See
Real Fish, Real Numbers, Real JobsLet 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.
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!