peano curves and 4 dimensional space

[otheronenorehto]

I am not interested in getting overly complex at first. I like starting with a simple idea and exploring the complex ramifications of it. Recently I had a very interesting idea while researching complexity and fractals for a project.

Here is my idea. You will have to know what a peano curve is to understand it. Information is readily available about peano curves.

(remember like I said I am going to keep it perhapse overly simplistic)

A given sequence or set of points in a one dimensional space represent a line.

it does not matter what the distribution of points is they all represent the same line in 1 dimensional space.

it could be
.........................................................
or
. . . . . . . . . . . . . . . .. .

Any given line in one dimensional space when curved can occupy a two dimensional space. A peano curve is a curved set of 1 dimensional points that fills a two dimensional plane.

Similarly you can apply the concept of a peano curve to a plane, in which case it would fill a volume.

Again a volume can be curved to fill a 4 dimensional space.

I personally believe that the way 3 dimensional space curves is like a peano curve and is infact what we percieve as time. I believe that gravity is a propety or results from the way space is curved. It seams to me that in order for gravity to exist it needs time! and is rather a property of the type of time (read: way 3D space is curved) we have in this universe.

Take from this idea what you will. I do not want any pretense of being an expert in math or physics even if I had studied those fields I would never want to tout around an expertise. It is a mule I do not want to carry. I would rather carefully consider and build on all perspectives.

So if you are coming here to express your expertise only then please don't if you want totake any ideas in this post and build on them so they can become an evolving thing then please, start writing.

[houserichichi]

I personally believe that the way 3 dimensional space curves is like a peano curve and is infact what we percieve as time. I believe that gravity is a propety or results from the way space is curved. It seams to me that in order for gravity to exist it needs time! and is rather a property of the type of time (read: way 3D space is curved) we have in this universe.

Care to elaborate on your thoughts? Clearly your thoughts aren't all written here because there are a lot of jumps in your logic here. How did you decide that our 3-space is a peano curve and, more importantly, that it is what we measure as time?

[otheronenorehto]

well I guess that maybe instead of trying to clarify I can boil it down into several possibilites...

Time seems different to us than the other dimensions.

Possibility A: Time is completely different from dimensional space.

Possibility B: Time is the extension of 3 dimensional space into the 4th dimension.

We tend to think of the fourth dimension as being seperate from the first 3. I percieve that there is a debate that spawns from the nature of gravity.

Gravity is explained very well by the curvature of 3 dimensional space.
But it doesn't fit for me to think of an extra dimension just to explain gravity. Rather I like to think of it as a property of the way in which space is curved.

To explain why I think 3 dimensional space is a peano curve or rather like a peano curve I gues I have to clarify further.

The nature of a peano curve is that it is an asembly of self similar units that are assembled to fill an aditional dimension (in the clasical example).

(By the way these are all opinions I have based on thinking, they make sense to me but have no grounding in "reality" so to speak. I am not interested in proving something about reality than I am about exploring a set of ideas, and I invite you to take anything I have said if it inspires an idea for you and expand on it

The self similar assembly of an uncurved set of points does nothing other than define a line. But space is not a line and trying to describe the universe within the context of only lines does not yield many results...

However, the self assembly of a set of points on a complexly curved line can not only describe a line but also describe a plane. (note there is not just one way for a set of points to fill a plane) But a plane in only moderately more usefull in describing the universe.

However a plane complexly curved (which is really just a peano curve, curved and a peano curve is just a curved set of points) can easily describe a volume. Volumes are even more usefull than the previous two conceptualizations at describing the universe. Remember that this type of volume can be decribed as a set of self similar points which is even more useful.

Remember that untill this point everything has been an assembly of self similar sets of points, curved points (2d) and curved curved points (3d) but essentially there is no distiguishing between the 3 they are one and the same thing at the most basic level an assembly of points.

Now to curve it into the fourth dimesion we take 3 dimensional space which we can concieve of fairly easily, but without time, basically a single state static and unchanging (like a sculpture) when you asemble the self similar 3 D states you get a curved 3 dimensional space.

That is more detailed explanation of what I think...

However I think it is more complex than that (obviously duh . So remember how any set of points in 1 D space could equal a line there was not just one. Well I think points could be the equivilent of basic building blocks of matter. What if more than one type of "hyper complex" peano curve was filling the 4 dimensional space.

Still may be a little vague or have holes in it but I think it is unique and interesting. I hope that clarifies my thoughts.

[wendy]

The notion that one can fill a line, or a hedrix (2d space), with dots, is largely wrong, because there are always excluded instances. That is, you can create an illusion of a line, or a plane, but when you start to think the illusion is reality, you run into problems.

twenty dots is twenty instances, and this do not make a line. in fact, one can make a line only from higher substances (eg intersection of planes).

thinking of time as a fourth dimension leads one into serious errors as to the nature of both space-time and the fourth dimension.

One can replicate 2d-space + time by a stack of pictures. One gets the illusion of time by flicking the pictures one after the other. But you can't talk to a thing in there, because you ask picture 29 and get a reply from picture 97. Also, common 3d objects like cubes etc don't exist in 2d-space + time.

[otheronenorehto]

The notion that one can fill a line, or a hedrix (2d space), with dots, is largely wrong, because there are always excluded instances. That is, you can create an illusion of a line, or a plane, but when you start to think the illusion is reality, you run into problems.

twenty dots is twenty instances, and this do not make a line. in fact, one can make a line only from higher substances (eg intersection of planes).

thinking of time as a fourth dimension leads one into serious errors as to the nature of both space-time and the fourth dimension.

One can replicate 2d-space + time by a stack of pictures. One gets the illusion of time by flicking the pictures one after the other. But you can't talk to a thing in there, because you ask picture 29 and get a reply from picture 97. Also, common 3d objects like cubes etc don't exist in 2d-space + time.

Very insightful response. I am glad that you brought this up since I can not possibly go into all the things I think about in one sitting since I would be typing for way to long. Everything in moderation!

I do not believe that matter is infinately divisible so therefor there must be a smallest building block "space" can be infinately divisable. Space is a place where a unit of matter does not exist but could be occupied at some state by a unit or some portion of a unit of matter.

Trying to describe the nature of space is an excercise in describing the paterns of matter. "Space" does not exist except as a potential. When I am talking about a line or a cube these only exist in the world of ideas. They are used to point out a property of something that does exist. Matter is not a line or set of lines or even a cube Movement and change would be very limited in such a system I think and therefor it would be very unlikely that our universe would describeable by such an object. It is better to use the object in the world of ideas to describe things that do exist. A Peano curve is never a plane. It's limit approaches a plane. What kind of plane is determined by the type of curve or certain properties of the way the curve curves.

So what we have in my idea is not that space exists as a line cube or even a 4 dimmensional object (am I contradicting something I said here?) What exists is matter ( a set of units {points?}) and what my idea does I think is describes the way in which those points could fill the four dimensional world we experience.

Time is indeed not a sequence of states one right after another. I agree with you on this concept too! But I think that the reason for this is that our universe is not infact a single curve filling 4 dimensional space but multiple curves that represent the paterns of the sets that are the basic building blocks of matter. the meshing of these different complex curves is what makes it impossible for us to identify a sequence of states.

I think if there is anywhere that we disagree it is that time can (or should?) be conceptualized as an aditional dimension. I believe that the dimension that we percieve as time (and possibly gravity) is much like the other dimensions. With my way of thinking the structure of time naturally follows from the structure of the other dimensions. The self similarity in the other dimensions is also apparent in time. This is actually very important that time have this property of else nothing could evolve. could you imagine what it would be like if states that were relatively close in time were vastly different? The universe would be a much more random place!

There is a lot of anecdotal evidence that there is a fractal structure inherent at least at some range of scales of our universe.

To boot my idea is a little more complicated in that the distribution of "points" along the 4 dimensional curve is not nessecarily even there is some cosmic mecanism that determines the distribution. I have not though a lot about this extension of my idea.

one of the interesting things about this is idea is that time as we percieve it does not exist except in our perception. All the states of all the curves exist simultaneously in 4 dimensions but from 3 dimensions it is only evident in the self similarity of three dimensional "states" on diferent scales in different ways. So a memory is just a self similar state across a 4 dimensional distance represented in a slightly different way? I don't know... These ideas boggle my mind sometimes:) But I kind of like that fealing. Again I would like to encourage anyone who is inspired by anything I have said to take any idea or subsection of ideas and jam with them for a bit before bed or something. Just share the love and let us all know what you come up with

[otheronenorehto]

I just want to itterate that I am not trying to portray myself or my ideas in an athoratarian way. I think that my passion comes out in what could be percieved as athoratarian... I don't want my ideas to threaten anyones world view and I want to say that I believe that it is imporant to realize that we as humans barely know what we are talking about when it comes to this kind of stuff. There are people whos opinions and theories I respect because of thier personal histories but that does not make it "gospel".

The important thing is not so much to discover the absolute truth or some such nonsense but to have ideas and talk about those ideas with other people and have fun doing it. If you do not enjoy what I have to say or think that it is totally of base please express your side in a well thought out and (as much as possible) non confrontational way:) I will certainly try to entertain your views as I hope you are entertaining mine:)