Galileo's Paradox
in [Math]
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From: Bob Kolker on 5 Dec 2006 10:03 Eckard Blumschein wrote: > > According to Spinoza, I refer to infinity like the quality to be neither > enlargeable nor exhaustable. As a teacher of electrical engineering, I > wrote or read this notion oo an estimated 10 000 times. Spinoza's ideas are irrelevent for mathematics and physics. He was a lens grinder and a philosopher. Fortunately for him, he did not give up his day job. Bob Kolker
From: Eckard Blumschein on 5 Dec 2006 10:11 On 12/5/2006 12:03 AM, Virgil wrote: > And how much of Cantor's depressions were brought on, or at least > exacerbated, by Kronecker's relentless persecutions of him? 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 proof of CH. Having already made publich this claim, he realised being wrong. Since then he suffered form alternating depressive and manic phases. Many opponents exacerbated his mental illness. Cantor was also very stirred up in 1904 when Julius Koenig claimed to have disproved well-ordering.
From: Bob Kolker on 5 Dec 2006 10:14 > > 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. 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. Bob Kolker
From: Eckard Blumschein on 5 Dec 2006 10:25 On 12/4/2006 11:57 PM, Virgil wrote: > In article <45744E30.8090207(a)et.uni-magdeburg.de>, > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > >> On 12/1/2006 10:33 PM, Virgil wrote: >> > In article <45706AD1.808(a)et.uni-magdeburg.de>, >> > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: >> >> > You claimed many "imperfectins" but did not justify those claims with >> > anything mathematically valid. >> >> When I performed Fourier transform back and forth for a function >> stepping at t=a, cf. >> http://iesk.et.uni-magdeburg.de/~blumsche/M283.html >> I correctly returned to the original function iff I ignored the >> intermediate value at t=a and decided to extend integration from t<a >> instead. > > That Fourier transforms do not do precisely as you wish they might, does > not constitute an imperfection in the transforms so much as an > imperfection of your understanding of what they can do. > > If you choose to hammer with a wrench, you may not always get the result > a hammer would produce. You did not understand that I am using Fourier transform as an example. I do not criticize FT but the integral tables, and I did not have a problem myself but I recall several reported cases of unexplained error by just the trifle of two. The integral tables suggest using the intermediate value. Experienced mathematicians should indeed know that they must avoid this use. Some tables give the intermedite value for the sake of putative mathematical correctness. Others omit it. As long as one knows the result in advance, there is almost not risk. FT and subsequent IFT may perform an ideal check of set theory. Feel free to suggest a better one. >> >> >> >> I guess, point-set topology and measure >> >> >> theory do not require the claim of set theory to rule all mathematics. >> >> > >> >> > They cannot exist without a foundation of set theory. >> >> >> >> In this case they could not exist. Set theory does not have a solid >> >> basis. So I doubt. >> > >> > There are a lot of textbooks on point-set, and other, topologies and on >> > measure theory. I have yet to see one of them that is not based on set >> > theory. If EB claims these books do not exist, he is even more foolish >> > than usual. >> >> I do not claim this. I just guess that not a single one really needs the >> transfinite numbers and nonsense cardinalities like aleph_2. > > They certainly need the cardinality of the (real) continuum. A continuum is continuous. Uncountable is a sufficient characterization. One has to be pretty miseducated in order to need the fancy aleph_1.
From: Eckard Blumschein on 5 Dec 2006 10:28
On 12/4/2006 11:52 PM, Virgil wrote: >> I am an electrical engineer > > Shocking! Why? We love mathematics. |