On Dec 28, 1:12 am, Virgil <vir...@ligriv.com> wrote: > In article > <a5a8214e-204a-49f4-8bbe-50b960b2c...@uc4g2000pbc.googlegroups.com>, > "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote: > > > Now, Hancher, I'll accept that you're quite familiar with crazy > > With sterling examples of it like you and WM, and others, everyone who > reads much of sci.math is. > --
There are varieties of mathematicians, and they derive different values from our study of the same principles. Some derive value from the very closedness of things, that there are right and wrong answers to our most fundamental questions. Some derive value from the very openness of things, that there may be right and wrong answers to all our questions. There are various motivations for its study and application. Yet, it is largely so that given strong fundamental principles, there are available general results, and mathematics is for that those with totally different thinking, can share in truths, given the principles of mathematics.
Clemens' law of conservation of truth: "For each Great Truth, there's an equal and opposite Great Truth." Apollo: "Everything in moderation, including moderation." There are a variety of fallacies, ad hominem here, or your appeal to the righteousness of the mob, that have as place in mathematics exhibits, not course.
monomania, check (determination, reliance on mathematical truth and proof) megalomania, check (belief in self) paranoia, reasonable (typical unknowns, and there are many) delusions, not so many (typical unknowns) depressive, no just relaxed (yawn) manic, from time to time (called high-energy, on-task, Olympian) hypochondriac (not so much) hyperchondria (not so much) psychotic (meh) sociopath, no neurotic (not so much)
Now I'm not a doctor and I don't play one on TV (MCAT top), but in terms of promoting the discovery of foundations of mathematics, including but not limited to those that are are discovered and well- covered, to me "different" doesn't mean "crazy", and here "infinite" and "counter-intuitive" don't mean the same thing. And, you can find someone who'll call you anything, and a quack who'll give you pills for it, and maybe they know of the schoolyard ribbing of rubber, and glue. You can trust anyone, to throw you in a ditch for a penny. And some, you can trust.
For some mathematicians, mathematics is a diamond and a single flaw would ruin the entire thing. For others, the existence of the flaw is the only way to cleave the diamond and cut the diamond from its rough aggregate to its perfect shape. So, when I throw light on the diamond, it is to see the flaws, not ignore them.
Then, when it comes to spending enough time working on infinities in mathematics, as one put it, "thinking about infinity makes people nuts". I think that's not necessarily so, instead that there are simply not so many people with the capacity and time to entertain the notions of the infinite for its cerebral beauty, and the mathematics of it for satisfaction of the mathematical conscience. Though, there are confounding results, that then for the purposes of establishing our rigor in mathematics, see requirements for limits in the discussion, to then work up that limited subset of all what may be true, to build a walled garden wherein all is true, consistent within its walls. Then, I'm among those that would have that there is a Universe, and there are mathematics of it, that tearing down the walls is not to let in the darkness, but the light.
So, if you think you're surrounded by crazy people, you're probably right. So, let us maintain decorum in our interminable discussions on interminability, toward progress, as you and Muckenheim joust each other keep in mind that if you're doctors of mathematics that a certain collegial courtesy is apropos, as it is anyways, know that I find myself quite in control of my faculties and don't so much care what you find of yours or think of mine, and that EF is a compelling construct that stands for its own and in the historical context, particularly as a touchstone in the foundations. I'm for the conscientious, and conscious, mathematician.
EF: it is what it is. EF: CDF, p.d.f.
Infinity: topic of our greatest thinkers. Ad hominem attacks: purview of the playground bully.
Take your ball and go home. Everybody's got one.
So, are you wading in a morass of incompetents, or, alternatively, engaging in the highest levels of mathematical discourse?
Good luck with that.
Then, for your attempt to divert the course from mathematical discussions, and there are hundreds of readers who comtemplate these writings, we return to the notion of _what would be_ the drawing of the line, _what would be_ the uniform distribution of the naturals here in the continuous and discrete, _what would be_ progress in mathematical foundations, and _what it is_.