The Gauss-Bonnet theorem asserts that the integral of the curvature of a (compact, oriented) surface equals 2 pi times its Euler characteristic, giving an extraordinary beautiful and deep formula.
(This is just one instance of what's called an index-theorem, which usually provide über-beautiful, über-general, über-deep formulas, but tend to be, well, less accessible to the masses...)
There is a semi-ugly rendition of Gauss-Bonnet'd formula into a GIF (Wolfram does GIFs...) here.
if you are not personally affected by some action now, it does not mean that you will not be affected later.
True -- but it does not mean that I will be affected later too. So...what now?
Well, it appears that the current administration is spying on citizens without going through the motions of getting a warrant &c. The fact that you personally have not been spyed upon is only circumstancial.
This has not happened in an indefinite later: it has already happened. Moreover, we know this has happened but it is not illogical to assume that other similar things are going on and have gone on in the past.
About your comment on the 4 safe years: as someone else said somewhere on this thread, you are confusing correlation with causation. Since 9/11 there have been no attacks here in Argentina either, and I would be a fool to think that that is because of the measures taken by the USian government, wouldn't I?
Well, yeah, but you haven't given me any proof that there isn't a correlation -- so what do we do now? I think there is, you think there isn't -- it's a matter of opinion.
The correlation is patent; what you mean is that I have not given you proof that there is no causation.
Regardless of that, you seem to think that the effectiveness of policies like the ones implemented (at least, of those policies we have heard about, as we can very reasonably conclude that there are policies that have been implemented but of which we have heard nothing yet) is a matter of opinion. I find that worrying. Indeed, any policy which is not accompanied at its inception by criteria as objective as possible to measure its effectiveness appears suspect in my view.
In a way, every policy works until it fails; for example, the homeland security policies that the US had in place before 9/11 worked pretty well, until they resoundlingly failed. And, notice, your argument about the current policies would have applied to the older policies just as well on the 10th of september.
You are clearly using the word "theological" in a different, significantly more general, sense that the original poster, and I am quite sure you realise this..
I certainly do realize this.
Good;-)
The abstract concept of "2", or of "gravity", or of "abstract concept" have no relation to religion whatsoever.
Actually they all do. 2 is related to the mathematical philosopher Pythagoreas, whose search for perfect numbers was a big time religion in ancient greece (more so the concepts of PI and the theorem that is named after him, but yes, mathematics was once a religion is the point).
The conecept of two and "twoness" was developed way before the pythagorean school. In fact, before the pythagorean school was even formed, the greek language had three numbers: singular, plural and dual, the third one being used when nouns and their accidents have two referrents; by the time the Iliad and the Odyssey were created, this third grammatical number had become less used, and only appears in those works fromtime to time. One can immediately deduce from a widely used language having a dual number, that the people speaking that language had a well developed concept of twoness.
Of course, very many other civilizations developed the concept of "twoness" independently of the greeks.
You are confusing the development of the concepty of two with the ulterior process of mystification of that concept. Yes: the pythagoreans loved to mystify numbers and such, and built a religion of sorts on them. Yet numbers, rectangular triangles, and what not existed as concepts before Pythagoras and his friends.
Let me be a little speculative here: "oneness" and "twoness" are probably among the abstract concepts that are indissolubly linked to intelligence, and it'd be hard to argue that a being with no grasp of those concepts can be described as intelligent.
Gravity was discovered as a part of Newton's philosophical musings about the mind of God. All abstract concepts discovered before 1800 or so are similar;
The fact that he may have stumbled upon the concept of gravity as part of his musings on God does not imply that the concept of gravity is in any way religious or based upon religion. The fact that I find a two dollar bill on my way to church in no way implies that that money is god-goven or based upon god or anything.
it's only after the American Revolution that we got the separation of Church and State, followed quickly by the separation of Church and Science.
Hmm. You might want to brush up your history! The separation of church and state as a concept, as an ideal, and as a implementation (imperfect as all are: look at the current USian implementation for an example...) predates not only the American Revolution, but the discovery of the American continent itself! Google for "magna carta" and/or behold it in its beautiful calligraphy.
The world is larger and older than the USA! Anyone claiming to be a marxist (whatever the variant) should know that;-)
To some more than others, that was a loss, not a gain. A significant sign of this loss is that you did NOT know that mathematics was once a religion. But don't take MY word for it- look it up for yourself.
It is certainly true that mathematics was taken up by quite a few cults, and developed significantly by them, too. Anything can be mystified. You can mistify the rain if you want, and it certainly has been; that does not make the rain religion-based, of religious nature or anything barely similar.
Your "think for yourself, little grasshopper" style fails not to amuse me.
You may want to start reading the news... And speding some time reflecting on the fact that if you are not personally affected by some action now, it does not mean that you will not be affected later.
Btw, you might want to look at history for examples of people who found that their freedoms had beed taken way too late to do anything.
About your comment on the 4 safe years: as someone else said somewhere on this thread, you are confusing correlation with causation. Since 9/11 there have been no attacks here in Argentina either, and I would be a fool to think that that is because of the measures taken by the USian government, wouldn't I?
These savages deserve no consideration and no mercy.
Great.
I know you Bush haters just love to think that everything Bush does is wrong and completely indefensible, but you must also know that there really are people out there who want to kill us all. I for one am glad that (despite their screwups) someone is trying to kill those very people.
You can bitch and whine all you want, but I sleep more comfortably at night knowing that our military machine is actively trying to kill everyone who beheads westerners for the glory of their god.
I very often wonder how well can one sleep when one knows the things being done there and elsewhere (now and before now) are being done in one's name. I very often wonder how much can one really believe that those things are being done in one's name.
I find myself quite lucky not to be an USian. I am responsible for many things done in my name, but the list would be much longer and much deeper if I were an USian.
But I think this is as silly as claiming that the concept of, for instance, multiplication is theological in nature.
It was originally. Theologies are just models for describing what we see.
You are clearly using the word "theological" in a different, significantly more general, sense that the original poster, and I am quite sure you realise this...
I hope so- but something tells me it hasn't. Abstract is the key word here- all abstract concepts have their basis in religious belief.
That is ridiculous.
The abstract concept of "2", or of "gravity", or of "abstract concept" have no relation to religion whatsoever.
The "randomness" could very well be introduced by normal physical means (such as radiation from Sun altering molecules within cell, which we know does happen).
And who set up the universal constants that allow the Sun to radiate? Sorry, all you've done here is move it back up a notch.
The "who set up the universal constants" is a question which is completely irrelevant to science. It belongs to metaphysics, religion or---this is the candidate I'd favor---is essentially nonsensical.
(Most of the proofs of existence of God and/or other similar stuff are based on arguments of infinite regression, like the one you are hinting at. I have failed, since I became aware of those arguments, that they prove not much more than the lack of imagination of the one using them. For example, in your case: why can it not be that universal constants are like they are just because they are? Or maybe because they cannot be otherwise?)
Science is merely interested in the fact that universal constants are as they are.
Introducing an agent assumed to have set the constants at the values they have, introduces in a big melodramatic move more problems than what it solves (it solves exactly zero problems...)
The use of the word "random" merely means that the causative effect is so minute and detailed that without tracking every single particle in the Universe, we can think of it as "random" from our macro point of view.
And thus, requires an intelligent designer who CAN track and influence every particle in the universe- and all we're discovering is his laws for doing so.
I have no idea where you see this requirement come from.
The fact that something is complex by no means whatsoever requires that something else exist which can keep track of its complexity and/or control it.
Now there is the issue of randomness within quantum mechanics, but I assume you are also arguing that our understanding of QM is wildly incorrect also.
Actually, I'm just arguing that human beings are too finite to get anything correct. Ever.
Well, there is no need in arguing that: that is essentially contained in the definitions of the words you are using. No one, absolutely no one, seriously pretends that humans are infinite, or that they can "get" anything 100% correctly, or anything remotely vaguely similar to that.
Indeed, it is not difficult to construe the scientific endeavor as precisely an attempt to do as much as is possible in the face of our finiteness.
Build time is only an issue for developers (and people with lots of time and a passion for watching gcc command lines pass by...), most importantly, usually no one needs to rebuild the whole thing: 99% of the time, you rebuild only the little part you are working on (and, notice, that little part migth have become littler with modularisation). Build time is essentially a non-issue.
It is quite boring to watch this "autotools suck" meme live on. Sure, they can be a pain, but that is usually solved by RTFM; sure they sometimes feel like you need to perform demonic invocations in order to do something, but they sure work, and do so well enough that the very people who maintain a huge beast like X.org are willing to cope with it. Come up with an alternative, good enough that people are willing to commit themselves to using it in real life projects, and then I'll listen with pleasure to your ramblings about how much autotools suck.
Oh, don't worry, it was quite explicit. If one were to read my comment looking for detail, one would see that I did in fact say that you were definitely explicit in calling my argument infantile, and that I did not have to rely on that most greatest of sins on Slashdot, infering someone's meaning from their implicit statements.
Also, perhaps you don't understand that telling someone their argument is childlike is rude, and derogatory. I don't mind you saying that it's ignorant, incorrectly founded, based on false premises, or other such things. These are constructive comments that state that I amm either missing information, or I'm making statements that are not logically based, or that I'm just making shit up.
Telling me that what I'm writing is exactly what a child would write isn't exactly constructive...
I was qualifying an attitude towards authority that I can really describe best by saying it is infantile. I am sorry if you find this derogatory.
Childishness can be grown out of; indeed, it is usually grown out of.
Because you feel a need to force me to go out and obtain a book, rather than using that vastly more mature and adult knowledge to simply assert a reasonably relavent reason to me.
I could do that, I guess. I simply do not have the energy.
One of the things I do is teach math, and I both love doing it and am quite good at it. I have practice explaining elaborate, complex reasoning to people. I know that doing so in writing is orders of magnitude harder and I know I am not very good at that. I believe that a bad explanation can do much more harm than no explanation.
Finally, I am forcing you to do nothing.
I hate this behavior of people. "I don't know how to spell 'eccentric'" "Look it up in the dictionary." "Awesome, thanks for the advice."
I'd tell you to look it up in the dictionary. The spelling of one word is irrelevant, yet knowing how to solve spelling problems is invaluable; my saying "E C C E N T R I C" to you would not solve your problem.
Perhaps I don't have the literary pedigree that you do to make any sort of passible progress attempting to read this book.
I'll try to find some commentary on the book for you. There must be some.
Meanwhile, you can read the prologue to the book's second edition, which was written by Alan Sokal and Jean Bricmont.
As you said, you're not certain if there exists an English translation.
You can get the book in Spanish, if that works better for you. I am quite surprised that it has not been translated into English: the book is quite related to the Sokal affair... (If you do not know what that is, look for "Alan Sokal" in Wikipedia, go to the guys' homepage, &c) USian academia is strange!
Well, do you mind being so kind as to grace us with an summary of an excerpt of the argument to show us that you're not just saying, "Well, there's this book, "EnAjAvUVes, Bej AlGer AlEnDov." and it says everything that I need to support my argument. Oh, by the way, I don't know if they have an English version, so I hope you can speak IoVeb."
Believe me: I know the feeling. If it only were the search for arguments! One of the ways I've tried to deal with this has been learning languages. English is not, as you have probably noticed, my first language.
You have to understand that the statement "6+6=0" in the theorry of Z_12 and the statement of "6+6!=0" in the theory of Z are using the same sign "6" to represent different things. They are conventionally represented with the same sign, by what is called in the jargon an "abus de langague", but they mean different things. It is not that one statement is true in one context and false in the other:
Thanks for using big words... you got me using tautological wrong, and nonetheless misspelling it.
You'll have to forgive me; I dislike using uncommon words, because they cause confusion and result in people misunderstanding you.
I am not a great fan of big words either, except when they mean exactly what I want to say, and, usually, precise, technical ideas are conveyed by big, uncommon words. It could somewhat playfully be argued that the reason behind that is quite simple: the short, common words are all taken by the more unprecise, everyday ideas, in a kind of Huffman encoding;-)
One can certainly avoid the word 'tautology' by paraphrasing, yet that in a way wastes the effort taken by humanity in the last couple of thousands of years to single out that precise idea in a specific term. The first time one comes across the word, as it happens with any other technical term, it looks and sounds a bit awkward. After a little while, though, when one has comprehended its meaning, it becomes a useful abreviation of sorts for a quite complex idea, and that is of undeniable value.
Confusion only arises when one does not know the meaning of a word, and instead of looking it up or asking for its meaning, guesses it wrong.
(You might want to look up the meaning of "nonetheless";-) )
My apologies for my ignorance of the word in question.
Never ever apologize for your not knowing something. You are not supposed to know everything. You are not even supposed to want to learn anything!
That said, I do personally prefer people who do...
I am sorry if it somehow appeared that I was implicitely implying that your stand on this points was somewhat childlike: I intended to be as explicit about it as I could. I firmly believe your attitude towards certain of the subjects we are dealing with, such as on how to deal with specific authority, to be quite of the romantic kind, cavalier if you like the word, and, in ultimate terms, quite childlike. Now, this does not mean, not at all, that I think you are worthless or an idiot or anything: it just plainly means what I said: that I think that some of your views are childlike.
But you'll agree that a scientific paper would look pretty stupid if you didn't put the relavent information into your text, and just said, "and as per This Guy Who Thinks Like Me, you'll see that I'm right." You're providing that the misapplication of Gödel's Theorem here is unjustified, but you don't actually justify your position here.
Actually, in a scientific paper I would simply provide a reference, and assume the reader to be able to go look at it for himself.
You are right that I did not provide a detailed explanation of my position that this was a misapplication of Gödel's theorem (in fact, what I was saying is that there is no possible application of Gödel's theorem: that any attempt at at an application of the theorem outside of its original scope is a misapplication); I did explain, though, why I did not provide such an explanation: I said quite clearly that there are explanations available, and I pointed to one. I do not think there is much I could add to the available explanations, and, in fact, I do not think there is any need to add anything to them in order to deal with the specific equivocal use of Gödel's results in the original poster comment.
I never said that Bouveresse's points should be taken as an article of faith: as whenever I am discussing anything with adults, I assume that references such as the one I made are to be taken critically by others.
Where you are reading "and as per This Guy Who Thinks Like Me, you'll see that I'm right" I say "and per this guy's arguments you'll see that I am right".
More to the matter here, the guy started this whole line of debate with the refusal to appeal to authority. So citation as proof is certainly the most unresponsive response you can make. It's like someone telling one that they would like one to not cuss, and one responds with "Well fuck that."
You are seeing "citation as proof"; as I said above, what this is is "proof by arguments contained in the reference". I am not relying on the authority of the reference but on the solidness of the arguments contained therein. I do not think this is subtle or implied: I think I am being quite explicit.
It's thought-ism. Rather than attempting to understand what the person actually believes, and attempting to help them understand their misapplication of Gödel's Theorem, you're just saying "you're wrong. Read this book if you want to know why." (By all means, if you provided any sort of justification or rationalization for the opinion that he is wrong, then let me know; I can't find it on my own, which may entirely be my fault.)
The argument is contained in Bouveresse's book. I cannot be more explicit about this than this. I will not repeat his arguments. That would be pointless.
On certainly can prove the correctness of arithmetic upon natural numbers (although, correctly applying Gödel's Incompleteness Theorem, you can't prove it simply with arithmetic upon natural numbers. You can though prove it with a higher level, that you need merely prove is consistent.)
You cannot prove consistency (correctness does not make sense in this context) of arithmetic.
But this doesn't mean that you can't prove different sets of different numbers. For instance, arithmetic in Z_12 (clock
Your statement about models is typical. It appears to be deep, but it is just a truism derived from the meanings of the words themselves, providing neither new information nor any insight into anything. What you are saying is that a model models.
It's more than just that. I'm saying that any model devised by a human being models IMPERFECTLY. And always will.
You seem not to understand that a model is by definition not a reproduction of the modelled thing. The IMPERFECTION you so upper-cappily talk about is the very essence of modelling: if the models we build out of reality reproduced reality perfectly they would be of no use because they would simply reproduce reality---this sounds tautological, and, well, it is.
This all-caps IMPERFECTION you seem to regard as negative is precisely the reason those models are useful.
Please oh please, do not mix Gödel into anything but formal logic. Gödel's theorem does not apply to anything but the formal theories it applies to, and in particular, it does not apply to anything even remotely related to "real life". Of course, there are no extensions of none of Gödel's theorems that apply to anything related to "real life" either.
So you say. And I believe that within your worldview it is correct.
The line of thought you pretend to follow always ends up in this kind of dismissive remark.
In any case, I could explain in detail why anything related to Gödel's work on the incompleteness of formal systems strong enough to contain arithmetic does not appply no anything but formal systems strong enough to contain arithmetic. I do not see the point, though: in the first place, there are already great expositions of this precise same point available, much better than anything I could cram into this textentry thingy for you to go read, and, second, you'd react with (some variant of) this "I believe that within your worldview it is correct" line. Forgive me if I care not that as much about you as would be needed to justify my forgetting these two points.
Mentioning Gödel is very "post-". It also usually signals the mind it is a good time to start thinking about dinner, because the speaker has no idea what he is talking about and it is not worth devoting neuron cycles to him. Unless, of course, you are discussing formal logic.
Actually, I'm discussing the basic flaw of human thinking modeling systems- of which formal logic is one such system.
This is plainly idiotic. What would be an alternative: thinking about systems in their full blown complexity without having recourse to simplifying assumptions and aproximating abstractions? Of course if you are going to make simplifying assumptions and aproximating abstractions, you better remember you are doing that: otherwise you'll soon enough be very, very wrong. But in any case, the only "flaw of human thinking" in sight in this context is the carelessness of some people that tend to forget about the assumptions and abstractions they have made.
There is an endearing discussion by Jacques Bouveresse, a philosoher who knows his logic, in his book "Prodiges et vertiges de l'analogie", of the Gödel-citing madness... I do not know if the book is available in English, though.
And I'm sure within his worldview, limiting Godel to formal logic makes sense as well- but his worldview is no better than any other religion.
Here it is, again: you must reach this point in which you essentially say "everything goes" in a complicated, fancy-if-you-are-in-the-60's way very, very often in your discourse...
That thing you are "battling" against is simply sillyness. And, much as fire is well-known to be a bad weapon against fire, sillyness does not fight
1. I don't imagine he's attempting to be deep, or informative. In except maybe that he just wants you to think.
"He just wants you to think" is a standard line to justify nonsensical babbling, when it is no longer possible to put forward arguments based on usefulness or infomativeness or even logical consistency. From koans to most of Lacan's seminaires.
2. Dude... don't point to another source in your debates with this guy. He doesn't care about what the authorities think... he cares what YOU think. Pulling out some form response to him only expresses his notion that people appeal far too greatly upon authoritarian figures instead of actually think for themselves.
Making reference to someone's work and ideas is by all means different from saying "go read this and believe every single word with absolute faith", and confusing the two is to be expected at most from a teenager. Reasonable adults, on the other hand, recognize that refering to other people's work is valuable, and acknowledge that complete acceptance of an author's thoughts is not the only option when dealing with them.
You read this book "Prodiges et vertiges de l'analogie", if you understood it, then apply it... don't point him to it and say "all your answers are here." Otherwise you're showing no intelligent thought, just regurgitated citation.
This is infantile. I never said anything remotely similar to "all your answers are here": I merely pointed to that book as a nicely detailed analysis of the complete mess people who do not understand formal logic and its scope make of things like Gödel's theorem, or, rather, of themselves, as Gödel's theorem is not messable with. Bouveresse has taken the time to understand the logic behind Gödel's results, and has taken the time (and the infinite patience, I might add) to go through some of the best-known and sadly very well-respected idiocy out there involving those results and its "applications to real life". It is infantile to think that his work is of no use to others, that the mere act of reading it and/or quoting it implies complete acceptance of his conclusions, that taking advantage of what he's already done is nothing more that "regurgitated citation"; indeed, all this goes against of thousands of years of history showing that it is false.
Moreover, your retorting "regurgitated citation" at me shows a rather insulting assumption on your part about me.
The GP was also not citing Gödel (since you put the Umlauts in I'll bother to also.), he was saying that in many ways it's LIKE Goedel's Incompleteness Theorem.
Well, Bouveresse's book is precisely about analogies involving Gödel's theorems. I'll not repeat his arguments; I am a scientist and firmly take part of the scientific tradition of acknowledging that others have done things of value.
3. You know, I thought at first the guy was full of it, too, but he's not. He's actually thinking, which is more than I can say for you. He's considered and constructed his own ideas, rather than relying on others to tell him what to think. Likely, he read about Gödel's incompleteness theorem, and thought that it sounded similar. But by no means was his authoritarian source of inspiration.
I have no idea what you mean by "authoritatian" source of insipiration.
He's not battling sillyness with sillyness, he's making an honest attempt to make people consider that hey, this fact we all "know" can't really be definitively proven (which it can't). So if everything is just as provable as anything else, then what good is it to say anything is "true" or "false."
That what we know cannot be definitely proven might need some publicity, I imagine; but that has been dealt with since the begining of time. His posture includes many other things which are not contain
Your statement about models is typical. It appears to be deep, but it is just a truism derived from the meanings of the words themselves, providing neither new information nor any insight into anything. What you are saying is that a model models.
Please oh please, do not mix Gödel into anything but formal logic. Gödel's theorem does not apply to anything but the formal theories it applies to, and in particular, it does not apply to anything even remotely related to "real life". Of course, there are no extensions of none of Gödel's theorems that apply to anything related to "real life" either.
Mentioning Gödel is very "post-". It also usually signals the mind it is a good time to start thinking about dinner, because the speaker has no idea what he is talking about and it is not worth devoting neuron cycles to him. Unless, of course, you are discussing formal logic.
There is an endearing discussion by Jacques Bouveresse, a philosoher who knows his logic, in his book "Prodiges et vertiges de l'analogie", of the Gödel-citing madness... I do not know if the book is available in English, though.
That thing you are "battling" against is simply sillyness. And, much as fire is well-known to be a bad weapon against fire, sillyness does not fight sillyness with any effectiveness at all. Throwing words like "axiom" and "Gödel" around is not much more than an attemt at doing precisely that---well, that, or an misguided attemt at tryingto gain others' respect by sounding deep.
Solipsism is not a steping astone on any journey towards anything: it is just another form of sillyness; a logically sound one, surely, but an useless one in so far as it as it precludes everything else, and a solipsist can be nothing but that.
I probably could but I find no will in me to respond to your (or anyone's, for that matter) variation of sollipsism du jour---which is actually of another jour, in fact. I used to find doing that kind of thing interesting when I was in my early teenager years---I'll candidly admit that---but it lost all of its attraction sometime while I was progressing into adulthood.
Yet: if any given situation it turns out that 1+3=1, well, then the "1" and the "3" and the "+" and the "0" that you are using in that situation are different from the ones that appear in the "usual" "1+3=4". There is absolutely no contradiction with any of these "axioms" you keep bringing up. You are talking about two "1"s, two "3", two, "+", &c, and your problem comes from that.
Now, that is a very boring fallacy... I imagine this is mostly due to the amazing frequency with which one comes across it: there are whole "theories" build upon an equivocation such as yours; a lot of them tend to like the prefix "post-" in their name, but they by no means exhaust the list.
What I had in mind is that the tax system is not out of control: it is being controlled in a very precise way. That precise way is motivated not by the national debt; that the results of taxation are being used to pay the national debt is completely irrelevant.
You must be a teacher or very young. Our literacy and educated rates have fallen as the public education system has grown.
This causality you are trying to show here is patently false.
It is a trivially verifiably fact that public education has been the major reason for the rise of literacy and education not only in the US but all over the world. One way to reach your false conclusion, though, is to disregard what happened in this world before, say, a few decades ago: but if you consider history in its entirety, you'll immediately see that public school is the one reason people read and write.
Now, it is true that literacy rates have fallen, in the US and elsewhere (though to various levels of depths in different places): and this has happened most noticeably in the public schools (but by absolutely no means only there). But "public school" is not constant in time: it changes; policy makers can alter what "public school" is and how it works and how much it succeeds. If you look diacronically at public school, you'll not fail to notice that there is a very strong correlation between the policies that have been implemented and the results we are observing.
Literacy levels have falled due to the policies implemented on the public schools. That much is true. Yet this tells us not much about public schools, but does tell a lot about the policies! If you study what's been done to public schools in the US and elsewhere, you can't help noticing that most opf the policies are quite obviously designed to impede any success.
There is a pattern here. In most of latin american countries, in Europe, and elsewhere, public companies have been in the past managed in what cannot be described as anything but a crash course towards utter failure, thus creating the consensus that this is intrinsic to these companies being public, then privatised. If you look around, you'll rapidly notice that things are not much better now.
There is absolutely nothing innocent in the design of "crash course" policies...
The fact is, that is not so. There may be private schools that value teachers considerably much more that public schools and pay them accordingly, but that is essentially exceptional. The compensation given to public school teachers is a reflection of the value society assigns to teachers. Last time I've checked, private schools are very much included in society.
Most of the deficit of the US is due to the state of the taxation system, which has of late decided to basically stop taxing the rich. You got it completely backwards.
Slashdot Mirror
Ouch.
The Gauss-Bonnet theorem asserts that the integral of the curvature of a (compact, oriented) surface equals 2 pi times its Euler characteristic, giving an extraordinary beautiful and deep formula.
(This is just one instance of what's called an index-theorem, which usually provide über-beautiful, über-general, über-deep formulas, but tend to be, well, less accessible to the masses...)
There is a semi-ugly rendition of Gauss-Bonnet'd formula into a GIF (Wolfram does GIFs...) here.
Well, it appears that the current administration is spying on citizens without going through the motions of getting a warrant &c. The fact that you personally have not been spyed upon is only circumstancial.
This has not happened in an indefinite later: it has already happened. Moreover, we know this has happened but it is not illogical to assume that other similar things are going on and have gone on in the past.
The correlation is patent; what you mean is that I have not given you proof that there is no causation.
Regardless of that, you seem to think that the effectiveness of policies like the ones implemented (at least, of those policies we have heard about, as we can very reasonably conclude that there are policies that have been implemented but of which we have heard nothing yet) is a matter of opinion. I find that worrying. Indeed, any policy which is not accompanied at its inception by criteria as objective as possible to measure its effectiveness appears suspect in my view.
In a way, every policy works until it fails; for example, the homeland security policies that the US had in place before 9/11 worked pretty well, until they resoundlingly failed. And, notice, your argument about the current policies would have applied to the older policies just as well on the 10th of september.
Good ;-)
The conecept of two and "twoness" was developed way before the pythagorean school. In fact, before the pythagorean school was even formed, the greek language had three numbers: singular, plural and dual, the third one being used when nouns and their accidents have two referrents; by the time the Iliad and the Odyssey were created, this third grammatical number had become less used, and only appears in those works fromtime to time. One can immediately deduce from a widely used language having a dual number, that the people speaking that language had a well developed concept of twoness.
Of course, very many other civilizations developed the concept of "twoness" independently of the greeks.
You are confusing the development of the concepty of two with the ulterior process of mystification of that concept. Yes: the pythagoreans loved to mystify numbers and such, and built a religion of sorts on them. Yet numbers, rectangular triangles, and what not existed as concepts before Pythagoras and his friends.
Let me be a little speculative here: "oneness" and "twoness" are probably among the abstract concepts that are indissolubly linked to intelligence, and it'd be hard to argue that a being with no grasp of those concepts can be described as intelligent.
The fact that he may have stumbled upon the concept of gravity as part of his musings on God does not imply that the concept of gravity is in any way religious or based upon religion. The fact that I find a two dollar bill on my way to church in no way implies that that money is god-goven or based upon god or anything.
Hmm. You might want to brush up your history! The separation of church and state as a concept, as an ideal, and as a implementation (imperfect as all are: look at the current USian implementation for an example...) predates not only the American Revolution, but the discovery of the American continent itself! Google for "magna carta" and/or behold it in its beautiful calligraphy.
The world is larger and older than the USA! Anyone claiming to be a marxist (whatever the variant) should know that ;-)
It is certainly true that mathematics was taken up by quite a few cults, and developed significantly by them, too. Anything can be mystified. You can mistify the rain if you want, and it certainly has been; that does not make the rain religion-based, of religious nature or anything barely similar.
Your "think for yourself, little grasshopper" style fails not to amuse me.
You may want to start reading the news... And speding some time reflecting on the fact that if you are not personally affected by some action now, it does not mean that you will not be affected later.
Btw, you might want to look at history for examples of people who found that their freedoms had beed taken way too late to do anything.
About your comment on the 4 safe years: as someone else said somewhere on this thread, you are confusing correlation with causation. Since 9/11 there have been no attacks here in Argentina either, and I would be a fool to think that that is because of the measures taken by the USian government, wouldn't I?
Great.
I very often wonder how well can one sleep when one knows the things being done there and elsewhere (now and before now) are being done in one's name. I very often wonder how much can one really believe that those things are being done in one's name.
I find myself quite lucky not to be an USian. I am responsible for many things done in my name, but the list would be much longer and much deeper if I were an USian.
And, sure, this is "war"...
Give me a break.
You are clearly using the word "theological" in a different, significantly more general, sense that the original poster, and I am quite sure you realise this...
That is ridiculous.
The abstract concept of "2", or of "gravity", or of "abstract concept" have no relation to religion whatsoever.
The "who set up the universal constants" is a question which is completely irrelevant to science. It belongs to metaphysics, religion or---this is the candidate I'd favor---is essentially nonsensical.
(Most of the proofs of existence of God and/or other similar stuff are based on arguments of infinite regression, like the one you are hinting at. I have failed, since I became aware of those arguments, that they prove not much more than the lack of imagination of the one using them. For example, in your case: why can it not be that universal constants are like they are just because they are? Or maybe because they cannot be otherwise?)
Science is merely interested in the fact that universal constants are as they are.
Introducing an agent assumed to have set the constants at the values they have, introduces in a big melodramatic move more problems than what it solves (it solves exactly zero problems...)
I have no idea where you see this requirement come from.
The fact that something is complex by no means whatsoever requires that something else exist which can keep track of its complexity and/or control it.
Well, there is no need in arguing that: that is essentially contained in the definitions of the words you are using. No one, absolutely no one, seriously pretends that humans are infinite, or that they can "get" anything 100% correctly, or anything remotely vaguely similar to that.
Indeed, it is not difficult to construe the scientific endeavor as precisely an attempt to do as much as is possible in the face of our finiteness.
It is quite sad, then, that such an important piece of software is in the hands of idiots, I guess, no?
Build time is only an issue for developers (and people with lots of time and a passion for watching gcc command lines pass by...), most importantly, usually no one needs to rebuild the whole thing: 99% of the time, you rebuild only the little part you are working on (and, notice, that little part migth have become littler with modularisation). Build time is essentially a non-issue.
It is quite boring to watch this "autotools suck" meme live on. Sure, they can be a pain, but that is usually solved by RTFM; sure they sometimes feel like you need to perform demonic invocations in order to do something, but they sure work, and do so well enough that the very people who maintain a huge beast like X.org are willing to cope with it. Come up with an alternative, good enough that people are willing to commit themselves to using it in real life projects, and then I'll listen with pleasure to your ramblings about how much autotools suck.
And, pray, build time is a metric for exactly what?
I was qualifying an attitude towards authority that I can really describe best by saying it is infantile. I am sorry if you find this derogatory.
Childishness can be grown out of; indeed, it is usually grown out of.
I could do that, I guess. I simply do not have the energy.
One of the things I do is teach math, and I both love doing it and am quite good at it. I have practice explaining elaborate, complex reasoning to people. I know that doing so in writing is orders of magnitude harder and I know I am not very good at that. I believe that a bad explanation can do much more harm than no explanation.
Finally, I am forcing you to do nothing.
I'd tell you to look it up in the dictionary. The spelling of one word is irrelevant, yet knowing how to solve spelling problems is invaluable; my saying "E C C E N T R I C" to you would not solve your problem.
I'll try to find some commentary on the book for you. There must be some.
Meanwhile, you can read the prologue to the book's second edition, which was written by Alan Sokal and Jean Bricmont.
You can get the book in Spanish, if that works better for you. I am quite surprised that it has not been translated into English: the book is quite related to the Sokal affair... (If you do not know what that is, look for "Alan Sokal" in Wikipedia, go to the guys' homepage, &c) USian academia is strange!
Believe me: I know the feeling. If it only were the search for arguments! One of the ways I've tried to deal with this has been learning languages. English is not, as you have probably noticed, my first language.
I am not a great fan of big words either, except when they mean exactly what I want to say, and, usually, precise, technical ideas are conveyed by big, uncommon words. It could somewhat playfully be argued that the reason behind that is quite simple: the short, common words are all taken by the more unprecise, everyday ideas, in a kind of Huffman encoding ;-)
One can certainly avoid the word 'tautology' by paraphrasing, yet that in a way wastes the effort taken by humanity in the last couple of thousands of years to single out that precise idea in a specific term. The first time one comes across the word, as it happens with any other technical term, it looks and sounds a bit awkward. After a little while, though, when one has comprehended its meaning, it becomes a useful abreviation of sorts for a quite complex idea, and that is of undeniable value.
Confusion only arises when one does not know the meaning of a word, and instead of looking it up or asking for its meaning, guesses it wrong.
(You might want to look up the meaning of "nonetheless" ;-) )
Never ever apologize for your not knowing something. You are not supposed to know everything. You are not even supposed to want to learn anything!
That said, I do personally prefer people who do...
I am sorry if it somehow appeared that I was implicitely implying that your stand on this points was somewhat childlike: I intended to be as explicit about it as I could. I firmly believe your attitude towards certain of the subjects we are dealing with, such as on how to deal with specific authority, to be quite of the romantic kind, cavalier if you like the word, and, in ultimate terms, quite childlike. Now, this does not mean, not at all, that I think you are worthless or an idiot or anything: it just plainly means what I said: that I think that some of your views are childlike.
Actually, in a scientific paper I would simply provide a reference, and assume the reader to be able to go look at it for himself.
You are right that I did not provide a detailed explanation of my position that this was a misapplication of Gödel's theorem (in fact, what I was saying is that there is no possible application of Gödel's theorem: that any attempt at at an application of the theorem outside of its original scope is a misapplication); I did explain, though, why I did not provide such an explanation: I said quite clearly that there are explanations available, and I pointed to one. I do not think there is much I could add to the available explanations, and, in fact, I do not think there is any need to add anything to them in order to deal with the specific equivocal use of Gödel's results in the original poster comment.
I never said that Bouveresse's points should be taken as an article of faith: as whenever I am discussing anything with adults, I assume that references such as the one I made are to be taken critically by others.
Where you are reading "and as per This Guy Who Thinks Like Me, you'll see that I'm right" I say "and per this guy's arguments you'll see that I am right".
You are seeing "citation as proof"; as I said above, what this is is "proof by arguments contained in the reference". I am not relying on the authority of the reference but on the solidness of the arguments contained therein. I do not think this is subtle or implied: I think I am being quite explicit.
The argument is contained in Bouveresse's book. I cannot be more explicit about this than this. I will not repeat his arguments. That would be pointless.
You cannot prove consistency (correctness does not make sense in this context) of arithmetic.
You seem not to understand that a model is by definition not a reproduction of the modelled thing. The IMPERFECTION you so upper-cappily talk about is the very essence of modelling: if the models we build out of reality reproduced reality perfectly they would be of no use because they would simply reproduce reality---this sounds tautological, and, well, it is.
This all-caps IMPERFECTION you seem to regard as negative is precisely the reason those models are useful.
The line of thought you pretend to follow always ends up in this kind of dismissive remark.
In any case, I could explain in detail why anything related to Gödel's work on the incompleteness of formal systems strong enough to contain arithmetic does not appply no anything but formal systems strong enough to contain arithmetic. I do not see the point, though: in the first place, there are already great expositions of this precise same point available, much better than anything I could cram into this textentry thingy for you to go read, and, second, you'd react with (some variant of) this "I believe that within your worldview it is correct" line. Forgive me if I care not that as much about you as would be needed to justify my forgetting these two points.
This is plainly idiotic. What would be an alternative: thinking about systems in their full blown complexity without having recourse to simplifying assumptions and aproximating abstractions? Of course if you are going to make simplifying assumptions and aproximating abstractions, you better remember you are doing that: otherwise you'll soon enough be very, very wrong. But in any case, the only "flaw of human thinking" in sight in this context is the carelessness of some people that tend to forget about the assumptions and abstractions they have made.
Here it is, again: you must reach this point in which you essentially say "everything goes" in a complicated, fancy-if-you-are-in-the-60's way very, very often in your discourse...
"He just wants you to think" is a standard line to justify nonsensical babbling, when it is no longer possible to put forward arguments based on usefulness or infomativeness or even logical consistency. From koans to most of Lacan's seminaires.
Making reference to someone's work and ideas is by all means different from saying "go read this and believe every single word with absolute faith", and confusing the two is to be expected at most from a teenager. Reasonable adults, on the other hand, recognize that refering to other people's work is valuable, and acknowledge that complete acceptance of an author's thoughts is not the only option when dealing with them.
This is infantile. I never said anything remotely similar to "all your answers are here": I merely pointed to that book as a nicely detailed analysis of the complete mess people who do not understand formal logic and its scope make of things like Gödel's theorem, or, rather, of themselves, as Gödel's theorem is not messable with. Bouveresse has taken the time to understand the logic behind Gödel's results, and has taken the time (and the infinite patience, I might add) to go through some of the best-known and sadly very well-respected idiocy out there involving those results and its "applications to real life". It is infantile to think that his work is of no use to others, that the mere act of reading it and/or quoting it implies complete acceptance of his conclusions, that taking advantage of what he's already done is nothing more that "regurgitated citation"; indeed, all this goes against of thousands of years of history showing that it is false.
Moreover, your retorting "regurgitated citation" at me shows a rather insulting assumption on your part about me.
Well, Bouveresse's book is precisely about analogies involving Gödel's theorems. I'll not repeat his arguments; I am a scientist and firmly take part of the scientific tradition of acknowledging that others have done things of value.
I have no idea what you mean by "authoritatian" source of insipiration.
That what we know cannot be definitely proven might need some publicity, I imagine; but that has been dealt with since the begining of time. His posture includes many other things which are not contain
Your statement about models is typical. It appears to be deep, but it is just a truism derived from the meanings of the words themselves, providing neither new information nor any insight into anything. What you are saying is that a model models.
Please oh please, do not mix Gödel into anything but formal logic. Gödel's theorem does not apply to anything but the formal theories it applies to, and in particular, it does not apply to anything even remotely related to "real life". Of course, there are no extensions of none of Gödel's theorems that apply to anything related to "real life" either.
Mentioning Gödel is very "post-". It also usually signals the mind it is a good time to start thinking about dinner, because the speaker has no idea what he is talking about and it is not worth devoting neuron cycles to him. Unless, of course, you are discussing formal logic.
There is an endearing discussion by Jacques Bouveresse, a philosoher who knows his logic, in his book "Prodiges et vertiges de l'analogie", of the Gödel-citing madness... I do not know if the book is available in English, though.
That thing you are "battling" against is simply sillyness. And, much as fire is well-known to be a bad weapon against fire, sillyness does not fight sillyness with any effectiveness at all. Throwing words like "axiom" and "Gödel" around is not much more than an attemt at doing precisely that---well, that, or an misguided attemt at tryingto gain others' respect by sounding deep.
Solipsism is not a steping astone on any journey towards anything: it is just another form of sillyness; a logically sound one, surely, but an useless one in so far as it as it precludes everything else, and a solipsist can be nothing but that.
I probably could but I find no will in me to respond to your (or anyone's, for that matter) variation of sollipsism du jour---which is actually of another jour, in fact. I used to find doing that kind of thing interesting when I was in my early teenager years---I'll candidly admit that---but it lost all of its attraction sometime while I was progressing into adulthood.
Yet: if any given situation it turns out that 1+3=1, well, then the "1" and the "3" and the "+" and the "0" that you are using in that situation are different from the ones that appear in the "usual" "1+3=4". There is absolutely no contradiction with any of these "axioms" you keep bringing up. You are talking about two "1"s, two "3", two, "+", &c, and your problem comes from that.
Now, that is a very boring fallacy... I imagine this is mostly due to the amazing frequency with which one comes across it: there are whole "theories" build upon an equivocation such as yours; a lot of them tend to like the prefix "post-" in their name, but they by no means exhaust the list.
As a member of that community... what on earth are you talking about?
Maybe they are interested in the 5.5 billion people out there in the world?
What I had in mind is that the tax system is not out of control: it is being controlled in a very precise way. That precise way is motivated not by the national debt; that the results of taxation are being used to pay the national debt is completely irrelevant.
This causality you are trying to show here is patently false.
It is a trivially verifiably fact that public education has been the major reason for the rise of literacy and education not only in the US but all over the world. One way to reach your false conclusion, though, is to disregard what happened in this world before, say, a few decades ago: but if you consider history in its entirety, you'll immediately see that public school is the one reason people read and write.
Now, it is true that literacy rates have fallen, in the US and elsewhere (though to various levels of depths in different places): and this has happened most noticeably in the public schools (but by absolutely no means only there). But "public school" is not constant in time: it changes; policy makers can alter what "public school" is and how it works and how much it succeeds. If you look diacronically at public school, you'll not fail to notice that there is a very strong correlation between the policies that have been implemented and the results we are observing.
Literacy levels have falled due to the policies implemented on the public schools. That much is true. Yet this tells us not much about public schools, but does tell a lot about the policies! If you study what's been done to public schools in the US and elsewhere, you can't help noticing that most opf the policies are quite obviously designed to impede any success.
There is a pattern here. In most of latin american countries, in Europe, and elsewhere, public companies have been in the past managed in what cannot be described as anything but a crash course towards utter failure, thus creating the consensus that this is intrinsic to these companies being public, then privatised. If you look around, you'll rapidly notice that things are not much better now.
There is absolutely nothing innocent in the design of "crash course" policies...
The fact is, that is not so. There may be private schools that value teachers considerably much more that public schools and pay them accordingly, but that is essentially exceptional. The compensation given to public school teachers is a reflection of the value society assigns to teachers. Last time I've checked, private schools are very much included in society.
Hmm. Now that's a strange statement.
Most of the deficit of the US is due to the state of the taxation system, which has of late decided to basically stop taxing the rich. You got it completely backwards.