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

Walking helps, even if you have to pace back and forth somewhere and mutter to yourself, or explain things to yourself, argue with yourself. 

And even if the Big Bad Real World would mock your secret interest in mathematics as "childish," then engage in it as though it were an illicit drug, and the notebooks, pencils, computers - the paraphenelia of a math(s) junkie.

I have observed that you use pencil for math not pen,why is that?

The reason why the series of notebooks I have been keeping have been mostly in pencil has to do with several factors:  cost of paper/notebooks and ink; for decades-long project, the use of pencil is more relaxing (for a perfectionist) ...

The reasons the cost of notebooks is a factor:  ink bleeds through cheaper paper

Often geometric diagrams require erasing.  I am no artist, so I must force myself to be careful.

When working with scrap paper, I prefer clipboard and cheap pen.

When you were a student in Rutgers University,you told me you had chosen to study multivariate analysis,but almost no one else wanted to study it.

Were you the only one in the entire batch to study it?

As for the Multivariable Calculus, I had transferred from community college (of Monmouth County) to Rutgers [NJ state] University (of New Brunswick) in January, 2000, at the ripe old age of 33.  All the computer science courses were full, so I wanted to get some of the required mathematics courses in, such as Linear Algebra.  Most of the required courses for math were behind me, so I chose to explore Mathematical Reasoning (on proofs) and Multivariable Calculus (analysis, yes - it is also called this).

Most students will choose less challenging courses for their "electives."
Multivariate analysis is not required for the Computer Science degree.  My true quest must be physics, so while at university I did not want to waste the opportunity.  I was the only compsci student in the midst of engineers and physics students.   You see, the three dimensions are crucial  for the vectors used in physics problems.   Also, all that "Trigonometry" and "Analytic Geometry" plays a huge role in physics.   If I live into my 60's, I may be ready for Computational Physics.  Who knows?   It doesn't matter.   In my head, I'll always be this student of mathematics, philosophy, physics ... the computer science is a branch of mathematics, and often physics is indistinguishable from "applied mathematics."

I still have not been able to give justice to the mathematics behind the digital computer revolution.  It is the concrete counterpart to all the abstract symbolic algebra-oriented mathematics most science students are exposed to.   There are some real brains out there.   I'm not the sharpest knife in the drawer, not by a long shot.  I was the sharpest knife in the drawer in that class, but I think this had to do with my age.  I was, after all, ready for that class.

You know, there were plenty of interesting literature courses I could have explored, but I chose that advanced analysis class out of pure interest.  It was not required for the degree I was pursuing.

I regret having lost my notebooks from Rutgers.  I wonder if they are out there somewhere.

They are a great tribute to the passion of a novice.  I still have the Beginner's Mind, fully resigned to embrace my great ignorance in genuine humility.

1.You must have read  Art of Being Right by Schopenhauer.
2.Its almost a book about Logic-would you agree?( Do you think that,if we could get hold of the transcripts of maths related courses which he took in the University of Berlin, we will find that he would have done rather well in the class tests, if there were any( I am not talking about research level/Gauss level maths-just class tests).He did take some maths classes).

I had never been interested in that book, the Art of Being Right.  It just did not appeal to me ... looked to be made up of previously published essays.

I see someone has done a "reboot": The NEW Art of Being Right: 38 Ways To Win An Argument In Today's World (Argument, How To Argue, Arthur Schopenhauer, Dialectic, Debate, Debating)

While I have been greatly influenced by Schopenhauer, I am not much of a fan of debating.

Still, most of the contents of that "book" can be found in "The Pessimist's Handbook" ( most of those popular essays published as the two-volumed Parerga and Paralipomena )

I would have really enjoyed seeing some of Schopenhauer's scratch work in computing and even formal symbolic algebra and/or geometry ... trigonometry ... yes, I'm sure he held his own.  Still, the notes would have revealed much.

The Logic class I took was a Philosophy class, Propositional calculus ...

Since the Computer Science department branches off the Mathematics department, these disciplines share some of the same philosophical roots.  Were not the very first philosophers Logicians, hence, Mathematicians?

Logic is always present in programming ...

There is a book coming out early this summer by Jens Lemanski, called Language, Logic, and Mathematics in Schopenhauer (prohibitively expensive).

The chapters in this timely volume aim to answer the growing interest in Arthur Schopenhauer’s logic, mathematics, and philosophy of language by comprehensively exploring his work on mathematical evidence, logic diagrams, and problems of semantics. Thus, this work addresses the lack of research on these subjects in the context of Schopenhauer’s oeuvre by exposing their links to modern research areas, such as the “proof without words” movement, analytic philosophy and diagrammatic reasoning, demonstrating its continued relevance to current discourse on logic.

Beginning with Schopenhauer’s philosophy of language, the chapters examine the individual aspects of his semantics, semiotics, translation theory, language criticism, and communication theory. Additionally, Schopenhauer’s anticipation of modern contextualism is analyzed.  The second section then addresses his logic, examining proof theory, metalogic, system of natural deduction, conversion theory, logical geometry, and the history of logic. Special focus is given to the role of the Euler diagrams used frequently in his lectures and their significance to broader context of his logic. In the final section, chapters discuss Schopenhauer’s philosophy of mathematics while synthesizing all topics from the previous sections, emphasizing the relationship between intuition and concept.

Aimed at a variety of academics, including researchers of Schopenhauer, philosophers, historians, logicians, mathematicians, and linguists, this title serves as a unique and vital resource for those interested in expanding their knowledge of Schopenhauer’s work as it relates to modern mathematical and logical study.

Some of this editor's work is available online:  Problems and interpretations of Schopenhauer’s World as Will and Representation  (with Daniel Schubbe)

From 'Euler Diagrams in Schopenhauer to Aristotelian Diagrams in Logical Geometry'. in: Jens Lemanski (ed.), Mathematics, Logic and Language in Schopenhauer. Heidelberg: Springer.

In a section called "On Mathematics" in Schopenhauer on Space, Time, Causality and Matter: A Physical Re-examination, by Shahen Hacyan [Mexico]:

6. On mathematics

Schopenhauer was not fond of mathematics. Without denying its practical use, he was convinced that mathematics could only yield a quantitative description of the material world, but could never provide an understanding of its causal relations. “Where calculating begins, understanding ends” was his statement on this matter (4R, §21; see also Chap. XIII of WWR). His view may seem to be anachronic nowadays, but it must be recalled that his dislike of mathematics was shared by many intellectuals of his time, who longed for a direct perception of nature and its laws without the intermediary of abstract concepts. Let us recall that even Isaac Newton was criticized in his time for having “only” described the motion of planets, without explaining the real cause of gravity. Goethe, a contemporary much-admired by Schopenhauer, was a strong critic of abstractions in the description of nature; they may be useful, he held, but “it does not occur to the architect to pass off his palaces as mountain sides and forests” (cited by Heisenberg 1990). Even among physicists, the case of Michael Faraday is noteworthy: he performed many crucial experiments that were the basis of a full theory of electromagnetism, but his knowledge of mathematics was quite limited and he deliberately avoided mathematical description in the treaties he authored.
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Why is mathematics so effective is a great mystery of modern physics. Indeed, its effectiveness is quite unreasonable, as Eugene Wigner (1960) has well pointed out. In conclusion, we could paraphrase Schopenhauer and assert that “where understanding ends, calculating begins...but it may go very far!”.

We may calculate without understanding, as when we program computers to operate on matrices beyond dimensions capable of diagramatic visualization.

When you were in the Rutgers University, you must have studied logic too, it must have been there somewhere in your syllabus. Do you think if someone is well versed in formal/symbolic logic, he would find learning programming languages/mathematics in general easier in comparison to someone who has never studied logic?

I was wondering when we were going to cross this bridge, this can of worms which goes by the name "Logic." 

Recall Korzybski and the General Semanticists' Non-Aristotelian Logic.

The goal of Korzybski’s system, as noted above, is to represent the world outside of our skins as accurately as possible within our nervous system.  We might call this a form of phenomenology – of perceiving and describing what appears through the senses and, more exactingly, through scientific methodology, instrumentation and mathematics.

Consciousness is supported by a nervous system that also provides us our language capacity.  You can’t have an “I” without a language to express the experience in.  The non-aristotelian system acknowledges that both our observational capacity and use of language can be badly flawed.  Further, that such flaws are deeply embedded in language, in culture and have been inherited (learned) from former generations.  This legacy he called Aristotelian and, below, we will review the reasons why he came to this conclusion and chose this convention.  This legacy allows us to think, in a highly logical and procedural style, about a world that just isn’t what it really is.  Korzybski asserted that this form of thinking is really little different from what we called insanity:  A detachment from “reality.”  Do we wonder why there are so many factions in theology and philosophy?  There is little, if anything, really real to agree about.

Before heading to Rutgers, around 1999, I was taking liberty with some research projects, combining philosophy with mathematics and computer science.   I found these discipline merge in the study of Fuzzy Logic.   Here is an entire chapter (12) from Ronald C. Pines Essential Logic:  Frontiers of Logic — Fuzzy Logic: Can Aristotle and the Buddha get along?

Fuzzy logic begins where Western logic ends . .
. . Fuzziness begins where contradictions begin,
where A and not-A holds to any degree. 

~ Bart Kosko, Fuzzy Thinking: The New Science of Fuzzy Logic


Everything must either be or not be, whether in the present or in the future.   
~ Aristotle, On Interpretation


I have not explained that the world is eternal or not eternal, I have not explained that the world is finite or infinite.
       
~ The Buddha


The fundamental idea of Buddhism is to pass beyond the world of opposites, a world built up by intellectual distinctions and emotional defilements.
         
~ D.T. Suzuki,  The Essence of Buddhism

Now we have a so-called state-of-the-art digital computerized system, intended to centrally control each room in each building and eliminate inconvenience and save taxpayers lots of money.  So now we all freeze and wear jackets in Hawaii, and waste lots of energy.  We don't dare complain.  If our comptroller adjusts the system it will be too hot, and for a teacher, having an office and a classroom that are too hot is a fate worse than death.  The mind shuts down, and suddenly even your best lecture becomes boring and students begin to fall asleep.

According to the gurus of a new logic, called fuzzy logic, the root of our problem is cultural and philosophical: Our air conditioning system thinks like Aristotle rather than like the Buddha. 

According to the proponents of this new logic, the all-or-nothing overshoot of our air conditioning system is the technological end-product of a cultural hasty conclusion fallacy in regard to truth.  Since the time of Aristotle and the ancient Greeks, Western logic has assumed that a proposition or statement must be wholly true or false with no in-between and no shades of gray.

  Small wonder that our computer systems are dumb, proponents of fuzzy logic say, if they are programmed on the basis of a black and white logic.  Based on such notions of categorical truth and falsehood, on-and-off systems have no common sense; they are incapable of mimicking the simple human process of smoothly adjusting a thermostat when a room is too hot or too cold.

Aristotle may have been stating the truth when he claimed that man is the animal that reasons.  There was an assumption that this reason is altogether crisp and accurate in describing reality.

Bivalent Logic and Paradoxes
According to the proponents of fuzzy logic, we did not have to wait for faulty air conditioning systems to know that something was seriously wrong with the foundations of Western logic and our assumptions regarding truth.  Classical Aristotelian logic is said to be founded on a
bivalent faith, propositions (statements) are "crisply" true or false.  But our experience tells us there are many areas of life where a crisp categorical bivalent map oversimplifies to the point of paradox by missing important shades of gray.  In short, by not recognizing that there are degrees of truth between the extremes of complete truth and complete falsehood, there is a mismatch problem between our logic and reason on the one hand, and our experience on the other hand.

Some might say,he is the one to talk, this one-time waiter,whose scr-otum and pe-nis were grabbed by the Chief Chef of the hotel publicly in order to humiliate him and all the onlookers did was to laugh at him,this man who was slapped in the hotels kitchen because he was not working hard enough,fast enough..and when he complained he was doubly punished.When his begged my parents to allow him to study something he saw meaning in,and it was as if he were talking to the wall,he who lives a third world sh-it-hole has the temerity to believe that he might have something to say to US, this man so repulsive he has never had a single girlfriend,has never been kissed or  kissed,who had to fall down on his knees and weep and beg in front of a lady training manager in the hotel to give him his certificate and let him go and not to extend his tenure ,this fellow who has just learned the names of a couple of famous thinkers and fancies that he can comment on math and logic and philosophy.What a joke! He cracks us up.
To them I can say,what van Gogh said:
All right, then - even if that were absolutely true, then I should one day like to show by my work what such an eccentric, such a nobody, has in his heart.

I merely want books that are very,very detailed.Books which would take three hundred pages to prove one plus one is two.

That's all one can ever hope to do.  Behold the immense ecosystem of computer languages and operating systems, and the diverse applications of computers and the kinds of programs we can write.  One has to have a feel for where one stands, for what one's interests really are.

I am drawn to numerics for obvious reasons, but that does not mean I won't have any opportunities for learning the craft of parsing, text manipulation, the use of regular expressions. 

You will already have the kind of intuitive understanding (that Schopenhauer praised as all the proof necessary) of Fuzzy Logic by realizing that it is merely a generic/general case of Classic Logic.

The Buddha contains Aristotle.  That is, the crisp logic (yes or no, 1 or 0, on or off) are the extreme endpoints between 0 and 1, between no power and full power.  The Buddha would represent [0,1] (which is not only between 0 and 1, but including 0 and 1 endpoints in domain of the Buddha).

It is far easier for humans to build switches that register a 0 if below 0.5, a 1 if registering above 0.5.

Imposing fuzzier logic can be done on the software level, but it would be a far different beast to implement on the hardware level.  If they were to do this (fuzzified hardware), would this dramatically change the way one programs?  Who can say?

I do not wish to be percieved as a university professor, although on the psychiatric ward, a few "residents" insisted I was as intelligent as any college professor they had ever encountered.   I prefer to be perceived exactly as I am, an honest man with genuine interests in fascinating crafts and disciplines who simply has never found a groove in the work force in which to practice this craft.    Witnessing the proliferation of "mobile applications" and the demand for GUI interfaces, multimedia, embedded systems, not to mention the industrial level headaches of chasing down other peoples' bugs, maybe it is best I just never got that "job interview" process down.   I'm just no good at it, Holden.  I can't pretend to want to be someone's code monkey.    It would be easier to clean their toilets and let them think I am the Village Idiot.

The key for me was hunting down very specific texts.  You have to really WANT to devote yourself to it, especially before you commit to it via a purchase.   You have to see it as honorable as attending some high cultured university.   Recall Charles Dexter Ward.  While he was interested in the occult, rather than mathematics and programming, it is no lie to insist that the solitary student outside formal institutions is capable of improving the mind without society's blessings.

You really have to have a "Fuck this world" attitude.  Who the fuck is anyone to deny one entrance into these Halls?   I am not trying to keep up with the eggheads.  This does not mean that I am not fascinated with what the eggheads produce.  I appreciate their efforts and I honor them by exploring their craft ... it is multidisciplinary.   They can't get away from the philosophical ... look at the problematization of binary logic, the law of the excluded middle.  This may be a cultural problem, but many problems are handled with yes/no logic.  Others require yes/maybe/no logic.

One may think of the Buddha as 0.5, halfway between 0 and 1 (0% and 100% ----> 0.00 and 1.00), but in reality, the Buddha is the entire domain 0 <= x <= 1, which includes the endpoints (Aristotle's crisp values 0 or 1).

The day happens to be mine today.  How to seize it?  Peck away ... consider yourself blessed if you have discovered you have a long lasting and genuine interest in more than one discipline.  It is humbling to be a man, a living man of flesh and blood.  Don't let the bastards deny you those days of study if you find yourself with such a day on your hands!   Many will not know what to do with themselves without a formal structure.

Now, with food insecurity growing, we will all have to get used to getting by with whatever is available to us.  Maybe our humble demands will also be a blessing.  This life can't be about who was right or who was wrong.  Do you know how often I have to stop writing for fear that I am "full of shit"?

One minor disturbance, and I can transform into a basket case.   That is, I am a living man.  May we never forget that we are shitting chimpanzee-like apes.  It is not possible for us to absorb the libraries of knowledge.  We, like everyone else, have to constantly look things up in documentation or even obscure text books.

When alone, walking, thinking, I let the mind wander.  It usually returns to demanding a cigarette, a cup of coffee, a banana ... I don't experience intrusive thoughts about a half-naked girating woman with long black hair and large brown eyes ... hardly at all anymore.   Believe it or not, such fantasies have been replaced by the technical details of computational algorithms. 

May you enjoy a few hours of peace.  I very much sympathize with your feeling that we do not have the right to engage in certain dialogues since neither of us is a professional academic; but we throw caution to the wind because I think we both can't deny this sense of having been "blacklisted" or "locked out" of the discussion.    I guess we will never know how, who, and why we had been blacklisted or "conspired against."

Poverty does make the genius deranged.  Take any pampered intellectual, whether in the UK or India or anywhere in the Americas, and place them in an environment not at all conducive to study or contemplation, and it is only a matter of time before they will become alcoholic dope addicts mumbling to themselves in the bushes.   

It certainly appears to be a discipline which attracts many oddballs.

I am not sure if coffee is as strong as speed, but thanks for bringing to my attention the source of a saying I repeat to myself half-jokingly many times without having any idea of where this came from:

As he once remarked, “A mathematician is a device for turning coffee into theorems.” [some sources attribute the original quote to Erdős’ friend and fellow Hungarian mathematican Alfréd Rényi.]

I am probably more familiar with his mathematics than the biography of the man himself.  In fact, I may have studied his work without even registering his name ... these are those I refer to, often with great affection, as the eggheads.   You might find the site, MacTutor History
of Mathematics archive a good resource ... that's where I went to look into the Benzedrine factor.

I would never have looked into this side of the equation.  I had to look elsewhere. Here, I found the following:

Erdos said, "I don’t want kids who are thinking about going into mathematics to think that they have to take drugs to succeed."

Of course, Sickmind Fraud sniffed a lot of cocaine, which may have inspired him to type so much - from brain to keyboard in a manic state.

Is it cheating?  Is it less authentic?   Hey!  It most likely has to do with BOREDOM and tedium and redundancy.  The drugs may slightly alter the mood enough to elude a sinking into depression, and then once one is in that hyper-mode (code mode? math mode?), one merges with pure cognition.  Maybe this becomes "addictive" - but addictive in a good way.   I have always used that analogy when I was collecting the math, programming, or physics textbooks.  I thought, wow, these are actually relatively "dirt cheap" drugs (the books and notebooks and pens and pencils as paraphernalia) ... just think of the potential for mental stimulation ... which, as it turns out, releases chemicals in the brain so that the brain is actually "enjoying itself" rather than short-circuiting via obsessive and morbid introspection.

Maybe it's just a sophisticated form of distraction, albeit, a superior form of distraction to, say, "watching a ball game."