I understand your point but past and present are still significantly different, for this one I do think it was mostly a stunt to get coverage.
Medal of horror would suit the brand name better after this
Hmmm maybe I am making a mistake but I don't see it, as far as I understand your post we must be agreeing because this is exactly what I meant:) (I am talking about the last part of your post)
What we are talking about here is about giving ourselves a certain level of confidence to say 'this is true', 'here is a proof of it'
Thanks to goedel we know we are limited in how far we can go this way as any formal system 'strong enough' as to support peano's arithmetic (not the oepration themselves, but as you say better than me, their 'truth assertion power') will necessarily be incomplete, you will need to add axioms to support some things you will have to or want to consider true when they are undecidable, that will give you a bigger system with its own limits and s on and so on
So anyway I was not disagreeing with Cyberax, I was just curious about what he meant with real numbers theory being complete
I believe it is misleading to present this fact as a way to show how much goedel's theorem is not all that relevant after all
What I do agree with in Cyberax's post is that goedel's theorem is shamelelly thrown at anything where some sort of science limitation is talked about
Hmm, sorry I don't know what is this theory, I'm sure there is one describing things you can do with things that will be called real numbers that happen not to be incomplete
There are many complete (or not incomplete:)) 'theories'
But at some point, when you have created your theory that alllows you to express statements, results, etc. you want your theory to be expressive enough to actually solve meaningful problems
This _theory_ of real numbers you are talking about will among other things fail to assert useful things about natural numbers (like their primality, and, I suspect, worse, their being actually natural or rational (I don't know, just guessing)), which are a part of the numbers it 'supports'.
Not to say that this makes it a useless theory, it is probably extremely useful if it allows you to establish some calculus or algebra results for instance, but whatever you have in mind with this theory of real numbers being complete despite arithmetic's incompleteness is not really a 'way to show hos goedel's proof is quickly limited' (which is how I understood why you were saying it)
But then again, I was also agreeing with your main point I was just puzzled by this particular example:)
What are you talking about ?
"all philosophical consequences of Godel's theorem are bunk" sounds fair but as you state probably falls in the undecidable set of assertions:)
but "real number theory is complete" ? are you confusing the "Gödel completeness" with the "Set completeness" (in the way that all Cauchy sequences are convergent in the same Set (unlike, say, rational numbers)) ?
Don't worry about it, this rule applies outside of the USA as well, and (in case (which I doubt) it is not the case in the USA too) it also applies to pretty much anything dying after having done or been known for anything even remotely popular except maybe scientists:)
I don' t know why you are "flamebaited"
I completelly agree with you, this is a very cool project, I am disapointed that they tag it 'wipeout', why not 'mario kart' ? that would be closer even
But I don' mean to uncool the project, this is awesome, I just don't get the wipeout tag (the track 'inspiration' just doesn not cut it)
(?)
alright, I don't see why you put so much emphasis on bad teachers not understanding how their gifted students get it so much better than themselves
Either you are no as stmart as you remotely think you are, or you had a terrible school experience and in this case you should get over it
But how should I know ? I am not a physics teacher (I wish) I am not a smart kid (I wish)
I just witnessed that students not really getting the whole of it would make fun of physics teachers that made a good point of explaining (or trying to) how inertia plays and what is has to do in the 'centripetal/centrifugal' argument
I think in the end it is more snobism than anything ele driving the argument, but however you look at it, there is indeed no such thing as a centrifugal force (when it is in fact a felt effect of inertia)
I remeber being exited as understanding why it was so, I also understand how it can be made a point "against it" (model, blahblah), but come on... WTF with your smart kids rant ?
Oh right, thanks for your answer
I didn't "state it" that's giving much more strenght thant what I meant as it was in fact not my point at all but thanks for your answer, I see how you interpreted it.
My point was not on this part, that's a separate thing to debate on I don't completely agree with what I wrote per se, it was just part of the main point
To me the point was that I don't like physics teachers being 'ridiculed' (so to speak) around the centripetal/centrifugal force argument because
- I see it out of context (as far as the teachers argument is concerned)
- it is not even right, I mean, teachers are right (as far as I kno/am concerned)
- to me the argument appears when trying to explain what inertia is in this case vs the 'magic centrifugal force'
Maybe this is something personal, of course, you never know, but it has always be clear to me, before studying physics (as achild at school, I am not talking about graduate level matters) I was shown by my grand-father and my father "how the centrifugal force works"
So when I got a better explanation of the phenomenon I bought the 'cebtripetal vs centrifugal' argument, you know, not that I don't understand you can model it any way you want, just as you could model an accelerating frame as a galilean frame with a force or just as you could say there is no difference between a gravitational pull on the referential and this frame being accelerated.
Anyway my point (and I probably shouldn't have detailed the part that you focused on which were poorly worded becasue my focus was on something else) was that I really don't apreciate physics teachers being ridicules out of context when they teach something very valuable arguaing against centrifugal force to let you inderstand about inertia
Sorry I don't see your point (and I am not saying this in a way that would try to diminish it (really this is not an agressive answer in any way), I just don't see what you mean as far as my point is concerned)
The overzalots teachers are right and misquoted.
When they say 'there is no centrifugal force but instead a centripetal force' they don't say it our of nowhere at any time just to hurt your feelings
Whenever a child get in school starting to learn basic physics, he almost always 'know' about the so called 'centrifugal force' meaning the force you experience when you are in a rotating wheel, orthe force that will prevent the water from falling in a fast rotating bucket attached to a rope (etc.)
So the teacher will rightly say that the observed effect is not due to any centrifugal force, and indeed it could not be modelled so, the only 'force' is centripetal (right of course it has its reaction) but what the children 'feel' and attribute to a centrifugal force is in fact inertia which by the way is not centrifugal since as soon as the centripetal force will cease the inertia will lend the mobile to follow a tangential trajectory
Of course you can still confront magnets or electrical charges to show that there are indeed such things as centrifugal forces but it has nothing to do with the 'evil stupid teachers' arguments when they want to make a point about the centripetal vs centrifugal force
No, parent was not meaning 'here is a winner genetic drift ' (that would be shoo-in) he meant, this is a genetic drift you can't easily get rid of because it has a shoe in, preventing you from closing the door;)
Also, I'm just kidding
Oh, no.. there's nothing euro-peon (:)) about it, I was just playing with the fact that moko is pronounced just like moco (which means booger in spanish, or at least in mexican spanish) I totally hate the name of the project because of it (but I have nothing against the project itself, on the contrary)
I don't think so no.. (why ? (??)) (what is Lisp anyway ? (does it have anything to do with the point ? (I don't think it has (just asking) (googling at the same time) (OIC !!!:p))))
Sorry, but I'm a metamathematician.... so everything you mathematicians do is just a model to me.
Göedel's (first incompleteness) theorem does not state that there aren't any complete and consistent theories for logic, it states that any system *complex enough* (it has some requirements to be met to be true) cannot be both complete and consistent.
Anyway I guess (sorry if I don't) I see your point but I don't think you are seeing your parent's, and (unless I missed it) your point is wrong (as in 'non sequitur', not as in 'not true' (which it might be))
This has nothing to do with completeness of logic vs models vs reality.
The parent was telling that relativity is much more than just a model in the way, 'epicycles' are (just) a model to make predictions to get result that should be in accordance with reality, while relativity tells you about deep 'truths', or 'concepts' about reality, and in doing so gives some tools to make predictions, but happens to be incomplete in not telling yet everything
Anyway, it could be interesting to debate if reality can be "completely" modeled at all even getting in your completeness reference (maybe the set of rules is simple enough that any 'happening' can be 'explained/proved' (I don't think so anyway)) but the thing is, the completeness the poster talks about has nothing to do at all with the incompleteness you are talking about, in fact, to some extent, goedel's *completenes* theorem could very well be more relevant (I'm stretching).
Slashdot Mirror
Funnily enough, it also sort of sounds like this: SCOTTEX
is it any better ?
What a nice, insightful post, I started reading it not getting it and pondering 'wtf' but eventually I got your point, thanks it was nice to read.
I understand your point but past and present are still significantly different, for this one I do think it was mostly a stunt to get coverage.
Medal of horror would suit the brand name better after this
Thank you I thought noone was getting it and was starting to despair :)
:) fantastic post !
Hmmm maybe I am making a mistake but I don't see it, as far as I understand your post we must be agreeing because this is exactly what I meant :) (I am talking about the last part of your post)
What we are talking about here is about giving ourselves a certain level of confidence to say 'this is true', 'here is a proof of it'
Thanks to goedel we know we are limited in how far we can go this way as any formal system 'strong enough' as to support peano's arithmetic (not the oepration themselves, but as you say better than me, their 'truth assertion power') will necessarily be incomplete, you will need to add axioms to support some things you will have to or want to consider true when they are undecidable, that will give you a bigger system with its own limits and s on and so on
So anyway I was not disagreeing with Cyberax, I was just curious about what he meant with real numbers theory being complete
I believe it is misleading to present this fact as a way to show how much goedel's theorem is not all that relevant after all
What I do agree with in Cyberax's post is that goedel's theorem is shamelelly thrown at anything where some sort of science limitation is talked about
Hmm, sorry I don't know what is this theory, I'm sure there is one describing things you can do with things that will be called real numbers that happen not to be incomplete :)) 'theories' :)
There are many complete (or not incomplete
But at some point, when you have created your theory that alllows you to express statements, results, etc. you want your theory to be expressive enough to actually solve meaningful problems
This _theory_ of real numbers you are talking about will among other things fail to assert useful things about natural numbers (like their primality, and, I suspect, worse, their being actually natural or rational (I don't know, just guessing)), which are a part of the numbers it 'supports'.
Not to say that this makes it a useless theory, it is probably extremely useful if it allows you to establish some calculus or algebra results for instance, but whatever you have in mind with this theory of real numbers being complete despite arithmetic's incompleteness is not really a 'way to show hos goedel's proof is quickly limited' (which is how I understood why you were saying it)
But then again, I was also agreeing with your main point I was just puzzled by this particular example
What are you talking about ? :)
"all philosophical consequences of Godel's theorem are bunk" sounds fair but as you state probably falls in the undecidable set of assertions
but "real number theory is complete" ? are you confusing the "Gödel completeness" with the "Set completeness" (in the way that all Cauchy sequences are convergent in the same Set (unlike, say, rational numbers)) ?
hmmmm not till lindemann
you forgot climate control weapons
Don't worry about it, this rule applies outside of the USA as well, and (in case (which I doubt) it is not the case in the USA too) it also applies to pretty much anything dying after having done or been known for anything even remotely popular except maybe scientists :)
I don' t know why you are "flamebaited"
I completelly agree with you, this is a very cool project, I am disapointed that they tag it 'wipeout', why not 'mario kart' ? that would be closer even
But I don' mean to uncool the project, this is awesome, I just don't get the wipeout tag (the track 'inspiration' just doesn not cut it)
exelent ! they will need to fix mine now though ;)
(?)
alright, I don't see why you put so much emphasis on bad teachers not understanding how their gifted students get it so much better than themselves
Either you are no as stmart as you remotely think you are, or you had a terrible school experience and in this case you should get over it
But how should I know ? I am not a physics teacher (I wish) I am not a smart kid (I wish)
I just witnessed that students not really getting the whole of it would make fun of physics teachers that made a good point of explaining (or trying to) how inertia plays and what is has to do in the 'centripetal/centrifugal' argument
I think in the end it is more snobism than anything ele driving the argument, but however you look at it, there is indeed no such thing as a centrifugal force (when it is in fact a felt effect of inertia)
I remeber being exited as understanding why it was so, I also understand how it can be made a point "against it" (model, blahblah), but come on... WTF with your smart kids rant ?
Oh right, thanks for your answer
I didn't "state it" that's giving much more strenght thant what I meant as it was in fact not my point at all
but thanks for your answer, I see how you interpreted it.
My point was not on this part, that's a separate thing to debate on I don't completely agree with what I wrote per se, it was just part of the main point
To me the point was that I don't like physics teachers being 'ridiculed' (so to speak) around the centripetal/centrifugal force argument because
- I see it out of context (as far as the teachers argument is concerned)
- it is not even right, I mean, teachers are right (as far as I kno/am concerned) - to me the argument appears when trying to explain what inertia is in this case vs the 'magic centrifugal force'
Maybe this is something personal, of course, you never know, but it has always be clear to me, before studying physics (as achild at school, I am not talking about graduate level matters) I was shown by my grand-father and my father "how the centrifugal force works"
So when I got a better explanation of the phenomenon I bought the 'cebtripetal vs centrifugal' argument, you know, not that I don't understand you can model it any way you want, just as you could model an accelerating frame as a galilean frame with a force or just as you could say there is no difference between a gravitational pull on the referential and this frame being accelerated.
Anyway my point (and I probably shouldn't have detailed the part that you focused on which were poorly worded becasue my focus was on something else) was that I really don't apreciate physics teachers being ridicules out of context when they teach something very valuable arguaing against centrifugal force to let you inderstand about inertia
Sorry I don't see your point (and I am not saying this in a way that would try to diminish it (really this is not an agressive answer in any way), I just don't see what you mean as far as my point is concerned)
The overzalots teachers are right and misquoted.
When they say 'there is no centrifugal force but instead a centripetal force' they don't say it our of nowhere at any time just to hurt your feelings
Whenever a child get in school starting to learn basic physics, he almost always 'know' about the so called 'centrifugal force' meaning the force you experience when you are in a rotating wheel, orthe force that will prevent the water from falling in a fast rotating bucket attached to a rope (etc.)
So the teacher will rightly say that the observed effect is not due to any centrifugal force, and indeed it could not be modelled so, the only 'force' is centripetal (right of course it has its reaction) but what the children 'feel' and attribute to a centrifugal force is in fact inertia which by the way is not centrifugal since as soon as the centripetal force will cease the inertia will lend the mobile to follow a tangential trajectory
Of course you can still confront magnets or electrical charges to show that there are indeed such things as centrifugal forces but it has nothing to do with the 'evil stupid teachers' arguments when they want to make a point about the centripetal vs centrifugal force
Thank's I would of right it so my self but you bit me to eat.
I guess its fine I should of been more fasterer
No, parent was not meaning 'here is a winner genetic drift ' (that would be shoo-in) he meant, this is a genetic drift you can't easily get rid of because it has a shoe in, preventing you from closing the door ;)
Also, I'm just kidding
Oh, no.. there's nothing euro-peon (:)) about it, I was just playing with the fact that moko is pronounced just like moco (which means booger in spanish, or at least in mexican spanish) I totally hate the name of the project because of it (but I have nothing against the project itself, on the contrary)
openmoko ? yuk, booguers...
rocket surgery.... *shivers*
(never did I (why should we ? (I'm sure you're sure it wasn't deserved (were you not ? (:p)))))
I don't think so no.. (why ? (??)) (what is Lisp anyway ? (does it have anything to do with the point ? (I don't think it has (just asking) (googling at the same time) (OIC !!! :p))))
Sorry, but I'm a metamathematician.... so everything you mathematicians do is just a model to me.
Göedel's (first incompleteness) theorem does not state that there aren't any complete and consistent theories for logic, it states that any system *complex enough* (it has some requirements to be met to be true) cannot be both complete and consistent.
Anyway I guess (sorry if I don't) I see your point but I don't think you are seeing your parent's, and (unless I missed it) your point is wrong (as in 'non sequitur', not as in 'not true' (which it might be))
This has nothing to do with completeness of logic vs models vs reality.
The parent was telling that relativity is much more than just a model in the way, 'epicycles' are (just) a model to make predictions to get result that should be in accordance with reality, while relativity tells you about deep 'truths', or 'concepts' about reality, and in doing so gives some tools to make predictions, but happens to be incomplete in not telling yet everything
Anyway, it could be interesting to debate if reality can be "completely" modeled at all even getting in your completeness reference (maybe the set of rules is simple enough that any 'happening' can be 'explained/proved' (I don't think so anyway)) but the thing is, the completeness the poster talks about has nothing to do at all with the incompleteness you are talking about, in fact, to some extent, goedel's *completenes* theorem could very well be more relevant (I'm stretching).