Galileo's Paradox
in [Math]
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From: Lester Zick on 6 Dec 2006 12:36 On Wed, 6 Dec 2006 00:58:24 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >Tonico wrote: >> Ps Have you, and anyone else, noted how all the anticantorian cranks >> are NEVER mathematicians? > >Kind of hard to survive graduate school if you can't think >mathematically. But apparently rather easy to survive graduate school if you can't define mathematics. ~v~~
From: Lester Zick on 6 Dec 2006 12:37 On Wed, 6 Dec 2006 01:06:15 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >Bob Kolker wrote: >> > >> > Cantor has won his psycho-battle against Kronecker who eventually got >> > ill and gave up when Cantor got admired for his masterly >> > misinterpretation. Kronecker died already in 1891. It was perhaps >> > Cantor's own feeling to be possibly wrong which prompted his mental >> > breakdowns for the first time in 1884 after Cantor believed to have a >> >> Depression is a purely physical/chemical condition. It is all about >> seritonin re-uptake. There is strong evidence that depression is >> hereditary. > >I doubt it is solely hereditary. However, your point that chemistry is >very important to depression is well taken. Two people can have very >different reactions to the same events. And, there are effective >medications for depression. > >> There is no such thing as a mental disease since there is no >> such thing as a mind. However the brain and nervous system, like any >> other subsystem of the physical body is subject to disease and disfunction. > >Analogy: mind is software, brain is hardware. What a brilliant insight. ~v~~
From: Eckard Blumschein on 6 Dec 2006 12:51 On 12/6/2006 5:19 AM, David Marcus wrote: > Eckard Blumschein wrote: >> >> Why do you think that the diagonal argument defines the reals? >> >> You all know that DA2 shows by contradiction that real numbers are >> uncountable. I carefully read how Cantor made sure that the numbers >> under test are real numbers. He did not use Dedekind cuts, nested >> intervals or anything else. > > Well, of course he did't use Dedeking cuts, etc. Cantor explained why he preferred his own definition. Read how he made sure that the numbers under test actually were real numbers. >> He assumed numbers with actually >> indefinitely much rather than many e.g. decimals behind the decimal >> point. Strictly speaking, he did not immediately show that the reals are >> uncountable but that these representation like never ending decimals is >> uncountable. > > That's because anyone who took an analysis course in college (or maybe > even freshman calculus) can prove (starting from the properties of a > complete ordered field) the existence of the decimal representation of > real numbers. Cantor took no analysis course. You are thinking backward. >> Being uncountable is the common property of these numbers under test. >> To my knowledge, sofar nobody was able to show that the numbers >> allegedly defined by Dedekind's cut or nested intervals are uncountable. > > Saying that to your knowledge no one has proved that the set of Dedekind > cuts is uncountable I did not say this. Please quote me carefully. The set of existing Dedekind cuts is finite. The set of feasible cuts is countable. > >> If we need the notion real numbers at all, then in connetion with the >> common property to be uncountable. >> >> You might wondwer that there is no chance to define the reals at will. >> Cantor made a false promise when he said the essence of mathematics just >> resides within its fredom. >> >> Do you still not yet understand why DA2 lets no room as to define the >> reals accordingly? > > Of course I don't understand it! What does "no romm as to define" mean? DA2 only works for actual infinity. >> but I don't see where you got this particular >> >> nonsense from. Did you read it in a book? >> >> I read several original papers by Cantor. The rest is reasoning. > > Well, I guess that explains it. If you want to understand/learn > mathematics, you pretty much have to take courses, read books, and do > the exercises. Kind of arrogant to think you can rediscover centuries of > mathematics on your own. Even Ramanujan read whatever books were > available to him. Be not so lecturing to me. Perhaps you are pretty young. I do my best, and so far my puzzle fits together. I feel myself by far not so arrogant how I consider Cantor who actually ignored many many centuries of science. I just try to revitalize the golden ideas by Archimedes, Aristotele, Galilei, Newton, Spinoza, Leibniz, ..., Gauss, Kronecker, Poincar� and many many others. >
From: Lester Zick on 6 Dec 2006 12:51 On Wed, 06 Dec 2006 06:11:30 -0500, Bob Kolker <nowhere(a)nowhere.com> wrote: >Virgil wrote:> >> EB's arguments give us a plethora of examples of both unfoundedness and >> the uselessness. > >That is why EB should be given the Zick Prize. High praise indeed coming from one who can integrate points into lines, Bob. ~v~~
From: Lester Zick on 6 Dec 2006 12:52
On 5 Dec 2006 17:03:08 -0800, cbrown(a)cbrownsystems.com wrote: > >Lester Zick wrote: >> On 4 Dec 2006 17:57:54 -0800, cbrown(a)cbrownsystems.com wrote: >> >> > >> >Lester Zick wrote: >> >> On 4 Dec 2006 11:29:33 -0800, cbrown(a)cbrownsystems.com wrote: >> >> >> >> > >> >> >Lester Zick wrote: >> >> >> On 3 Dec 2006 11:22:56 -0800, cbrown(a)cbrownsystems.com wrote: >> >> >> > >> >> >Of course it doesn't; "all of mathematics" is an extremely broad range >> >> >of discourse. >> >> >> >> So when mathematikers conflate mathematical ignorance with set >> >> "theory" ignorance they are being extremely overly broad? >> >> >> > >> >Not all of Italian cooking involves sauteeing things in olive oil; >> >however it is somewhat bizzare for someone to claim to be a >> >knowledgeable Italian cook without knowing how to sautee things in >> >olive oil. >> >> Then you undoubtedly qualify as an Italian cook and set mathematiker >> in your spare time. I'm just trying to ascertain the basis for your >> disdain of Italian cooks who don't choose to practice what you preach. >> > >Why do you assume that I disdain cooks (Italian or otherwise) who don't >know how to sautee things in olive oil? I simply think that it's >bizzare to claim to be a knowledgable Italian cook, when one cannot >sautee things in olive oil. I doubt such a person get a job at an >Italian restaurant. But you undoubtedly could. ~v~~ |