Author Topic: Quasi-Religious Speculation on Things Which Don't Exist  (Read 544 times)

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Nation of One

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Quasi-Religious Speculation on Things Which Don't Exist
« on: May 29, 2017, 07:35:56 am »
See Real Fish, Real Numbers, Real Jobs

Let x be a real number.

OK.  I accept the validity of the real numbers even though there may be something fishy about them.  I wish they would have called them anything else besides Real Numbers. 

Quote from: Wildberger
  What did we call this new number system consisting of largely chimerical creations of our imagination?  Did we call them Arbitrarials? or Way-out  numbers?  No.  In a flash of brilliance any PR person would be proud of, we called them real numbers, and designated them by the solid looking R


What I mean to say is, I have all these exercises I want to go through completely, and they deal with these things called "real numbers".  I then write mathematically oriented computer programs to run on the command line (NOT APPS!  ::)) ... Old School.  I keep accumulating these special little mathematical programs I make for my own personal use.  I first compile them in Linux, and then in Windows.  In each operating system I have created a bin directory where I place the binaries and include this directory in my $PATH so that I can just run them from the command line from whatever location.

This is the kind of thing that makes life worth living for me.  This is all I have ever aspired to be able to do.   In other words, I appreciate my little math programs, and I would encourage others to build some of their own (in C++ or whatever).

Now, it's all very intellectually stimulating, and if I have to profess to having some kind of religious belief in the real numbers, I will.  I don't care about them being mental constructs that cannot be constructed in actuality.   I really don't.  They prove to be useful in many ways.   They exist only in our minds.  What doesn't exist only in our minds?

While I am very interested in what NJ Wildberger has to say, since attention is a limited resource, I have to make some choices on a daily, if not moment to moment, basis.   

For now, I am studying in a classical manner.

I share some of Wildberger's preference for the rational numbers.  In fact, I am considering altering many of the programs I have written so that they compute with objects called Rationals or Fractions.

By the way, I am backing out of the other thread (Re-Imagining Mathematics) out of respect.  I will try to use self-restraint. 

I know there is a great deal of philosophical drama surrounding mathematics.  I humbly submit that I prefer to focus on the technical and computational aspects, albeit, with some attention paid to formal proof writing.

I will not take offense.  People are free to devote their energies to studying what they will.

Maybe, deep down inside, I really am just a hack.  This does not make me any less interested in mathematics than the "mathematical philosopher" or any less interested in programming than the "software designer".

Hell, to hell with all these labels and titles.

I hear some "software designers" complain that Sage was put together by a bunch of "mathematicians", and that is why it is so clunky.

Sage is very cool ... even though I find myself just using SymPy as a computer algebra system.   SymPy is under the hood of Sage anyway (along with everything else but the kitchen sink).   I don't complain about Sage.  Never.   I just learn to do things with SymPy since I installed Sabayon (Gentoo based) where I was not able to get sage to build.

Oh well, some people are professional mathematicians and even paid educators (academics).  Others get paid to develop actual commercial software - many more contribute to Open Source.  Regardless of whether someone is getting paid or not, the task of programming remains something which requires a great deal of care and devotion.  The complexity of it all is mind boggling and rather daunting.

It forces me to acknowledge my ignorance, and treasure the little that I have been able to learn over the years.   I tend to resent those who do not fully grasp the degree of their own ignorance, but such resentments are diminishing.  As I mellow out, as long as I am content with my intellectual endeavors, the contents of other peoples' consciousness has less and less an impact on my moods.

Me?  I am just another madman math/programming hobbyist even though the so-called hobby is what I engage in from morning into late at night, leaving myself only a little time for literature (such as some essays suggested by Maughan by Count Giacomo Leopardi, Darkness at Noon by Koestler suggested by Holden, and the Devil knows what else ...).

I work through a great deal of mathematical exercises and hack around with coding.

I thought maybe I could inspire you (Holden) to take an interest in some coding yourself, and, yes, to get into some algebra.  I was a little disappointed to read that you wanted to dismantle the whole of mathematics and rebuild it from the ground up.  It just sounds so outlandish; but, as we both know, a great deal of such projects happened over a hundred years ago, and Wildberger is reviving that project with the aim of altering the way mathematics is presented to future high school students.

Will they not still want to learn the "classical methods"?

I am certainly no academic nor have I ever aspired to be any kind of professional programmer.

I thought I remembered you saying you faced some difficulties with algebraic calculations, so I figured you might enjoy developing skills in that area.  I'm not going to even begin to speculate what would motivate you to pursue such philosophically radical projects rather than something more feasible and doable. 


I suspect there is a shiit storm of mind-fuuckery all over the Internet, and I want to stay focused on learning some actual mathematics to become more skillful in a technical sense.  In any case, I am on my own with what I study, and I neither request nor require any blessings or approval.  My interest and devotion in no way depends on anyone besides me.   So, I am willing to take the risk (of wasting time) studying the mathematics I have decided to return to and go over more intensely.  I am not at all discouraged by these claims that the real numbers don't really exist.


One day we'll all be dead, and nothing will exist; and eventually there will be no evidence of anyone even ever being here.  In the meantime, I can work factor integers over the set of primes and a great deal more ... even if it is all in my head, it is still INTELLECTUALLY STIMULATING.

Today I want to bone up on some algebra and tinker with some mathematical programming.  I get a thrill when I can check my work with a program I created ... and to solve algebraic problems with integers or ratonals or real numbers.

I don't care if I am in my own orbit. 

No wonder there are so many cantankerous, frustrated, and downright grouchy math nerds and computer geeks, not to mention suicidal philosophers!

Before it's all over, I wouldn't be surprised if I forsaken all these terms that signify some kind of profession.

In the end, like Kurt Vonegut said, we are just a bunch of chimpanzees who can read, write, and do a little math (and computer programming).

Bananas!
« Last Edit: May 29, 2017, 03:58:23 pm by Raskolnikov »
Things They Will Never Tell YouArthur Schopenhauer has been the most radical and defiant of all troublemakers.

Gorticide @ Nothing that is so, is so DOT edu

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Holden

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I need to think about these things more thoroughly.
La Tristesse Durera Toujours                                  (The Sadness Lasts Forever ...)
-van Gogh.

Nation of One

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The ironic thing about the so-called real numbers is that an infinite amount of them cannot be constructed, which is made even more evident when trying to represent them as a decimal number with a digital computer.  We have to learn to live with approximations and "error tolerance".

I find working with integers and rational numbers far more elegant, and I think this is their appeal to a "Finitist" like NJ Wildberger. 

Maybe we can compartmentalize as far as what parts of the brain will be doing the thinking.  When it comes to the validity of infinite sets, limits, and nonconstructible "real numbers", for me, it is safe to put these on the back burner.  It doesn't mean I am ignoring the issues or that they are exempt from philosophical inquiry, doubt, skepticim, etc.   It just means that the part of the brain that is writing now, the part that computes and calculates and manipulates algebraically, must take certain concepts for granted in order to concentrate on the tasks at hand.

I am not equipped to challenge the mathematical community on foundational issues.

Please forgive my low frustration tolerance as I am easily overwhelmed.

When it comes to methematics [sic! I'm leaving this typo], I suspect I use the Husserlian epoche to bracket off the entire universe other than what it is I am trying to juggle in our limited short term memory capacity.

Feel free to post anything you wish here.  Just also realize I can be very close-minded at times and consumed with my own little world of ideas, which is limited.

« Last Edit: May 30, 2017, 07:53:43 pm by Raskolnikov »
Things They Will Never Tell YouArthur Schopenhauer has been the most radical and defiant of all troublemakers.

Gorticide @ Nothing that is so, is so DOT edu

~ Tabak und Kaffee Süchtigen ~

Holden

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As you so rightly say "Nothing that is so,is so." The idea maybe to try & not  reduce mathematics to a structural configuration. What we may seek out in mathematics is a conceptual apparatus, a deep structure, that explains the way in which motion is actually instantiated in the world all around us. Consequently, the mathematical concepts maybe formulated around relations rather than stand-alone principles, they maybe about transformative activity.
La Tristesse Durera Toujours                                  (The Sadness Lasts Forever ...)
-van Gogh.

Holden

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Please understand that it is not that I dont wish to study mathematics.It is that I fail to concentrate when I try to study it.If you have a formula/method which can help me to concentrate and develop prolonged interest in math,then please give it to me and I promise that I will give it my best shot.

The blindman wants to see very much,one cannot say that he keeps his eyes closed deliberately all the time.
« Last Edit: June 01, 2017, 01:01:26 pm by Holden »
La Tristesse Durera Toujours                                  (The Sadness Lasts Forever ...)
-van Gogh.

Holden

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Do you think this is a good approach.
http://www.amesa.org.za/amesap_n68_a2.pdf
La Tristesse Durera Toujours                                  (The Sadness Lasts Forever ...)
-van Gogh.

Nation of One

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I'll print it out and take a look at it. 

I'm heading into my hometown today for a rather short visit (just to check in on my Dad).

I was going to suggest always returning to the fundamentals when thinking about numbers and polynomials ... to think about prime factorizations, greatest common divisor, least common multiple, how they are related to the prime factorization, where these come into play with the arithmetic of fractions ... reflecting on actual numerical computations alongside algebraic ones ...

It's a shame we can't develop our telepathic powers.

There is no rush though.  Sometime today I will read through what you have asked me to look at.

Things They Will Never Tell YouArthur Schopenhauer has been the most radical and defiant of all troublemakers.

Gorticide @ Nothing that is so, is so DOT edu

~ Tabak und Kaffee Süchtigen ~

Nation of One

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As I post this, cold rains pour down, and I reflect upon how utterly dependent my very being is upon the roof over my head.  With that said, I wish to link this thread to another one by taking a small excerpt from a link you left in the  Schopenhauer's Philosophy of Mathematics thread.

Quote
In the 19th century, the German mathematician Leopold Kronecker said "God made the integers, all else is the work of man".

Mathematics has been happening for a very, very long time. Long before ancient Greece and Pythagoras.

Is it real? Most cultures agree about some basics, like the positive integers and the 3-4-5 right triangle. Just about everything else in mathematics is determined by the society in which you live.

 :o
« Last Edit: October 31, 2021, 03:03:52 am by mike »
Things They Will Never Tell YouArthur Schopenhauer has been the most radical and defiant of all troublemakers.

Gorticide @ Nothing that is so, is so DOT edu

~ Tabak und Kaffee Süchtigen ~