Galileo's Paradox
in [Math]
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From: David Marcus on 9 Dec 2006 01:55 Virgil wrote: > In article <4579bdf2(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > > > >> When challenged to support his fool theories, TO resorts to nonsense. > > > > > > At least he admitted that his fool theory has no relevance to any of the > > > number systems commonly used in Mathematics. > > > > Of course I did. It depends on some substantially different assumptions. > > When is TO going to come out with that promise axiom system in which his > various assumptions do not trip over each other? And, all the number systems and other stuff that his axiom system leads to and which will be so much more useful than all those boring ones that people have been using for centuries. -- David Marcus
From: Tonico on 9 Dec 2006 05:16 Tony Orlow wrote: > Tonico wrote: > > Tony Orlow ha escrito: > > > >> 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. > > > > ***************************************************** > > Lemme see: troll....yup, it makes me feel better....ah. > > ***************************************************** > > > > Well, that's very nice for you and your diminutive ego.... ******************************************************** "Diminutive ego"...hehe. I supose that was intended to be an offense, but I just can't see why.. ******************************************************* .. .................. >Amazing ammount of nonsenses in such a short paragraph >> Yes, be amazed, and now make sense of it... ****************************************************** Pssst! Perhaps you use to try to "make sense" out of nonsenses. I don't. ****************************************************** > As a matter of fact, even if > > there existed a widely accepted definition of what "reality" is, and > > EVEN if some parts of math doesn't fit in there, that's not reason to > > believe that mathematicians MUST change their rules of games within > > mathematics, and this is one of the toughest parts for some of you to > > understand: who ever told you, you weird, weird creatures, that > > mathematics MUST fit into reality, whatever that is?!? > > When there is a balance between one assumption and another, we are in a > position to justify one or the other. That's logic.... > ********************************************************* "Balance"..."assumption"...what does this have to do with LOGIC? ********************************************************* > > The increidibly dense stupidity of those not willing to see the above > > is what moves me, and perhaps others, to call you, Eckie, Mueck and > > others trolls...and cranks. > > "Incredibly dense stupidity" - I don't suppose you're being at all > prejudgidicial? > ******************************************************** On the contrary: I think I was being too cautious. You people (the crank-trolls bunch) think (figure of speech...) that you can bark your nonsenses about what YOU BELIEVE math SHOULD be... to mathematicians!!, and even accuse, offend and mock those that don't believe the nonsenses you do, and people (and mathematicians) HAVE to respect you and your position?? Common....you've got to be joking. Just read the unbelievably stupid and ranting posts of Eckie talking of fictitious numbers, Cantor and Dedekind's "fantasy", etc. ********************************************************** > > There are some VERY simple definitions in set theory (either naive or > > ZF, AC or not), and some of them are REALLY as simple as one can > > expect: a set is called "infinite" if there exists a bijection (which > > already has been completely and fully WELL defined) between that set > > and at least one of its proper subsets. Period. That is all there is to > > it. > > Cardinality, yes, is simplistic - no argument. Very simplistic... > > > You don't wanna accept this definition? Good, propose > > yours..."potencial infinity", "actual infinity", shminfinity: give us > > DEFINITIONS, axioms to work with...and let's hope that upon checking > > and re-checking, those axioms and definitions aren't shown to be > > inconsistent, which has NOT been proved for ZF, AC or not AC....and > > that they are sufficiently interesting to deal with, of course. > > Okay, a "potential" infinite set is one where each element, like the > naturals, has a specific string associated with it, which has a > left-hand end. *********************************************** Ok, so now you've given a definition of something. Of course, we still have to know what a "string" is in this definition. Let's now hope (or better: YOU hope) this definition is sound and interesting. For me it isn't, but who knows? Perhaps after some mathematical applications are found I will be interested in this. *********************************************** > > I still wonder what is what pisses off so much some trolls about this: > > Eckie's anger against Dedekind in special is laughable, and one of the > > most interesting sides of a crank I've seen in the last years... > > After some time interchanging posts, some of these trolls/crankis begin > > to REALLY believe that they have proved inconsistencies, > > contradictions, etc. Just read some of Eckie's posts to see what a diet > > low in potassium can do to human brain. > > No one here claims any such thing. One can only claim that certain > logical constructions involved are invalid. You can dismiss it as a > nutritive deficiency, but that may be on your own part... ************************************************** "Logical constructions"?? Which ones? You people think that if you throw fancy words then you're ACTUALLY saying something: sad, HUGE mistake. And in order to really show that something in logic is invalid you HAVE TO show it is a contradiction, which is a very well defined term in logic. When have you, or any other crank, proved something even CLOSE to this? To mock and call names to great works of great men is not proof of anything. **************************************************** > > So the above, and very specially the despise and offensive tone many > > idiotic trolls/cranks use to refer to PROFESSIONAL mathematicians just > > because they don't abide by their whims is what makes me call you > > people what you are: trolls/cranks. > > There is nothing wrong with expecting science to satisfy intuition. ***************************************************** And there's nothing wrong with expecting Pittsburgh Steelers to win the Superbowl next year, so what? I won't begin ranting and offending people because they do not share my expectations. You may expect science to satisfy intuition (by the way: whose intuition? Yours, mine, the president's...whose??), but the crank's characteristic is to DEMMAND from all the others to have the same expectation, and this is utterly ridiculous in science. ****************************************************** > > And one last question from me to you: what do you think of my remark, > > some 5-6 days ago, that as far as I know, NONE of the megacranks is a > > mathematician? Don't you wonder about this? I don't doubt there are > > mathematicians that don't like this ir that part in math, but I bet > > they won't troll about it as you people do, and that's a huge > > difference. > > Tonio > > > > > > > > I chose to work within computer science, after having planned to become > a mathematician, for the obvious reasons.... > ****************************************************** I will refrain, making a huge effort, from making an easy joke here about "the obvious reasons" that pushed you to go into computers instead of math.... ****************************************************** > >> 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 > > > > No anwswer? Hmmm. Why does 2's complement work? Can you explain that? I can. > ******************************************************** I don't know what does "Why does 2's complement work?" can possibly mean. I could direct you to my graduate thesis in modular curves and supersingular ones, but I think it'd be a waste of time since you obviously aren't neither interested nor capable to understand it, just like I probably am not capable to understand some computer work you may be doing now. The difference though is that I don't care nor I crank in some computer group about that, and you DO crank and rant nonsenses in a math group without being a mathematician. Tonio ******************************************************* > TonyCo
From: Tony Orlow on 9 Dec 2006 12:42 Tonico wrote: > Tony Orlow wrote: >> Tonico wrote: >>> Tony Orlow ha escrito: >>> >>>> 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. >>> ***************************************************** >>> Lemme see: troll....yup, it makes me feel better....ah. >>> ***************************************************** >>> >> Well, that's very nice for you and your diminutive ego.... > > ******************************************************** > "Diminutive ego"...hehe. I supose that was intended to be an offense, > but I just can't see why.. > ******************************************************* > . .................. >> Amazing ammount of nonsenses in such a short paragraph > >>> Yes, be amazed, and now make sense of it... > > ****************************************************** > Pssst! Perhaps you use to try to "make sense" out of nonsenses. I > don't. > ****************************************************** > >> As a matter of fact, even if >>> there existed a widely accepted definition of what "reality" is, and >>> EVEN if some parts of math doesn't fit in there, that's not reason to >>> believe that mathematicians MUST change their rules of games within >>> mathematics, and this is one of the toughest parts for some of you to >>> understand: who ever told you, you weird, weird creatures, that >>> mathematics MUST fit into reality, whatever that is?!? >> When there is a balance between one assumption and another, we are in a >> position to justify one or the other. That's logic.... >> > ********************************************************* > "Balance"..."assumption"...what does this have to do with LOGIC? > ********************************************************* > Axioms are assumed facts, upon which logical arguments can be built. Not all axioms are mutually compatible. >>> The increidibly dense stupidity of those not willing to see the above >>> is what moves me, and perhaps others, to call you, Eckie, Mueck and >>> others trolls...and cranks. >> "Incredibly dense stupidity" - I don't suppose you're being at all >> prejudgidicial? >> > ******************************************************** > On the contrary: I think I was being too cautious. You people (the > crank-trolls bunch) think (figure of speech...) that you can bark your > nonsenses about what YOU BELIEVE math SHOULD be... to > mathematicians!!, and even accuse, offend and mock those that don't > believe the nonsenses you do, and people (and mathematicians) HAVE to > respect you and your position?? Common....you've got to be joking. Just > read the unbelievably stupid and ranting posts of Eckie talking of > fictitious numbers, Cantor and Dedekind's "fantasy", etc. > ********************************************************** > Sure, sometimes those that go against the norm here enjoy riling things up with such language. It gets Virgil all foaming at the mouth. But, there are serious questions regarding the measure of infinite sets, as Six Letters points out. It's not unreasonable to consider the proper subset as always smaller than the superset, though that is clearly not how cardinality works for infinite sets. So, there is an ongoing attempt in various directions to develop a better theory, or to reject it as an absurdity. I prefer the first route, where IFR and N=S^L grow out of infinite-case induction and provide a means for finely ordering all sorts of infinite sets, countable and uncountable. > > > There are some VERY simple definitions in set theory (either naive > or >>> ZF, AC or not), and some of them are REALLY as simple as one can >>> expect: a set is called "infinite" if there exists a bijection (which >>> already has been completely and fully WELL defined) between that set >>> and at least one of its proper subsets. Period. That is all there is to >>> it. >> Cardinality, yes, is simplistic - no argument. Very simplistic... >> >>> You don't wanna accept this definition? Good, propose >>> yours..."potencial infinity", "actual infinity", shminfinity: give us >>> DEFINITIONS, axioms to work with...and let's hope that upon checking >>> and re-checking, those axioms and definitions aren't shown to be >>> inconsistent, which has NOT been proved for ZF, AC or not AC....and >>> that they are sufficiently interesting to deal with, of course. >> Okay, a "potential" infinite set is one where each element, like the >> naturals, has a specific string associated with it, which has a >> left-hand end. > > *********************************************** > Ok, so now you've given a definition of something. Of course, we still > have to know what a "string" is in this definition. Let's now hope (or > better: YOU hope) this definition is sound and interesting. For me it > isn't, but who knows? Perhaps after some mathematical applications are > found I will be interested in this. > *********************************************** > It means the same thing as "countably infinite", so you probably already know whether you think it's "interesting" or not. >>> I still wonder what is what pisses off so much some trolls about this: >>> Eckie's anger against Dedekind in special is laughable, and one of the >>> most interesting sides of a crank I've seen in the last years... >>> After some time interchanging posts, some of these trolls/crankis begin >>> to REALLY believe that they have proved inconsistencies, >>> contradictions, etc. Just read some of Eckie's posts to see what a diet >>> low in potassium can do to human brain. >> No one here claims any such thing. One can only claim that certain >> logical constructions involved are invalid. You can dismiss it as a >> nutritive deficiency, but that may be on your own part... > > ************************************************** > "Logical constructions"?? Which ones? You people think that if you > throw fancy words then you're ACTUALLY saying something: sad, HUGE > mistake. And in order to really show that something in logic is invalid > you HAVE TO show it is a contradiction, which is a very well defined > term in logic. When have you, or any other crank, proved something even > CLOSE to this? To mock and call names to great works of great men is > not proof of anything. > **************************************************** > "Logical constructions" is fancy words? Mebbe in your neck of the woods.... To my knowledge, no one has detected an internal contradiction within the current form of set theory. That doesn't mean that it provides the conclusions we desire. While the axioms may not be mutually contradictory, they also may not be the best formulation of the problem. The "paradox" that Six Letters points out is a prime example among many. Many feel that the proper subset must be considered smaller, and that any theory in this area should not fail to reflect that. Such a theory is possible. >>> So the above, and very specially the despise and offensive tone many >>> idiotic trolls/cranks use to refer to PROFESSIONAL mathematicians just >>> because they don't abide by their whims is what makes me call you >>> people what you are: trolls/cranks. >> There is nothing wrong with expecting science to satisfy intuition. > > ***************************************************** > And there's nothing wrong with expecting Pittsburgh Steelers to win the > Superbowl next year, so what? I won't begin ranting and offending > people because they do not share my expectations. > You may expect science to satisfy intuition (by the way: whose > intuition? Yours, mine, the president's...whose??), but the crank's > characteristic is to DEMMAND from all the others to have the same > expectation, and this is utterly ridiculous in science. > ****************************************************** > I don't think I've demanded everyone to have the same expectation, but many others besides myself share many of the same concerns, as is evidenced by the ongoing discussions here. I think Eckard's use of the word "fictitious" is a little inflammatory. So what? Cantor's "paradise" is hyperbole too, especially for something that more closely resembles a junk yard. :) >>> And one last question from me to you: what do you think of my remark, >>> some 5-6 days ago, that as far as I know, NONE of the megacranks is a >>> mathematician? Don't you wonder about this? I don't doubt there are >>> mathematicians that don't like this ir that part in math, but I bet >>> they won't troll about it as you people do, and that's a huge >>> difference. >>> Tonio >>> >>> >>> >> I chose to work within computer science, after having planned to become >> a mathematician, for the obvious reasons.... >> > ****************************************************** > I will refrain, making a huge effort, from making an easy joke here > about "the obvious reasons" that pushed you to go into computers > instead of math.... > ****************************************************** > How civilized of you. >>>> 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 >> No anwswer? Hmmm. Why does 2's complement work? Can you explain that? I can. >> > ******************************************************** > I don't know what does "Why does 2's complement work?" can possibly > mean. I could direct you to my graduate thesis in modular curves and > supersingular ones, but I think it'd be a waste of time since you > obviously aren't neither interested nor capable to understand it, just > like I probably am not capable to understand some computer work you may > be doing now. The difference though is that I don't care nor I crank in > some computer group about that, and you DO crank and rant nonsenses in > a math group without being a mathematician. > Tonio > ******************************************************* >> TonyCo > A little science would be no idleness in mathematics, as Han likes to cryptically say. In other words, mathematics could stand a little feedback from those trying to apply it. TO
From: Tony Orlow on 9 Dec 2006 12:51 Virgil wrote: > In article <MPG.1fe4233fd1946032989a0c(a)news.rcn.com>, > David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > >> Tony Orlow wrote: >>> Okay, a "potential" infinite set is one where each element, like the >>> naturals, has a specific string associated with it, which has a >>> left-hand end. >> What do you mean "a specific string associated with it", and what is a >> "left-hand end"? > > If TO means a string having a first character but not a last one, the > set of all such is uncountable, so cannot represent a merely > "potentially infinite" set. I mean a finite string. By a specific string, I mean one which differs from all other strings in the language in at least one position. Countably infinite means potentially infinite.
From: Tony Orlow on 9 Dec 2006 12:56
David Marcus wrote: > Tony Orlow wrote: >> David Marcus wrote: >>> Tony Orlow wrote: > >>>> Isn't the purpose of math be to quantify? >>> No. >> What,in mathematics, has a solution which is neither a real measure, or >> the measure of truth of a statement, 0, 1, or somewhere in between? >> Measure=maths. > > You have a very limited view of what mathematics is. A better > description is, Mathematics is the study of patterns. I believe Saunders > MacLane presented this view in his book "Mathematics, Form and > Function". You might like this book. MacLane believed set theory is not > the best foundation for mathematics. > I have a simplistic view of it. There is measure, the language of measure, and the operations within the language. To me, logic is a form of mathematics where all values lie within the first unit interval. I try to stick to the basics - Occam's Razor, eh? Thanks for the reference, by the way. TOny |