Consider a point. A point is a reference and thus has an infinitely small dimension, on an infinitely small plane. Everything in geometry is based on the point, so we'll call it's plane zero-dimensional, or 0-D, the dimensional origin.
From a 0-D plane we move to a 1-D plane, usually denoted as an x-axis. Now a 1-D has a dimensional value, usually called length, and a geometric figure, denoted as a line. A line of course is simply an infinite number of points across given interval. A 1-D plane can be said to be perpendicular to a 0-D plane, being that any plane beyond a 0-D plane is perpendicular to a 0-D plane due to the fact that it is without dimension.
A 2-D plane is simply two 1-D planes perpendicular to each other, which suggests that a 1-D plane is two 0-D planes perpendicular to each, which reinforces this compound perpendicularity theory. The 2-D geometric figure is a polygon, which can be defined as an infinite number of lines, either of varing lengths and/or continuity or not, across a given interval. With this definition one can construct any kind of 2-D geometric figure.
A 3-D plane is three 1-D planes perpendicular to each other (or one 1-D plane perpendicular to a 2-D plane) following this logical pattern. A 3-D geometric figure, following the respective patter of geometry, can be defined as an infinite number of 2-D geometric figures, either of varying lengths and/or widths, and/or continuity, or not, across a given interval. Thus one can construct any kind of 3-D geometric figure.
Continuing with this logic, one can mathematically define an infinite number of dimensions.
For example, a 4-D plane must be four 1-D planes perpendicular to each other (which is equal to one 1-D plane perpendicular to a 3-D plane, as well as two 2-D planes perpendicular to each other. Each axis of the plane must be perpendicular to every other axis of the plane.) A 4-D geometric figure would be an infinite number of 3-D figures of varying lengths and/or widths and/or heights, and/or continuity, or not, across a given interval.
Taken to infinity, the n-D plane must be n 1-D planes perpendicular to each other, one 1-D plane perpendicular to one (n-1)-D plane, etc etc. An n-D geometric figure would bee an infinite number of (n-1)-D figures of varying values, and/or continuity, or not, across a given interval.
From a 0-D plane we move to a 1-D plane, usually denoted as an x-axis. Now a 1-D has a dimensional value, usually called length, and a geometric figure, denoted as a line. A line of course is simply an infinite number of points across given interval. A 1-D plane can be said to be perpendicular to a 0-D plane, being that any plane beyond a 0-D plane is perpendicular to a 0-D plane due to the fact that it is without dimension.
A 2-D plane is simply two 1-D planes perpendicular to each other, which suggests that a 1-D plane is two 0-D planes perpendicular to each, which reinforces this compound perpendicularity theory. The 2-D geometric figure is a polygon, which can be defined as an infinite number of lines, either of varing lengths and/or continuity or not, across a given interval. With this definition one can construct any kind of 2-D geometric figure.
A 3-D plane is three 1-D planes perpendicular to each other (or one 1-D plane perpendicular to a 2-D plane) following this logical pattern. A 3-D geometric figure, following the respective patter of geometry, can be defined as an infinite number of 2-D geometric figures, either of varying lengths and/or widths, and/or continuity, or not, across a given interval. Thus one can construct any kind of 3-D geometric figure.
Continuing with this logic, one can mathematically define an infinite number of dimensions.
For example, a 4-D plane must be four 1-D planes perpendicular to each other (which is equal to one 1-D plane perpendicular to a 3-D plane, as well as two 2-D planes perpendicular to each other. Each axis of the plane must be perpendicular to every other axis of the plane.) A 4-D geometric figure would be an infinite number of 3-D figures of varying lengths and/or widths and/or heights, and/or continuity, or not, across a given interval.
Taken to infinity, the n-D plane must be n 1-D planes perpendicular to each other, one 1-D plane perpendicular to one (n-1)-D plane, etc etc. An n-D geometric figure would bee an infinite number of (n-1)-D figures of varying values, and/or continuity, or not, across a given interval.
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Re: Logic of Dimensions
Tue, January 31, 2006 - 12:32 PMok...how would u then explain 5-D, 6-D and the 7th (the last) dimension?
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Re: Logic of Dimensions
Sat, July 14, 2007 - 9:30 AMby definition an n dimensional figure can only have one form because a variation is a deviation from an infinate space that defines a said space as a shape or form, secondly your logic of dimensions is flawed as is Newtonian logic which your premise seems to be based on because newton couldn't define a point because a point can not be defined with in physical space that doesn't have the same properties as all other things in physical space such as three dimensiality no matter how small of a point you select it will always be three dimensional so a plane is not a 2D object it is a 3D object defined by 2 dimensions. look up Riemann and Einstein and spherics for referance. -
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Re: Logic of Dimensions
Tue, July 17, 2007 - 2:04 PMFirst let me say that I am not a mathemetician or a physicist, so I may be totally and painfully wrong, but I don't think that a point always has to have three dimentions.
A point, as I understand it, is a simple location. It is a property of something else...or anything else. If it was a point in the 3rd dimention, it would have three dimentions, yes, but if it were a point in the sixth dimention it would have all of the properties of that dimention. The possible properties of a point, then, are infinite. Infinity includes the empty set.
Before you start arguing that if a point was located in the empty set, it wouldn't be empty and therefore have a dimention of some kind...what if the point is itself the empty set. The actual location of nothing?
I hope I didn't miss the point! ;)
Leo
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Re: Logic of Dimensions
Sun, July 22, 2007 - 7:58 PMThis empty set logic seems to be flawed as well. The origin of this logic is ignorance itself, which also seems to be emptyness in the form of a lack of knowing something. Yet the creative human mind fills in the missing pieces when it has to cram them in to make them close to fiting even when the piece is not the correct one. When the human mind sees a space beyond its comprehension it often labels it as empty. people once thought the air was empty untill observational technology evolved, and some people still believe that the space in between stars is empty even though scientific evidence shows that non light emitting bodies and sub atomic particles are moving constantly through these spaces. In conclusion there is no completely empty place in our universe except the one you and other ignorant people made up in your heads. -
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Re: Logic of Dimensions
Sun, July 22, 2007 - 11:29 PMLet me clarify that.
If you are going to call me ignorant ( and I have admitted that I may be) you should be able to back up your assertion that there is no such thing as the empty set. Fine, I am willing to be enlightened.
Your claim that I am ignorant implies that you are not... so my question is, do you your self really know and undertand what you are putting forth as fact? I am asking you to prove that by supporting your claim that in all possible dimensions there is not and cannot be any state of nothingness.
That is what I meant by "Can you prove that?"
Leo -
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Re: Logic of Dimensions
Sat, August 18, 2007 - 11:22 PMzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz zzzzzzzzzzzzzzzzzzzzzzzzzz zzzzzzzzzzzzzzzzzzzzzzz...........
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Re: Logic of Dimensions
Tue, August 28, 2007 - 4:25 PMIgnorant people... So what exactly do you get out of calling a person ignorant? Vindication? Some kind of validation? Ignorance is also self indulgence, would you not agree? Loki, for all your cleverness, and all your intelligence, your demeanor is at best arrogant, and self indulgent. You may know how to be a mathematician, but apparently you have no clue how to be a person. Good luck in that man... -
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Re: Logic of Dimensions
Thu, August 30, 2007 - 12:42 AMAs an average PERSON who has a healthy brain I Feel it is nesessary to point out flaws in logic when I see them it helps keep peoples minds in check and also active. this is the way a free intellectual society is, ideas clashing no need to kiss ass by not acknowleging obvious flaws. "hmmmm.. this patient is about to contract diabetes I don't wanna be rude by calling him obese and irresponsible so i'll just let him die happy" a doctor like that wouldn't cut it. A doctor and PEOPLE in general should be honest. Ignorance is not a bad word it is just used in diagnosis of a persons mental state and all people have ignorance in one form or another. Your ignorance seems to be similar to that of a bad politician trying to make a big statement attacking someone's morality based on one little neutral fact, trying to create a B.S. facade around a little fact with no chain of logic or supportive facts.
Secondly, what is your definition of indulgence? sex ? food? sleep? would you then prefer life to be free of indulgences? If honest intellectual discussion is an indulgence and by your definition also ignorance, as is sex,food, and sleep. Should all these things not be included in a HUMAN PERSON?
Thirdly, a gorilla is knows the value of competition and conflict, maybe your name should be chiuaua. So if you got trash to talk, throw it away; if you got facts to talk throw'em up. And good luck learning how to back up your statements with facts ..........man................. -
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Re: Logic of Dimensions
Thu, August 30, 2007 - 12:21 PMI think I touched a nerve... man... Ok so lets break this down.
There is nothing wrong with pointing out flaws in logic. If the argument has a hole in it, then you expose that hole for what it is. Your analogy is the diabetes patient. The patient is overweight, has a bad diet, poor lifestyle choices, which in the end have resulted in a disease. Frankly, that has nothing to do with the subject, and is a horrible analogy because we aren't dealing with diabetes. First off the guy who post a response admitted that it was an "idea" and I believe that he also readily admitted that it had flaws and if I am not wrong he was looking for some kind of interjection that would help to develop his idea. Therefore your response to him in your diabetes argument would be close to informing the patient that they have diabetes, telling them it is because they are overweight, they have a poor diet, and a poor lifestyle, and then ending it all by saying, "You stupid fucking imbecile!" See what the doctor would be lacking in this case is a word called "professionalism."
>Your ignorance seems to be similar to that of a bad politician trying to make a big statement attacking someone's morality based on one little neutral fact, trying to create a B.S. facade around a little fact with no chain of logic or supportive facts.
So you feel that I attacked your morality and that I took a small instance and BLEW it up into something that does not truly reflect your character with "little fact" and "no chain of logic or supportive facts." I disagree... In fact I think that you gave quite a bit away about your character.
>Loki: "In conclusion there is no completely empty place in our universe except the one you and other ignorant people made up in your heads."
>Leo: "Can you prove that?"
>Leo: "Let me clarify that. If you are going to call me ignorant ( and I have admitted that I may be) you should be able to back up your assertion that there is no such thing as the empty set. Fine, I am willing to be enlightened. Your claim that I am ignorant implies that you are not... so my question is, do you your self really know and understand what you are putting forth as fact? I am asking you to prove that by supporting your claim that in all possible dimensions there is not and cannot be any state of nothingness. That is what I meant by "Can you prove that?"
>Loki: "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz zzzzzzzzzzzzzzzzzzzzzzzzzz zzzzzzzzzzzzzzzzzzzzzzz..........."
Lets put this in context of the patient doctor scenario. "You have diabetes because you eat like a pig and you live like a cur, you stupid fucking imbecile. Furthermore, your diagnosis bores me and you should consider yourself lucky that I don't hit you over the head with a cord of wood for your 'ignorance'... Moron."
It's a good thing you aren't a doctor isn't it Loki. . .
>Secondly, what is your definition of indulgence? sex ? food? sleep? would you then prefer life to be free of indulgences? If honest intellectual discussion is an indulgence and by your definition also ignorance, as is sex,food, and sleep. Should all these things not be included in a HUMAN PERSON?
First off lets get something straight. What do I mean by "indulgence" in context to "you"? You indulge your intelligence. In fact you do so in such a manner as to raise the appearance of being intelligent by actively trying to dumb other people down (If there is any doubt to this please reread the quoted exchange you had with Leo above.) that you perceive as not being of your intellectual caliber. Is this an assertion into "you" as a person, no... it's an observation of your actions.
>If honest intellectual discussion is an indulgence and by your definition also ignorance, as is sex,food, and sleep. Should all these things not be included in a HUMAN PERSON?
Once again you muddle up what I was telling you. What you did with Leo was not: 1. Honest. nor 2. Intellectual. What you did with Leo was an "indulgence" of your own intellectual superiority over another human being. To make matters worse, you have exhibited that not only are you arrogant, but that you not able to admit when you have made a mistake. Apparently your version of rationality is not about a process of exploration, but a process of affirming your ego. There is no doubt in my mind that you are a very intelligent fellow. However, an "individual little snowflake" you are not. You are not the first intellectual fascist that I have met in my past, and frankly (this will be "irrational", but I think that I can allow myself this one slight "indulgence") most intellectual fascist aren't interested in rationality, or the love of knowledge, or humbling themselves down before the alter of learning. They are interested in bolstering their own version of the world even at the peril of other people who may actually have something to show them about the world in which they live. In other words, you are so busy relishing in your own intelligence that you don't have the time to find wisdom in anyone else except yourself, or others like you.
>Thirdly, a gorilla is knows the value of competition and conflict, maybe your name should be chiuaua. So if you got trash to talk, throw it away; if you got facts to talk throw'em up. And good luck learning how to back up your statements with facts.
1. I don't talk trash, I point trash out, which I think that I have effectively (in your case) done.
2. I think that I have effectively pointed out the facts about your demeanor, therefore I have "thrown'em up".
3. Lastly, I have backed up my statements with facts, perhaps it is you who should consider reading back through your posts and reviewing what you have said and take accountability for them, that is what grown-ups do.
>Thirdly, a gorilla is knows the value of competition and conflict, maybe your name should be chiuaua.
I understand the value of competition and conflict. Perhaps what you don't understand are the consequences of competition and conflict. I however must applaud you on your creative play on words comparing me to a "chiuaua", or as we "irrational" gorillas would spell it, "chihuahua".
>As an average PERSON who has a healthy brain I Feel it is nesessary to point out flaws in logic when I see them it helps keep peoples minds in check and also active.
"I Feel it is nesessary to point out flaws in logic when I see them it helps keep peoples minds in check and also active."
It helps you keep peoples minds in check? And also active? Sorry to loose my "professionalism", but, who the hell are you to keep anyone's mind in check but YOUR OWN. Once again, this is the arrogant, pompous behavior that I am talking about. Reality check, you are what, 21 years old? Son, you haven't seen shit. Your a kid. A smart kid, but a kid none the less. You don't have the experience to keep anyones mind in check but your own. So kindly pull your head out of your anus.
I am sure that you are quite average, I have no doubts about that. I being a student, one who has been humbled countless times, who has been wrong, and wronged, as one who understands that no matter what kind of crap I fill my head with, I am still not "knowing" of anything because of my inability to prove that my knowledge is nothing more than justified belief, and not TRUE justified belief. Being all these things and more I understand what it means to be humble. My demeanor is that of a person who is passionate about wanting to learn, which has constantly (and will constantly) force me to kneel before the alter of knowledge as a life time student, a moron, an idiot, ignorant, irrational, and meek. In these things I have found my ability to be the teacher, brilliant, intelligent, aware, rational, and proud of who I am as a person. Call me an ankle biter if you choose, but you grossly underestimate me, and that is no fault of mine. It in the end is you who must deal with the consequences of your own behavior. As far as I am concerned, you have been shut down. -
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Re: Logic of Dimensions
Thu, September 6, 2007 - 11:20 PMWow! a philibuster just what I would expext from a bad politician, although it does humor me that you would take time out of your busy student life to correct my spelling errors and attempt to psycoanalyze me. It seems the only nerve you touched in me is the ulnar nerve.
Let me make one thing clear; this is the internet. There is almost no use in getting "butt hurt" about any said dialouge. There is little use in correcting spelling errors on a conversational dialogue and it is a big waste of time to interject into conversations and like so many other internet folk; try to play hero by attacking the character of the individual who you percieve as the bad guy.
Now let me clarify my previous dialogue. The diabetes anlaogy may have not been the best choice since it seems to be distortable by people like yourself. The simple message of that analogy is that honesty is more important than politeness. You also seem to assume I prefer to insult people because I enjoy belittling them. Since you seem to be a man who likes to emphasize the details I am surprized you didn't quote my entire dialogue including the most constructive parts, like the point. In my dialogues I am Clearly offering my insight. Then some one tries to contradict and/or doubt my point instead of building on it. That is when I made my counter points. The fact that the counterpoints had a sting in them, which no one should be offended for; does not take away the fact that I proved my initial point which was contradicted. I made puns yet I did not rant and rave as you assume I would. As for the zzzzzzzzzz response, again if you were a true man of details you would have noticed the date;
>>>>Sat, August 18, 2007 - 11:22 PM<<<<<
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz zzzzzzzzzzzzzzzzzzzzzzzzzz zzzzzzzzzzzzzzzzzzzzzzz...........
and the date and the content of my actual response;
>>>>>Tue, July 24, 2007 - 10:56 PM<<<<<
My explanation of your ignorance doesn't imply my complete lack of ignorance it shows that you revealed your ignorance and I didn't. Secondly the simplist of the numerous proofs of the falsity of the empty set is a mathmatical one besides the historical one I pointed out. 0x1=0, 0+1=1.All numbers can be combined accumitively in the same way to get a completely different result each time, except 0. All practical math equations and figures are interconnected and intercorrelated. No matter what mathmatical action you take with 0 its either 0 or it has no effect. That's why any figure w/a 0-D plane has no space or mass what so ever 4x4 is a16square unit figure, 2x2x2 is an 8 cubic unit figure, 2x2x0 is not a figure at all because it has no dimension no space no mass.The empty set seems to have no place in applied mathmatics and no place in physics and thus no place in theoretical dimensional math.It is only a mental tool used by newtonian mathematicians to isolate equations and numbers in a false equilibrium in order to isolate them and make them easier to dissect. SO FEEL FREE TO PROVE THE PRESENCE OF THE EMPTY SET OUTSIDE OF THE ABSTRACT HUMAN MIND.
The zzzzzzzzz response was for the fact that leo did not attempt any more dialogue after my last response.
I also wonder why indulgence has a different definition when used to adress me.
As far as my age goes it does not take away the relavence of any points I have made. What really demeans ones words is when one is as old and cultured as yourself yet still probably makes the same mistakes as when he was a young knucklehead.
The reason you probably see knowlege as justified belief is because you don't know it's value probably because you never applied it in a way that has any relevance to anything important. That is most likely the reason you go online trying to be a hero by first insulting people and then trying to psychoanalyze them and giving them a ramanticized synopsis of your life in order to prove you are morally superior and they are lacking in good character.
In conclusion, you trying to insult my morale character online is the same as saying you're going to kick my ass. You can't really prove it. What you can prove is known facts that people actually know and have been using all thru out history in order to survive and prosper. Speaking of facist you seem to be alot like Hitler, trying to convince yourself and others that you are a hero probably because of some guilt or shortcoming in your life. If you would like to conversate again please have something much more relavent to discuss instead of declaring your morale superiority over others which can not be verified. If you are a person passionate about learning please learn how to deal with your own hang ups instead of trying to analyze others and "shut them Down." Instead of pretending to be a psychologist online you should try to find a real one so you can take care of your own baggage instead of trying to find people who are more F'd up than you thus making you're self look like a hero in comparison.
Good Luck with that!!
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Re: Logic of Dimensions
Fri, September 7, 2007 - 5:40 PMI can't really finish your response. I feel bad because as I put a lot of work into mine, as you did yours, I feel bad because I didn't give you the benefit of finishing yours as you did mine. Sorry about that... In the end however, it's rather meaningless in the grand scheme of things. This can continue forever... My point behind all this is this and this alone. Loki, quit being a penis. Dude, very few of us hold degrees that would qualify us as anything more than spectators in fields like this. People toss around ideas, some good, some not so good, but in the end what is to be learned is not from any one person, but from a collective of ideas, perspectives, etc. etc. etc. My issue with you I made clear, and it doesn't require being a psychotherapist to identify when someone is being less than civil. Yes your right, this is the internet, nothing more. Am I "butt hurt"? No... Try to play hero? No... I called you out on your bullshit, thats all. So pretend like your an adult, and take it for what it is. I could be dead on about you, I might not be, what does it matter? Well I will put it like this, I said what I needed to say, yet you responded. You more than likely will respond to this too. In fact, I would bet that for every time I make a comment back to you about this particular subject, you will respond. I said what needed to be said, now go do what you suggested that I do, go live your life, and move on. -
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Re: Logic of Dimensions
Mon, September 10, 2007 - 10:32 AMDude, my my point which always seems to be lost on you is this; if you feel like calling out my bullshit please try to find it in my anwser to the logic of dimensions. Anything else you can't really prove, only facts you can prove. Ideas aren't meant to be just "tossed around" they are meant to be applied. These ideas make modern life possible which also makes useless intellectuals like yourself possibe. People who use the vastness of the universe as a petty excuse in order to avoid trying to prove anything relavent. All these people can do is complain and criticize others who are actively trying to find and prove ideas that will better our lives. You are not a guru just an insecure man so quit telling strangers what to do with their lives its pointless. If you want to complain please make a point about my anwser to the Logic of Dimensions, not my unprovable morale character, any thing else you say is useless, pointless bullshit. That is all.
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Re: Logic of Dimensions
Tue, July 24, 2007 - 10:56 PMMy explanation of your ignorance doesn't imply my complete lack of ignorance it shows that you revealed your ignorance and I didn't. Secondly the simplist of the numerous proofs of the falsity of the empty set is a mathmatical one besides the historical one I pointed out. 0x1=0, 0+1=1.All numbers can be combined accumitively in the same way to get a completely different result each time, except 0. All practical math equations and figures are interconnected and intercorrelated. No matter what mathmatical action you take with 0 its either 0 or it has no effect. That's why any figure w/a 0-D plane has no space or mass what so ever 4x4 is a16square unit figure, 2x2x2 is an 8 cubic unit figure, 2x2x0 is not a figure at all because it has no dimension no space no mass.The empty set seems to have no place in applied mathmatics and no place in physics and thus no place in theoretical dimensional math.It is only a mental tool used by newtonian mathematicians to isolate equations and numbers in a false equilibrium in order to isolate them and make them easier to dissect. SO FEEL FREE TO PROVE THE PRESENCE OF THE EMPTY SET OUTSIDE OF THE ABSTRACT HUMAN MIND.
