Galileo's Paradox
in [Math]
|
From: Eckard Blumschein on 8 Dec 2006 12:37 On 12/7/2006 3:57 PM, David Marcus wrote: > Lots of people have trouble with math. Neither HvH nor I. > That doesn't mean > there is something wrong with mathematics. What is wrong in mathematics? Good question. First of all I see mounting evidence for a lack of evidence which could support some bizarre fancies related to the elusory belief introduced by Dedekind, Cantor, et al. "there must be more reals than rationals because the latter are a subset of the former" Secondly, I got the impression that the praiseworthy intention to get more rigorous led to inappropriate pseudo-basic theories because some basic questions are not yet correctly understood. What about the misleading intermediate values, I see them one more indication for side-effects of incorrect basics. > >> >> >> 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. >> >> > >> >> > You are criticizing integral tables? >> >> >> >> Some of them are rather eclectic and difficult to overlook. Others are a >> >> bit slim. Sometimes the intermediate values are given, sometimes they >> >> are omitted which i consider the better decision. >> > >> > I haven't a clue why you think integral tables have any relevance to set >> > theory. >> >> The intermediate values, given in integral tables "for mathematical >> reasons", are misleading and perhaps unnecessary. > > No idea what "mathematical reasons" these are. Please give a full quote > where the book says what the "mathematical reasons" are. Sorry, I was not given a book where this was to read but it was simply repetitiously said to me. I am already happy if people are ready to utter so frankly what made them sceptical. In this case it is pretty understandable what they meant: A function like y=sign(x) has to have just one value y for every value of x. If I hide my daring smile and ask if |sign(0)|=1 might be correct, than people wonder why I have such a silly idea. >> The "mathematical >> reasons" relate to the somewhat inappropriate arbitrarily distorted >> notion of real numbers adapted to the illusion by Dedekind and Cantor, >> real numbers and infinity are numbers with full civil rights. > > You really should learn to speak concretely. Telling us what they > "relate to" tells us nothing, especially since the rest of your sentence > just contains your usual prejudiced, uninformed rant. My point is: Not just irrational numbers but all real numbers are categorically different from rational numbers. D. & C. declared infinity and the belonging irrational as well as real numbers numbers with "full civil right within the kingdom of numbers". In more scientific words: They denied the categorical difference. This denial was demanded from mathematical practice and it was reasonable to some extent. Kronecker did not understand that. He was correct, in principle, when he declared irrational numbers no numbers at all. More wise views already by Galilei, Spinoza, Leibniz, Gauss, etc. were ignored. I would like to follow Leibniz who considered irrationals as fictions with a fundamentum in re. Do not get me wrong. I never suggestet to numerically operate with really real numbers. As Peirce wrote, they are mere potentialities. They must not have full numerical addresses. Otherwise they are rational numbers. Do not confuse these reals with the reals according to the still mandatory definitions. The latter are strictly speaking rationals with as many decimals as you like. You will perhaps already understand that there is a categorical borderline between the world of numbers and the world of continuum. Really real "numbers" belong to the continuum and have different properties. They are not countable. Mathematicians learned that this means: there is no bijection to the set of naturals. This is correct but it can also be explained quite simply: The continuum is smooth. It does not have outstanding points. Single out of the imagined actually infinite amount of reals do not have any significance. > >> >> >> Experienced mathematicians should indeed know that >> >> >> they must avoid this use. Some tables give the intermedite value for the >> >> >> sake of putative mathematical correctness. >> >> > >> >> > Please give an example. >> >> A gave >> http://iesl.et.uni-magdeburg.de/~blumsche/M283.html > > That link produces a page saying the search didn't produce any results. I see a typo: iesl should read iesk, try again http://iesk.et.uni-magdeburg.de/~blumsche/M283.html The pertaining calculation is easily to find. >> >> I just have my old Bronstein-Semendjajew Teubner 1962 at hand. >> >> On p. 351, number 13 does not give intermediate values, number 15 does. >> > >> > Please quote the entire example. Not everyone is next to a library. >> >> No. 15: Integral from 0 to oo dx over sin x cos x / x = >> = pi/2 for |a|<1 >> = pi/4 for |a|=1 (intermediate value) >> = 0 for |a|>1 > > There is no "a" in int_0^oo sin x cos x / x. > >> No. 13: just over tan(ax)/x > > Huh? Integral ... like 15 but no intermediate value given, perhaps 13 and 15 were quoted from different sources. >> >> >> 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. >> >> > >> >> > What do you mean "ideal check of set theory"? >> >> >> >> Set theory leads to intermediate values. >> > >> > What do you mean? Do try to be specific. >> >> Set theory considers real numbers to be existing numbers, not just >> fictions. > > Nonsense. The words "existing" and "fictions" are your own creation. Christian Betsch got 1,000,000,00 Mark in 1926 for his book fictions in mathematics. Beware of saying nonsense. You will lose me because I conclude that you are not willing to learn from me. Set > theory says nothing of the sort. If you discuss something, you should > have at least some knowledge of it. Be sure, I have, and I found set theory unfounded from the very beginning. > >> From this point of view, one cannot admit that a number may be >> void even if it turns out to be useless and maybe even misleading. > > More made-up words: "void", "useless", "misleading". My command of English does not provide more appropriate words.
From: Virgil on 8 Dec 2006 13:23 In article <457988FD.2060201(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/7/2006 8:05 PM, Virgil wrote: > > In article <457822A4.1000103(a)et.uni-magdeburg.de>, > > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > > > >> On 12/7/2006 1:30 AM, David Marcus wrote: > >> > Eckard Blumschein wrote: > >> >> On 12/6/2006 5:35 AM, David Marcus wrote: > >> >> > Eckard Blumschein wrote: > >> >> > >> >> >> You did not understand that I am using Fourier transform as an > >> >> >> example. > >> >> > > >> >> > Example of what? > >> >> > >> >> a typical mistake when using the immediate value. > >> > > >> > Be specific: what is the mistake? > >> > >> Ask Hendrik van Hees who could not explain a result differing from a > >> printed one just by the factor 2. He uttered this in sci.physics.research > > > > Examples of physcists phucking up are not relevant to mathematics. > > > > > >> Set theory considers real numbers to be existing numbers, not just > >> fictions. From this point of view, one cannot admit that a number may be > >> void even if it turns out to be useless and maybe even misleading. > > > > Examples of physcists phucking up are not relevant to mathematics. > > You meant physicists. HvH is a reputable one. But what phucking stands for? "Phucking up" is idiomatic English for making mistakes.
From: Tony Orlow on 8 Dec 2006 13:33 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. 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 So, Bob, is that to say that depression cannot be caused by major life losses, such as the death of a loved one, the loss of employment, or failure in a major endeavor or challenge? If it can, and we all know it can, then how do these events cause a phsyical/chemical condition? I am not saying that they don't. I am asking you to consider that these physical and chemical changes may have their roots in psychological phenomena, which have to do with love, and the loss thereof. There remains a mind-body connection question. Yes, one can "treat" depression through manipulation of serotonin, dopamine, and (nor)epinephrine levels, either through reuptake inhibition, or release stimulation, or both. One can also treat depression through full-spectrum light therapy, especially when it's seasonal. However, those are all inadequate replacements for the missing element that is the root cause: love. Do you know what treats depression? Knowing that someone actually cares about you. Is that physical? What is your physical explanation for "love", or even a definition? Does love exist? Is it physical? What are the atomic constituents of love? Or, is love simply a poetic illusion devised to turn girls on? And, if the last, how does THAT work, in the world of physics and atoms? Tony Orlow
From: Virgil on 8 Dec 2006 13:41 In article <4579A2D7.2030500(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/7/2006 3:57 PM, David Marcus wrote: > > Lots of people have trouble with math. > > Neither HvH nor I. > > > That doesn't mean > > there is something wrong with mathematics. > > What is wrong in mathematics? > Good question. Nothing! Good answer! > > First of all I see mounting evidence for a lack of evidence which could > support some bizarre fancies related to the elusory belief introduced by > Dedekind, Cantor, et al. "there must be more reals than rationals > because the latter are a subset of the former" That is an extremely convoluted way of saying nothing. If there were evidence of anything wrong, present it. Otherwise quit carping. > > Secondly, I got the impression that the praiseworthy intention to get > more rigorous led to inappropriate pseudo-basic theories because some > basic questions are not yet correctly understood. Impressions of impressions of impressions do not impress. > > What about the misleading intermediate values, I see them one more > indication for side-effects of incorrect basics. What about ephemeral accusations, such as those EB is making. > >> > I haven't a clue why you think integral tables have any relevance to set > >> > theory. > >> > >> The intermediate values, given in integral tables "for mathematical > >> reasons", are misleading and perhaps unnecessary. > > > > No idea what "mathematical reasons" these are. Please give a full quote > > where the book says what the "mathematical reasons" are. > > Sorry, I was not given a book where this was to read but it was simply > repetitiously said to me. I am already happy if people are ready to > utter so frankly what made them sceptical. So that EB is justifying his attack on mathmatics on rumors which he cannot even verify? > > In this case it is pretty understandable what they meant: A function > like y=sign(x) has to have just one value y for every value of x. > If I hide my daring smile and ask if |sign(0)|=1 might be correct, than > people wonder why I have such a silly idea. As a "sign()" function is not standardized across mathematics, one can chose to define one's own in any way one likes, but unless one has some fairly good reasons for one's definition, it is not likely to gain much acceptance.
From: Tony Orlow on 8 Dec 2006 13:45
Tonico wrote: > Tony Orlow ha escrito: > >> Eckard Blumschein wrote: >>> On 12/4/2006 9:56 PM, Bob Kolker wrote: >>>> Eckard Blumschein wrote: >>>> >>>>> 2*oo is not larger than oo. Infinity is not a quantum but a quality. >>>> But aleph-0 is a quantity. >>>> >>>> Bob Kolker >>> >>> To those who belive in the usefulness of that illusion. >>> >>> >> Aleph_0 is a phantom. The aleph_0th natural starting from 1 would be >> aleph_0. It's not a count of the naturals. There is no smallest infinity >> but, sorry to have to tell you, Eckard, a whole spectrum of infinities >> that extend above and below any given infinite expression. Sure, >> transfinitology is quasi-religious. Actual infinity can be quite >> sensible, though. :) >> >> Tony > *********************************************************** > Just like good'ol Mad Journal with Spy vs Spy, but here it is "Troll vs > Troll"...fascinating. > Tonio > You can call me a troll if that makes you feel better. You seem to need to bolster your ego by piling it on top of others. Hopefully you'll work that out eventually. I won't concern myself with your spiritual development too deeply, but I do have some questions. What is your definition of "troll"? From what I understand, in this context, it's someone who just wants to make inflammatory comments which foment argument, someone who evaluates their performance based on the number of responses they get. That's not necessarily an unworthy endeavor, if the area you address is too complacent and needs stirring, but what makes you think that's what I or Eckard are doing? Can you really be so ignorant as to think there aren't major problems with set theory in the transfinite arena, at least intuitively? Surely you must see that defending the conclusions of the theory regresses into defending pure deduction, as having complete priority over the inductive process of establishing the axiomatic rules in the first place? The question we both address and agree on is whether set theories axioms are appropriate or applicable to anything real, when it comes to infinite sets. Eckard is an anti-Cantorian, choosing like WM and others to reject the very notion of an "infinite set" as inconsistent, since "infinite" implies a process, and "set" implies something static, "set in stone". That's not unreasonable, though too conservative for me, and so I look for other ways to formulate "infinite" and "set", so that they can be integrated with "measure". You may find it amusing that those that think for themselves don't agree on everything like those that take their answers from the same history books, and think it proves you are right because you agree more. It's easy to agree, when you don't think for yourself. What was your last discovery? TonyCo |