t be taught.  They can only be learned.

Of course, there will be those who claim that just being in a position to study mathematics is tainted with the guilt of privilege, and yet how many find themselves wasting away in a redundant job or languishing in poverty, or worse still, in a jail cell.

I am not suggesting that studying mathematics, at whatever level, is a means to escaping poverty or securing economic security.  No, far from it.  I am suggesting it as a way to make the most of one’s poverty by attaining a life of the mind, where the most essential ingredient is leisure.

In modern mass-industrial society, those with the most leisure are the very rich and the somewhat poor.  When industrialization and computerization has automated many jobs, there will be more and more superfluous members of the population whose main activity will be the securing of, the enjoyment of, and the recovering from intoxicants whose main function is to enable the user to endure its own existence.

Is self-education a social privilege?

If early education has lasting value, maybe it is simply the value as a cultural artifact, that one will have things to think about even if one finds oneself in the growing army of mind-bodies who have become apparently useless to society.

How shall the over-educated, underemployed and long-term unemployed masses continue to develop their mental lives outside the prohibitively expensive buildings of the Church of Reason if not via their own secretive self-education?

You know what, while it is interesting to talk about the masses, it is unrealistic to think in terms of mass society.  That’s why, for the time being, I will only consider my own psychology.  I will proceed as though learning things for the first time.  Also, I have found that including a verbal explanation (to myself) of each step may convince myself (whatever that is) that I have a grasp of the concepts.  Proceeding in this calm manner, from the ground up, may help me to develop a certain approach to problem solving that can be carried with me into whatever areas I choose to explore (or re-explore) in this manner.

Maybe I am just looking for a different style of education than what I experienced as a formal student.  I am not promoting this style for “mass consumption”.  I’m just keeping records of my learning experiences.  In “planning for future studies”, I am only thinking of a few key subjects, and I foresee the study of these key subjects as lasting the rest of my life.

Isn’t it peculiar that a realistic assessment of the proper time I want to devote to these studies is in direct conflict with the pace at a university?

This makes me wonder how much intuitive understanding is actually being retained after the exams are “aced”.

Maybe I am not aiming to be a “mathematician” and will be satisfied as a kind of “mathematical technician”.

I feel the same way about computer programming.

I never had any ambitions to be a “software engineer”.

I’m just a curious chimpanzee who can read some code, and I appreciate seeing mathematical algorithms come to life in computer programs, especially computer algebra systems.

Maybe I will never possess the “mathematical maturity” to really appreciate proofs, and maybe I will never have the expertise to manage a very sophisticated piece of software.

And yet, what I do hope to attain is enough emotional maturity to be able to appreciate whatever I am able to grasp, and to stay curious.

I don’t demand too much of myself, and yet I feel I am eons ahead of those who would damn me to Hell, screaming, “Get a job you a-s-s-hole!”


related:  How to Attain a Studious Life

(why bother?)


FFF: Forget Football Fans !

I can’t sit back and witness a total gort yammering on about football, as if a gort buster really gives a shit about such gortville matters.  It wouldn’t be so bad, but this gort named his new website “Gort Busters” and is using the name “Mike”.

I tried to leave a comment there, but this is not allowed.

His latest post is “Football Weather“.

We have a blizzard in Dirty Jersey.  That should keep the goddamn gort mobiles off the road.  Nature shut down gortville.  Definitely not “football weather” here in dirty fuckin’ jersey.

{∅, {∅}, {∅, {∅}}}

implies { }

The singleton of the void is written here as {∅}.

The name of the void is written here as ∅, meaning the empty set, { }, NULL.

{∅} is the formation-into-one of the name of the void. Its sole element is ∅.

What would the parts of the power set of p(∅) be?

There is {∅} itself; there is also ∅ because the void is universally included in every multiple.

∅ is part of every set. The multiple p(∅) has two elements, ∅ and {∅}.

Here, woven from nothing apart from the void, we have the ontological schema of the Two, which can be written {∅, {∅}}.

The element ∅ is part of the Two.

The element {∅} is also part since ∅ is an element of the Two (it belongs to it).

The two elements of the two are also two parts of the two. The mathematical concept of transivity is therefore possible. Transitivity tells us, “everything which belongs is included.”

The inverse is impossible.

It is not possible for everything which is included to belong.

Not only is the Two a transitive set, but its elements, ∅ and {∅} are also transitive.

Nothing inside ∅ is not “a part” since the void is no thing, the empty set, null.


A Few Comments About ∅

As stated, ∅ is a symbol for the empty set, { }, “the void” —-> NULL.

The void is a subset of any set: it is universally included.

The void possesses a subset, which is the void itself.

Examining these properties of the void is an ontological exercise.

The first property testifies to the omnipresence of the void.

The void, to which nothing belongs, is by this very fact included in everything!

The State considers the individual as a subset – not as Your-Government-Name (the proper name of an infinite multiple) but as {Your-Government-Name}, an indifferent figure of unicity, constituted by the forming-into-one of the name.   The individual is included within the State.

Coercion consists in not being held to be someone who belongs to society, but as someone who is included within society.

Does this make sense?  Note the difference between BELONGING to society and being INCLUDED within society.  A stateless person doesn’t “belong to” any state.  A de facto stateless person is someone who is outside the country of his or her nationality and is unable or, for valid reasons, unwilling to avail himself or herself of the protection of that country.

The relation of belonging is the fundamental non-logical relation that structures all sets, and is written ‘∈’.    The relation of being included is written ‘⊂’.  I’m not sure if the difference is clear to me.

Given a set A = {a, b, c, d}, the elements that belong to it are: a, b, c and d.

But what about sets that share coincident elements, such as B = {a, b} for example?

Such a set is said to be included in A, or to be a subset of A, and is written: B⊂A.

If all the elements of a set B are also elements of A, then B is included in A.

The Power Set Axiom then states that if a set A exists then so does the set of all A’s subsets.

Taking the example C = {a, b, c}, the power set of C is: p(C) = {{a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}, ∅}.

The new set, p(C), has eight, or (2 to the 3rd power) (2^3) elements. Perhaps the only two surprising inclusions are the empty set and the set C itself. Given the definition of a subset, their inclusion becomes clear. Although the original set cannot belong to itself, on pain of paradox and inconsistency, it can include itself as it obviously shares all its elements.

The empty set, ∅, has the unique property of being universally included in all sets; there is no element belonging to ∅, which is not also an element of any other set, as ∅ has no elements.

If sets present their elements, they represent their subsets. The full representation of a set is equivalent to its power set, and Badiou calls this the State of a situation. The State represents the situation, and it will be in the minimal relation between an infinite set/situation and its power set/State that novelty will be possible.

Badiou’s set theoretical universe is sparse; only the empty set exists.

The first new set he produces is p(∅) = {∅}, a set with one element, a singleton.

This is not too surprising either, if the general rule is that the number of elements of a power set are 2^n, where n is the original number of elements, if n = 0 then 2^0 = 1.

From this Badiou derives the rule that given any set A, then its singleton, {A}, also exists.

We are now in a position to consider the construction of the finite ordinals. The void, or empty set, ∅, can be considered as the first natural ordinal 0, with its singleton {∅} corresponding to the ordinal 1.

The successor of these two ordinals is the union of these two: ∅∪{∅} = {∅, {∅}}, the ordinal 2.

The process of succession is to form the unity between the current ordinal and the singleton of this current ordinal. The construction of the ordinal 3 is accomplished as follows: the union of {∅, {∅}} with its singleton {{∅, {∅}}}: {∅, {∅}}∪{{∅, {∅}}} = {∅, {∅}, {∅, {∅}}}. In general if a is an ordinal the successor of a is a∪{a}.  This is equivalent to the idea of adding one. The interesting feature of this construction of the ordinals is that all the previous stages of the construction appear within the current level as elements. Every element of an ordinal is itself an ordinal.  It is this feature of nesting and homogeneity that qualifies a set as transitive:

∀A∀B (A∈C & B∈A) → B∈C

This reads, if A belongs to C and B belongs to A, then B belongs to C.

Now we go insane.


{∅, {∅}}

{∅, {∅}, {∅, {∅}}}

{∅, {∅}, {∅, {∅}}, {∅, {∅}, {∅, {∅}}}}

{∅, {∅}, {∅, {∅}}, {∅, {∅}, {∅, {∅}}}, {∅, {∅}, {∅, {∅}}, {∅, {∅}, {∅, {∅}}}}}


~ H : {∅, {∅}, {∅, {∅}}}

On Being Honest

When I come right out and confess how limited my mental capacity is, I do so in a private setting. I consider this message board (or even a small blog) to be private even though it is “public.”

The point I am trying to make is not that I feel “stupid”. I know I am not stupid. I am simply aware of how much I do not know, and that what I have studied has not brought about a tremendous amount of understanding. On the other hand, I am also aware that those who do not even attempt to explore the kinds of things I have looked into are not even dimly aware of their own ignorance, so they may not experience the “limits of their mental capacity” as strongly as I do.

Paradoxically, I walk around feeling “not very bright” … since I continuously stretch my mental faculties to their limits, often becoming frustrated and a little depressed in the process.

When I encourage honesty of this sort, I certainly do not mean to encourage false modesty.

It is just a sad paradox any solitary student will face when venturing on this path alone. Attending some kind of formal setting may boost one’s confidence since one may pick up on things and be able to explain what one understands to one’s peers. Alone though, one does not experience this. One feels always behind the eight ball.

The kind of honesty I propose is about knowing one’s limitations and not competing with others.

I have never been outwardly ambitious, but I have had some intellectual ambitions which have left me feeling as though I will never reach the kind of knowledge and understanding I thought I might have reached by this time in my life.

I remember Schopenhauer telling his readers that it is important for us to know ourselves so that we don’t go around pretending we are something we are not. I would not walk into a boxing ring knowing my opponent could crush me with one blow to the head or a short jab to the ribs. There is no shame in facing our limitations. An animal in the wild does not feel ashamed when it must flee from another animal that can clearly devour it.

Likewise, with intellectual pursuits, we may be curious to just skim the surface of a subject, and then lose interest, or we may truly desire to master a craft only to find that it is just too much for us. I say, take it slow. I say, do not aim to be great. I am not a motivational speaker who is going to tell someone they can be anything they want to be in this world. That is bullshiiittt.

In fact, considering my lowly non-position in society, I guess I have no business advising anyone. How do we measure failure or success? Why is it that some of the brightest minds walk around with a sense of their limitations, while those who do not stretch their minds may walk around with confidence, having never pondered too long over anything too difficult?

The type of honesty I encourage is a very personal and private kind of honesty. It’s the kind of honesty where, were one to be called a “genius”, one would fiercely deny it.

The whole idea of self-esteem is false. We are what we are, and that is all there is to it.

If I proclaim myself to be an idiot, that is not humility! Surely I know that, in comparison to the multitudes, I most likely am more well read and have exposed my brain to some of the higher and deeper levels of thought. Do I judge those who are not inclined to self-education? Well, I guess I can be rather judgemental using terms like gort and drone and sheeple and knuckle-dragger and what not. I never said I was a saint.

I do not live a lie. Nor can I appreciate how much I have learned over the years. Maybe I can be satisfied that I study things that interest me, and I may finally be emotionally mature enough to face the fact that I may never master any craft … but I am still a fairly bright chimpanzee … just not a trained professional cog in the machine.

Maybe every morning I wake up I can remind myself that I am a chimpanzee-like creature. OK, and at the same time I ought to really consider the fact that Schopenhauer and Husserl and Cioran and some other intellectual heroes of mine were also chimpanzee-like creatures.

This exercise is not meant to demean myself or detract from my heroes’ contributions to our species’ private quest to think honestly about our real situation, not to just mouth lines like a parrot so as to secure a position in the social machinery.

I respect what each individual creature endures just in being born. I am not a humanist. I respect all creatures.  I respect all intelligence, not just the academic or literate kind.

There may be a bitter resentment that is not easily overcome which arises from spending years studying something difficult only to find oneself no better off than those who did not spend all those hours trying to understand something obscure. So, we just deal with it. If we become bitter over time, so be it. There’s nothing we can do about it. It’s evidently how we are wired.

I just like to explore this kind of thinking because I see a path leading out of total frustration. To use a spiritual term, I see my psychological salvation in an honest appraisal and acceptance of my limitations.

This may enable me to even accept the limitations of all others. We are the products of a great evolutionary accident … a series of accidents … However it feels is how it is. So some of us feel despair and anguish, doubt and confusion. We may refuse to be comforted by the mantras of our societies because we are not after “pleasant feelings” but after authentic feelings.

We want to know how we really feel. Feeling good is not as important to us as knowing how we really feel.

Why do I say We instead of I? Why do I write “us” instead of me???

It’s just the way it comes out. In psychiatric wards those who run the group sessions bully inmates (clients – HA!) into using me statements, I statements.

Sometimes we rebel against such demands. 😉

Besides, fortunately for now, at least when we write on the Internet in a semi-private dialogue, we are not policed by those who want to control our language.

A Computational Diary, A Hacking Diary, and the Dead End Philosophical Diary

Irony or Paradox or Contradiction?  You decide.  I am posting a “blog” at a wordpress site in which I declare that I am not blogging, but simply keeping track of non-bloggable projects.

  1. My sketch pad has turned into a math diary.  I call this “A Computational Diary” since most of the mathematical ideas get transformed into magic recipes that I type at the command line, recipes in Python and C.  I like to be able to turn functions from Python modules into C or C++ codes that can be run from the command line with parameters.  So, that stuff is non-bloggable unless I were to get my own site where I uploaded scanned copies of my notes.  That might work for someone if many people were also interested in what one was computing, but, for me, it’s just not necessary.
  2.  My “philosophical diary” has turned into a “hacking diary”.  I call it The Book of Nonsense.  It has many notes about what I am currently studying … it has become a kind of supplemental text to the math diary.
  3. So, this morning, as I changed the Books of Nonsense from “philosophical diaries” to “hacking diaries”, I wondered where I will write when I want to philosophize.  Eureka, I already have Dead End: A Philosophical Diary.  I’ll just add chapters as needed.

It will come down to this:  Whatever can be most easily communicated with alphabetic symbols will end up being typed into forthcoming chapters of Dead End.   Like this blog, it’s not really a project so much as a bucket waiting to catch rain water.

Maybe that’s why I called it Dead End.  It’s all I will need for such “meditations” …

That’s my story and I’m sticking to it.  Now, back to the Extended Euclidean Algorithm … I want to alter some code so that I can display the entire process of applying the Extended Euclidean Algorithm.   It’s a pedagogical exercise.

The Great Literary Experiment: Introduction

I face a ridiculous dilemma. I was only able to burn about 25 of the 135 diaries I intended to burn tonight. I have already digitized what I want to save from them, but I can’t just put them to the curb. As a collection, they are quite tempting to read. No, if I am to do this properly, I have to burn each. I have been dragging them along. They have become a burden.

Hence, the problem I face with storing all my scribblings is what has motivated me to type these very words into a document which I will save as a file. My plan is to organized such notes into folders. Sure I continue to keep hand-written notes, but I have to start utilizing the current technology at hand when I have access to it, when I am not homeless, incarcerated, or lost in alcoholic oblivion.

I guess this is an introduction of sorts. Trust me, I prefer writing with a pen in a journal, but I am trying a different strategy here. I don’t even know where I’m going with this. Hundreds of pages from the diaries have been digitized into PDF files, but I still face the ridiculous dilemma of having to destroy the original notebooks. This is proving to be quite a challenge.

Tossing and turning on my cot, the feeling of panic and anxiety returns as I can’t prevent my mind from coming to certain conclusions about the nature of the world in general, and the nature of the society I was born into in particular. I can’t be the only one to see it for what it is: nightmare. As far as literature is concerned, is there a vast conspiracy suppressing the truth? Oh, it’s vast alright. The conspiracy is the tyranny of public opinion.

Who would be interested in reading the ideas of a deadbeat? I don’t care. I am not writing to the gorts who uphold the status quo and defer to mainstream values such as the work ethic, marriage, or “go forth and multiply.” As a man at odds with his society, and indeed, at odds with Being-in-the-world itself, what drives me to type these words has nothing to do with wanting to please an audience. Occasionally I choose this medium rather than jotting down handwritten notes in a journal because it gives me an added sense of addressing an audience. As Dostoyevsky’s Underground Man stated, I am better able to critique my own thoughts in this format. I gain actual relief from writing, especially if I can face my human suffering with humor while gaining psychological insight.

Since I defy pressure to conform to social norms, I don’t have any delusions about reaching the masses. I will direct my rhetoric to the few, the outcasts and outsiders.

I am going to call this work The Great Literary Experiment. I will try to destroy the fear of public opinion. What this comes down to is preparing to be mocked, ridiculed, and ultimately condemned as some kind of weirdo creep. Rather than continue to toss and turn for hours, I rise at 4AM and eat some scrambled eggs. I clean the dishes in my mother’s sink. Yes, I live with my aging mother in a 55+ community. Myself, I am only 48, about the age of Harry Hallar in Hermann Hesse’s Steppenwolf.

I am a bit like Harry Hallar, the Steppenwolf, except that I am not a fictional character created by a writer to represent himself. I intend to remain strictly committed to autobiographical philosophy. I could call it fiction, maybe even science fiction. This may allow me to further speculate upon the vast conspiracy which compels writers to burn their diaries and format their hard drives. Subversive thoughts, subversive thoughts … can somebody please deliver the reading public something to guide the suicidal insomniacs of the world to the morning light?

Forgive me, I’m looking for my style and how exactly to go about describing my anxieties about Being in the World. Once and for all I have to forget about reaching some kind of readership or audience. It does not effect my theories one iota if the entire reading public makes a total mockery of me. I will be a pioneer and face down the specter of public opinion.

Like Dostoyevsky’s Underground Man, I will want to unload my resentments against those who keep up the farce of the status quo … the hangmen, the enforcers, and, yes, even the breeders who keep the absurd comedy going. Ah, but now the reader will protest, “Come now, sir, you seem to be enjoying life out of harms way in your aging mother’s domicile devouring her eggs and typing into some kind of digital contraption. At least you’re not scribbling with one of those security pens on scrap paper in the county jail.”

Yes, yes, dear blessed reader, but I am ready for that too, I suppose. I know about image devices (scanners), so I intend to scan through my jail house scribblings to see which pages will be concatenized into PDF files. Why this compulsion to preserve my rantings? I sense that my perspective is worth noting and passing on to the future. Since what I scribble in diaries takes up entirely too much space, and the collection of such a tome becomes absurdly problematic as the years pass, whenever I have access to a device, I might as well bite the bullet and type these words into a document as if anyone really cares.

At least you’re not being held hostage by crack cocaine and its side-kick, Traveler’s Vodka. Yes, but that is because of environment. Fortunately my mother and I are close enough that we were able to figure out the dirty details of the vast conspiracy. Part of that vast conspiracy includes being corralled into residences where I would be preyed upon to the point where my day to day reality would drive me to seek relief in alcoholic oblivion. For the moment, I am side-stepping that trap.


Peace and Greetings!

Since I have limited access to the Internet I have returned to the old school message board format.  I appreciate dialog, and with the blog format, comments are awkward, requiring “approval” to filter spambots and/or haters.   One individual in particular took to engaging me in dialog via email.  I find a message board, even if it is just two or three participants, is a better way to organize our chaotic thought processes.

All are welcome to register there or even just lurk.

I left this post because there was a comment which kind of requested I keep this blog updated.

I have been posting fairly regularly at:
{∅, {∅}, {∅, {∅}}} .
  Presently we were pecking away at Madness Theory.

Again, peace.