> Even if "God" is defined in such a way to make it meaningful, it becomes a > case of > "OK..Next..."
> RJ Pease
> --- > Outgoing mail is certified Virus Free. > Checked by AVG anti-virus system (http://www.grisoft.com). > Version: 6.0.419 / Virus Database: 235 - Release Date: 11/13/02
Next? Ok. This is what Descarte said: "Accordingly I shall now suppose, NOT that a true God, Who as such must be supremely good and the fountain of truth, but some malignant genius exceedingly powerful and cunning, has devoted all his powers in deceiving me; I shall suppose that the sky, the earth, colors, shape, sound and all external things are illusions and imposters of which this evil genius has availed himself for abuses of my crudility; I shall consider myself as having no eyes, no flesh, no blood, nor any senses, but as falsely opining myself to possess all these things," If God is a mathematician then he (not HE) cannot ceceive you, YOU ARE YOURDELF GOD or at least you can be sure that you possess all you believe you possess.
> > "Lovecraftesque" <Lovecraftes...@yahoo.com> wrote in message > > news:pan.2002.11.22.21.50.59.94395.30884@yahoo.com... > > > Which God would that be? Until you define precisely > > > what you mean by "God", the assertion is pretty meaningless.
> > Even if "God" is defined in such a way to make it meaningful, it becomes a > > case of > > "OK..Next..."
> > RJ Pease
> > --- > > Outgoing mail is certified Virus Free. > > Checked by AVG anti-virus system (http://www.grisoft.com). > > Version: 6.0.419 / Virus Database: 235 - Release Date: 11/13/02 > Next? Ok. This is what Descarte said:
[snip]
> If God is a mathematician then he (not HE) cannot ceceive > you, YOU ARE YOURDELF GOD or at least you can be sure that you > possess all you believe you possess.
Bizarre. There are plenty of people who believe they posess a winning system for roulette or picking horserace winners, but as a matter of verifiable fact they do not. There are plenty of people who believe they possess some sort of eternal life, but they could be wrong. There are plenty of people who believe they possess useful arguments to post on Usenet, but they don't. Etc.
Hey, VG, how come you haven't responded to my detailed reply to your "What is wrong in geometry-part2". And how about giving a specific response to each of my points, rather than your usual all-run-together-at-the-end style?
-- --------------------------- | BBB b \ barbara minus knox at iname stop com | B B aa rrr b | | BBB a a r bbb | | B B a a r b b | | BBB aa a r bbb | -----------------------------
Lovecraftesque wrote: > Which God would that be? Until you define precisely > what you mean by "God", the assertion is pretty meaningless.
Most of the time that people ask other people to "define God" it's a category error. "God" is a proper name; "define God" makes no more sense than "define Abraham Lincoln".
That's why the supposed logical proofs that God exists or does not exist are doomed from the word go. They all necessarily start with some "definition" of God -- how else could you expect to prove either proposition from just logic? But such definitions inevitably change the question being asked, and in a detrimental way. I'm not frankly very interested in whether there is "that than which nothing greater can be imagined"; that could be something purely abstract. If God is an abstraction, that's not *God*, not as I think of God anyway.
Your point is well taken. My question was a very prosaic one though: given the large number of vastly different, antagonistic deities that have been, and many still are, worshipped by different societies, I was just wondering which one of them is the greatest mathematician.
On Sat, 23 Nov 2002 19:25:54 -0800, Mike Oliver wrote: > Lovecraftesque wrote:
>> Which God would that be? Until you define precisely what you mean by >> "God", the assertion is pretty meaningless.
> Most of the time that people ask other people to "define God" it's a > category error. "God" is a proper name; "define God" makes no more > sense than "define Abraham Lincoln".
> That's why the supposed logical proofs that God exists or does not exist > are doomed from the word go. They all necessarily start with some > "definition" of God -- how else could you expect to prove either > proposition from just logic? But such definitions inevitably change the > question being asked, and in a detrimental way. I'm not frankly very > interested in whether there is "that than which nothing greater can be > imagined"; that could be something purely abstract. If God is an > abstraction, that's not *God*, not as I think of God anyway.
s...@sig.below (Barb Knox) wrote in message <news:see-2411021155050001@192.168.1.2>... > In article <38af3945.0211230652.70f4f...@posting.google.com>, > vgopa...@rediffmail.com (V.Gopal) wrote:
> > > Even if "God" is defined in such a way to make it meaningful, it becomes a > > > case of > > > "OK..Next..."
> > > RJ Pease
> > > --- > > > Outgoing mail is certified Virus Free. > > > Checked by AVG anti-virus system (http://www.grisoft.com). > > > Version: 6.0.419 / Virus Database: 235 - Release Date: 11/13/02
> > Next? Ok. This is what Descarte said: > [snip]
> > If God is a mathematician then he (not HE) cannot ceceive > > you, YOU ARE YOURDELF GOD or at least you can be sure that you > > possess all you believe you possess.
> Bizarre. There are plenty of people who believe they posess a winning > system for roulette or picking horserace winners, but as a matter of > verifiable fact they do not. There are plenty of people who believe they > possess some sort of eternal life, but they could be wrong. There are > plenty of people who believe they possess useful arguments to post on > Usenet, but they don't. Etc.
> Hey, VG, how come you haven't responded to my detailed reply to your "What > is wrong in geometry-part2". And how about giving a specific response to > each of my points, rather than your usual all-run-together-at-the-end > style?
Dear BK, In "What is wrong in geometry? part2" Your questions did not pertain to the topic raised by me, they were personal and had nothing to do with mathematical logic. I do not want to answer any question that is not concerned with mathematical logic. Please forgive me. I am not running away, I am eager to answer any question, provided the question is impersonal and relevent to the topic raised by me.
andi babian <abab...@cruzio.com> wrote in message <news:3DDE499D.95076B9A@cruzio.com>... > > Brilliant proof, George. Could you address this one small doubt about > > "2. God is not a human being."? > Cool, a doubt I can remedy! I won't put the argument in numbered > step form, but it goes like this:
> God is all-powerful. > He or she can be whatever he or she wants. > He or she may want to be human if he or she wants. > Thus, though, translation from hypothetical statements to statements > of fact is not a well studied branch of logic theory, we can > add a concluding step that: > God _can_ be the greatest mathematician if he or she wants.
Your counter-argument depends on only one premise (which I will number, only because I'll refer to it later) that:
i. God is all powerful.
That is a reasonable enough premise, I think, if we interpret it correctly.
First of all, we shouldn't interpret it as meaning God can do things that are logically impossible - that eliminates such paradoxes as the question, "Can God create a rock so big that He or She can't lift it?" So we have to add a rider that:
ii. Even an all-powerful being cannot do anything logically impossible.
What we do want to capture is the notion that God can do things that human beings cannot do. So, I think, we need a further premise that:
iii. Human beings are not all-powerful.
That is sufficient to criticize your conclusion, that:
iv. God can be a human being (and thus the greatest mathematician) if God wants to.
There is nothing logically impossible about becoming a human being - indeed, all of us managed it - then God can be a human being. If God became a human being, then He would not be all-powerful (by iii), and if he were not all-powerful, then He would not be God (by the converse of i). In order for Him to be both God and a human being, he would have to be both all-powerful and not all-powerful; and since this last is a logical impossibility, then God cannot (by ii) both become a human being and still be God. For God to become a human being, then (given the premises) would mean for him to cease to be God - forever, since, no longer being all-powerful, he would not be able to change himself back into God at a later time.
So if God became a human being (and thus the greatest mathematician), he would not be God, and "God is the greatest mathematician" would still be false.
> It really does depend on the logical system you wish to accept, > but it can be shown that the proof is in error.
Lovecraftesque <Lovecraftes...@yahoo.com> wrote in message <news:pan.2002.11.24.03.49.49.74638.20312@yahoo.com>... > Your point is well taken. My question was a very prosaic > one though: given the large number of vastly different, antagonistic > deities that have been, and many still are, worshipped by different > societies, I was just wondering which one of them is the greatest > mathematician.
> On Sat, 23 Nov 2002 19:25:54 -0800, Mike Oliver wrote:
> > Lovecraftesque wrote:
> >> Which God would that be? Until you define precisely what you mean by > >> "God", the assertion is pretty meaningless.
> > Most of the time that people ask other people to "define God" it's a > > category error. "God" is a proper name; "define God" makes no more > > sense than "define Abraham Lincoln".
> > That's why the supposed logical proofs that God exists or does not exist > > are doomed from the word go. They all necessarily start with some > > "definition" of God -- how else could you expect to prove either > > proposition from just logic? But such definitions inevitably change the > > question being asked, and in a detrimental way. I'm not frankly very > > interested in whether there is "that than which nothing greater can be > > imagined"; that could be something purely abstract. If God is an > > abstraction, that's not *God*, not as I think of God anyway.
If large number of different deities are worshiped by different societies then it is not His mistake. If one day scientists successfully construct a predictable system or develop a Theory of Everything then we will find that God cannot interfere in the affairs of the world. But Theory of Everything will prove that there can be only one God and one religion. If man imagines different deities then the deities names can only serve as different names or proper nouns of one and the same God. What I mean is man and God are identical in essence, both are mathematicians. The only difference is man cannot create something out of nothing.
V.Gopal wrote: > If large number of different deities are worshiped by different > societies > then it is not His mistake. If one day scientists successfully > construct > a predictable system or develop a Theory of Everything then we will > find > that God cannot interfere in the affairs of the world. But Theory of > Everything will prove that there can be only one God and one religion.
> If large number of different deities are worshiped by different > societies > then it is not His mistake. If one day scientists successfully > construct > a predictable system or develop a Theory of Everything then we will > find > that God cannot interfere in the affairs of the world. But Theory of > Everything will prove that there can be only one God and one religion. > If man imagines different deities then the deities names can only > serve > as different names or proper nouns of one and the same God. What I > mean > is man and God are identical in essence, both are mathematicians. The > only difference is man cannot create something out of nothing.
A TOE can only be a matter of faith. Even if we discover a Theory of Everything through the requirement of logical consistency, it would still be a matter of faith that everything in the universe complies with that theory. For we cannot measure all things and observe all events to confirm that this theory holds everywhere. But if we do find a theory that does seem to explain everything in terms we can understand, then that would only show that things are as we believe they are and according to our faith will it be done - faith being defined as something we understand.
> I believe, and everybody with capacity to think must realize that Zeno, > Euclid, Newton, Einstein and for that matter every individual who > contributed to the advancement of human knowledge was a human being just > like any body - you or me.
> Mathematics has advanced on the basis of logic > of sense of sight - we can find nothing wrong in mathematics as long as > we try to understand it using the logic of sense of sight - judge the > truth and falsity of each mathematical proposition by checking whether > mind and eye reach a total agreement or not. We always find that whatever > we have accepted as true in mathematics, our mind and eyes always reached > total agreement. The act of making our mind and eye reach total agreement > does not always constitute thinking, although in some cases it does. > That part of mathematical logic, which cannot be understood by using the > logic of sense of sight is revealed by geometry. Geometry contains > certain knowledge that is incommunicable. If one tries to expalin it > and in the process if many of our conventional ideas are proved wrong > it is not going to have any effect on progress in technology. This > way nobody brings any disgrace to any individual living or dead. No body > can become the greatest mathematician; only God is the greatest > mathematician
If one believes in God and if one believes that he created the universe, _and_ if one sees the universe as having a mathematical "pattern". Then that might tempt one to the view that God is a mathematician. But, might it not be the case that we see the universe as having a mathematical pattern because we are trying to make sense of something (so far) inexplicable by imposing our order on it; and our order is a man-made mathematical order? That is possible even if there is a God, though I don't believe in Him myself.
> (Premise A) > > I believe, and everybody with capacity to think must realize that Zeno, > > Euclid, Newton, Einstein and for that matter every individual who > > contributed to the advancement of human knowledge was a human being just > > like any body - you or me.
> snip
> > No body > > can become the greatest mathematician; only God is the greatest > > mathematician and any difference between one man to another man is > > negligible, even if you compare Newton and Einstein with Bob or Knox.
> Is God the greatest mathematician?
> 1. By Premise A, every individual who contributed to the advancement > of human knowledge was a human being.
> 2. God is not a human being.
> 3. God has not contributed to the advancement of human knowledge. (1,2 > MT)
This only follows if God is an indivdual. I know too little about theology to know whether God is considered an individual or not.
> 4. The greatest mathematician must necessarily be a great > mathematician.
> 5. All great mathematicians have contributed to the advancement of > human knowledge.
Perhaps not. Perhaps God is the One Exception?
> 6. God is not a great mathematician. (3,5 MT)
> 7. God is not the greatest mathematician.
Going a bit further, and assuming that your argument _is_ valid: the op's Subject and your 7 lead by reductio to the conclusion that at least one premise is false. Perhaps the Trinity requires the denial of your 2?
If our assumptions are incorrect, and mathematics cannot accurately model the universe, perhaps because it is not operate by any set of universal laws, then we will soon find that our observations disagree with the predicted model. Our observations include more than just sight, but every recording of every type of instrument devise from sound to heat to IR and EUV, etc. In attempting to reconcile our mathematical models with our observations of our universe (telescopes can see very far out there), we will find that any universe that refuses to follow any sort of order will introduce inconsistencies into our mathematical models. Mathematics allows for no inconsistencies and requires perfect order/universal laws. If there is no order in the universe, then we MUST ask, "What directs the affairs of the universe?" Something MUST dictate the interactions that we observe. If it is a supreme being, then how does that being come to decide what happens. If every interaction is determined by the decisions of the smallest particles, then how do they decide and how is it that we can observe any consistencies in this world and predict anything? While we find it difficult to predict many things perfectly, we can predict most things with remarkable accuracy. Therefore our observable universe follows laws that are very close to our mathematical models. Note: That we refrain from imposing any specific mathematical model, but instead we allow the universe to describe the model that it follows. Before we ask how that model was chosen (a question reserved for God), we must first know the laws perfectly. God may act in a world of laws just as we also may act. Should we compare His power to act versus ours, an easy analog could be seen with our own power to act versus the cavemen of ancient times. The laws have never changed by our learning them, but our power to act has increased with our understanding of them. So also with God, a being who has such great mastery of the knowledge of the laws (which He Himself ma y have created), that comprehension of His power would require a complete knowledge of His understanding and skills.
"Moufang Loop" <Moufang.L...@btinternet.com> wrote in message
> > I believe, and everybody with capacity to think must realize that Zeno, > > Euclid, Newton, Einstein and for that matter every individual who > > contributed to the advancement of human knowledge was a human being just > > like any body - you or me.
> That's a nice thought! Thank you.
> > Mathematics has advanced on the basis of logic > > of sense of sight - we can find nothing wrong in mathematics as long as > > we try to understand it using the logic of sense of sight - judge the > > truth and falsity of each mathematical proposition by checking whether > > mind and eye reach a total agreement or not. We always find that whatever > > we have accepted as true in mathematics, our mind and eyes always reached > > total agreement. The act of making our mind and eye reach total agreement > > does not always constitute thinking, although in some cases it does. > > That part of mathematical logic, which cannot be understood by using the > > logic of sense of sight is revealed by geometry. Geometry contains > > certain knowledge that is incommunicable. If one tries to expalin it > > and in the process if many of our conventional ideas are proved wrong > > it is not going to have any effect on progress in technology. This > > way nobody brings any disgrace to any individual living or dead. No body > > can become the greatest mathematician; only God is the greatest > > mathematician
> If one believes in God and if one believes that he created the universe, > _and_ if one sees the universe as having a mathematical "pattern". Then > that might tempt one to the view that God is a mathematician. But, > might it not be the case that we see the universe as having a > mathematical pattern because we are trying to make sense of something > (so far) inexplicable by imposing our order on it; and our order is a > man-made mathematical order? That is possible even if there is a God, > though I don't believe in Him myself.
> ML
> > and any difference between one man to another man is > > negligible, even if you compare Newton and Einstein with Bob or Knox.
From below, #5 is wrong and must be restated that: All great mathematicians, of which we have record (or know), have contributed to human knowledge. Neither 6 nor 7 must follow from this revised premise. We do not have record or know of God. Furthermore, "Greatness" does not require the individual(s) to share that greatness. Finally, we cannot prove that he has not shared some of his knowledge with at least many of the great mathematicians or scientists or philosophers by the revelation of ideas into their minds. Interesting that few men give God any credit, but that those who do are often the ones who contribute the most to human knowledge.
"Moufang Loop" <Moufang.L...@btinternet.com> wrote in message
> > (Premise A) > > > I believe, and everybody with capacity to think must realize that Zeno, > > > Euclid, Newton, Einstein and for that matter every individual who > > > contributed to the advancement of human knowledge was a human being just > > > like any body - you or me.
> > snip
> > > No body > > > can become the greatest mathematician; only God is the greatest > > > mathematician and any difference between one man to another man is > > > negligible, even if you compare Newton and Einstein with Bob or Knox.
> > Is God the greatest mathematician?
> > 1. By Premise A, every individual who contributed to the advancement > > of human knowledge was a human being.
> > 2. God is not a human being.
> > 3. God has not contributed to the advancement of human knowledge. (1,2 > > MT)
> This only follows if God is an indivdual. I know too little about > theology to know whether God is considered an individual or not.
> > 4. The greatest mathematician must necessarily be a great > > mathematician.
> > 5. All great mathematicians have contributed to the advancement of > > human knowledge.
> Perhaps not. Perhaps God is the One Exception?
> > 6. God is not a great mathematician. (3,5 MT)
> > 7. God is not the greatest mathematician.
> Going a bit further, and assuming that your argument _is_ valid: the > op's Subject and your 7 lead by reductio to the conclusion that at least > one premise is false. Perhaps the Trinity requires the denial of your > 2?
> > Hey, VG, how come you haven't responded to my detailed reply to your "What > > is wrong in geometry-part2". And how about giving a specific response to > > each of my points, rather than your usual all-run-together-at-the-end > > style?
> Dear BK, In "What is wrong in geometry? part2" > Your questions did not pertain to the topic raised by me, they were > personal and had nothing to do with mathematical logic.
A couple of my questions were personal, so if that's what puts you off I've edited them to eliminate the personal questions. So, VG, please now provide some answers to the several non-personal questions, below.
> I do not want to answer any question that is not concerned with > mathematical logic. Please forgive me.
You will be forgiven if you answer the non-personal questions below.
> I am not running away, I am eager to answer any question, provided > the question is impersonal and relevent to the topic raised by me.
OK, here's your chance to not run away...
In article <38af3945.0211030641.722c8...@posting.google.com>,
vgopa...@rediffmail.com (V.Gopal) wrote: > It seems that the cunning policy: "It is better to be vague and partly > correct than to be precise and completely wrong" is applied > particularly to coordinate geometry form the very beginning.
[personal question snipped]
> It seems > that even among mathematicians there is a difference of opinion on the > following fundamental issues:
Seems to whom? Please cite a *single* bona-fide mathematician (not some Usenet crank) who has the slightest problem with the foundations of co-ordinate geometry.
> (1) Whether a point occupoies space or does not occupy space.
This actually can be a meaningful question in point-set topology. As applied to Euclidean space, a point does NOT occupy space. Do you have a cite of some mathematician who claims that it does?!?
> (2) Does a point specify only 'location' and not a number?
Huh? In co-ordinate geometry, a location IS a tuple of numbers. Do you have an example of the distinction between the two that you are trying to get at?
> (3) Whether each point has to represent the same number > OR a point can represent any number from 0 to infinity,
Since each point IS a tuple of numbers, why ask whether it can be several different tuples? Clearly it can not.
> e.g. any value of TanA.
[personal question snipped]
> (4) Whether a line becomes contiguous/continuous if we > ADD points to a line one AFTER another (assign value of X, then > calculate the value of Y and finally place the point on its > appropriate position) or it requires a different condition.
There is no disagreement among mathematicians about this; it does require "a different condition" in the general case. Clearly, a line with a countable number of point holes in it can be filled in by the procedure you describe. But, as Cantor showed, the number of points in a line segment (such as a gap in your discontinuous line) is vastly greater than the number that can be filled in one-at-a-time.
HTH, really.
-- --------------------------- | BBB b \ barbara minus knox at iname stop com | B B aa rrr b | | BBB a a r bbb | | B B a a r b b | | BBB aa a r bbb | -----------------------------
> > > Brilliant proof, George. Could you address this one small doubt about > > > "2. God is not a human being."?
> > Cool, a doubt I can remedy! I won't put the argument in numbered > > step form, but it goes like this:
> > God is all-powerful. > > He or she can be whatever he or she wants. > > He or she may want to be human if he or she wants. > > Thus, though, translation from hypothetical statements to statements > > of fact is not a well studied branch of logic theory, we can > > add a concluding step that: > > God _can_ be the greatest mathematician if he or she wants.
> Your counter-argument depends on only one premise (which I will > number, only because I'll refer to it later) that:
> i. God is all powerful.
> That is a reasonable enough premise, I think, if we interpret it > correctly.
> First of all, we shouldn't interpret it as meaning God can do things > that are logically impossible - that eliminates such paradoxes as the > question, "Can God create a rock so big that He or She can't lift it?" > So we have to add a rider that:
> ii. Even an all-powerful being cannot do anything logically > impossible.
> What we do want to capture is the notion that God can do things that > human beings cannot do. So, I think, we need a further premise that:
> iii. Human beings are not all-powerful.
> That is sufficient to criticize your conclusion, that:
> iv. God can be a human being (and thus the greatest mathematician) if > God wants to.
> There is nothing logically impossible about becoming a human being - > indeed, all of us managed it - then God can be a human being. If God > became a human being, then He would not be all-powerful (by iii), and > if he were not all-powerful, then He would not be God (by the converse > of i). In order for Him to be both God and a human being, he would > have to be both all-powerful and not all-powerful; and since this last > is a logical impossibility, then God cannot (by ii) both become a > human being and still be God. For God to become a human being, then > (given the premises) would mean for him to cease to be God - forever, > since, no longer being all-powerful, he would not be able to change > himself back into God at a later time.
> So if God became a human being (and thus the greatest mathematician), > he would not be God, and "God is the greatest mathematician" would > still be false.
> > It really does depend on the logical system you wish to accept, > > but it can be shown that the proof is in error.
On Sun, 24 Nov 2002 07:11:18 -0800, V.Gopal wrote: > If large number of different deities are worshiped by different > societies > then it is not His mistake.
So, you answer would be - what? Which of those deities, if any, are talking about?
s...@sig.below (Barb Knox) wrote in message <news:see-2511021228490001@192.168.1.2>... > In article <38af3945.0211232249.7a4ef...@posting.google.com>, > vgopa...@rediffmail.com (V.Gopal) wrote:
> > > Hey, VG, how come you haven't responded to my detailed reply to your "What > > > is wrong in geometry-part2". And how about giving a specific response to > > > each of my points, rather than your usual all-run-together-at-the-end > > > style?
> > Dear BK, In "What is wrong in geometry? part2" > > Your questions did not pertain to the topic raised by me, they were > > personal and had nothing to do with mathematical logic.
> A couple of my questions were personal, so if that's what puts you off > I've edited them to eliminate the personal questions. So, VG, please now > provide some answers to the several non-personal questions, below.
> > I do not want to answer any question that is not concerned with > > mathematical logic. Please forgive me.
> You will be forgiven if you answer the non-personal questions below.
> > I am not running away, I am eager to answer any question, provided > > the question is impersonal and relevent to the topic raised by me.
> OK, here's your chance to not run away...
> In article <38af3945.0211030641.722c8...@posting.google.com>, > vgopa...@rediffmail.com (V.Gopal) wrote:
> > It seems that the cunning policy: "It is better to be vague and partly > > correct than to be precise and completely wrong" is applied > > particularly to coordinate geometry form the very beginning.
> [personal question snipped]
> > It seems > > that even among mathematicians there is a difference of opinion on the > > following fundamental issues:
> Seems to whom? Please cite a *single* bona-fide mathematician (not some > Usenet crank) who has the slightest problem with the foundations of > co-ordinate geometry.
> > (1) Whether a point occupoies space or does not occupy space.
> This actually can be a meaningful question in point-set topology. As > applied to Euclidean space, a point does NOT occupy space. Do you have a > cite of some mathematician who claims that it does?!?
> > (2) Does a point specify only 'location' and not a number?
> Huh? In co-ordinate geometry, a location IS a tuple of numbers. Do you > have an example of the distinction between the two that you are trying to > get at?
> > (3) Whether each point has to represent the same number > > OR a point can represent any number from 0 to infinity,
> Since each point IS a tuple of numbers, why ask whether it can be several > different tuples? Clearly it can not.
> > e.g. any value of TanA.
> [personal question snipped]
> > (4) Whether a line becomes contiguous/continuous if we > > ADD points to a line one AFTER another (assign value of X, then > > calculate the value of Y and finally place the point on its > > appropriate position) or it requires a different condition.
> There is no disagreement among mathematicians about this; it does require > "a different condition" in the general case. Clearly, a line with a > countable number of point holes in it can be filled in by the procedure > you describe. But, as Cantor showed, the number of points in a line > segment (such as a gap in your discontinuous line) is vastly greater than > the number that can be filled in one-at-a-time.
> HTH, really.
My observation, "It seems that the cunning policy ....." is not directed to you or any person; it is a general remark and may not be applicable to you. Any concept that does not occupy even a 'point' cannot indicate location. If a point does not occupy space then location will be forgotten as soon as our attention shifts to the next location. A countable singularity must occupy at least a point. The gentleman who postes the 2nd answer in the thread does accept that a point occupies point and you differ! In geometry a point or a location cannot represent more than one number. Here the number itself is a countable singularity! I do not know the meaning of "tuple of numbers". In any case you cannot associate one point with "tuple of numbers" or any plurality. All the 'points holes' on a line, however small the line may be, can not be filled, for however long you may try (1mm*N/N=1mm here N can be infinite.)In all my postings I found disagreements between mathematicians.
Thank you for finally replying to the substance of my comments, sort of.
It really would help if you interspersed your replies in-line after each comment you're replying to, like most posters manage to do. It would then be clearer when you were actually addressing the issues, and when you weren't. For the sake of clarity, I've moved each of your replies to after the comment being replied to.
> > > > Hey, VG, how come you haven't responded to my detailed reply to your > > > > "Whatis wrong in geometry-part2". And how about giving a specific > > > > response to each of my points, rather than your usual > > > > all-run-together-at-the-end style?
> > > Dear BK, In "What is wrong in geometry? part2" > > > Your questions did not pertain to the topic raised by me, they were > > > personal and had nothing to do with mathematical logic.
> > A couple of my questions were personal, so if that's what puts you off > > I've edited them to eliminate the personal questions. So, VG, please now > > provide some answers to the several non-personal questions, below.
> > > I do not want to answer any question that is not concerned with > > > mathematical logic. Please forgive me.
> > You will be forgiven if you answer the non-personal questions below.
> > > I am not running away, I am eager to answer any question, provided > > > the question is impersonal and relevent to the topic raised by me.
> > OK, here's your chance to not run away...
> > In article <38af3945.0211030641.722c8...@posting.google.com>, > > vgopa...@rediffmail.com (V.Gopal) wrote:
> > > It seems that the cunning policy: "It is better to be vague and partly > > > correct than to be precise and completely wrong" is applied > > > particularly to coordinate geometry form the very beginning.
> My observation, "It seems that the cunning policy ....." is not directed > to you or any person; it is a general remark and may not be applicable > to you.
I didn't take it personally. And even if I had done so I would just have ignored it. It usually doesn't pay to be personally touchy on Usenet.
> > > It seems > > > that even among mathematicians there is a difference of opinion on the > > > following fundamental issues:
> > Seems to whom? Please cite a *single* bona-fide mathematician (not some > > Usenet crank) who has the slightest problem with the foundations of > > co-ordinate geometry.
> > > (1) Whether a point occupoies space or does not occupy space.
> > This actually can be a meaningful question in point-set topology. As > > applied to Euclidean space, a point does NOT occupy space. Do you have a > > cite of some mathematician who claims that it does?!?
> Any concept that does not occupy even a 'point' cannot indicate location.
We agree that in Euclidean co-ordinate geometry a point is defined by its location (the X and Y co-ordinates for 2D). Therefore a point does "occupy" a location in one sense. But it isn't any sort of "exclusive occupancy". That is, a point does not "take up" any space; other points can be arbitrarily close to it.
> If a point does not occupy space then location will be forgotten as soon > as our attention shifts to the next location.
Huh? A co-ordinate pair doesn't change behind my back when I'm not looking at it. And an isolated geometric point would be invisible in any case, since it has zero area (and therefore would have a zero cross-section for reflecting photons). Human perceptual intuitions can be VERY MISLEADING when considering things other than our usual macroscopic physical reality. In particular, visual intuitions can lead one astray when dealing with geometric abstractions that do not exist in the macroscopic world (such as points and lines).
> A countable singularity must occupy at least a point.
Huh? What's a "countable singularity"? What sense of "occupy" are you using?
> The gentleman who postes the 2nd answer > in the thread does accept that a point occupies point and you differ!
Not my problem. Just please answer my objections; if you have replies for other posters then deal with them directly.
> > > (2) Does a point specify only 'location' and not a number?
> > Huh? In co-ordinate geometry, a location IS a tuple of numbers. Do you > > have an example of the distinction between the two that you are trying to > > get at? > In geometry a point or a location cannot represent more than one > number.
Huh? In 2D co-ordinate geometry each distinct point corresponds to a distinct pair of real numbers. So each point represents 2 numbers. In higher dimensions each point represents more than 2 numbers.
> Here the number itself is a countable singularity!
This reads as gibberish. It would help if you tell us what you mean by "countable singularity".
> I do not know the meaning of "tuple of numbers".
Then that would appear to disqualify you from any serious discussion of co-ordinate geometry. Your highly idiosyncratic terminology also indicatea that you haven't really studied the subject. At the risk of asking a personal question, is that indeed the case?
> In any case you cannot > associate one point with "tuple of numbers" or any plurality.
Since you just said you don't know what a "tuple of numbers" is, how can you claim with any certainty that a point cannot be "associated" with one?
Your use of "plurality" at the end seems to imply that you view a point as a "singularity" (which it is in one sense) but a pair of numbers as a "plurality". Well, the fact is that in co-ordinate geometry each 2D point IS DEFINED TO BE a pair (2-tuple) of numbers. If your metaphysics chokes on that elementary fact then a serious re-think on your part seems called for.
> > > (3) Whether each point has to represent the same number > > > OR a point can represent any number from 0 to infinity,
> > Since each point IS a tuple of numbers, why ask whether it can be several > > different tuples? Clearly it can not.
> > > e.g. any value of TanA.
> > [personal question snipped]
> > > (4) Whether a line becomes contiguous/continuous if we > > > ADD points to a line one AFTER another (assign value of X, then > > > calculate the value of Y and finally place the point on its > > > appropriate position) or it requires a different condition.
> > There is no disagreement among mathematicians about this; it does require > > "a different condition" in the general case. Clearly, a line with a > > countable number of point holes in it can be filled in by the procedure > > you describe. But, as Cantor showed, the number of points in a line > > segment (such as a gap in your discontinuous line) is vastly greater than > > the number that can be filled in one-at-a-time.
> All the 'points holes' on a line, however small the line may be, can > not be filled, for however long you may try (1mm*N/N=1mm here > N can be infinite.)
> > HTH, really. > In all my postings I found disagreements between mathematicians.
As requested earlier, please provide A SINGLE CITE from a bona-fide mathematician supporting your views. I specifically asked for cites for your points (1) and (4), and so far you haven't provided any. (I would be very surprised if you had any to provide.)
-- --------------------------- | BBB b \ barbara minus knox at iname stop com | B B aa rrr b | | BBB a a r bbb | | B B a a r b b | | BBB aa a r bbb | -----------------------------
s...@sig.below (Barb Knox) wrote in message <news:see-2811020021080001@192.168.1.2>... > In article <38af3945.0211251004.132f6...@posting.google.com>, > vgopa...@rediffmail.com (V.Gopal) wrote:
> Thank you for finally replying to the substance of my comments, sort of.
> It really would help if you interspersed your replies in-line after each > comment you're replying to, like most posters manage to do. It would then > be clearer when you were actually addressing the issues, and when you > weren't. For the sake of clarity, I've moved each of your replies to > after the comment being replied to.
> > s...@sig.below (Barb Knox) wrote in message > <news:see-2511021228490001@192.168.1.2>... > > > In article <38af3945.0211232249.7a4ef...@posting.google.com>, > > > vgopa...@rediffmail.com (V.Gopal) wrote:
> > > > > Hey, VG, how come you haven't responded to my detailed reply to your > > > > > "Whatis wrong in geometry-part2". And how about giving a specific > > > > > response to each of my points, rather than your usual > > > > > all-run-together-at-the-end style?
> > > > Dear BK, In "What is wrong in geometry? part2" > > > > Your questions did not pertain to the topic raised by me, they were > > > > personal and had nothing to do with mathematical logic.
> > > A couple of my questions were personal, so if that's what puts you off > > > I've edited them to eliminate the personal questions. So, VG, please now > > > provide some answers to the several non-personal questions, below.
> > > > I do not want to answer any question that is not concerned with > > > > mathematical logic. Please forgive me.
> > > You will be forgiven if you answer the non-personal questions below.
> > > > I am not running away, I am eager to answer any question, provided > > > > the question is impersonal and relevent to the topic raised by me.
> > > > It seems that the cunning policy: "It is better to be vague and partly > > > > correct than to be precise and completely wrong" is applied > > > > particularly to coordinate geometry form the very beginning.
> > My observation, "It seems that the cunning policy ....." is not directed > > to you or any person; it is a general remark and may not be applicable > > to you.
> I didn't take it personally. And even if I had done so I would just have > ignored it. It usually doesn't pay to be personally touchy on Usenet.
> > > [personal question snipped]
> > > > It seems > > > > that even among mathematicians there is a difference of opinion on the > > > > following fundamental issues:
> > > Seems to whom? Please cite a *single* bona-fide mathematician (not some > > > Usenet crank) who has the slightest problem with the foundations of > > > co-ordinate geometry.
> > > > (1) Whether a point occupoies space or does not occupy space.
> > > This actually can be a meaningful question in point-set topology. As > > > applied to Euclidean space, a point does NOT occupy space. Do you have a > > > cite of some mathematician who claims that it does?!?
> > Any concept that does not occupy even a 'point' cannot indicate location.
> We agree that in Euclidean co-ordinate geometry a point is defined by its > location (the X and Y co-ordinates for 2D). Therefore a point does > "occupy" a location in one sense. But it isn't any sort of "exclusive > occupancy". That is, a point does not "take up" any space; other points > can be arbitrarily close to it.
> > If a point does not occupy space then location will be forgotten as soon > > as our attention shifts to the next location.
> Huh? A co-ordinate pair doesn't change behind my back when I'm not > looking at it. And an isolated geometric point would be invisible in any > case, since it has zero area (and therefore would have a zero > cross-section for reflecting photons). Human perceptual intuitions can be > VERY MISLEADING when considering things other than our usual macroscopic > physical reality. In particular, visual intuitions can lead one astray > when dealing with geometric abstractions that do not exist in the > macroscopic world (such as points and lines).
> > A countable singularity must occupy at least a point.
> Huh? What's a "countable singularity"? What sense of "occupy" are you using?
> > The gentleman who postes the 2nd answer > > in the thread does accept that a point occupies point and you differ!
> Not my problem. Just please answer my objections; if you have replies for > other posters then deal with them directly.
> > > > (2) Does a point specify only 'location' and not a number?
> > > Huh? In co-ordinate geometry, a location IS a tuple of numbers. Do you > > > have an example of the distinction between the two that you are trying to > > > get at?
> > In geometry a point or a location cannot represent more than one > > number.
> Huh? In 2D co-ordinate geometry each distinct point corresponds to a > distinct pair of real numbers. So each point represents 2 numbers. In > higher dimensions each point represents more than 2 numbers.
> > Here the number itself is a countable singularity!
> This reads as gibberish. It would help if you tell us what you mean by > "countable singularity".
> > I do not know the meaning of "tuple of numbers".
> Then that would appear to disqualify you from any serious discussion of > co-ordinate geometry. Your highly idiosyncratic terminology also > indicatea that you haven't really studied the subject. At the risk of > asking a personal question, is that indeed the case?
> > In any case you cannot > > associate one point with "tuple of numbers" or any plurality.
> Since you just said you don't know what a "tuple of numbers" is, how can > you claim with any certainty that a point cannot be "associated" with one?
> Your use of "plurality" at the end seems to imply that you view a point as > a "singularity" (which it is in one sense) but a pair of numbers as a > "plurality". Well, the fact is that in co-ordinate geometry each 2D point > IS DEFINED TO BE a pair (2-tuple) of numbers. If your metaphysics chokes > on that elementary fact then a serious re-think on your part seems called > for.
> > > > (3) Whether each point has to represent the same number > > > > OR a point can represent any number from 0 to infinity,
> > > Since each point IS a tuple of numbers, why ask whether it can be several > > > different tuples? Clearly it can not.
> > > > e.g. any value of TanA.
> > > [personal question snipped]
> > > > (4) Whether a line becomes contiguous/continuous if we > > > > ADD points to a line one AFTER another (assign value of X, then > > > > calculate the value of Y and finally place the point on its > > > > appropriate position) or it requires a different condition.
> > > There is no disagreement among mathematicians about this; it does require > > > "a different condition" in the general case. Clearly, a line with a > > > countable number of point holes in it can be filled in by the procedure > > > you describe. But, as Cantor showed, the number of points in a line > > > segment (such as a gap in your discontinuous line) is vastly greater than > > > the number that can be filled in one-at-a-time.
> > All the 'points holes' on a line, however small the line may be, can > > not be filled, for however long you may try (1mm*N/N=1mm here > > N can be infinite.)
> > > HTH, really.
> > In all my postings I found disagreements between mathematicians.
> As requested earlier, please provide A SINGLE CITE from a bona-fide > mathematician supporting your views. I specifically asked for cites for > your points (1) and (4), and so far you haven't provided any. (I would be > very surprised if you had any to provide.)
If you talk of 'distinct pair of real number numbers' then each real number is a set and each set (real number) is a countable singularity. Please try to understand, IF YOU CAN, that if one (single) point in Euclidean space is a 'tuple of numbers' then you cannot talk of 'relation' between those two numbers, which obviously means that YOU CANNOT TALK OF ANY "RELATION" BETWEN X AND Y, THEY BECOME INDEPENDENT VARIABLES SIMPLY BECAUSE THEY ARE "TUPLE OF NUMBERS" AT ONE POINT. If geometry is not a subject of relation between X and Y then it the whole of geometry is useless. I think I have to explain it to many of those like you whose mind works like digital and not like the human brain.
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