After Schopenhauer,you are the greatest philosopher we've had.(Did Cioran study math?)
No, Holden, I am not. I actually prefer to see myself more clearly as I truly am, if you don't mind. This is not false modesty.
I am not Nietzsche or Heidegger or Husserl or Merleu-Ponty (none of which impressed me the way Schopenhauer did, as you are well aware). Schopenhauer is my "spiritual grandfather". He told me things I wished my biological grandfathers would have told me. Alas, it takes a village to raise a child. Schopenhauer has helped me get through this life and to understand why I have not paired off with a woman and reproduced. He has helped me make sense of my existence.
I will never publish anything I have ever written, unless, of course, if I live to be a very old man, maybe I might write something aimed at teenagers since that was the most difficult period of life for me. You see, I lose patience with those who explain the world to us. We each can only try to explain this world to ourselves as best as we can just to get through each moment.
I think it is best for both of us if we divorce ourselves from those competing to solve the great riddles. When the sun expires and the surface of the earth looks like the surface of the moon, there will be no memory of Schopenhauer or even of the Vedas or Upanishads. It will be as though no one had ever been born.
I am going to join you in this exploration of the translations of Kant, but I must say I am a little skeptical about any attempts to make sense of lived experience. I think that life will take all my marbles away before it's over.
So, while I am still able, all I aspire to do is go over some fundamental mathematics and work on some problems whenever I am in the state of mind to do so.
Life is hard enough to endure without thinking of oneself as "the greatest philosopher since Schopenhauer".
It could only lead to a rude awakening. My view of myself is far more humble. While Schopenhauer was an outsider due to his views and in the manner which he expressed those views, he was a tremendous scholar so he more than held his own when taking on the established "academic philosophers". I am, in contrast, an outsider because I am an amateur. I am certainly no intellectual heavy weight.
What you may find appealing about my way of expressing myself is my attempt to be as intellectually honest as possible. I think we both share an extreme contempt for the pretentious, the pompous, and the downright snotty attitudes found among those who play the role of academic philosophers or officially sanctioned "students of
analytic philosophy". Let's not even get started thinking about actual "mathematicians". My god, you would think they own the branch of knowledge, as if it were some kind of well-guarded priesthood.
No, we are outsiders, outcasts, untouchable nobodies. We shall study Kant to the best of our ability, regardless. Maybe our understanding of Schopenhauer's work will give us an unexpected advantage in that we might try to see the work through Schopenhauer's eyes.
Really, though, I don't think reading Kant will give me the mental stimulation I get from writing a simple computer program.
I get a thrill just being able to write a computer program in C/C++ that factors a quadratic equation, showing each step. This is about the limit of my mental capacity. I do not possess the kind of brain Schopenhauer had as far as learning other languages and pouring through difficult and ancient Indian texts. It's ok. I am ok with just being me.
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I get a kick out of making simple programs like this even though I could use a CAS or do this with pencil and paper. Suppose I want to factor 2*x^2 - 3*x - 14, I type my homemade program, tfac2, at the command line:
hentrich@coyote:[~]: tfac2
To factor quadratic trinomial of the form a*x^2 + b*x + c,
Input a (>0), b, and c (!=0):
2 -3 -14
We want to find the binomial factors of 2*x^2 + -3*x + -14
of the form (m*x + p)(n*x + q), where
m*n = 2
p*q = -14
m*q + p*n = -3
The integral factors of 2 are {1, 2}
The integral factors of -14 are {1, -1, 2, -2, 7, -7, 14, -14}
TRIAL FACTORIZATION LINEAR TERM
--------------------------------------------------------------------
(m) (p) (n) (q) m*q + n*p = b
--------------------------------------------------------------------
(1*x + 1) (2*x + -14) 1*-14 + 2*1 = -12
(1*x + -1) (2*x + 14) 1*14 + 2*-1 = 12
(1*x + 2) (2*x + -7) 1*-7 + 2*2 = -3
(1*x + -2) (2*x + 7) 1*7 + 2*-2 = 3
(1*x + 7) (2*x + -2) 1*-2 + 2*7 = 12
(1*x + -7) (2*x + 2) 1*2 + 2*-7 = -12
(1*x + 14) (2*x + -1) 1*-1 + 2*14 = 27
(1*x + -14) (2*x + 1) 1*1 + 2*-14 = -27
--------------------------------------------------------------------
The unique complete factorization is:
(1*x + 2)(2*x + -7)
_______________________________________________________
That was the output.
The code is below:
-----------------------------------------------------------------------------------
// Factoring a quadratic trinomial of the form a*x^2 + b*x + c is just a matter of brute force:
// plugging in the factors of the second degree coefficient a and the factors of the constant c
// and seeing which combinations add up to first degree coefficient b.
#include <iostream>
#include <cmath>
#include <vector>
using namespace std;
vector<int> factors(int number, int negative = 0);
int factorTrinomial(int a,int b,int c);
int main() {
int a, b, c;
cout << "To factor quadratic trinomial of the form a*x^2 + b*x + c," << endl;
do {
cout << "Input a (>0), b, and c (!=0):" << endl;
cin >> a >> b >> c;
} while ( (a <= 0) || (c == 0) );
factorTrinomial(a, b, c);
return 0;
}
int factorTrinomial(int a,int b,int c) {
// factors a polynomial of the form a*x^2 + b*x + c'''
vector<int> afactors = factors(a,0);
vector<int> cfactors = factors(c,1);
int irreducible = 0;
// variables used for "Trial Factorizations and Linear Term"
double a2, c2;
cout << endl << "We want to find the binomial factors of " << a << "*x^2 + " << b << "*x + " << c;
cout << endl << "of the form (m*x + p)(n*x + q), where " << endl;
cout << "m*n = " << a << endl;
cout << "p*q = " << c << endl;
cout << "m*q + p*n = " << b;
cout << endl << endl;
cout << "The integral factors of " << a << " are {";
for (int i = 0; i < afactors.size(); i++) {
cout << afactors
;
if (i < afactors.size() - 1) { cout << ", "; }
else { cout << "}" << endl << endl; }
}
cout << "The integral factors of " << c << " are {";
for (int i = 0; i < cfactors.size(); i++) {
cout << cfactors;
if (i < cfactors.size() - 1) { cout << ", "; }
else { cout << "}" << endl << endl; }
}
cout << "TRIAL FACTORIZATION LINEAR TERM" << endl;
cout << "--------------------------------------------------------------------" << endl;
for (int i = 1; i <= abs(a); i++) {
a2 = double(a)/double(i);
if ( abs(a2) != int(abs(a2)) ) { continue;}
if ( a2 < i ) { break; }
cout << endl << "(m) (p) (n) (q) m*q + n*p = b" << endl;
cout << "--------------------------------------------------------------------" << endl;
for (int j = 1; j <= abs(c); j++) {
c2 = double(c)/double(j);
if ( abs(c2) != int(abs(c2)) ) { continue; }
cout << "(" << i << "*x + " << j << ") ("
<< a2 << "*x + " << c2 << ")"
<< " ";
cout << i << "*" << c2 << " + " << a2
<< "*" << j << " = "
<< i * c2 + a2 * j;
cout << endl;
// include negative factors of c (-c2 = -c/j, and -j)
cout << "(" << i << "*x + " << -j << ") ("
<< a2 << "*x + " << -c2 << ")"
<< " ";
cout << i << "*" << -c2 << " + " << a2
<< "*" << -j << " = "
<< i * -c2 + a2 * -j;
cout << endl;
} // end inner for loop
}// end outer for loop
cout << endl << "--------------------------------------------------------------------" << endl;
cout << "The unique complete factorization is: " << endl << endl;
for (int i = 0; i < afactors.size(); i++) { // try all the factors of a
for (int j = 0; j < cfactors.size(); j++) { // and all the factors of c
// see which combinations add up to b
if ( afactors * ( c / cfactors[j] ) + ( a / afactors ) * cfactors[j] == b ) {
cout << "(" << afactors << "*x + " << cfactors[j] << ")("
<< int(a / afactors) << "*x + " << int( c / cfactors[j]) << ")" << endl << endl;
return 0;
}
} // end inner for loop
}// end outer for loop
/* DEBUG:
cout << "What happened?" << endl << endl;
cout << "The integral factors of " << a << " are {";
for (int i = 0; i < afactors.size(); i++) {
cout << afactors;
if (i < afactors.size() - 1) { cout << ", "; }
else { cout << "}" << endl << endl; }
}
cout << "The integral factors of " << c << " are {";
for (int i = 0; i < cfactors.size(); i++) {
cout << cfactors;
if (i < cfactors.size() - 1) { cout << ", "; }
else { cout << "}" << endl << endl; }
}
// end DEBUG */
if (irreducible == 0) { cout << endl << "IRREDUCIBLE" << endl << endl; }
return 0;
}
vector<int> factors(int n, int neg) {
// returns a list of the positive and negative factors of a number n'''
vector<int> factorList;
n = abs(n);
for (int i = 1; i <= n; i++) {
if (n % i == 0) { // if n is divisible by i (i divides n)
factorList.push_back(i); // i is a factor
if (neg == 1) { factorList.push_back(-i); } // so is -i
}
}
return factorList;
}
// a*x^2 + b*x + c = (m*x + p)(n*x + q)
// Given a*x^2 + b*x + c, we want to output the factorization
// in the form (m*x + p)(n*x + q), where
// m*n = a
// p*q = c
// m*q + n*p = b
______________________________________________________
All I am trying to say is, I am content to tinker around with stuff like this. I do not want to be "one of the great philosophers" or even some kind of "writer".
I just want to honor whatever mental capacities I have. I don't see myself as some kind of genius at all. Please view me as just another creature who happens to be passing through the world the same time you are.
Thanks for taking me seriously. The respect you grant me is a rare thing. I do appreciate it, and I try to give you a similar kind of respect.
There are moments where it is all i can do to keep a grip on my temper, but I do have a handle on it. I think I have a high degree of psychological insight, which helps me keep things in perspective.
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