{∅, {∅}, {∅, {∅}}} : Rage Against the Meat Grinder
General Category => Why Mathematics? => Topic started by: Nation of One on April 30, 2016, 10:53:58 am
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Here is an interesting book that was just released. The only problem is that it is unreachable by our "usual means". Not only that, but the Kindle edition is more expensive than the hardcover (http://www.amazon.com/Burn-Math-Class-Reinvent-Mathematics/dp/0465053734/ref=tmm_hrd_swatch_0?_encoding=UTF8&qid=1462026868&sr=1-85). Strange, right?
It may be right up our alley though.
Forget everything you’ve been taught about math. In Burn Math Class, Jason Wilkes takes the traditional approach to how we learn math—with its unwelcoming textbooks, unexplained rules, and authoritarian assertions—and sets it on fire.
Focusing on how mathematics is created rather than on mathematical facts, Wilkes teaches the subject in a way that requires no memorization and no prior knowledge beyond addition and multiplication. From these simple foundations, Burn Math Class shows how mathematics can be (re)invented from scratch without preexisting textbooks and courses. We can discover math on our own through experimentation and failure, without appealing to any outside authority. When math is created free from arcane notations and pretentious jargon that hide the simplicity of mathematical concepts, it can be understood organically—and it becomes fun!
Following this unconventional approach, Burn Math Class leads the reader from the basics of elementary arithmetic to various “advanced” topics, such as time-dilation in special relativity, Taylor series, and calculus in infinite-dimensional spaces. Along the way, Wilkes argues that orthodox mathematics education has been teaching the subject backward: calculus belongs before many of its so-called prerequisites, and those prerequisites cannot be fully understood without calculus.
review - Scientific American (http://www.scientificamerican.com/article/book-review-burn-math-class/)
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I have been thinking of something similar,can I derive everything from +,-,x & /?
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... its [calculus] so-called prerequisites, and those prerequisites cannot be fully understood without calculus.
This would explain why I keep returning to these subjects every 10 years or so ... because I want to study logarithms, exponents, natural logarithms, e, and trigonometric functions AFTER I've seen them in action in calculus or physics. So I keep coming around full circle over and over again.
It's not always a regression or a "falling behind" or "going backwards" ... It's just that some concepts make more sense that way. It's all fuucked up and beautiful at the same time.
It makes no sense to race to get through a textbook, since you can never be "done" with anything.
Even though I wish I could just get through the Poole text and forget linear algebra, I know I will be checking out Axler's Linear Algebra Done Right. We can be all over the place. All these different branches and "formal courses" give the illusion of covering an entire subject when we can only think of so much at a time ...
There are other areas I am far more interested in, but I can't shake it. I lust after mathematical understanding and comprehension. The Will to Know?
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Last post: 2016.04.30
Today: 2020.03.30
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days: 1430
The following work shown for 3 exercises displays how I would go about sketching the graph of a curve without computer technology.
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Solutions to Section 6-6 Exercise 1 (https://archive.org/download/work_6-6_8/work_6-6_1.pdf)
Solutions to Section 6-6 Exercise 8 (https://archive.org/download/work_6-6_8/work_6-6_8.pdf)
Solutions to Section 6-6 Exercise 9 (page 1) (https://archive.org/download/work_6-6_8/work_6-6_9p1.pdf)
Exercise 9 (page 2) (https://archive.org/download/work_6-6_8/work_6-6_9p2.pdf)
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I am no purist, and am naturally quite fond of graphing calculators and computer algebra systems. I would encourage others to use both technological resources as well as rational analysis via classical, modern, and postmodern theorems. I do not deny the fallability of our mental apparatus and how prone to error we are, not to mention our fagile mental and/or physical and/or emotional health. [or legal status, depending upon the severity of chaos in geographical location] ... If you have time, please do investigate "the nature of my sketches." Notice that I extract the "Qualitas Occulta" of the actual sketched curve via rational techniques [analysis]. Schopenhauer appreciated the instant communication of the figure, but such a figure is found in a pain-staking manner. For me, the "Window" space becomes the first mystery to be demystified before I even draw the axes, which is the symbol at the heart of all "natural science," by the way. Schopenhauer could not help but be interested in the sciences. As I have said before, I do not mind being of far more mediocre and less educated peasant compared with our patron genius, Arthur Schopenhauer. In fact, being the son of a refrigeration mechanic and grandson of scientists gives me a certain natural disposition toward mystical ecstacy when it comes to the representation of mathematical concepts and phenomena via electro-mechanical digital brains, which become a kind of "assistant."
We could transform prisons into monestaries of mathematical, philosophical, and technological wonderment ... if not for the necessity to eat food and poop. In my mind, I could be in some kind of inner circle with the Pythagoreans, but the authorities will always see me as deadbeat, emotionally disturbed, "troubled." Existential nightmare.
Please do stubbornly resist the crushing of the human spirit. All you need to nurture is wonder. Working with mathematics is a slow process. One page might trigger the scribbling in many pages within a notebook, perhaps even scrap paper before that --- not to mention coding projects inspired by the "exercises."
The rulers would have us fearing death at the expense of enjoying our higher mental faculties, the world as representation, that is ... the world that is our idea, the galaxies dependent upon a breathing sentient organism in order to exist as "representation" or Lebenswelt [lifeworld].
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The very fact that you are studying maths inspired me a great deal.By the way,a question, if it appears absurd to you then you could invite it.
You have said repititions are very important when it comes to studying maths.If I were so study,say, geometry today ,after a while I tend to forget it.I am also aware that spaced repititions are really helpful.
My question is,what would you say the ratio between new material and revision/repititions should be.
For example,if you wanted to study a few maths concepts and ,for the sake of the example, say you had 200 hours to do it.You see ,one could easily spend thousands of hours studying just new material.But in order to really grasp the concepts one needs repititions as you well know.
So, the point is ,would you spend ,say,160 hours studying new material and then revise for 40 hours or some other ratio.
Take care.
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The material in the above exercise would have been first exposed to my young 17 year old brain, but this time through it is a totally different experience.
So, 53-17 = 36 years ...
But I encountered it at 17 (1984) as a frightening and overwhelming blur. My emotional life trampled under foot. By 1990, an attempt to revive interest but confounded by computer-oriented changes. By 1994, I was interested in combining computing with algebra, calculus, etc ... So, a good 10 year hoop, cycle ... Revived by 1998 then surpassing my expectations, but possibly burning out some fuse before a long drunken binge [2003 - 2015] 12 year hoop ...
Leave it in the lap of the gods, and do what you can, in the days you might seize from the jaws of human society.
Think in units of decades, not hours. :D
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I lost touch with maths in 2002,when father made me to choose biology instead of maths despite obtaining distinction in grade 10.Since then I have been studying it on my own.I studied almost no math from 2002 to 2009,between 2010 and 2012 very little.From 2014 to 2015 I studied a great deal.Since July,2018, I have again been studying it.I have no hopes for resurrection and healing. I just broke my reading glasses by mistake and to now I will have to do without it for a while.There is no doubt that your own studies in philosophy and mathematics have helped me a lot.I am not looking for any kind of professional career in maths.But it is important for me to find it if I am capable of doing maths or not.It is perhaps the very last thing that holds my interest.I just saw my broken glasses and they do look like me,in that they are broken beyond repair.
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We may be broken machinery, born into madness in fact, but I have proven to myself that there exists a passionate intellectual connection between the texts and myself, whatever it is a self even "is" ... Only you can advise yourself on this path.
My interest in mathematics (and music) may have led me nowhere, but as we are all nothing, all nobodies in a Cosmic Void, where does anything else lead? Your mind for a job, your mind for a TV.
That part of "me" which may recall having studied and made note of all manner of proof and applications and exercises does not seem to exist in the Embodied Animal Mind, or Animal Body. And yet professors hold positions. How many of them would care to go over Trigonometry or solve triangles? Maybe they want to study some "important" obscure theory? The world is a Crock of ShiiT.
There is the emotional animal presence breathing and traumatized and terrorized. All human animal creatures are born weak, vulnerable, manipulable. My god, look at what slaves we have been transformed into by our mere dependence on the Hive for sustenance!
Apes transfromed into insects for what purpose? What is the aim of all this eating and fuucking? It's too depressing to contemplate!
I am no musician, but I love music and I would sing or drum if alone and away from human society. If left on my own, if I have access to machines, writing implements and paper, especially paper without lines, then it's ON. That is, I have my own personal and intimate relationship with Mathematics and Computer Technology.
and philosophy, as do we all --- all human animals of a strange and diabolical species.
No one can deny you this connection as you have inherited from all our ancestors.
If you find something worthy of years of devotion, then you can't go wrong with mathematics. It may be there for you when no human being can bring comfort, as in a dungeon or nightmarish global quarentine.
I think that one must be fine with the idea of most of society thinking you peculiar, touched in the head, or impractical if you display strong tendencies to personal mathematics-learning inducing behavior.
You must recognize the Confederacy of Mutter Futters we have been born into. They do not want to learn so much as they want to Qualify for Credentials and Authority, so that they might be granted access to lines of credit, so that they may be depended upon to put their lives in harms way. They have become one with the apparatus they serve, that which they bow down to as Lord, their Employer, the Corporate State.
We are rebels, Holden, intellectual outlaws who must be starved by the mob, for we are full of contradictions. I wish you or even I myself, for that matter, had access to some secular monestary where we might offer refuge from the world as it is, but, in the end we each must live out the drama of the hero (or, in our cases, antihero).
I am leaving notes of what I am trying to document for posterity, but we live in a Planet of the Madhouses, Jails, and Asylums, not to mention the factories, mines, hospitals, 18-wheelers, etc ...
Even when society tosses one overboard, when they have no use for the likes of one with such passionate intellectual interests, this still can't lock the gates to the Engine of Reason hard-wired into our sensory apparatus.
There is a herd morality which condemns passive non-participation, but then orders masses to hole up in a room and die quietly, which we do lock-step on command, but there has always been a wall keeping me firmly in "outsider status". It is as Kafka describes in the Castle. Villians everywhere, all up in the State apparatus like some play about "Roman times," Biblical times, pfffft ...
What Nietzsche claimed, about philosopher dressed in rags and mocked in the streets by gangsters with jewels, narcotics, access to a vulnerable women, the same can be said for anyone who aspires for intellectual integrity during their lives, throughout their lives. You have to be willing to be mocked by the herd, whether en masse, or just your local kin and nation. Commit yourself to mathematics/philosophy/computing interspersed with as much literature as you wish.
They can't lock anyone out of this quest. It is personal.
Even if you just wanted to reflect upon something in your death bed ...
It's been such a petty, brutal, mere existence; but there is still some intellectual wonder in the computing power of some second hand 64-bit laptop device. You may wish to "imagine" the notebooks you keep to be "holy" in your own Inner Domain, that is, in your own little world. That's where this quest takes place, a million miles from the every day Real World.
In fact, you might be enclosed in one of the cells in a Giant Prison Hive, and you may still invite the Spirit of Learning into that cell, if only you are spared the torments of vulgar jailers and fellow-prisoners, who often might be following orders to knock you on the head.
It is hard to trust anyone who claims to have authority, but they themselves, personally, are following one order after another all day, or barking orders based upon orders they have been given, which come from the top only.
We are instructed to remain calm; the authors of the texts we read write them as though we were in a timeless dimension without need for a toilet or eggs on rice. And yet!
After all, in the end, we are some gruesomely vulnerable creatures. We depend on water sold in plastic bottles. It is too frightening to think about too long, our vulnerability, that is ... the huge delusion of social security. Social insecurity, social death ... in a realm in between.
There is a great contradiction between our intellectual aspirations and our actual predicament as animal bodies with brains which start to go haywire the moment the body's equillibrium is off balance. You understand, Holden, that there is a certain amount of deception taking place in any incarnation of any text ...
I will attempt to continue with the exercises. It is a hard call for me. There are several texts I wish to devote myself to, but each one devours me ... it takes effort and time, and the world is not a hospitable place for a daydreaming mathematician/poet-philosopher Holy Fool, Sacred Clown, everyday madman disguised as village idiot.
It's the threads that barely fit me, and the rotten teeth. The gorts take me for an idiot!
Never mind my devotion to the core ideas about the programming at the very heart of technological apparatus [all the devices] compartmentlizing their computerized monetary system into "entities" we call corporations ... which do not really answer to, as much as own, States.
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You have said repititions are very important when it comes to studying maths.If I were so study,say, geometry today ,after a while I tend to forget it.I am also aware that spaced repititions are really helpful.
My question is,what would you say the ratio between new material and revision/repititions should be.
I would not be much help in guiding you in the details of how you will incorporate "new" and "old" ...
the concepts we encounter had often been hard-won, thought out in detail ...
The reason I like programming is because it forces me to understand the mathematics. In fact, i must be able to understand the concepts before I can represent them as phenomena in the form of some Structure. Before creating an interactive command line program which analyzes "conics," I might spend several months revisiting Analytic Geometry. You can never get enough of anything having to do with vectors, especially three-dimensional vectors, which play such a huge role in Physics.
Not to be too openly blasphemous, but, I only wish people would contemplate mathematical phenomena with as much veneration as they do, say, the symbol of the crucifix, with all that it has to say: GodMan on the electric chair, that is, upon an instrument of death used by the State to execute prisoners, convicted criminals, or perhaps even entire villages of "witches" or "Commies" or "suicidal maniacs" ... :D
People behold paintings and writers have published book after book about such symbols. Even Schopenhauer gave great attention to the symbolic truths revealed in the kernel of Christianity. He did so, quite respectfully, while simultaneously maintaining an intellectually hostile stance against the Church Fathers, School Masters, and Church-Attending Slave Owners.
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Thank you, you are already helping me in compressing maths better.I am quite determined to learn it well.
The tortoise might be slow but it keeps moving without sleeping.
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So, 53-17 = 36 years ...-Herr Hauser
As the Eagles sang-
And maybe someday you will find
That it wasn't really wasted time.
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or, it has all been in vain ... :D
In which case, let's hope I have a damn good sense of humor.
I suppose it takes a bitter person to sympathize with another bitter person.
What makes me such a contradiction is that while I admit all this studying has not been bad for me, I do not claim that such devotion has spared me from the general misery of existence. Also, I do have a great deal of bitterness in my heart which I barely allow myself to express if only for the simple reason that I am tired and bored with the usual responses, such as to "think positive" --- or the implications that I need to "man up" and accept "life on life's terms."
Should I outlive both my parents, I can imagine myself studying in a room by myself and feeling the immense burden of my own existence weighing down on me. Do we allow oursleves to become overwhelmed with bitter hatred toward the Creation itself?
Do we lie to ourselves the way Nietzsche did, so as to "appear hard," to be "tough" or heroic? Is it possible to be honest about our bitterness without drawing the infinite number of would-be-therapists lecturing us on things like "gratitude" ?
I understand that I have contradictory feelings about just about everything.
Even were my entire existence one cruel joke, I don't think that studying mathematics can ever be a waste of time. After all, how long can I just sit and sulk and brood? :-\
Sometimes I am just one ball of frustration and repressed rage. It is right there just below the surface. I remember feeling this as a child. I feel this way now.
I can't honestly tell you that it is not a waste of time. I just know that it is something I value, even if this vulgar world only values its obedient and well-disciplined slaves. They have no love for a rebel slave who just wants to study more math, or just go over the math he has studied in this life already. This world would only love me were I to disinfect its toilets or follow "Doctor's orders." :P
In fact, the only way to flip the script on these gorts is to nurture disdain and contempt for their values. In that case, working through math-drills rather than chasing a "career in the medical industry" or the "food industry" might be a sign of immaturity ...
I guess I am just trying to be totally honest with you Holden. I feel betrayed by life ... it is not easy to describe. I have been thoroughly deceived, even by my own brain.
When I see this world for what it is, my heart breaks. I mean, how brutal, how selfish we all are made to be. How much hatred and frustration in our hearts!
You may wonder if it is possible to study when brooding and bitter. No, at that time, I must stop - call it a day ... and just brood.
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… and the Snail …
At noon, a tortoise moving south at 8 inches per minute is 25 inches due north of a snail that is moving west at 6 inches per minute. When will they be closest together and how far apart will they be then ?
I work out a solution on paper since all communication is more powerful in that medium, as far as symbols go - symbols that have deep and powerful meaning shared across a multitude of cultures.
What you would want to visualize is a "dynamic" [transformable] right triangle with horizontal side 25 - 8t, vertical side to the right of and perpendicular to it the side with length 6t. The distance between them is represented by hypotenuse with length s.
The Pythagorean theorem says s^2 = (25 - 8t)^2 + (6t)^2 = 625 -400t + 64t^2 + 36t^2 = 100 t^2 - 400 t + 625
To minimize the distance s between the tortoise and the snail,
find the derivative ds/dt :
d/dt [s^2] = d/dt[100 t^2 - 400 t + 625]
2 s ds/dt = 200 t - 400 = 200 * (t - 2)
ds/dt = 0 when t = 2 minutes, that is at 12:02 PM
s^2 = (25 - 8*2)^2 + (6*2)^2 = (25 - 16)^2 + 12^2 = 9^2 + 144 = 81 + 144 = 225
s = sqrt(225) = 15
Note that the second derivative of s, s''(t) = 200 > 0, therefore s has minimum distance 15 inches at t = 2 minutes (12:02).
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Thanks for the maths problem.Here is the kind of things I am working on at the moment:
There are three equal circles of unit radii touching each other. Find the area of the triangle circumscribing the three circles.
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What would be the area of the remaining portion if the same three circles are circumscribed by another circle?
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Here is the kind of things I am working on at the moment:
(1)
There are three equal circles of unit radii touching each other. Find the area of the triangle circumscribing the three circles.
(2)
What would be the area of the remaining portion if the same three circles are circumscribed by another circle?
How are your exercises coming along? Do you have a solution?
Did you draw a sketch? Is Schopenhauer's method of constructing a visual representation conducive to your understanding?
It would be easy if it were a triangle whose vertices connect the three centers, but the diagram I drew does not reveal anything exact. I would have to think about these.
It is good to stay calm and work with scrap paper, allowing the lazy part of the brain doodle … then maybe look for theorems which would help derive an exact rational solution. It's like, first Schopenhauer, then Euclid.
You would want to scribble before walking outdoors in solitude to mumble to yourself. That was also another modus operandi of the Great Schopenhauer: thinking while walking with dog, speaking out loud to dog, ignoring those who might mock him from afar. So much of any of our thinking or emoting occurs while we are walking around or sitting alone, maybe purposefully constructing a fortress to shield us from DISTRACTIONS. If you hear hushed but cold laughter from a short distance, coming from the shadows, you can ignore those (dogs barking at the elephant). The activity of engaging your brain with an exercise or problem should have no time constraints. Look at it at night, continue it whenever.
See if any clues come from the unconscious during slumber …
I am currently in the process of switching gears from some rigorous introductory analysis back to the last section of the "generic programming" sections of the Stroustroup text … but I paused to take a look at the board.
Do you draw diagrams? Do you use straightedge ruler and some kind of make-shift compass? I tend to sketch rough (cartoon like) approximations. It's less stressful.
https://www.youtube.com/watch?v=hV_zQopwUjQ
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(1)
There are three equal circles of unit radii touching each other. Find the area of the triangle circumscribing the three circles.
The area is of the triangle is 6 + 4*sqrt(3), about 12.9282032302755
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Explanation:
I drew diagram with side a = 2*x + 2*r, where r is radius of circles (here r = 1), and r/x = tan(30) = sqrt(3)/3
x is the distance between the left bottom vertice and the vertical projection foot of the left bottom circle center.
If an equilateral triangle's angle has 60 degrees (pi/3), the bisection has 30 degrees (pi/6).
Since r/x = sqrt(3)/3, x = 3*r/sqrt(3) = sqrt(3)*r
Since radius r = 1, x = sqrt(3)
Let height of triangle h = sqrt(a^2 - (a/2)^2)
Area of triangle is (1/2)*a*h = (a/2)*sqrt(3*a^2/4) = (a^2/4)*sqrt(3)
Each side a = 2*x + 2*r = 2*sqrt(3) + 2 = 2*(sqrt(3) + 1)
Therefore, area = sqrt(3)(2*sqrt(3) + 2)^2 / 4 = sqrt(3)*(4*3 +8*sqrt(3) + 4)/4
= sqrt(3)*(16 + 8*sqrt(3))/4 = (16*sqrt(3) + 24)/4 = 4*sqrt(3) + 6
about 12.928 square units
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(2)
What would be the area of the remaining portion if the same three circles are circumscribed by another circle?
Area of circle minus area of triangle?
area of circle = pi*(a*sqrt(3)/3)^2 = pi*a^2/3 = pi*(2*sqrt(3) + 2)^2/3
= pi*(8*sqrt(3) + 16)/3
area of triangle we found was 4*sqrt(3) + 6
So, area of circle - area of triangle = (1/3)*[ 8*pi*(sqrt(3) + 2) - 3*(4*sqrt(3) + 6) ]
~ 18.33735 .... ?
I had sketched a circle around the triangle, and shaded in the desired space. I noticed the center of the outer circle was also the center of the triangle. I doodled an equilateral triangle with radius R (of outer circle) as its sides! It was the lazy part of the brain finding the solution, just as Schopenhauer implies in his arguments against Euclid's manner of "proof."
I noticed that the height H of this equilateral triangle with sides R was a/2, that is, half the length of a side of the triangle.
With this I found the relationship a/2 = sqrt(R^2 - (R/2)^2), from which I was able to extract the value of R = a*sqrt(3)/3, hence, area of circle is pi*R^2
Bankruptcy case over ... That was "fun". Please spare my sensitive ego if my attempts did not lead to the correct solution. I am a haywire bipolar lunatic.
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Scribblings and reckonings on scrap paper saved and uploaded for your inspection, if you would wish to catch me in the "act of thinking" ...
page 1 (https://archive.org/download/scrapwork_20200407_02/scrapwork_20200407_01.pdf), page 2 (https://archive.org/download/scrapwork_20200407_02/scrapwork_20200407_02.pdf), page 3 (https://archive.org/download/scrapwork_20200407_02/scrapwork_20200407_03.pdf), page 4 (https://archive.org/download/scrapwork_20200407_02/scrapwork_20200407_04.pdf).
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I am sorry I have been calling you Herr Hauser for so long,when your real name is Herr Gauss!
I am just focusing on the first question at the moment and yes your solution is right.
Please help me understand it one step at a time-you as well my book are saying that the triangle we are talking about must always be an equilateral triangle, not acute ,not obtuse but equilateral,is it because all the circles have the same radius?
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I am no Gauss, for he was a genius as a child. I am just an old Steppenwolf who knows some monkey tricks. Those three circles are tangent to one another, and their centers form an equilateral triangle, by inspection. The triangle formed inscribing the triad of unit circles with radii 1 has sides of equal length.
At first I was distracted by the question, but then I began to scribble. It was challenging if only that it forced me to prove each step to myself, and then check my work with a computer algebra system. It all depends on my moods. It was a good distraction. Thank you for confirming the result.
The key work is on scrap work page 2 (https://ia801507.us.archive.org/20/items/scrapwork_20200407_02/scrapwork_20200407_02.pdf), with the relationship r/x = tan(pi/6) = tan(30) = sqrt(3)/3
Since r = 1, x = 3/sqrt(3) = sqrt(3)
From the diagram you can see r is the perpendicular distance from left circle center down to base of triangle, total length 'a'.
a = 2*x + 2*r = 2*sqrt(3) + 2
That is the key idea. From there you can find area = (1/2)*a*h
You find the relationship h = sqrt(a^2 - (a/2)^2) and substitute, then expand.
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Thanks to you Herr Hauser ,my great benefactor,I have understood the first problem.
https://ibb.co/kKCwKnz
I want to show you the very bad diagram that is there in my book-
https://ibb.co/tM3MMmm
I can understand about 80 percent problems I attempt but some of them have very unclear solutions and that frustrates me a lot.About the last thing I aspire to in this life is to gain the kind of understanding you have as regards mathematics and then ,I can die with zero desires.
I do really hope that comes true for me,for I don't want to stay for too long in this wretched,pitiless world.
Thanks for everything.You are most kind.
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Yes, that is a bad diagram. it is difficult to see what A and B refer to.
Also, the area of a triangle circumscribing the three circles is (1/2)*base*altitude.
In that book's awful diagram, I suppose the A and B are vertices of the triangle, so segment AB is the length of a side (what I call 'a'), which is therefor, the length of the base.
To find the altitude, I use h = sqrt(a^2 - (a/2)^2) = sqrt(3*a^2/4) = (a/2)*sqrt(3)
and area = (1/2)*a*(a/2)*sqrt(3) = (a^2/4)*sqrt(3)
After substituting length a = 2(1+sqrt(3), we get area = 6 + 4*sqrt(3)
That book, for exercise 14, states area = sqrt(3)*(1 + sqrt(3))^2, which comes out to the same thing: sqrt(3)*(1 + 2*sqrt(3) + 3) = sqrt(3)*(2*sqrt(3) + 4) = 6 + 4*sqrt(3)
As for the second question in your original post, I am not sure what they are asking for, so I would have to look at it. I answered it with the assumptions shown on page 4 (https://ia801507.us.archive.org/20/items/scrapwork_20200407_02/scrapwork_20200407_04.pdf) of scratch work.
Thanks for everything.You are most kind.
This life is so thoroughly dissatisfying, and our exchange of ideas has to be one of the highlights of my day to day existence. I wish I would be better able to share my math notes with you.
I do not wish a long life for either of us, but if we should live much longer, maybe we might manage to get you far more detailed explanations. I myself, am an amateur hobbyist. I call myself a math junkie so as to assure the world at large that I do not take myself too seriously. Although I can hold my own with many problems, I do get shell-shocked (overwhelmed with self-doubt) rather easily.
My life has been a crazy roller coaster ride, and yet I have experienced some enthusiasm for learning ... and yet it is only one aspect of my life.
I get very bored with it all every now and then. The wind has been taken out of my sails decades ago, and then repeatedly. I've been engaged in this kind of "secret inner life" since around 1991 ... It is a part of me. I may be mad, you know; and yet, from you I sense a definite respect for my particular style of madness. That is, you respect that I have been a fairly attentive and dedicated student. You also must sense a certain chip-on-my-shoulder that I may have toward "academics" and even "professionals."
Schopenhauer had a similar chip-on-his-shoulder.
Learning is a slow process, and it takes privacy and honesty just to break things down to oneself enough to understand a little better. Often it is best to take a long walk, or, if at all possible, rest in a tub of very warm water away from paper ... to give that part of the brain a rest.
You make me appreciate how much time I have spent studying, and how precious that particular mood conducive to spending an evening thinking mathematically ... or just breaking down some code into understandable blocks ... This understanding is all happening inside the head. It is a private domain.
I can pick out any of my notebooks and look at the exercises - and I would be just as challenged today as I was when doing them, more so ... It takes thought. Sometimes we are not in any mood to think nor derive nor prove nor show nor explore ...
You really have to know yourself and try to approach the subject when that mood strikes you. I have not figured out a way to "summon" that mood. It does not appear on command. One must wait for the "spirit to move" ...
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About the last thing I aspire to in this life is to gain the kind of understanding you have as regards mathematics and then ,I can die with zero desires.
I do really hope that comes true for me,for I don't want to stay for too long in this wretched,pitiless world.
Mine is a very depressing path. A library of books that I can barely peck, peck, peck away at, and all for what? Only to endure the present moment lest I be eaten alive by my own consciousness.
https://www.youtube.com/watch?v=Ab6ST1q43c4
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not acute ,not obtuse but equilateral-Holden
I should have said not scalene,not isosceles.
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https://ibb.co/3CdNkT1
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To amuse myself ,in my mind , sometimes I like to imagine that the two world wars never happened and your ancestors never migrated to the US,that you are based out of Germany,Berlin, the greatest place to do maths in and that you are to this century what Gauss was to his and that you are also the editor of the world's most important maths journal-The German Mathematician, and I am sending you my ground breaking research papers, to you and the magazine :)
I would make a great Don Quixote:)
In Pessimism: Philosophy, Ethic, Spirit
Joshua Dienstag says that Don Quixote was a pessimist par excellence.
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A great book:
https://www.goodreads.com/book/show/6684592-perfect-rigor
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I just said it with. a tongue in the cheek.I like your way a lot.
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I have observed that you use pencil for math not pen,why is that?
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?
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Thanks.
I really liked your statement that physics is applied mathematics. My next question is related to it. I am trying see it there is an overlap among mathematics, coding/programming and formal symbolic logic.
You once said that Schopenhauer had much better educational opportunities compared to you .You will also agree that you yourself have gained a great deal from the kind of exposure that he received by way of the written word.Unlike me,you have attended a great university and so please be so kind as you help me just as Schopenhauer helped you-by way of the written word( and you have already been helping me a great deal)-
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).
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?
You told me you read Pricipia Mathematica once.I think its full of symbolic logic. I think you studied it after the Uni( or was it before).If it was after the Uni, due to you think, the fact that you knew programming by that point of time and a lots of maths too,helped you to understand symbolic logic and can it work the other way around too-someone who knows symbolic logic well can take up coding/maths in general better than someone who does not.
I think when you were in the Uni,you might have seen that logic was being taught in three different departments-computer science, to which,I think you belonged, the Mathematics Department,and also the Philosophy Department.
So, the question is, someone who has learnt logic well in one of three aforementioned departments, do you think he would find that, if he were to study the logic being taught in the other two departments,that is ,after all, not all that different?
Thanks.
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I am merely telling you what I know,and not necessarily believe in it-in Hindu theology it is believed that a woman cannot attain salvation under any circumstances. She is earth bound.She is Nature herself...
I,for one, would never want an existence on this earth.No existence of any kind for me.
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Note that I went a little bonkers trying to hold posts at 3666, but having a second registered user, Gorticide, might cause more confusion than it's worth in the long run. So, I am cleaning up after myself.
To amuse myself ,in my mind , sometimes I like to imagine that the two world wars never happened and your ancestors never migrated to the US,that you are based out of Germany,Berlin, the greatest place to do maths in and that you are to this century what Gauss was to his and that you are also the editor of the world's most important maths journal-The German Mathematician, and I am sending you my ground breaking research papers, to you and the magazine
I was aiming at something more down to earth. I really just want to appreciate mathematics. To each his own, though. I can't control the things you might imagine or wish for. There is great wonder to be found outside the society of great journals. I prefer to daydream of a realm beyond the one where egos get bruised and there is just so much prick-waving. One must be fully prepared to be looked upon as a naive flunky.
I was hoping to infect you with my genuine appreciation for incremental development of understanding, and possibly even some of my disdain for the priesthoods of the Church of Reason.
One need not be a great mathematician in order to study mathematics any more than one need to be a great musician in order to appreciate music ...
I like to imagine my notebooks making it to India, being copied and distributed for actual manifestations in some future education system. Someone might really make something out of them, not for any ground-breaking acheivements, but simply an attempt to salvage a novel approach with some rigor.
For me, the key is in claiming oneself worth the time to explore as a student (explorer). This is a precious kind of humility. Suddenly, confusion becomes your invitation to mathematics, rather than something to take the wind out of your sails.
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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.
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One might strive to be the Schopenhauer of documenting programming and mathematics in the least terse manner possible. Here is one for a daydreamer: If Schopenhauer were a technical writer, mathematical wordsmith that he would have become ...
an aside: When writing code with pen on paper, when I get to the comments sections (that part of the text file which is not read by the machine/compiler, but only by humans), I switch to pencil, and even add little notes in smaller print with possible diagrams.
The documentation becomes an art in itself since programs designed at such a high level of abstraction are intended to bring understanding to the "Kantian Subjective Consciousness" of the human reader (of the code itself, the code read by compiler-to-the-Machine).
The details of interactions with hardware components of the electro-mechanical machinery are hidden from the programmer herself.
a second aside: The spirit is Feminine? in honor of an ancient custom, Spirit is "She" and "Her" as opposed to "He" and "Him" ... for what its worth. Maybe the Frankensteinian Industrialists will discover a way to breed better slaves with mostly female pods, and we males will be eliminated from the process, more or less. In that case, if one wishes to be read on the most intimate level with a future "audience," it may be best to re-introduce that custom, that is, of referring to the reader/spirit/intelligence as "she" or "her".
;)
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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 (https://www.amazon.com/Art-Being-Right-Arthur-Schopenhauer-ebook/dp/B00UCWDW92/ref=sr_1_4?dchild=1&keywords=The+Art+of+Being+Right&qid=1587087640&s=books&sr=1-4). 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) (https://www.amazon.com/NEW-Art-Being-Right-Schopenhauer-ebook/dp/B01DB8CAPU/ref=sr_1_5?dchild=1&keywords=The+Art+of+Being+Right&qid=1587087250&s=books&sr=1-5)
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 (https://www.amazon.com/Language-Mathematics-Schopenhauer-Studies-Universal/dp/3030330893/ref=sr_1_1?dchild=1&keywords=Language%2C+Logic%2C+and+Mathematics+in+Schopenhauer&qid=1587085613&s=books&sr=1-1)).
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 (https://periodicos.ufsm.br/voluntas/article/download/37246/pdf) (with Daniel Schubbe)
From 'Euler Diagrams in Schopenhauer to Aristotelian Diagrams in Logical Geometry (https://lirias2repo.kuleuven.be/rest/bitstreams/518776/retrieve)'. 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 (https://arxiv.org/pdf/1803.07603.pdf), 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.
___________________________________________________________
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.
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I experienced a nervous breakdown as an aging teenager (young adult). Neither religion nor mathematics could save me.
SCHOPENHAUER WAS NOT FOND OF MATHEMATICS.
Holden,
I appreciate not only your interest but your patience with contradictions, paradoxes, riddles, problems, errors ...
This is not so very scandalous since it was quite "in fashion" among the well-to-do "intellectual class" to show disdain toward computational "work" - as there was really something tedious and downright difficult in the DRUDGERY of Mental Labor.
Schopenhauer would have despised Assembly Language Programming, but may have shown an interest in the development of programming languages to transform coding from drudgery to a more creative interaction with the machinery.
While I honor Schopenhauer as a great Teacher of mankind, and as my own personal "Master" when it comes to his writing a potential Holy Book without a Creator God, I would not have wished to be charged with the task of teaching Schopenhauer mathematics. It would be best to just leave the best texts I could find, with my own WORK shown, and leave them there for him to get to in his own time, should he show any genuine interest.
Maybe the "mathematicians" and "educators" did not make a very good impression on the youthful Arthur.
Can one find a small dose of sanity in such a world which allows such contradictions?
Maybe we ought to explore this GIANT PINK ELEPHANT in the room, which is the fact that SCHOPENHAUER WAS NOT FOND OF MATHEMATICS.
Here is an 8-page essay to download: Goethe and Schopenhauer on Mathematics (https://core.ac.uk/download/pdf/60548862.pdf) by Arnold Emch.
I understand that you may share Schopenhauer's disdain for the drudgery of arithmetic (which would be a close cousin to the tediousness of programming). I do not claim to have formed an opinion on the matter, and am actually only skimming the surface of the possibility that I might be hiding some thoughts about "the Master" from myself.
And yet! Schopenhauer was always pinching those pennies ever so tightly, so he must have at least been a "closet reckoner" ... :-\
I openly compute ... and I delight in learning about the craft ... but, in my heart, there are deeper yearnings. Would Schopenhauer have been mentally stimulated by the work of Alex Stepanov (http://stepanovpapers.com/)? I mean, would he be drawn to the mathematics then?
I'm afraid Schopenhauer and I might have a heated argument ... when it comes to calculating and understanding.
I might have to beg to differ, but as I am fully aware that his genius would make minced-meat out of my mediocre intelligence, I might just have to accept his conclusions that a "sub-genius" would be drawn to calculating and computing, whereas a true genius would find such "work" too mechanical, something better suited for machines rather than for someone like, say Arthur Schopenhauer, Johann Wolfgang von Goethe, or any of the many who find themselves "above" such things as reckoning. I would say they represent a tendency that still exists to this day among the "elite intellectuals" who care very little for mathematics. In fact, I recall a fellow student explaining to me how only the very wealthy are at liberty to study literature and "high culture," for when one of the lowly (of the lower "working class") has an opportunity to attend University, they feel obligated to study the most difficult technical subjects that they can handle without having a nervous breakdown. That is, it is a sign of one's lower "caste" - to be devoted to the "hard," the difficult, the tedious, the rather overwhelming ...
I had also been motivated to see if I might learn something that would help me find "gainful employment." This was motivated by my being a regular human being with absolutely no financial resources.
Did Schopenhauer want to burn down the Mathematics Department?
Is the entire Church of Reason (the University) even trustworthy ? Who do the universities serve? Businessmen? Industrialists? People who are part machine?
I am going to continue to humbly make my way through programming exercises (Stroustrup) --- but I am also captivated by this little discrepancy I have with Schopenhauer. I may have to think against myself, but in so doing, I may have to think against Schopenhauer every now and then, since, after all, I am no wealthy genius --- just an "over-educated janitor" in a 25-year long rebellion against being who society tells me to be.
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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 (http://korzybskiinstitute.blogspot.com/2016/08/korzybskis-non-aristotelian-systems.html).
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? (http://www.chinabuddhismencyclopedia.com/en/images/a/a8/Chapt12-EL-am.pdf)
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.
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( I wrote this before your last post)
Thank you for answering my questions.First off, I want you to be clear that I hold your -maths- project in high esteem and it has rekindled my own desire to do more -math-.To attack it in anyway is the last thing I want to do.Having said that, I think you are talking of the following apparent paradox,that on one hand:
1.One considers Schopenhauer a great philosopher.
2.One accepts,for the most part,Schopenhauers world view.
3.One has come to believe that Schopenhauer somehow looks down upon -mathematics-.
On the other hand:
One spends a lot of time doing -mathematics-.
This is an apparent paradox,and channeling Wittgenstein,I suggest we do not try to resolve it,but that we dissolve it.
The dissolution will come about when one ponders the meanings of the words-Mathematics,Logic, and Philosophy and looks at them the way Schopenhauer used them. The way we use them.And most importantly the way the Gort uses them.
The apparent paradox will dissolve on its own when one considers the fact that our captains of the industry find it acceptable, nay,extremely useful,to teach -mathematics- in schools,(speaking only of the Indian Schools here, but I suspect that it might be true in your neck of the woods too), but NEVER logic( of any kind), NEVER philosophy(of any kind).
They teach- mathematics-, because they want clerks. In millions.They dont teach it because they want more Herr Hausers and Holdens. Maybe the way we are looking at -mathematics- ,was not the way Schopenhauer looked at it.Maybe he looked at it more radically .And maybe there is after all a non-gortish -mathematics-, which you practice and the gortish -mathematics-,which Schopenhauer was denigrating & is taught today in our schools.
Why do you think they lionise speed maths tricks?Why do they think mental maths is a big deal?
In the last analysis,it might be Schopenhauer himself who would show the fly the way out of the fly bottle.The gort says yes to Science, to Technology, to Engineering and to- Mathematics-.The gort laughs at ,or at best ignores logic and philosophy at the school level.There is something fishy here.
I am afraid the word -mathematics-,Deleuze would say, has been absolutely territorilized by the gort.
Maybe we need a new word,a better defined word. A deterritorilized word.
(No quotation marks in my keyboard so I am using -X- instead.I have used the word -math- in quotations everywhere as while I wish to use a better word,I am forced to use it due to the convention)
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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.
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Powerful writing, Holden.
I also wish to leave a trail of carefully-crafted notes to show what a penniless "village idiot" might be up to any given decade. It surely is a case of Nothing that is so, is so - for the lot of us. One has to nurture a sense of humor and just pray someone who is worthy and ready for such notes should benefit by their "hand-craftedness" --- including supportive code if that should be found.
I wonder how many madmen's works are left on the curb in the rain simply because that is the kind of vacuum we have been born into, the emptiness. We are reaching out for something that is simply not there. So was Schopenhauer, although his penetrating intellect did reveal he had an inkling of the absolute indifferent nature of our world. Hence, his analogies about a man isolated on an island finding a logbook of a previous inhabitant who has since passed. The notes, if legible, might bring comfort or consolation.
Schopenhauer was aware of the impending futility of all human striving. He may have been instinctually aware of things to come. Maybe the "fantasy" of endless improvements, tweaks, upgrades, enhancements, etc., is about to be DE-Fantasized.
We may very well be flies trapped in a jar, and even especially when we are engrossed in studying, we have to find a way out of these linguitic traps, these pigeonholes: novice vs professional, academic vs ex-convict :P ...
Our discussions help me focus on whatever might be actual reality. Whatever spirit moves through one to leave traces of "some higher interest," it is more kin to wind or rain, something that happens to us ... Some programs I wrote a couple years ago were like being possessed by some Schopenhauerian Holy Ghost --- and it was deeply math-oriented. I could not plan for such a creation. I was caught up in it.
Schopenhauer would have appreciated some of my code since I was able to experience creative intellectual stimulation while creating a mechanism which would be able to show the "work=math" for any number of candidates in the domain.
Yes, I do believe the stubborn Buddha of Berlin would not disapprove of computer programming as a respectable and mentally stimulating craft, especially when used in a "mathematically-oriented" manner, rather than a monetary-oriented manner.
Interesting distinction between types of math ... gort math ... They did not want people teaching "New Math" in the 1960's in the USA mainly because they, like India, did not require masses of "mathematical philosophers" who studied the structure, but only drones, just educated enough to operate the machinery and run the software ... and they may have had a point from their perspective.
After all, they are to feed the corporations from this Human Farm. They wanted people to get the "right" answer even without understanding why it was the right answer.
Whatever it was, I got caught up in the tail end before the transition, so I have been haunted all my life with this passionate desire to deepen my understanding. I am, as you probably have discerned by now, a kind of freak.
I have to be true to my "self" as Schopenhauer would have wished it, anyway. He would not wish that we appeal to loyalty:
The appeal to loyalty is a logical fallacy committed when the premise of an argument uses a perceived need for loyalty of some sort to distract from the issue being discussed.
Example
B questions A's statement of x.
Anyone who questions A is disloyal.
Therefore, B is wrong.
Problem: Even if B is disloyal, that doesn't mean that B is wrong, as A is not necessarily always right.
There is something to exploring code with a debugger. Schopenhauer and I are are wired differently. You see, I sometimes rise out of depression at night, and then i do not wish for it to end, so I ride it like a wave. Schopenhauer slept regularly, keeping "regular hours" --- with a structured, ritualistic lifestyle - not extravagant ...
I smoke tobacco like a mental patient, consume large quantities of strong dark coffee, to mention just a couple of my "morally degenrate" traits. There is also this compulsive obsession with math textbooks, specific ones for long periods of time ...THIS exhaustive, extraordinary, and insane devotion to just trying to get a grip on it, if that's even possible. Maybe we really do just have to get used to feeling what essentially amounts to fear=anxiety=paranoia=discomfort.
The really creepy thing is that our own awareness of this anxiety does not necessarily begin to alleviate it. As a nervous wreck myself, I am not qualified to advise others on how they might reduce their own anxiety, or whether the diminishing of anxiety is even advisable.
Anxiety must play a key role in our "wiring," what's more, in the wiring of all organic life.
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I merely want books that are very,very detailed.Books which would take three hundred pages to prove one plus one is two.
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It is true,I concede, there are so many things I dont know about maths and logic.But I will continue to learn.
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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. ;)
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Herr Hauser,
Thanks for your response.
Would you say that coffee and tobacco are to you what amphetamines in the form of Benzedrine/Ritalin were to Erdos.He seemed to think this that it helped him to do math.He worked for as many as 19 hours a day.
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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 (http://mathshistory.st-andrews.ac.uk/) a good resource ... that's where I went to look into the Benzedrine (http://mathshistory.st-andrews.ac.uk/Biographies/Erdos.html) factor.
I would never have looked into this side of the equation. I had to look elsewhere. Here (https://amphetamines.com/paul-erdos/), 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." :)
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https://ibb.co/BcZPrFh
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I took a look at that, Holden. Very powerful how you could surmise that the unit digit would be zero just by inspecting the first few elements of this set of prime numbers between 1 and 11^11 (== 285311670611): {2, 3, 5, 7, 11, 13, ..., 285311670569}
You will be pleased to know that using brute force caused SageMath computer algebra system to crash, and sympy is still churning away ... Actually, running this on just the first several prime numbers verifies your conclusion.
sage: for i in srange(1, 285311670611):
....: if (is_prime(i)):
....: p *= i
....: print p
....:
Killed
I suppose the point you have made is that a little reflection may save a great deal of unnecessary computing.
In [25]: def doit():
...: p = 1
...: for i in range(13):
...: if (isprime(i)):
...: p *= i
...: print(p)
...:
In [26]: doit()
2310
In [27]: def doit():
...: p = 1
...: for i in range(11**11):
...: if (isprime(i)):
...: p *= i
...: print(p)
...:
In [28]: doit()
(Sympy has been churning away in the background ... I will see if it crashes or spits out a long number that fills the screen several times.)
-----------------------------------------
This would be an awfully large number requiring a Big Integer library like the one I used to build the rational calculator (https://github.com/Gorticide/PPP_LAB/blob/master/calculators/rational_calculator.cpp) for factorials, combinations, and permutations.
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Thanks a lot.I genuinely like these kind of problems.As van Gogh said-I am seeking, I am striving, I am in it with all my heart.
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I wrote a program using the Big Integer GMP library <gmpxx.h>,
compiled with:
g++ -lgmpxx -lgmp -g product_BIG.cpp -std=c++17 -o product
I made it so I could at least see the primes being added to the vector. I had to do this since I kept thinking the program was freezing up, when it was just doing as I programmed it to do. So, I am running it, witnessing how long it is taking. I added the <chrono> header so that I could time it. In the morning I will check to see if we can capture that huge product of primes. We will also know how long it took.
I am just curious to see what it takes.
__________________________________________________
#include <numeric>
#include <functional>
#include <cmath> // for pow(11, 11) = 285311670611
#include <vector>
#include <iostream>
#include <gmpxx.h> // g++ -lgmpxx -lgmp -g product_timed.cpp -std=c++17 -o product
#include <chrono>
#include <unistd.h>
using std::cout;
using std::endl;
mpz_class prod (const std::vector<mpz_class> v)
{
mpz_class accum = 1;
for (const auto& p : v)
accum *= p;
return accum;
}
int check_prime(mpz_class n)
{
mpz_class c;
for (c = 2 ; c <= (n - 1); c++ ) // replaced c <= sqrt(n)
{
if ( n%c == 0 )
return 0;
}
if ( c == n )
return 1;
}
// for ( c = 2 ; c <= (int)sqrt(n) ; c++ )
// Only checking from 2 to square root of number is sufficient.
// but would not convert real to mpz_class
int main ()
{
auto start = std::chrono::steady_clock::now();
std::vector<mpz_class> primes; // sage: prime_pi(11^11) = 11262113374
// This is how many primes less than 11^11
std::cout << "Maximum size of a 'vector' is " << primes.max_size() << "\n";
mpz_class count = 0;
for (mpz_class i = 2; i < std::pow(11, 11) ; ++i) // 11^11 = 285311670611
if (check_prime(i)) {
cout << "\nprime[" << count << "] = " << i << '\n';
primes.push_back(i);
++count;
}
cout << "\n\nThere are " << count << "prime numbers multiplied together!";
cout << "\n\nBig Product is " << prod(primes) << endl;
auto end = std::chrono::steady_clock::now();
cout << "Elapsed time in seconds : "
<< std::chrono::duration_cast<std::chrono::seconds>(end - start).count()
<< " sec";
cout << "Elapsed time in minutes : "
<< std::chrono::duration_cast<std::chrono::minutes>(end - start).count()
<< " min";
return 0;
}
_______________________________________________________________
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The few versions I launched late last night were running through the night, but were only up to about the millionth prime (there are 11262113374 primes less than 11^11 = 285311670611), so it would be 11262 times as long as "all god damn night"). I had to hunt down some special function for finding the square root of Big Integers so that I (the machine, actually) could "check primes" faster. The changed code is below. I have to venture out to the grocery store ... not much sleep, so I have to be careful not to get into any altercations with any of my beloved fellow nervous wrecks.
I just launched this program, and it is already zooming into the 10 millionth prime in about 5 minutes! I think that, by the time I return, it will be done, and I will have a time elapsed for you.
I am leaving the code above since it did work ---- and I will run it one week just to see how much longer it takes using the basic "check_prime()" code.
____________________________________________________________________________
#include <numeric>
#include <functional>
#include <cmath> // for pow(11, 11) = 285311670611
#include <vector>
#include <iostream>
#include <gmpxx.h> // g++ -lgmpxx -lgmp -g product_sqrt.cpp -std=c++17 -o product
#include <chrono>
#include <unistd.h>
using std::cout;
using std::endl;
mpz_class prod (const std::vector<mpz_class> v)
{
mpz_class accum = 1;
for (const auto& p : v)
accum *= p;
return accum;
}
int check_prime(mpz_class n)
{
return mpz_probab_prime_p(n.get_mpz_t(), 15); // see Notes below (Number Theory)
}
int main ()
{
auto start = std::chrono::steady_clock::now();
std::vector<mpz_class> primes;
// std::cout << "Maximum size of a 'vector' is " << primes.max_size() << "\n";
mpz_class count = 0;
for (mpz_class i = 2; i < std::pow(11, 11) ; ++i) // 11^11 = 285311670611
if (check_prime(i)) {
cout << "\nprime[" << count << "] = " << i << '\n';
primes.push_back(i);
++count;
}
cout << "\n\nThere are " << count << "prime numbers multiplied together!";
cout << "\n\nBig Product is " << prod(primes) << endl;
auto end = std::chrono::steady_clock::now();
cout << "Elapsed time in seconds : "
<< std::chrono::duration_cast<std::chrono::seconds>(end - start).count()
<< " sec";
cout << "Elapsed time in minutes : "
<< std::chrono::duration_cast<std::chrono::minutes>(end - start).count()
<< " min";
return 0;
}
/* Notes
sage: prime_pi(11^11) = 11262113374
11^11 = 285311670611
Number Theoretic Function: int mpz_probab_prime_p (const mpz_t n, int reps)
Determine whether n is prime.
Return 2 if n is definitely prime,
return 1 if n is probably prime (without being certain),
or return 0 if n is definitely non-prime.
This function performs some trial divisions, a Baillie-PSW probable prime test,
then reps-24 Miller-Rabin probabilistic primality tests.
A higher reps value will reduce the chances of a non-prime being identified as “probably prime”.
A composite number will be identified as a prime with an asymptotic probability of
less than 4^(-reps). Reasonable values of reps are between 15 and 50.
*/
_______________________________________________________________
By the way, Holden, can you imagine how big this product is? It gotta be Bernie Sanders' HUGE.
More than HUGE! It's a Big Mother Fuckin' Integer, baby! (sorry, no sleep!)
I can't wait to see it. Stay tuned, weirdos. ;)
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The last three entries before crashing:
prime[67108862] = 1339484149
prime[67108863] = 1339484197
prime[67108864] = 1339484207
terminate called after throwing an instance of 'std::bad_alloc'
what(): std::bad_alloc
Aborted
I am unable to reserve the space for the vector of BIG INTEGERS. Maybe the computer runs out of RAM, just like what was happening with Sage. Damn, Holden, thank goodness there will always be that 2 and 5 within the first three primes, so the product will always have that 0 in the unit place.
And yet, are you not curious to behold the number of digits in that big product?
I'm going to try to get a little tricky ... maybe work on it a little before collapsing, then I will just return to the Matrix library in the Stroustrup text. It will be cool to revisit the code for solving systems of linear equations.
These big integers present a real challenge requiring much hidden code, most likely written by the weirdest of the weirdos. I am not such - but only an explorer of sorts, just ever so slightly weird.
My apologies for being so absorbed in something like this "off the wall," but most likely I've gone completely mad. (hyperbole)
over and out
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Yes,it's a very big number.Maybe someday I will be able to write programs like you to solve such problems.
But for the present,this is all I have:
https://i.postimg.cc/mgtfJL4Q/IMG-20200423-114046.jpg
-
I'm gonna put that code on a back burner somewhere. It is humbling to face the limitations of hardware (memory, RAM) and the difficulty of representing such huge numbers. It forces me to respect the analytical approach when the numbers are so big.
Surely, that product from your other example is far larger than 32^32^32. I mean, the computer itself, as hardware, even with the special GMP library techniques, has actual limitations. It was choking on just filling the vector with the numbers. Imagine the tax on the random access memory when those products started reaching larger and larger numbers.
I will take a look at this other example, preferably outside with scrap paper, clipboard, and pen, so that the Computing Lizard in My Head doesn't try any brute force methods. Still, it is cool to at least, only after analyzing on paper first, to have the assitance of at least a computer algebra system for seeing just how large is large. If a program chokes, I do not take it as a failure on my part, but simply as a brute fact : some numbers are too big for the hardware (even with software written by the number crunching freakazoids).
Not only are the large numbers humbling, but there is a very creepy realization that we exist in such times where one may have access to a relatively powerful computer and sophisticated software, and yet is still vulnerable to food insecurity and even "mental health insecurity." :-\
PS: the last solution is difficult for me to follow. Could you expound a little more, even if on a napkin?
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Note that the author of "Goethe and Schopenhauer on Mathematics," this Arnold Emch (https://en.wikipedia.org/wiki/Arnold_Emch), may have had strong gort-tendencies (believing strongly that that which is so, is so).
He had wife and two sons, one of which became a well-known "management consultant" - whatever the fuck that's supposed to be. :o (I have never heard of him, but - then again, who the hell am I? I'm just some old suicide who has lived long beyond what would be expected (beyond 50, that is). )
Maybe it has been a desire to understand more math(s), to rejuvenate my interest in programming by focusing primarily on mathematics-oriented and educational code, that has enticed "the will to live" to endure the redundancy of "doing what we do to stay alive" (much of which is beyond our personal control).
If the food trucks stop hauling the animal parts to the spooky stores, then I don't know what we become. We certainly will see, won't we?
On some level I realize that much of what I think I am (a personality? a soul?) is just the energy from food consumed, and that a starving me might be so drawn inward that articulating myself might not be possible.
Essentially, as long as I am an Eater-of-Food, I am full of shit. When the animal body dies, no more food, no more stomach, no more shit ...
:P
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A book mentioned in this thread (back here (http://whybother.freeboards.org/math-diary/burn-math-class/msg8766/#msg8766)) has appeared at Library Genesis: Language, Logic, and Mathematics in Schopenhauer (Studies in Universal Logic) 1st ed. 2020 Edition (http://gen.lib.rus.ec/search.php?req=Language%2C+Logic%2C+and+Mathematics+in+Schopenhauer&lg_topic=libgen&open=0&view=simple&res=25&phrase=1&column=def). (editor: Jens Lemanski)
____________________________________________________________________________
Also, this 5 page article, Who Won the Math Wars? (https://faculty.fordham.edu/tampio/who_won_the_math_wars.pdf)
One may rightly speak of a Common Core goldrush.
Phillips notes that New Math advocates wanted for-profit publishers to make aligned textbooks. According to Phillips, however, New Math leaders respected the American federal system with its constitutional prohibitions on centralized education authority. The New Math may have fallen, in part, because its leaders still respected democratic procedures for the ways in which states and localities make curricular decisions. CommonCore advocates, however, leveraged the power of the federal government and billionaire philanthropy to create a market where education entrepreneurs stand to make fortunes. Who won the math wars? Follow the money.
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I have taken your advise of focusing on math problems with regard to which I have "some hope of understanding them" .
This approach has helped me quite a bit.
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This book you mention sounds very interesting to me.
-
This book you mention sounds very interesting to me.
Yes, Holden, it is melting my brain even just in the Introduction. I will have to devote at least an entire notebook just to this collection. I will want to read notes from it somewhere besides attached to a terminal or reading device.
I am tired and a little emotionally drained (not too bad), and yet still parts of me have a gut intuition that this book will have a great impact on me as I have been alarmed throughout my life by certain comments I've read from the 1900's disparaging to Schopenhauer's mathematical insight. I have never felt qualified to defend him, or where even to begin. Fortunately, we have "elder brothers" (and a handful of sisters, i suppose) who have stepped up to throw this wonderful pie into the face of The Church of Reason, whose representatives have conveniently written Schopenhauer off as "the artists' and musicians' philosopher."
Well, I would not mind a strong dose of Schopenhauer's genius. Indeed, logarithms may have become like poetry to me, but only as a personal technique for warding off decades of general dissatisfaction. Sometimes I am able to capture a mood where I feel fortunate or blessed to have gained a bit of familiarity with the small but fundamental branches of mathematics I have studied.
I wish I could be to young mathematics students what Schopenhauer was to me, even though I do not see Schopenhauer as one who has had any mathematical influence upon me other than to remind me what drudgery arithmetic is, and how a man can actually fry his brain via number crunching. Schopenhauer knew he was better off playing the flute! :D
Don't get me wrong, I do sometimes slip into my number-crunching (manic? WTF) modes, but it is usually kind of disturbingly stimulating, in that I become entirely obsessed and engrossed in the computations. It is similar to a drug-induced trance.
No matter what level of understanding of mathematics or calculating and computing I have developed over the decades, I am fully aware that Schopenhauer's grade of intelligence and "spirit" or "character" was superior to mine. That is, I have no problem with being under any kind of delusions that I have deeper insight just because I have been exposed to more recent methods of analysis (which were being developed in Schopenhauer's time). No, and AGAIN NO! I am very grateful to those who authored the contents of Language, Logic, and Mathematics in Schopenhauer 1st ed. 2020 Edition. (editor: Jens Lemanski) ! Right out of Germany ... maybe some of the authors are researchers who had access to Schopenhauer's research "library" and "notes" ...
I know Schopenhauer had a different kind of mind than my own, and that he possessed an enormous wealth of knowledge, not to mention the confidence to question authorities that I would be too intimidated by to ever even think of doubting.
Maybe I am setting myself up for a disappointment, but this is quite a rare collection of essays. I am intrigued. I will read into the night, having finally put away the math texts for the night.
I know the human world is filled with misery, want, and need, and I am not ignoring the ever-present annoyance of the burden of my own existence, but kindling such interest in two areas I have been influenced to believe were not even remotely related. Now I come to find out that there are others ... others who have delved into it.
Maybe Hell really is about to freeze over.
We were scratching at this very surface a while back with your Schopenhauer's Philosophy of Mathematics (http://whybother.freeboards.org/math-diary/schopenhauer's-philosophy-of-mathematics/). I was even gathering specific parts of Schopenhauer's opus when we were zeroing in on those gems ... if only because they were so few and far between.
It is great to know someone else has been eagerly leaning in this particular direction, just waiting for some guidance and fellow-students-of-life to forge a bit of a trail into that woodlands.
The freaking bloody Berlin Lectures are out of the bag, and they thought nobody in the world would notice.
Again, I feel we are blessed to have the haven/fortress prepared for paying respect to those who might greatly benefit, spiritually and even emotionally, by having access to lectures Schopenhauer intended for the most genuine students. That "Prince Vault" has yet to be translated, and to remains as mysterious to me as, say, an old Sanskrit text might be to Holden. I am linguistically far removed from understanding the German language. I struggle just to remember the numbers in German. I will be delighted to take note of some of the more significant German words that I am sure to be exposed to in the readings.
Those lectures might reveal the details I crave! I'm sure some of the Berlin Lectures will make it into this or future incarnations of this or similar scholarship.
His wished for his published (paid for out of his own inherited pocket) work to be received by lone scholars throughout several ages, and did not wish to bore the reader or tax his memory with mathematical abstractions or chains of formal logic diagrams. Maybe someone inspired by this collection will be motivated to fund such research and translation ...
To have something out of Academia, at least, unknowingly respond to our willy-nilly inquiries, our little elephants in the room ... might qualify as uncanny. Deeper Understanding would be appreciated, especially for one who goes from one set of [school mathematics] exercises to the next ... it is cool to step outside of the structure and method, an opportunity to reflect upon the foundational genesis of logic, the queen of mathematics --- maybe the combination of Fourfold Root + both volumes of WWR really does reflect the world as it is, but with the abstract symbols of language, logic, and mathematics. These are all from the first of the four parts of WWRv1. Hmmmm ...
I had definitely paid much more attention, especially when going back over (and over) ideas pertaining to salvation, to Book Four, on Ethics, so this book will challenge me to reflect upon the very parts of Schopenhauer's system which I may have paid least attention to, due to the literary slander against him in this respect from the early 1900's. They were bad-mouthing him, Schopenhauer, that is, making him out to be mathematically naive or immature, rudimentary, even. Ha! Without logic, there is no mathematics or philosophy. (opinion or fact? I am not certain.)
The World as Will is Blind Appetite, Hunger, Thirst, Lust ... It is what it is. Chaotic, irrational, absurd. The world of logic is an abstract world of symbols, but we take it all so much for granted that we don't appreciate that Schopenhauer's quest for an intuitive understanding of the Thing-in-itself is what he was attempting to shoot into the future for the benefit of mankind. He possessed the confidence to create a kind of "holy book." He would often mention the realm of dreams, where the most abstract sorts of meaning and logical relations might be represented by spatial relations.
I suppose this editor is going to be "taking us to school." That is, it has the potential to ignite, not only more Schopenhauer scholarship, but also may breathe new life into those parts of Schopenhauer's system that place knowledge in the realm of intuition.
I am reaching an age where forced friendships reveal themselves as such, and rather than cursing Fate, I may simply acknowledge the nature of this world, the nature of other human beings, the unpleasantness of my own moody and irritable Thingy-in-Itselfy.
No One Knows The Big News :
we ourselves are the dark light
https://www.youtube.com/watch?v=vAa9wKKyvSY
This type of scholarship is the type of material I wish to spend my energy on, not on people I feel obligated to because of past history. When we walk in the woods with others, there comes a time in the middle of the night when we wander off our separate ways. Maybe the mental world of ideas is similar to those woods in that, well, when it comes to thinking about ideas or the very structure of our mental faculties, we have no other choice but to think for ourselves. No one can do your thinking for you, and, truth be told, as Ligotti points out in the song, No One Knows the Big News, not many others are concerned with the big news (in the world of ideas). Their heads are just too heavy with so many plans and schemes, thousands of tasks that will not allow them to focus on something that is so strange, anything that is so uncertain. They have no time to confront some ultimate revelation. They have no desire to find out some incredibly big news. Such a thing would take everything they know and arrange it in another way altogether, telling a story so different than the one that is already familiar to them. No one knows the big news. Yet the big news is always there.
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I have taken your advise of focusing on math problems with regard to which I have "some hope of understanding them" .
This approach has helped me quite a bit.
I was surprised by this also, by returning to areas one has some familiarity with, instead of always taxing with the newest, latest, and greatest, helps us develop intellectual honesty as we continue our intellectual adventure. What happens is, each time around you have notes from your last interaction with those ideas, notes of certain tangents you go on, such as my "calculating without instruments" phases. Those notes are a pleasure to read a few years later when returning to those fundamental concepts.
You want your quest to be deeply personal, since, well, we get out of it exactly what we put into it, like a bread machine.
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In a thread called,
Arctangent Without a Calculator ...Why Bother? (http://whybother.freeboards.org/math-diary/arctangent-without-a-calculator-why-bother/msg2798/#msg2798),
Mathematical reasoning, Schopenhauer argued, is fundamentally different from ordinary logical or syllogistic reasoning in being based on intuition or construction, not on deduction from premises to conclusion; and accordingly Schopenhauer advocated the revision of Euclid, who, he believed, mixes the genuinely geometrical with the spurious logical proof. Schopenhauer even offered specimens of the right kind of proof. While the idea is interesting, I feel daunted by complexity of the problem S. has raised.Do you think his work on the logical foundations of mathematics has any value to-day?
I think that, if I invest a little time at the end of each night to read through, reread, and take notes from the recently mentioned collection, I will be able to respond in a more intelligible manner. Your question is a great motivation for zooming in on those particular parts of his work, as well as being on the look out for the rare scholarship going on in this area.
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Well,I have downloaded the book,finished the introduction and now I am reading the first article in the collection.
I wish someone translated the Berlin Lectures. Maybe Schopenhauer is ,after all, checking out this message board from the other side,from time to time, and sent this book as the answer to our queries ;)
I always maintained the thesis that the book puts forth in a far more articulate manner than I could have possibly been able to do on my own.
My parents, made me call up a young lady, who possess a post graduate degree in mathematics .I talked to her over the telephone and she seems to me to be obsessed with getting married and even more obsessed with having kids.
I ,on the other hand, am determined to dedicate all of the life to pessimistic philosophy(language, logic and mathematics being very much a part of it).
The paradox here is that ,generally speaking, people who are good at maths are supposed to wise.
The incontrovertible fact here is that,she is maths postgraduate major and I continue to struggle with even basic mathematics(but I grown to rather like this struggle). Yet, she is one who is determined to cause more suffering, more chaos.I just want to cease to exist.
https://youtu.be/gxEPV4kolz0
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I wish someone translated the Berlin Lectures. Maybe Schopenhauer is ,after all, checking out this message board from the other side,from time to time, and sent this book as the answer to our queries.
In the collection, Language, Logic and Mathematics in Schopenhauer (https://www.springer.com/gp/book/9783030330897), in one of the chapters written by the editor Jens Lemanski, Pages 47-71, Concept Diagrams and the Context Principle, in section 4 (Schopenhauer's Concept Diagrams and the Context Principle, I quote:
I only refer to Schopenhauer's Berlin Lectures, which are published in the Manuscript Remains. These lectures were elaborated in the 1820's, edited by Mockrauser for the first time in 1913, and reprinted in 1986. In what follows, I am referring to the Mockrauser edition of 1913.
I, maybe not by luck or coincidence, but by conscious deliberation at the time of tracking down and purchasing, have in my possession, Volume 3 of the Manuscript Remains, that is, Berlin Manucripts (1818-1830) ... in English ... very small print, so it has been slow-going. I actually require a magnifying glass to read it. I think I had found a copy for less than 50 frog skins at the time. Well, one thing is certain: this presently released Language, Logic, and Mathematics in Schopenhauer will inspire, motivate, and most likely guide my careful inspection of the large volume 3 of Manuscipt Remains. Just flipping to a random page, I was struck by a paragraph discussing word and concept. Already, I think the scholars, including the editor, who wrote the chapters of the book I've read so far, have influenced my reading of the Manuscript Remains. I have been spoiled by the ability to increase font sizes on terminals and screens, so, as with the mathematics texts, which are always hard copies, rarely digital, I just have to use magnifying glass (and for laying on back, reading glasses).
Also, on the inner flap/cover of Volume 3 [Berlin Manuscripts], it is written that the English version of The Manuscript Remains represents the first five parts; the sixth (Vol V: Notes on Books) was declared untranslatable by Payne.
It was back in 2016 that Holden made me aware of the Manuscript Remains. I was not at all aware of their existence.
The Will's Harmonic Motion (http://whybother.freeboards.org/what-now/the-will's-harmonic-motion/msg2692/#msg2692) (2016)
Schopenhauer Manuscript Remains (http://whybother.freeboards.org/math-diary/being-and-number-overcoming-mathematics/msg2756/#msg2756)
Schopenhauer's Philosophy of mathematics (http://whybother.freeboards.org/math-diary/schopenhauer's-philosophy-of-mathematics/msg8853/#msg8853)
My parents, made me call up a young lady, who possess a post graduate degree in mathematics .I talked to her over the telephone and she seems to me to be obsessed with getting married and even more obsessed with having kids.
I ,on the other hand, am determined to dedicate all of the life to pessimistic philosophy(language, logic and mathematics being very much a part of it).
The paradox here is that ,generally speaking, people who are good at maths are supposed to wise.
The incontrovertible fact here is that,she is maths postgraduate major and I continue to struggle with even basic mathematics(but I grown to rather like this struggle). Yet, she is one who is determined to cause more suffering, more chaos.I just want to cease to exist.
I am not so sure if those who have the discipline and support to excel in the formal study of mathematics are necessarily wise. In fact, all scientific professions require the scientist to be proficient in the language of mathematics. Not all scientists are necessarily wise.
Is wisdom related to formal academic training?
I would not think so, since there are wise people with little formal education. I have made the efforts to get some formal education, but I sense any wisdom I have attained came from my lived experience, and certainly not from the Field Axioms or finding roots of polynomials.
Those of us who shy away from marriage and reproduction may be tapping into a wisdom that transcends the dictates of the survival of the species.
I suppose many men might be intimidated by this young woman, with her knowledge of advanced mathematics. Did you explain to her your apprehensions about bringing sentient life into this?
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I did not say anything unconventional to her,I just said to her that while it is true that I am in a very big city at the moment, mine is a transferable jobs and most of the organization's projects are in remote areas of country.It is highly likely that within a couple of years ,I would once again find myself in the middle of nowhere. So, even if we did have kids, they would have to study in third rate schools with very bad teachers.
Now, this is not necessarily false,in fact,its quite true. It worked to a certain extent. She said her kids are going to be her top priority and she wants the best possible education for them.
If push comes to shove,I have decided that I would stop taking my parents' calls. I cannot win verbal arguments with anyone.
I will do that I do best-hide.
I am not rich and the most valuable asset that I possess is my solitude during my off-duty hours. I would guard it with my life.
https://youtu.be/4OTBkzyxg4U
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By the way, I found it difficult to sustain motivation for taking notes from the collection, Language, Logic and Mathematics in Schopenhauer, edited and partially authored by Jens Lemanski. I suppose I might have to skip many of the chapters (contributions) on language and search for the sections on logic and mathematics.
It is humbling to face the limits of our reason, the limits of what we are actually able to devote our conscious attention to. :-\
I hope you, Holden, are continuing to stand your ground as far as "whether or how you want to live in this world."