The following is a hypothetical conversation which explains some basic things about dimensions.   Use the index to skip around in the conversation if you want.

space time
  space-time uses
  energy versus matter
knowledge integration
natural machines
dimensional swapping
tilting dimensions

me: I've figured out a fifth dimension.

you: And just what does that mean?   What is the fourth dimension anyway, time?

me: Sure, you could assign time to be the fourth dimension, but which number it is is actually arbitrary.

you: Wait, so then what are the first three dimensions?

me: They are the simple ones I guess.   They're height, width, and depth.   People tend to see height, width, and depth as being contained somehow by time.   It's more natural for humans to do that since they see themselves as three-dimensional objects moving through time.   But it's not the only way.

you: Well why shouldn't you see height, width, and depth as going through time?

me: I'm not saying you shouldn't.   As a human, eventually you have to organize the dimensions in a way that's useful to you.   The standard way is probably pretty useful or else not everyone would believe it.   But it can be useful to organize the dimensions differently.   Doing that can let you see things you couldn't otherwise.

you: Interesting.   So how else can you organize the dimensions?

me: Before you can organize the dimensions you need to know what you are organizing them for.

you: Oh great.

me: Heh... well it's not so complicated.   Just consider some more why people normally organize the dimensions as height, width, and depth moving through time, in other words, space moving through time.   They do it that way because their consciousness is moving through time.   So for people to best understand what's going on around them, they organize the dimensions as space going through time.   Make sense?

you: Maybe it'll make more sense if you tell me how else people can organize the dimensions and why.

me: Ok, here is another way you can organize them.   You know how people who are talking about relativity and so forth often refer to space-time?   Well space-time is another way to organize the dimensions.   Instead of seeing three of the dimensions moving through the fourth, you see all the dimensions at once.

you: All at once?

me: Well if we go back to the space-moving-through-time perspective, it's just like when you look at a person and you see vus height, width, and depth all at once.   Only with the space-time perspective you see the person's height, width, depth, and time all at once.

you: What does a person look like from the space-time perspective?

me: They look like a worm.   The worm is thin where it begins because the person is small.   The worm get's thick when the person is middle-aged.   Then the worm gets thinner and eventually ends as the person gets old and dies.   Just imagine a time line, like they use in history books.

you: Ok.

me: Now imagine the time line like it is a string floating in front of you.   Then imagine the string going through the center of a cube, so the cube is like a bead and you can slide it back and forth on the string.

you: Ok.

me: Now move the cube to the left end of the string and we'll have that point along the string represent when the person's life began.   The right end of the string represents when the person died.   Now visualize the person as a fetus inside the cube.   You got that so far?

you: Yep.

me: Ok, now imagine sliding the cube slowly to the right along the time-line string.   As you do it, see the person inside the cube get older.   Try to see the person in 3-d, not just as a movie.   Keep moving the cube right until you get to the end of the person's life.   Then keep moving the cube right and see that the person has disappeared and there is nothing in the cube.

you: So is that what a person looks like in space-time?

me: Prettymuch.   But you have to make sure you're doing this visualization exercise with the right perspective.

you: What's the right perspective?

me: Hmm... you should do it just as if you were scanning along a peice of paper with a magnifying glass.   The key is that you know the whole paper is there all at once.   All the magnifying glass is doing is focusing in on one part of the paper.   As you move the magnifying glass, you're just looking at a different part of the same paper.

you: And so the cube is sorta like a magnifying glass for the timeline.

me: Exactly.   By focusing in on the different parts of the space-time person you get a feel for what a space-time person looks like.   The best part though is that by visualizing the parts along the time line, you automatically integrate all those parts into one in your mind.

Space-Time Uses
you: Cool.   Now I'm beginning to get it.   So what can I use the space-time perspective for?

me: For starters, you can create a whole new paradigm of what types of machines can be built, and what machines are.   You see, almost all machines today are made according to the space-moving-through-time perspective.   Take a car for instance.   Engineers see a car as a three-dimensional object, it has height, width, and depth.   And when the engineers try to make the car do something, they set up the car so that as it progresses through time, things happen.

you: How exactly do they do that?

me: It's a matter of objects and events.

you: Objects and events?

me: Right well, the objects are the peices of the car, like the parts of the engine.   The engineers make names for each of these.   Then events are things these objects do as time progresses.   I guess basically what I'm saying is that that is their perspective on how to make machines.   You just construct 3-d objects and arrange them so that they do something useful as time progresses.

you: Ok, I see.   So how would you make machines according to the space-time perspective?

me: Heh... that's a pretty neat one.   Basically, you only deal with objects.   But instead of 3-d objects, you deal with space-time objects.

you: Are space-time objects like 4-d objects?

Energy Versus Matter
me: Yep, just like that.   Now you're beginning to see how the metaphors and analogues help you to understand dimensions.   Anyway, space-time objects fall into several categories.   Again, it helps to see what the categories are in the space-traveling-through-time perspective.   First there are static physical objects, like cars, lakes, and tables.   Then there are dynamic physical objects, like radio waves, sound waves, and light.

you: Is there really any difference between those two?

me: Well people generally lable static physical objects as matter, and they see dynamic physical objects as energy.   Of course, technically matter and energy are the same thing, but in practice, people distinguish between the two because it is very useful for making machines.   People use matter to contsrain energy and create useful patterns out of it.   Just look at a computer.   But remember that the cut-off point between matter and energy is arbitrary.   In a car, for example, the gasoline and air are treated as energy and the metal parts are treated as matter.

you: But isn't gasoline matter?

me: It all comes down to your situation.   I mean, technically, both gasoline and metal are both energy and matter.   But all that really makes a difference is that people cognitively view things as either matter or energy in order to cope with making machines.   So although the cut-off point between matter and energy is arbitrary, different cut-off points are more or less useful in different situations.

you: Ok, so now I'm beginning to see how machines are made in the space-through-time perspective.   So how do you decide what's matter and what's energy in the space-time perspective?

me: Actually, there is no energy in the space-time perspective, there is only matter.   You can see the reason if you go back to the space-through-time perspective and see that energy is inherently dynamic.   And since you are only dealing with static objects in the space-time perspective there can be no energy.   Well, specifically, it isn't useful to see anything as energy.

you: Ugh... well then why did we go through all that discussion about matter and energy?

4-d coherence
me: Well, knowing how and why matter and energy are distinguished is useful in its own right.   But it's also useful to see why there is no useful notion of energy in the space-time perspective, and knowing that helps give you a grasp of what the space-time perspective is all about.   It is all about 4-d objects, static 4-d matter.   It's all about arranging 4-d objects into coherent structures.

you: Coherent?

me: Yes, in order to build a useful space-time machine, you have to arrange space-time objects into coherent structures.   Visualize coherence this way: visualize a ball.   Now let's assume the ball is coherent.   Ok, now if you split the ball into two peices, it's not coherent anymore.   Specifically, the left half and the right half are not coherent by themselves.   But, if you push the two peices up against each other, they become coherent again because they form a ball again.

you: Ok, I can see that.   So what is coherence like in space-time?

me: A good example for space-time is a jet going from take-off to landing.   Can you see how the jet going from take-off to landing is a space-time object?

you: Sure, because it involves a Jet in various states over a period of time.

me: Good.   Well, if you want, you can split the jet's flight up into the pilot's movements as one space-time object and the jet's movements as another space-time object.

you: Ok.

me: Ok, now that you know what the components are, let's make a space-time machine.   Imagine you place just the jet's movements into your machine.   In other words, you don't include the pilot's movements in your machine.   What will happen then?

you: Heh... well without the pilot to fly the jet, it would never work.   The jet would never get off the ground or it would crash.

me: So basically all you're saying is that your machine wouldn't work, right?

you: Right.   So to make my machine work I would have to add the pilot right?

me: Right, but remember you aren't adding the pilot per se, you are adding the pilot's movements.   The pilot is a 3-d object, but the pilot's movements is a 4-d object, and we're only dealing with 4-d objects here.   Anyhow, so what happens when you add the pilot?

you: Well I guess then the machine works.   Since the pilot's movements correspond with the jet's movements, the jet's flight happens.

me: Excellent, you've just designed your first space-time machine.

you: Well ya, but couldn't I have made the same machine just coming at it from the space-through-time perspective?

me: Sure you could.   And the reason why is because whether you use the space-through-time or the space-time perspective you are still dealing with the same four dimensions, height, width, depth, and time.   So it makes sense that as long as you include all those dimensions then somehow you can come up with anything.   It's also true that if you lock a thousand monkeys in a room they'll eventually produce the great american novel.

you: Heh.

me: But it's also true that all of your monkeys will probably die before they do it.   Sorry.   Sorry.   I'm getting a little obtuse.   But what I'm trying to say here is that many machines are much easier to invent and create using the space-time perspective.   In other words, why use monkeys when you can use authors?

you: Oh, I see.   So you would want to use the space-time perspective because it's much easier to create using it.

me: Exactly.   I mean think about it.   It is actually pretty hard to create using the space-through-time perspective.   If it wasn't for the fact you have a memory it would be impossible.   First off, you have to use your memory to make an internal model of the 3-d objects you are creating with.   Then you have to actively deduce what the interaction of those objects will be as time passes.   Then based on your deductions you must induce the arrangement of 3-d objects which will produce the desired 4-d event.   And if you mess up, you can't go back and correct your mistake because time has passed for you at the same time as it passed for the machine.   It's almost like trying to defeat the enemy with the enemy's might when you are the enemy and aren't the enemy at the same time!

you: So, in practice, how would you actually produce space-time machines?

me: I hope you're not too disappointed, but actually making the machines if the tough part.

you: Oh really.

me: The thing is, you shouldn't be disappointed.   I mean think about how long humanity has been working on making machines according to the space-through-time perspective.   It required many generations of technologies leap-frogging off of each other to produce today's machines.

you: Right, first you need material science, chemistry, physics, dynamics, statics, etc., etc.

Knowledge Integration
me: The good news though is that you don't have to go through the same long process with the development of space-time engineering.   All you have to do is integrate what we already know, and I don't mean integrate in the usual sense.   I mean integrate like you integrate equations in calculus.

you: Oh god, not calculus.

me: Yes calculus.   I won't go into too much detail, but basically you do this: first you take some space-through-time machine you understand; then, you look at the machine from the space-time perspecitve and map your space-through-time understanding onto the space-time object using metaphors and analogues.

you: I see, that's basically what you were doing with the whole matter-energy problem.   But I still don't see what this has to do with calculus.

me: Well, time-based equations can be integrated to produce new equations which describe space-time properties of objects.   So you can use integration to abstract our mathematically-defined knowledge to space-time.   You can still integrate knowledge that isn't mathematically defined, you just do it according to abstract integration.

you: Eh?   Abstract integration?

me: Heh... we'd best not get into that right now, it's pretty complicated.   But let me tell you another way to make space-time machines.

you: Ok.

Natural Machines
me: Basically, you harness naturally-occuring space-time machines.

you: Cool.   What exactly are those like.

me: They're just like the naturally-occuring space-through-time machines that people have harnessed in the past.

you: Oh, so then using a horse to ride on would be one.

me: Right, plus people used oxen to pull troughs in agriculture.   Then later on people learned how to make artificial machines and started using them instead of oxen.

you: I see.

me: Some natural machines hinted at the underlying forces going on.   For instance, no one uses lightning.   But if people had taken the time to understand what lightning was, electronics might have developed much sooner than it did.   So, I figure that similar space-time phenomena will guide us to forces we have yet to discover.

you: Sounds like a whole new frontier.

me: Would you believe that's only the beginning?

you: Oh god.   What else is there?

me: Well there are quite a few other perspectives which result from organizing the dimensions differently.   And I haven't even mentioned the fifth dimension yet.

you: Oh that's right, I can't wait, what's the fifth dimension?

me: Abstraction.

you: Abstraction is the fifth dimension?

Dimensional Swapping
me: Yep, but we better not go into that right now.   I aught to tell you about dimensional swapping first.

you: Oh joy, dimensional swapping.

me: Ok, so dimensional swapping is when you exchange, say, height for time.

you: What?   How can you possibly exchange dimensions?

me: Well, you know how in the space-through-time perspective height, width, and depth are contained in time?

you: Right.

me: Well, if you exchange height for time, the result is that time, width, and depth are contained in height.   And the result is the time-height perspective, whereas the normal space-through-time perspective is called "time-time perspective".

you: My god.   How can you visualize that?

me: Like most things, using an analogue.   First, I'll show you how the time-time perspective you are familiar with is derived from the space-time perspective.   Then, I'll show how the same process can produce the time-height perspective.

you: Sounds like a plan.

me: Ok,first off, think of the space-time perspective as being sort of like the fundamental perspective.   It's the basic one because it doesn't arbitrarily place some dimensions inside other dimensions like space-through-time does.   In space-time all the dimensions are on equal footing and all are shown at once.

you: So how do you get time-time from space-time?

me: You look at space-time from a certain perspective.   You see, dimensional organizations only exist relative to an observer.   The space-through-time perspective is produced by being a spatial object and travelling through time.   The space-time perspective is produced by being a space-time object and not travelling at all, everything is static.

you: I don't understand.

me: Hmm... maybe an analogue is in order to explain this analogue.   Imagine a big mountain in the middle of a plain.

you: Ok.

me: Now, the mountain is a 3-d object right?   So that means that you could look at it from infinite different angles.   But, the image you get from the mountain when you look at it from a particular angle is a 2-d object, a photo.   Basically what has happened then is that by looking at a 3-d object from a certain perspective you produced a 2-d object.   Well, an analogous thing happens when time-time is derived from space-time.

you: Ah, that makes more sense now.   It the same thing just with 4-d objects and 3-d objects.

me: Right.   So that points out that you can take an infinite number of 3-d perspectives of a 4-d object.   Or in this case, you can produce an infinite number of 3-d universes from one 4-d universe.   And time-time is one of those.   It's the one we happen to be in.

you: I'm starting to get confused.

me: Hmm... let's link this back to what we were originally talking about, swapping dimensions.   I know.   I'll describe dimension swapping in just three dimensions first.   I'll show you what dimension swapping is like in a movie.

you: Ok.

me: Ok, a movie has three dimensions, height, width, and time right?   Well what we're gonna do is swap height and time and see what we end up with.   Try to imagine that each of the frames of the film has been transferred onto a stack of transparent sheets of paper.   Sort of like if you took the film strip, cut it into frames, and stacked all the frames on top of each other in order.   Ok, now imagine the stack of frames on a table in front of you and orient yourself in your mind as to which dirrection is up in the film.

you: Ok.

me: Alright, now I want you to imagine a magic plane that you control in your mind.   It's not solid so you can move it through the frame stack.   Now what this magic plane does is display on the movie screen whatever it is touching.   So, in other words, if you move the plane right on top of frame 1, then frame 1 will be show up on the movie screen.   So now try moving the plane from frame 1 up through the stack to the end of the movie and imagine what is happening on the movie screen as you do it.

you: It's just as if the movie is playing normally.

me: Right, good.   Now I want you to run the movie backwards using the magic plane.   Start from the top of the stack and move the plane down to frame 1.

you: Right, the movie goes in reverse on the screen.

me: Ok now for the tough part.   Visualizing the frame stack in front of you again, I want you to place the magic plane against the left side of the stack.   Now what do you see on the movie screen?

you: Well, the plane is just touching the left edge of every frame.   So the movie screen shows a single thin line from each of the frames.   Frame 1's line is at the bottom edge of the screen, and the final frame's line is at the top edge of the screen.   It's like I'm seeing everything that happened during the whole movie at the left edge of the normal movie.   Only, I am seeing it all at once, in one frame.

me: Good, now we're going to turn on time so to speak.   Start moving the plane through the frame stack to the right and try to visualize what is happening on the movie screen as you do it.

you: Weird.   It's like I'm seeing a completely new movie.

me: Right, the movie you are seeing now is what the original movie would look like if you swapped the width and time dimension.   I'm assuming here that height dimension on the original frame stack was away from you.   Anyway, do you see how the time information became the height information in the new movie?   And how the original height information became the time information?

you: Yes.

me: Ok, now I'm not gonna ask you to do a similar visualization with space-time because that can lead to some major headaches.   But the point is, the same process produces the time-time perspective and the height-time perspective I was originally trying to explain.   If you imagine space-time as a transluscent blob, then things like time-time are produced by moving the magic plane through that blob in a particular direction.   Only in the 4-d case it is actually a magic cube, but you get the point.   Just visualize it as a plane, it'll make it easier to understand.

you: Now I'm beginning to understand swapping dimensions.

Tilting Dimensions
me: Good, now the next craziest thing is tilting dimensions.

you: Does that have to do with swapping dimensions?

me: Yep, tilting is just like partial swapping.   Before we were exchanging one-hundred percent of time for one-hundred percent of height.   But tilting is when you just exchange like twenty percent or something.

you: Wow, how does that fit in with the frame stack model?

me: It's pretty simple really.   It all comes down to the magic plane.   When we were visualizing the frame stack before, the magic frame was either horizontal or verticle.   But imagine what happens if you tilt the magic plane thirty degrees and then move the plane perpendicularly to itself.

you: Well you get a new movie just like before!

me: That's right, there are an infinity of angles the magic plane can use to traverse through the frame stack.   And each of those angles corresponds to a new dimensional perspective.   Actually, since the perspective you take is directly linked to what you are consciously aware of, you might say that the magic plane is consciousness.   You could even allow the consciousness plane to meander haphazardly, perhaps even discontinuously, through the space-time universe.

you: Consciousness?   That makes me wonder if there is some form of life in tilted dimensions.

me: That's a really intriguing question.   It makes sense that evolution would occur no matter what perspective you took.   And that means that complex objects would form in all perspectives at once.   They might not be so complex that people would call them life according to laymen's terms.   But surely you would have things such as rocks.   It's troubling tough that complex objects might form in all perspectives at once since the same space-time matter is being manipulated in every perspective.

you: So they're all competing then?

me: Ya, and it makes sense that over time, one perspective would become the locus of success and one would be the locus of failure.   Wow, it's almost like a life and death force.   It's just what would explain the presence of both entropy and evolution.   Entropy is evolution in reverse time.   But it's strange that orthogonal perspectives don't seem to pull.   Oh but wait, that is because they are counter balanced by evolution on the other side of our perspective axis.

you: What?

me: Sorry.   I was just pushing onto some new ground.   Anyhow, before I diverge any further lets finally get to the fifth dimension, abstraction.

you: Good.

me: Ahem... ok abstraction is a dimension because that is the only way to account for things like societies.

you: Why are societies abstractions?

me: Well, specifically, societies are an epiphenomenon of the interaction of people.   And people are an epiphenomenon of the interaction of molecules.

you: Epiphenomenon?

me: That just means something that arrises from something else.   It's something that is a level of abstraction up from what you started with.   The key point here though is that no one level is the real one.   They are all on equal footing.

you: What, atoms aren't real?

me: Well they are just one level of the abstraction.   If fact, it shouldn't even be called a level because it is more of a continuum of abstraction.   And the abstraction doesn't go up, it doesn't go down either.   You could just as easily say that the spirit is the epiphenomenon of the body as the body is the epiphenomenon of the spirit.

you: So how do people normally view abstraction.   Is it a containing dimension like time?

me: Yes.   Abstraction is normally viewed as a containing dimension just like time.   The reason for this is that abstraction can't be viewed without the viewer being at a certain complimentary abstraction level already.

you: Complimentary?

me: Ya, like the way an ant wouldn't be able to notice an argument between people.   Hmm... I just thought up some complexities that are going to make my head explode if I don't stop, at least for a while.   I'll talk to you some more later ok?

you: Ok...

John LeFlohic
February 25, 1999