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I enjoy contemplating the nature of time and trying to conceptualize different dimensional realities. I can't help but feel that all dimensions are just different manifestations of the same thing, providing different "dimensional" perspectives. Although each being very different, I wonder if they may be equal mathematically. Is this conceivable? Would be interested in any feed-back on these ideas. Thanks

- raindog
- Mononian
**Posts:**7**Joined:**Fri Feb 21, 2014 2:47 am

I enjoy contemplating different numbers of dimensions as well. I'm not sure exactly what you mean when you say that all dimensions are different manifestations of the same thing.

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- anderscolingustafson
- Tetronian
**Posts:**312**Joined:**Mon Mar 22, 2010 6:39 pm

Lets look at the 3rd and 4th dimensions. In my opinion the difference between the 2 are how time is perceived. In the 3rd dimension time is linear and we perceive it in "slices" moving toward the future. In the 4th dimension, all exists together simultaneously. A person's life would be a trail of energy through space. It would exist in it's entirety. So everything that existed in the 3rd dimension, it exists in the 4th. The only difference is perspective. I think the way we perceive time in the 3rd dimension allows organized energy to create this very real "illusion" of matter which we experience in the 3rd dimensional physical universe. In the 4th this "illusion" of matter would not be possible and everything would exist simultaneously in the form of energy. Past, present and future would exist together, but none of it would be "physical". What I was trying to say is that both the 3rd and 4th dimensions contain the same thing, the difference being manifestation and perspective. Having physical perspective in the 3rd dimension is like wearing blinders as far as the others are concerned. We can only experience it one moment at a time. I'm am now inclined to believe that ALL dimensions are just different manifestations and perspectives of ONE thing. Of course ALL ideas about dimensions are only speculation, but that is where my train of thought about this has taken me in 50 years of thinking about this.

- raindog
- Mononian
**Posts:**7**Joined:**Fri Feb 21, 2014 2:47 am

Now I see what you mean. Sometimes I use time to help me visualize the fourth dimension by forming 3d images in my head in sequences. Using time to help visualize the fourth dimension helps me understand the fourth dimension.

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- anderscolingustafson
- Tetronian
**Posts:**312**Joined:**Mon Mar 22, 2010 6:39 pm

Well, time + 3D is a good way to understand it. The flow of time is something we're all familiar with. We are all stuck in the now-moment slice moving along 4D. We can meet someone on the 11th floor on 21 street and 2nd avenue, but WHEN should we be there? We still have to think in 4 degrees of freedom, even though we can freely move around in 3. Our entire life is a bent and kinked time-worm with frayed ends, where we existed along the trunk. The frayed ends are the trajectories our atoms took to combine then disassemble.

However, the 4 and 5D stuff that this website is focused on are geometric solids, that do not use time for their extra dimensions. These are mathematically possible shapes, that require 4 or 5 degrees of freedom to exist. They don't extend into time with their 4D part, they extend into another 4th direction of space. Using time as 4D is a good way to get there, to nail down the concept. Once you understand where it is, and what it really means to us 3D-ers, then you can apply the same visual tricks. They translate over fairly well, which is where 5D comes in. 5D is only another even higher direction, that branches off of all 4, right-angled axes. Probably the best way I learned how to visualize 5D is with near-side, far-side projection. This is a universal tool for rotating shapes around, and viewing them from other angles.

Take the triangle prism, for example. This 3D shape has flat 2D panels joined together, encasing a central void of 3D space. They are two triangles and three squares. This means we can view the triangle prism from two unique perspectives. If we looked through one of its triangle-panels, we'll see another triangle at the far end. In between will be the three squares. Now, rotate around to a square-panel, and we will always see a line at the far side. Connecting these are two squares and two triangles.

Now take a cube pyramid. This 4D shape has "flat" 3D panels joined together encasing a central void of 4D volume. It has a flat cube and 6 flat sq-pyramids on the surface. We can view the cube pyramid from two unique vantage points. Looking through the near-side cube, we see a point at the far end, connected by 6 sq-pyramids. If we look through one of the square pyramid panels, we will see a line at the far side, laced by the cube and 5 remaining sq-pyr.

At last, we come to a cylconinder. This 5D container had three "flat" 4D panels, and a 2D pointy corner. It's actually very cone-like, with a largeish base tapering down to a smallish vertex on top. Viewing through the bottom, we see a duocylinder as the near-side. Scaling along 5D, it tapers down to a circle at the far-side. Lacing these are two torus-type shapes, as the 2 curved rolling sides. They are a cone torus ( innertube with 3D cone crosscut ), and a torinder ( innertube with 3D cylinder crosscut ). Both of these attach to the one circle at the top, making a pyramid-like structure extended along 5D.

I like playing with near-side far-side projections for shapes. The different angles help you feel the shape out, and put together how it's composed on the surface.

Here's some more, using Klitzing's near-side || far-side notation :

sq-pyramid : triangle || line , square || point

tetrahedron : line || ortho line

triangle prism : triangle || triangle , square || line

coninder : cylinder || line , cone || cone

cube-pyramid : sq-pyramid || line , cube || point

triangle-prism-pyramid: sq pyramid | line , triangle-prism || point

sq-pyr-prism : triangle prism || square , cube || line , sq-pyr || sq-pyr

dipyramid : tetrahedron || line , sq-pyr || point

cyltrianglinder - cylinder || circle

dicone - cone || circle

cylconinder : duocylinder || circle

tricone : dicone || circle

cyltetrahedrinder : cyltrianglinder || circle , cylinder || ortho cylinder

cylhemoctahedrinder : tesserinder || circle , cyltrianglinder || cylinder

cyltriandyinder : cubinder || cylinder

contrianglinder - cyltrianglinder || triangle , coninder || cone

cone diprism : cubinder || square

cyltrianglindrone - cylindrone || circle

--Philip

However, the 4 and 5D stuff that this website is focused on are geometric solids, that do not use time for their extra dimensions. These are mathematically possible shapes, that require 4 or 5 degrees of freedom to exist. They don't extend into time with their 4D part, they extend into another 4th direction of space. Using time as 4D is a good way to get there, to nail down the concept. Once you understand where it is, and what it really means to us 3D-ers, then you can apply the same visual tricks. They translate over fairly well, which is where 5D comes in. 5D is only another even higher direction, that branches off of all 4, right-angled axes. Probably the best way I learned how to visualize 5D is with near-side, far-side projection. This is a universal tool for rotating shapes around, and viewing them from other angles.

Take the triangle prism, for example. This 3D shape has flat 2D panels joined together, encasing a central void of 3D space. They are two triangles and three squares. This means we can view the triangle prism from two unique perspectives. If we looked through one of its triangle-panels, we'll see another triangle at the far end. In between will be the three squares. Now, rotate around to a square-panel, and we will always see a line at the far side. Connecting these are two squares and two triangles.

Now take a cube pyramid. This 4D shape has "flat" 3D panels joined together encasing a central void of 4D volume. It has a flat cube and 6 flat sq-pyramids on the surface. We can view the cube pyramid from two unique vantage points. Looking through the near-side cube, we see a point at the far end, connected by 6 sq-pyramids. If we look through one of the square pyramid panels, we will see a line at the far side, laced by the cube and 5 remaining sq-pyr.

At last, we come to a cylconinder. This 5D container had three "flat" 4D panels, and a 2D pointy corner. It's actually very cone-like, with a largeish base tapering down to a smallish vertex on top. Viewing through the bottom, we see a duocylinder as the near-side. Scaling along 5D, it tapers down to a circle at the far-side. Lacing these are two torus-type shapes, as the 2 curved rolling sides. They are a cone torus ( innertube with 3D cone crosscut ), and a torinder ( innertube with 3D cylinder crosscut ). Both of these attach to the one circle at the top, making a pyramid-like structure extended along 5D.

I like playing with near-side far-side projections for shapes. The different angles help you feel the shape out, and put together how it's composed on the surface.

Here's some more, using Klitzing's near-side || far-side notation :

sq-pyramid : triangle || line , square || point

tetrahedron : line || ortho line

triangle prism : triangle || triangle , square || line

coninder : cylinder || line , cone || cone

cube-pyramid : sq-pyramid || line , cube || point

triangle-prism-pyramid: sq pyramid | line , triangle-prism || point

sq-pyr-prism : triangle prism || square , cube || line , sq-pyr || sq-pyr

dipyramid : tetrahedron || line , sq-pyr || point

cyltrianglinder - cylinder || circle

dicone - cone || circle

cylconinder : duocylinder || circle

tricone : dicone || circle

cyltetrahedrinder : cyltrianglinder || circle , cylinder || ortho cylinder

cylhemoctahedrinder : tesserinder || circle , cyltrianglinder || cylinder

cyltriandyinder : cubinder || cylinder

contrianglinder - cyltrianglinder || triangle , coninder || cone

cone diprism : cubinder || square

cyltrianglindrone - cylindrone || circle

--Philip

in search of combinatorial objects of finite extent

- ICN5D
- Pentonian
**Posts:**1047**Joined:**Mon Jul 28, 2008 4:25 am**Location:**Orlando, FL

I agree, there is no "time" in the 4th dimension...at least, not as we perceive time in this dimension. What I was trying to say is that if you took the 3rd dimension and could see it in it's entirety, past, present and future...from beginning to end, that's the 4th dimension. All 3rd dimensional time relative to a specific location would correlate to a point in the 4th dimension. But technically it would not be time as we know it. Just saying... all dimensions are just a different view, or dimensional perspective of all the others...in my opinion. A "translation" of sorts only meaningful to someone capable of the perspective.

- raindog
- Mononian
**Posts:**7**Joined:**Fri Feb 21, 2014 2:47 am

Well, yes, you would be correct. If you were viewing all of 3D's past, present, and future at once, you would have to be in 4D, if 4D were time. That's actually a good concept analogy, because you would be essentially capturing all of the extra 4D spatial volume, by seeing all time at once. Each slice of that temporal solid is an infinitely thin 3D snapshot in time.

in search of combinatorial objects of finite extent

- ICN5D
- Pentonian
**Posts:**1047**Joined:**Mon Jul 28, 2008 4:25 am**Location:**Orlando, FL

I would say what we call "dimensions" can factored down to continua of displacement of objects and events. This is what I got into here: viewtopic.php?f=4&t=1318#p15106 where I surmised that both space and time dimensions were actually a manifestation of a continuum containing all alternate realities.

You connect to the displaced points either randomly (where you can go back and forth between points, and measure the displacement with a fixed ruler as "distance"), or one points leads to the next in a fixed sequence, that we measure with a clock, as "duration".

(And "alternate reality" would be anything displaced neither in space nor time, such as the way an event would be if other events leading to it had been different).

You connect to the displaced points either randomly (where you can go back and forth between points, and measure the displacement with a fixed ruler as "distance"), or one points leads to the next in a fixed sequence, that we measure with a clock, as "duration".

(And "alternate reality" would be anything displaced neither in space nor time, such as the way an event would be if other events leading to it had been different).

- Eric B
- Trionian
**Posts:**79**Joined:**Wed Jul 20, 2005 11:46 pm**Location:**NYC

Yep, that's how I started seeing things a while back, too. Time can be considered a fourth dimension, though it's not necessarily the 4th. When making sense of our reality, I often feel like everyone's now moment, that we are all perceiving, is a speed of light 3D energy pulse racing along the time axis. Our atoms and chemistry is moving so very fast, our planets so very slow, and we are right in the middle. We're these giant chemical reactions that have no idea what the hell is going on, and we're just trying to make sense of the world. Luckily, we have language and education, which helps us make more sense of it.

I liken our space-time to this neat picture I found a while back : http://hddb.teamikaria.com/forum/viewtopic.php?p=23149#p23149 . A 5D being would perceive our 4D spacetime the same way, from completely outside.

I liken our space-time to this neat picture I found a while back : http://hddb.teamikaria.com/forum/viewtopic.php?p=23149#p23149 . A 5D being would perceive our 4D spacetime the same way, from completely outside.

in search of combinatorial objects of finite extent

- ICN5D
- Pentonian
**Posts:**1047**Joined:**Mon Jul 28, 2008 4:25 am**Location:**Orlando, FL

Wonder why they didn't include Back to the Future.

- Eric B
- Trionian
**Posts:**79**Joined:**Wed Jul 20, 2005 11:46 pm**Location:**NYC

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