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How much science, math, physics theory, posts, books, etc., would come to nothing if one could simply demonstrate that the most correct geometrical ideas were expressed by Euclid. There there is one and only one true geometrical grammar? Compile a list.
This all of course comes with the massive caveat that Euclid's ideas are in fact not the best description we currently have of geometry; that prize goes to Einstein's theory of General Relativity.
Maths can never 'fall down'. Observational evidence may lead to mathematics previously regarded as 'applicable' becoming obsolete in some physical situation or other, but the mathematics itself will remain unassailably correct, and will probably be continued to be studied and developed if it is interesting.
Theoretical physics would be the worst affected area; the main areas I can think of being cosmology, and also the attempts to unify physics into a single theory.
I think all other areas would largely remain unaffected however.
With respects to applied physics, very little indeed would change. I think the only major practical use our understanding of non-Euclidian geometry has been put to so far is satellite technology where accurate times are needed. I think I'm correct in saying that satnavs would not work, though I could be confused with special relativity there.
The Elements are a grammar system, Relativity is not.
Secondly, the Elements are a relatiologic. This means that the difference is a given, and the boundaries are applied. Or one can say that it is the first Grammar of Relativity.
The 'grammar system' of general relativity is differential geometry. It is just as rigorous.
Rhetoric will never change the fact that if you actually try to obtain empirical evidence you will discover that GR is a better model than EG.
Or does your GPS work because there's a little magical man inside with a penchant for map-reading?
One of the outcomes of my solving the delain problem with euclidean geometry and plain algebra, and writing the equations in plain algebra, is that it demonstrates a one to one correspondence between simple arithmetic, euclidean geometry and simple algebra. Now, do you suppose that you can negate the one grammar system, and preserve the other two? Not by language theory. So, there is the empirical evidence. Filling in equations with ad hoc variables is not a grammar system.Quote:
Originally Posted by Xei
I was not the first to parallel euclidean geometry and siimple algebra. Nor did Descartes even come close. I do not use anything he formulated.
I also wrote a lot about how to do exponential manipulation in euclidean geometry, something books on algebra said did not exist.
Therefore, to negate the one, one must negate them all, leaving no math to support your claim.
I have also done a little paper demonstrating the four basic moves of math using euclidean geometry. One figure multiplies and divides, and incorporates a triplicate ratio in the figure, a natural. I did it some time ago, I suppose I should post it on the archive. Just so little time and resources.
However, it has been accepted that if one can demonstrate a grammar closed to the four basic moves in math, then it was complete. However, that is not the reason why, with one modification, Eucldiean Geometry is true, it is true because of something more basic in grammar theory, something non-euclidean geometries are not even aware of.
The Delian problem has been proven is impossible. Trying to actually solve these problems (squaring the circle being the most famous) is a favourite obsession of pseudomathematics.
Simple algebra cannot be equivalent to geometry, geometry is consistent and complete whereas algebra is not.
Stop trying to do maths with words. Maths uses symbols and strict syntax.
The Delian Problem is not impossible. I have solved it. The solution follows from something you learned in Elementary Set Theory. There are two, and only two methods of constructing a set. If you are able to generalize this fact, you find that it is the foundation for not only predication itself, determines primitive predication, but also demonstrates that there are two, and only two groups of geometries. One group is not based on judgment, therefore not true, and only one that is true. I.e. a geometry based on definition. Just what a definition is, has not been taught. But I will give you a leg up.
When it was said that Euclidean Geometry can use only a straight edge and compass, it enumerated the foundation of geometry. However, from what you already know, it should have been defined, such as, a geometric tool provides one and only one difference between two points. Now, you have made the unit the foundation of geometry, and have three tools. You should know what they are. The unit of discourse, the universe of discourse, and every ratio between them.
The figure I present gives everything to use for these three tools, the figure itself does, and the solution to the Delian Problem.
Secondly, you missed a PBS special. Mathematicians themselves admitting that they do not know what is wrong with their understanding of math, that they can write the equations to say whatever they want. I.E. they lost the importance of definition.
There are principles of grammar, logic, math that a very few ancients were exercising in their work, that have been forgotten in history, but which is the key to truth in reasoning. That is the focus of my work, because they lay at the foundation of language itself.
For example, there is no process that is valid in a grammar that results in the violation of that grammars naming convention. Something you find in no book. Another, one can not predicate of a first principle, the why is obvious if you understand predication. Example, one cannot say that space bends. It violates fact and grammar.
I trust you have never read a book on math or logic that even explained naming conventions nor the paradigms they may be based on. Nor seen any regard on how to preserve or maintain it.
It is no idle talk "In the begining was the word."
If you understand the concept that there is no idea, practice, or theory in a grammar system that violates the original naming convention, and realize the naming convention of simple arithmetic, it might dawn on you that the problems in mathematics started very early and that every advancement from simple arithmetic has multiplied the conceptual errors. math has become a patchwork of errors masking errors. Any advancement from simple arithmetic must preserve the original naming convention, and it does not.
The very fact that involved mathematical proceedures often produce not one, but several results which must be further sifted by non-mathematical proceedures just demonstrates how little is the desire for examining the faults in comprehension has been. Perhaps it is just desperation because they don't understand.
lol. Okay, can we move this thread out of the science forum now?Quote:
Originally Posted by Philosopher8659
No, you haven't solved it. The problem has been completed in the sense that it has been proven - an unassailable mathematical proof, not some kind of political debate - impossible. That's a perfectly satisfactory answer.
Please either post your 'proof' or stop talking about it.
Mathematics was never claimed to have a one-to-one correspondence with reality.Quote:
Secondly, you missed a PBS special. Mathematicians themselves admitting that they do not know what is wrong with their understanding of math, that they can write the equations to say whatever they want. I.E. they lost the importance of definition.
There are principles of grammar, logic, math that a very few ancients were exercising in their work, that have been forgotten in history, but which is the key to truth in reasoning. That is the focus of my work, because they lay at the foundation of language itself.
For example, there is no process that is valid in a grammar that results in the violation of that grammars naming convention. Something you find in no book. Another, one can not predicate of a first principle, the why is obvious if you understand predication. Example, one cannot say that space bends. It violates fact and grammar.
I trust you have never read a book on math or logic that even explained naming conventions nor the paradigms they may be based on. Nor seen any regard on how to preserve or maintain it.
It is no idle talk "In the begining was the word."
If you understand the concept that there is no idea, practice, or theory in a grammar system that violates the original naming convention, and realize the naming convention of simple arithmetic, it might dawn on you that the problems in mathematics started very early and that every advancement from simple arithmetic has multiplied the conceptual errors. math has become a patchwork of errors masking errors. Any advancement from simple arithmetic must preserve the original naming convention, and it does not.
The very fact that involved mathematical proceedures often produce not one, but several results which must be further sifted by non-mathematical proceedures just demonstrates how little is the desire for examining the faults in comprehension has been. Perhaps it is just desperation because they don't understand.
Mathematics in its most basic form simply takes a set of facts, and a set of valid inferences, and then deduces further facts.
If those basic facts closely resemble reality in some way then the mathematics you do should also closely resemble reality.
If the basic facts do not resemble reality in any discernible way then neither will the mathematics.
If the basic facts resemble reality to a certain degree then the mathematics will resemble reality to a certain degree.
There is absolutely no problem with this. The process of mathematics can never be incorrect. The only thing that can be incorrect is if you claim certain facts are true of reality when they are not. The only way of discerning said facts is by empirical investigation.
Names mean nothing. Names are only ever an abbreviation, a convenience; they have no bearing on actual truth. As long as you define what exactly you mean by a name, and stick to that definition for as long as you are using it, there can never be a problem. If everybody calls a fox a fox and a badger a badger on weekdays but call a fox a badger and a badger a fox at weekends, the statement 'foxes are smaller than badgers' will be true on weekdays and 'badgers are smaller than foxes' will be true on weekends, and anything you further deduce from these statements will still be correct, and anything you tell other people about foxes and badgers will still be correct. The statement 'foxes are badgers' will never be correct. There is no problem and words have no substance.
It is posted. The Delian Quest. Archive.org. One thing you should notice right away, I did what Descartes could not do, and did it quite naturally--second nature.
Second, language has a function, the manipulation of reality. math is a language. If there is no one to one correspondence with reality, it is gibberish.
math is layered number of grammar systems, all resolving back to simple arithmetic.
A number is a name from an ordered naming convention. The fact that you cannot even manipulate the synonyms name and number speaks a great deal of your conceptual ability. If they mean nothing, so does your conception of math.
And, since every word you use is a name, what in the hell are you molesting your keyboard for?
And please, don't spit Eintein's gibberish back at me, that moron could not even say what truth was. Give me a break.
One will not find any rave reviews on my work, as is to be expected when you make an ass out of the entire intellectual community. Self preservation trumps honesty.
I will grant this, when you can demonstrate to me that evolution is driven by the not real, I will join your side, however, if you can understand that this concession is an oxymoron, there is hope for your and your kind.
What do you mean by gibberish?Quote:
Originally Posted by Philosopher8659
If you look at the history of maths you will find that maths is often developed 'for its own sake' because it has interesting properties, but then later turning out to have useful applications. Differential geometry, for instance. It was originally studied just because it was inherently interesting, but later it was discovered that it corresponds to the real world. But even when it does not, there is nothing 'gibberish' about investigating beautiful structures and patterns. Is art jibberish just because the pictures are not real?
If you had bothered to ruminate over what I had said, you would know the answer to this.Quote:
math is layered number of grammar systems, all resolving back to simple arithmetic.
A number is a name from an ordered naming convention. The fact that you cannot even manipulate the synonyms name and number speaks a great deal of your conceptual ability. If they mean nothing, so does your conception of math.
And, since every word you use is a name, what in the hell are you molesting your keyboard for?
I am not saying words cannot be used. I am saying that words are not objects with inherent existence. The word 'cow' is not something one discovers. There is simply an agreement between English speakers that 'cow' should refer to cows, and this relationship is only established by a posteriori, empirical means (in this case, your parents pointing at examples of cows and saying 'cow').
There is no difference between the word 'cow' and any other word. The word has no independent existence. Only the objects embodied by the words have existence. One could have used any other sound for the word 'cow'. Obviously there are hundreds of other language which do so. One could create a new language identical to English except that 'woc' means cow.
The key point is that languages are constructed, and do not have independent existence. They are simply useful due to a mutual understanding between language speakers what the various things refer to.
As I have said before, with mathematics, we start with some basic facts, and work from there. This is how Euclidean geometry comes about, for example. As mathematics is a posteriori, how on Earth do you propose to 'prove' that it is 'correct'? You can't prove axioms. The mathematics is always 'correct' in the sense that it uses a rigorous formal approach; Euclidean geometry is correct, and so is differential geometry. How could they be incorrect? They are two totally different conceptual structures so it is impossible that one could contradict the other. It is like saying the population of France cannot be 100 million because the population of Germany is 105 million.
The only potential issue one could have is which conceptual structure can best said to be equivalent to the object we call 'space', and the only way of establishing that is by observation, and, unless you really do think that your GPS contains a minuscule magical man inside (do you? You never answered that one), observation tells us that differential geometry is the answer to this question.
You have become incoherent by this point. Einstein was an idiot and you know better? Okay. We're talking about evolution now? Okay. You made an ass out of the intellectual community? Okay, about that:Quote:
And please, don't spit Eintein's gibberish back at me, that moron could not even say what truth was. Give me a break.
One will not find any rave reviews on my work, as is to be expected when you make an ass out of the entire intellectual community. Self preservation trumps honesty.
I will grant this, when you can demonstrate to me that evolution is driven by the not real, I will join your side, however, if you can understand that this concession is an oxymoron, there is hope for your and your kind.
Firstly, I don't have time nor ability to read hundreds of pages of totally incoherent work, so could you please explain to me in brief: by precisely what method did you establish that your construction does indeed allow you to double the cube?
Secondly: what is the flaw in the proof that the Delian problem is insoluble?
Tell mathcad and geometers skechpad that they produce incoherent work. Nice try genius.
At least the college teachers that have seen it were more honest, saying they would need many more math courses to understand it. However, Each work up has two live documents, Sketchpad and Mathcad--both agreeing for every detail.
I work in a factory, ditch the suit and add grease. I live in the real world.
If you really think that then that's the most pitiful act of self-delusion I've ever encountered.
You really think you're the guy in the right here? The guy who's resorted to simply asserting 'I am right' and refusing to answer any questions?
Oh, how pathetic. You asked for proof then dismiss it like a teenage girl. Get a life.
^ Dismissal.Quote:
so could you please explain to me in brief: by precisely what method did you establish that your construction does indeed allow you to double the cube?
It is published. You know where. If you cannot follow it, your problem. you can verify every figure and every equation available by software.
PS, dont get married and then ask someone to sleep with your wife so you know what it is like. That really don't make sense.
If you would have even looked at the figure, you will notice that it does cube roots period. Two at a time, A^2B and AB^2. Which should have been expected.
Oh, this is not my only work, by far. Did you know that I can demonstrate that angular division is also based on an elliptic function? Any number of divisions you want. I can only get to it by the back door, not the front yet. And, if it is true what they say, then squaring the circle follows from an elliptic function.
For a piece of work which took you ten years I find it quite an outstanding performance of doublethink to claim that it isn't worth the time to spend a single minute giving me a brief outline of the proof, especially as any acceptable proof would have such an outline in the first place, and especially as you have a prime opportunity to talk about your hereto ignored work with a not completely untalented mathematician who is listening to you.
How art thou out of breath when thou hast breath to say to me that thou art out of breath? It's taking more time making excuses than if you just answered the bloody question. Deep down you know what you are doing and why you are doing it.
Can you direct me to the final figure which is actually the answer to the problem?
Also, what was your methodology? How did you go about this?
You aptly demonstrate your hearing problem. So, go back to the original post, a what if question, since not even a real demonstration is able to penetrate your keen mind. The appendix has a step by step, the intro shows you that it is from a very primitive geometric figure. Basically it is one of the many square root figures available in geometry. It gives you everything you need to simply draw in the ellipse. The figure itself points to the next geometric tool to use.
And why did you think you were allowed to draw ellipses in the Delian problem?
Apparently you are not even reading the posts. Take a hike. I am not reexplaining what is in the text itself and what has been posted here. You are arguing for the sake of arguing. Be an ass anywhere else you like.Quote:
Originally Posted by Xei
Elementary Set Theory, which is a shadow of The Two-Element Metaphysics. There are two, and only two ways to construct a set. Do the conceptual generalization. There are two, and only two ways to formulate a geometric grammar. Enumerated or Defined. Straight Edge and compass is an enumeration. A geometric tool is that tool which provides one, and only one difference between two points. I.e. straight edge, compass, and ellipse. Hell, one can even find this hint in geometry books written in the 1800's. Start with a definition of unit. I.E. a standard.
There is no non-Euclidean Geometry that starts with a definition of the unit, therefore by basic metaphysics they are not true. I.E. no standard.
Oh, and I failed to mention it. Why do you even think of proof when your notion of what proof is is pointless. What good is a notion of proof when by it you cannot even distinguish which of the many so called geometries are true? What in the hell are you proofing it to other than your imagination? Just what in the hell are you claiming it is true to? You don't even suspect how conceptually sterile you are. You worship so called mathematicians just as pointless--those who fantasize that they rediscovered numbers!
So, since you seem to be a bit slow, like you just woke up or something.
1) The metaphysics of a grammar system said I could.
2) The figure itself said so, by giving everyting needed to simply lay it down.
There are two witnesses. Pun intended.
Did you notice that in order to facilitate some of the work, I had to generalize the Pythagorean Theorem for any triangle. It took me about 1 day to figure it out.
And why have you never questions the foolish rigour in examining euclid, but failing to use even one tenth of that rigour to examine non-euclidean geometries?
Why is it more important to imagine that one is reinventing a grammar, than understanding one to begin with? Ego, self-delusion.
And why are you so upset by me showing you that Eucidean geometry can do what was said it could not? Are delusions really more important than understanding?
Correct, I am an ass. I should take a hike! I'm just arguing for the sake of arguing, after all.
These are your responses to somebody who has only ever asked you legitimate questions about your work. You are intellectually abhorrent.
Just so you can't delude yourself that I'm evading you:
Euclidean geometry does not start with the definition of a unit. It starts with the axioms of Euclidean geometry, none of which say anything about units.Quote:
Originally Posted by Philosopher8659
Strange thing for somebody who wrote a book about a 'proof' to think.Quote:
Oh, and I failed to mention it. Why do you even think of proof when your notion of what proof is is pointless.
Once again you utterly fail to understand anything I've said. Is this because of memory problems, or are you just in denial?Quote:
What good is a notion of proof when by it you cannot even distinguish which of the many so called geometries are true?
Here's what I said to this exact same misunderstanding a few posts ago:
"As I have said before, with mathematics, we start with some basic facts, and work from there. This is how Euclidean geometry comes about, for example. As mathematics is a posteriori, how on Earth do you propose to 'prove' that it is 'correct'? You can't prove axioms. The mathematics is always 'correct' in the sense that it uses a rigorous formal approach; Euclidean geometry is correct, and so is differential geometry. How could they be incorrect? They are two totally different conceptual structures so it is impossible that one could contradict the other. It is like saying the population of France cannot be 100 million because the population of Germany is 105 million.
The only potential issue one could have is which conceptual structure can best said to be equivalent to the object we call 'space', and the only way of establishing that is by observation, and, unless you really do think that your GPS contains a minuscule magical man inside (do you? You never answered that one), observation tells us that differential geometry is the answer to this question."
No I didn't, please either refer me to the page in question or quote your result here so I can check it for you.Quote:
Did you notice that in order to facilitate some of the work, I had to generalize the Pythagorean Theorem for any triangle. It took me about 1 day to figure it out.
This from the guy who just told me,Quote:
And why are you so upset by me showing you that Eucidean geometry can do what was said it could not? Are delusions really more important than understanding?
And why have you never questions the foolish rigour in examining euclid, but failing to use even one tenth of that rigour to examine non-euclidean geometries?
As you're now admonishing me for being rigorous of all things, I think you are qualified to answer your own question.
When you're complaining because somebody is trying to use logic, you know that you failed utterly. I'm not using 'rigour to examine other geometries' right now because this is a thread about your ideas; although naturally when I do study those geometries I expect there to be fully coherent proofs for each and every result used in the course which I would have to learn, as you would know if you had any experience of mathematical education.
Here's an assorted bunch of questions for you, most of which you keep ignoring:
1. How can you establish that a set of a posteriori truths (in this case geometries) are correct without actually investigating reality?
For example, you claim that we live in R^3; three dimensional Euclidean space. As an example of your answer, please explain to me how you could establish that we inhabit R^3 and not R^2 or some other dimension without investigating reality, but rather from a priori principles.
2. Following from the previous point: do you really think there is a tiny magical man inside GPSs? If Euclidean geometry is so perfect, how come when we try and use it we get results that are wrong, whilst when we try to use general relativity we get results that are correct?
3. What is the flaw in the established proof that the Delian problem is impossible?
4. What was your methodology for creating your proof? How did you know you were going in the right direction?
5. How in brief does your proof establish that you have doubled the cube? You directed me to the appendix at one point, but I trawled through that and I found no reference to any kind of method of proof there. The final result is a formula using the symbols N1 to N4, the relevance of which is not stated.
Your not up to par on anything. Sorry. You cannot even correctly abstract the meaning of a common sentence. How old are you anyway?
I was a prodigy for comprehension, I don't think I have diminshed that much with age.
If you want to start with a common understanding, you can abstract the Two-Element Metaphysics from the work of Plato and Aristotle, which Set-Theory is only a shadow, if you can, or you can wait till I have written it up and am satisfied with my work. Choice is yours.
My question is, why has not one developed it? Perhaps reading comprehension? I don't know. However, the Elements, in the title of Euclid's Geometry refered to the Two-Elements, form and material difference. I am astonished when I read that there has been a question as to its meaning.
Synonyms. Absolute, form, boundary, one, unchanging, eturnal, definition, etc.
Material difference, many, relation, changing, corruptible, undefined, etc.
The two elements of any thing are that things form, and that things material difference. As the form determines what is inside, so too its synonym, definition. Restudy Aristotle. He did not get it right, but he did show the way. Plato was much better at it, a great deal better, and demonstrated that the exercises started with Parmenides. There was a small group, a budding idea, preserved enough for someone with intelligence to formalize it, but it never happened. The Elements was the first attempt, with less flaws than any geometry since.
The one and the many, means the absolute and the relative, the form and the material in the form,
General Semantics, the map is not the territory. The boundary is not the bounded. the point (boundary) is that which has no part (material difference).
If you were well versed even in set theory, synonym recognition should be near automatic. And it should have been near automatic response that a theory of relativity, by definition cannot ever be true, the absolute is not the relative. Spinoza wrote intellectual parodies, which Einstein took as legit philosophy, that is how smart he was. If you need a demonstration that logic follows not through the relative, but through the absolute, then you don't even know what A = A means.
One of the ways one can tell if a mind thinks by rote, or processes by definition, is their synonym recognition ability. Aristotle was a synonym freak, and often forgot how he defined one. A good exercise is to do as I did, make a table of his definitions and usages.
Now I have presented you with a document that made an ass out of the Cartesian Coordinate System by paralleling Algebra with figures without it. It contains a generalization of the Pythagorean Theorem covering every triangle, solves the Delian Problem, Points to the correct reconstruction of geometry based on set theory, demonstrates exponential manipulation, which has been claimed not to be exampled geometrically, shown the path to multiplication and division of linear segments straight on, and you, are still whinning.
That says everything. If your mind thinks by rote genetically, no amount of communication can make you advanced enough to think by definition. It is in your psych books. Extrememly high IQ people think by definition, unlike even normal genius. This is why Plato was never understood. You cannot talk someone into being something they are not. However, even you have imagination, so try to get back to the original topic, one more time.
What?Quote:
Originally Posted by Philosopher8659
Common Characteristics of Cranks - Wikipedia
1. Cranks overestimate their own knowledge and ability, and underestimate that of acknowledged experts.
CHECK, HE'S A PRODIGY.
2. Cranks insist that their alleged discoveries are urgently important.
SEMI-CHECK.
3. Cranks rarely, if ever, acknowledge any error, no matter how trivial.
OR JUST IGNORE EVERYTHING, CHECK.
4. Cranks love to talk about their own beliefs, often in inappropriate social situations, but they tend to be bad listeners, and often appear to be uninterested in anyone else's experience or opinions.
CHECK.
5. Seriously misunderstand the mainstream opinion to which they believe that they are objecting.
CHECK.
6. Stress that they have been working out their ideas for many decades, and claim that this fact alone entails that their belief cannot be dismissed as resting upon some simple error.
SEMI-CHECK.
7. Compare themselves with Galileo or Copernicus, implying that the mere unpopularity of some belief is in itself evidence of plausibility.
NO CHECK, BUT EINSTEIN IS AN IDIOT.
8. Claim that their ideas are being suppressed, typically by secret intelligence organizations, mainstream science, powerful business interests, or other groups which, they allege, are terrified by the possibility of their revolutionary insights becoming widely known.
DEFINITELY CHECK.
9. Appear to regard themselves as persons of unique historical importance.
EPIC CHECK.
10. Exhibit a marked lack of technical ability.
UNEQUIVOCAL CHECK.
11. Misunderstand or fail to use standard notation and terminology.
CHECK, CHECK, CHECK.
12. Ignore fine distinctions which are essential to correctly understand mainstream belief.
CHECK.
Ooh, and
13. Some cranks exhibit a lack of academic achievement, in which case they typically assert that academic training in the subject of their crank belief is not only unnecessary for discovering "the truth", but actively harmful because they believe it "poisons" the minds by teaching falsehoods.
CHECK.
Congratulations, you obtained an extremely high score!
Well, that was fun, but let's continue swinging a sledgehammer at that incredible bubble of yours. You really are a fascinating case study.
Well versed in set theory, hmmm...Quote:
Originally Posted by Philosopher8659
Okay. There are 1,000 numbered boxes, each containing a piece of paper with the same number as the box on it. The pieces of paper are taken out, shuffled, and replaced in individual boxes at random. How many ways of there of doing this so that no piece of paper ends up in its original box (e.g. paper 500 back in box 500)?
This can be established very quickly and easily with basic set theory. Have fun!
Yes yes, I'm well aware that having a low IQ allows for a freer mind and hence your incredible genius, well done you.Quote:
Now I have presented you with a document that made an ass out of the Cartesian Coordinate System by paralleling Algebra with figures without it. It contains a generalization of the Pythagorean Theorem covering every triangle, solves the Delian Problem, Points to the correct reconstruction of geometry based on set theory, demonstrates exponential manipulation, which has been claimed not to be exampled geometrically, shown the path to multiplication and division of linear segments straight on, and you, are still whinning.
That says everything. If your mind thinks by rote genetically, no amount of communication can make you advanced enough to think by definition. It is in your psych books. Extrememly high IQ people think by definition, unlike even normal genius. This is why Plato was never understood. You cannot talk someone into being something they are not. However, even you have imagination, so try to get back to the original topic, one more time.
However, I believe the original topic was whether or not Euclidean geometry is correct or not. I'm confused as to why you are telling me to get on topic after an entire post of ad hominems, self-praise, and so-vague-it's-meaningless philosophy, which you could instead have spent addressing the concise set of questions I asked you in the previous post which were directly about your original post. The only answer I can think is that you are unable to answer them, and that your reaction is a basic reaction of self-misdirection so as to doublethink yourself into denial. Brilliant!
1. How can you establish that a set of a posteriori truths (in this case geometries) are correct without actually investigating reality?
For example, you claim that we live in R^3; three dimensional Euclidean space. As an example of your answer, please explain to me how you could establish that we inhabit R^3 and not R^2 or some other dimension without investigating reality, but rather from a priori principles.
2. Following from the previous point: do you really think there is a tiny magical man inside GPSs? If Euclidean geometry is so perfect, how come when we try and use it we get results that are wrong, whilst when we try to use general relativity we get results that are correct?
3. What is the flaw in the established proof that the Delian problem is impossible?
4. What was your methodology for creating your proof? How did you know you were going in the right direction?
5. How in brief does your proof establish that you have doubled the cube? You directed me to the appendix at one point, but I trawled through that and I found no reference to any kind of method of proof there. The final result is a formula using the symbols N1 to N4, the relevance of which is not stated.
6. Where is the proof and final result for your generalisation of the Pythagorean theorem? / state the result here.
7. Precisely what proposition do you think you are disproving when you talk about geometric exponentiation? Precisely what are you claiming to have achieved, and precisely where have you achieved it?
Xei. Point Set Match.
Fucking Christ! That was tedious.
Could you elaborate on that? Specifically, what do you mean by algebra? I'm sure you're aware that R^n is a model of Euclidean geometry and that all Theorems of Euclidean geometry can be derived purely from that relationship. So you must mean something other than what I think you mean. There's also the possibility that you temporarily caught a slight case of stupidity (perfectly understandable given the vast amount of it flying around at high velocities on this thread)Quote:
Originally Posted by Xei
]
Well, it is my understanding that Euclidean geometry is known to be simple enough that it is complete and consistent, whereas Godel's incompleteness theorem applies to arithmetic. I can't really remember what inane point was originally being made here, but I was basically indicating that the two aren't equivalent.
You're right. Tarski formulated it as complete. If you include the ability to measure angles (which I always assumed, not being incredibly interested in it), then it is powerful enough to describe arithmetic and then Godel applies.Quote:
Originally Posted by Xei
Hey I read through the debate between you guys, and I just couldn't
understand what was the argument about. So can someone tell me
what was the "main" topic about? It looks interesting but I just seem not
to understand.
Thanks,
P.S. : If you can direct me to a website to understand theses kind of stuff
that will be grate thanks.