dimensions of our reality
dimensions of our reality
earlier today i was thinking about the dimensions of our reality and we have 2D and 3D. 1D is from a view point kind of impossible but a 4th Dimension isnt. so think...if there were to be a 4th dimension, what do you think it would be?
I don't know what it is, but I know about how you'd see it.
Picture this: You're underwater, say in a swimming pool, and someone dives in over you. (We'll just ignore the safety regulations that are being broken here...) Looking at what passes the plane of the surface (from underwater it's like a mirror):
First thing you see is 8-10 round pinkish things. They suddenly coalesce into 2 elliptical things. They narrow, and a hairy round thing appears between them. The objects are joined into a large elliptical. Eventually the large elliptical separates into 2 round objects that taper off into 2 ellipticals followed, finally, by 10 round things again.
So, you'd be able to see things but you wouldn't be able to understand what it is until the whole has passed you by and you could try to put the pieces of what you saw together.
Picture this: You're underwater, say in a swimming pool, and someone dives in over you. (We'll just ignore the safety regulations that are being broken here...) Looking at what passes the plane of the surface (from underwater it's like a mirror):
First thing you see is 8-10 round pinkish things. They suddenly coalesce into 2 elliptical things. They narrow, and a hairy round thing appears between them. The objects are joined into a large elliptical. Eventually the large elliptical separates into 2 round objects that taper off into 2 ellipticals followed, finally, by 10 round things again.
So, you'd be able to see things but you wouldn't be able to understand what it is until the whole has passed you by and you could try to put the pieces of what you saw together.
Juliaki is right. 
I'll add to this by saying that one can actually describe reality by many more than four dimensions, at least mathematically, which is obviously what you're talking about when you talk of three and four dimensional real vector spaces.
One example:
Given a four dimensional real vector space: P = { x, y, z, t }, x, y, z, t are Reals, where points P are the Gaussian coordinates in space-time of our current reality.
Let T( P ) be the temperature at a given point.
We can now build a five dimensional space: P1 = { x, y, z, t, T( P ) }, however T is dependent on P = { x, y, z, t }, so generalize T( P ):
let T1( P, w ), w is a Real, be the temperature at a given point in all possible realities where T1( P, 0 ) = T( P ).
We now have a proper five dimensional real vector space P2 = { x, y, z, t, w }, x, y, z, t, w are Reals and are independent of each other, which describes all universes like ours with all possible temperature distributions (in Gaussian coordinates).
How can you tell if you've 'escaped' our reality and are moving into a parallel world along the 'heat' dimension? It's simple, if you ever observe the heat equation being violated, you are most likely moving along 'w' into a parallel world.
hope that helps,
T. Guy.

I'll add to this by saying that one can actually describe reality by many more than four dimensions, at least mathematically, which is obviously what you're talking about when you talk of three and four dimensional real vector spaces.
One example:
Given a four dimensional real vector space: P = { x, y, z, t }, x, y, z, t are Reals, where points P are the Gaussian coordinates in space-time of our current reality.
Let T( P ) be the temperature at a given point.
We can now build a five dimensional space: P1 = { x, y, z, t, T( P ) }, however T is dependent on P = { x, y, z, t }, so generalize T( P ):
let T1( P, w ), w is a Real, be the temperature at a given point in all possible realities where T1( P, 0 ) = T( P ).
We now have a proper five dimensional real vector space P2 = { x, y, z, t, w }, x, y, z, t, w are Reals and are independent of each other, which describes all universes like ours with all possible temperature distributions (in Gaussian coordinates).
How can you tell if you've 'escaped' our reality and are moving into a parallel world along the 'heat' dimension? It's simple, if you ever observe the heat equation being violated, you are most likely moving along 'w' into a parallel world.
hope that helps,
T. Guy.
Re: dimensions of our reality
earlier today i was thinking about the dimensions of our reality and we have 2D and 3D. 1D is from a view point kind of impossible but a 4th Dimension isnt. so think...if there were to be a 4th dimension, what do you think it would be?
the 4th dimension is time, it's prettry well esptavblished by Those With Such Authority.
However....if you have an interest...and some basic background (read: have taken high school physics, or are really good at following unfamiliar subjects), I HIGHLY recommend Brian Greene's book The Elegant Universe...which is basically a layman's introduction to string theory and quantum physics. It's some pretty mindbending stuff, but it's supposed to be one of the best intro books out there on the subject.
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Ouch, my head hurts just trying to decypher the math. BUt I will run with it as I can not prove or disprove otherwise.
ThatGuy: I do a off and on comic wth a couple of friends. My contribution is a anime catgirl named "Shrody" who once lived in a box for an unspecified amount of time. (Cudoes to ANYONE who gets the joke.) As she tends to switch from vapid, innocent and cute fluffball to science/ mathmatical whiz. I have to ask. May I use this post of yours as a gag? It'd be histerical to have her all of a sudden just blurt these formula out for any number of random reasons.
WW.
ThatGuy: I do a off and on comic wth a couple of friends. My contribution is a anime catgirl named "Shrody" who once lived in a box for an unspecified amount of time. (Cudoes to ANYONE who gets the joke.) As she tends to switch from vapid, innocent and cute fluffball to science/ mathmatical whiz. I have to ask. May I use this post of yours as a gag? It'd be histerical to have her all of a sudden just blurt these formula out for any number of random reasons.
WW.
The greatest advice I was ever given: It matters not what you believe. Only that you believe it wholeheartedly.
Heh heh, nice. I used to be a Martian Successor Nadesico fan (if you've ever heard it this). Do you put your comic online? Is there anywhere to go see it?Ouch, my head hurts just trying to decypher the math. BUt I will run with it as I can not prove or disprove otherwise.
ThatGuy: I do a off and on comic wth a couple of friends. My contribution is a anime catgirl named "Shrody" who once lived in a box for an unspecified amount of time. (Cudoes to ANYONE who gets the joke.)
Sure thing, I wrote it as a gag anyways, it's only fitting.As she tends to switch from vapid, innocent and cute fluffball to science/ mathmatical whiz. I have to ask. May I use this post of yours as a gag? It'd be histerical to have her all of a sudden just blurt these formula out for any number of random reasons.
WW.

cheers,
T. Guy.
if themath hurts your brain, but you're still interested, I suggest again the book by Brian Greene mentioned above. It's all theoretical, no math. And it's still a great intro to the subject.Ouch, my head hurts just trying to decypher the math. BUt I will run with it as I can not prove or disprove otherwise.
ThatGuy: I do a off and on comic wth a couple of friends. My contribution is a anime catgirl named "Shrody" who once lived in a box for an unspecified amount of time. (Cudoes to ANYONE who gets the joke.) As she tends to switch from vapid, innocent and cute fluffball to science/ mathmatical whiz. I have to ask. May I use this post of yours as a gag? It'd be histerical to have her all of a sudden just blurt these formula out for any number of random reasons.
WW.
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[quote="thatguy
Heh heh, nice. I used to be a Martian Successor Nadesico fan (if you've ever heard it this). Do you put your comic online? Is there anywhere to go see it? [/quote]
At the moment it is a collection of random sketches and gag strips that I have sent amongst friends. I am getting up the nerve to put it online but web pages are not my specialty. "Shrody" only shows up in the gag strips. the bulk of the comic involves other char. and situations.
She started as a joke to a friend after watching a debate for two weeks on Schrodengers theory. As an artist and only partime science buff, I chimed in my two cents as only I could. With a cute little cat girl insisting that she was alive and pleading for people to believe in her. She kinda grew from there into a unique little charicter with a lively personality and an off again/on again genius level understanding of the upper sciences.
The last gag I drew was of someone teaching her a dice bassed strategy game and her not getting a single bit of it until the dice are shown to her. She starts spouting out formulae on Bell curve and probability and ends up winning by sheer mathmatic theory... Then gets distracted by a passing ball of foil.
WW.
Heh heh, nice. I used to be a Martian Successor Nadesico fan (if you've ever heard it this). Do you put your comic online? Is there anywhere to go see it? [/quote]
At the moment it is a collection of random sketches and gag strips that I have sent amongst friends. I am getting up the nerve to put it online but web pages are not my specialty. "Shrody" only shows up in the gag strips. the bulk of the comic involves other char. and situations.
She started as a joke to a friend after watching a debate for two weeks on Schrodengers theory. As an artist and only partime science buff, I chimed in my two cents as only I could. With a cute little cat girl insisting that she was alive and pleading for people to believe in her. She kinda grew from there into a unique little charicter with a lively personality and an off again/on again genius level understanding of the upper sciences.
The last gag I drew was of someone teaching her a dice bassed strategy game and her not getting a single bit of it until the dice are shown to her. She starts spouting out formulae on Bell curve and probability and ends up winning by sheer mathmatic theory... Then gets distracted by a passing ball of foil.
WW.
The greatest advice I was ever given: It matters not what you believe. Only that you believe it wholeheartedly.
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