Fractals for integration and of thinking.

[think]

The idea and the reason for that first posting was to get links to places that might cover this idea in more detail. Since the concept is really not on a wiki other then my source but not my ideas directly I wanted to see what others thought of the idea of going between the standard natural numbered dimensions into irrational and imaginary numbered dimensions?

below is some defined dimensions as we know them.

zero dimension a point
one dimension a line
two dimensions a plain surface like area type
two point five dimensions some basic fractal geometry
three dimensions field representations or vector surfaces.
three and a half dimensions =- unknown (possibly part time and not time dimension)


Integrating functions are given as whole number values but what of other values for integration and or differentiation? If there is a link between the theory then we can find the math to prove these things.

see the first lecture here for commentary on the fractal dimension plus other places in the course, and no I am not taking this course but I am just interested in this.

---------------object thought creation----------------irrelevant questions------

So as with any objective, the idea that learning new things is not really new.(paradox)

How fast can a person's mind think? (, and why does that even matter?) Is the speed of thought measurable?

 

[sojourner]

Maybe you should stick to miscellaneous.

 

[think]

Maybe you should stick to miscellaneous.

maybe you should join us in the RA lounge sometime for some creative fun?

============

anyway...

the idea of new math is the same as interesting math but why is something interesting when it is new? Even if it is not new to me but knew to someone else?

of the object of new as it is implied to mean something that was not old and or of past creations that we "know" of what is there left?

Anyway?

============

I am asking if anyone has any "leads" to fractal math? you know other then the kind the computer uses or fractal programs create/use and develop? mathematics in part dimensions like two and a half dimension math? anyone hear of that? anywhere? Has anyone see that before? or if they are from the future having seen that again soon. ?

 

[Robert Maxwell]

It took me a while to figure out what the hell you were talking about, then I realized you were pulling this whole notion of "partial dimensions" from the fact that fractals are self-similar--therefore, you don't need all the information of an additional dimension in order to plot it.

This page explains the concepts in very simple terms and even shows you how to calculate the dimensionality of any arbitrary figure.

There is really nothing magical about it, in any case. It's just a mathematical abstraction.

As for what you said about integration/differentiation besides "whole number" values (I assume you mean integers), there's nothing novel or unique about that. Here is a method for integrating with partial fractions. It's freshman-level calculus.

If you are trying to come up with some sort of philosophical insight based on this stuff, you are probably wasting your time. Mathematics is a formal system and an abstraction of the real world. It doesn't really work as philosophy, unless perhaps you are Pythagoras.

 

[think]

We are all Pythagoras in one way or another just some of us are not in full realization of this.
---------------
I knew that I would have a difficult time with the integration half integrals since there is no reference i could find that would let me adapt the correct words to use...

consider the analogy ...

the integration of a function is of order one
the double integration of a function is of order two
the triple integration of a function is of order three

how does one find the order two and a half?

same with the derivatives ...

the first order differential is that 1st order
second order and third order...

but first and a half order...

It seems like half a quantum ? or somehow the whole divided when it is never divided.

(I have to go to work[yes they pay me to work ;p ], but will think about easier ways to explain and solve this if possible.)

Bill

 

[Robert Maxwell]

I'm thinking you don't understand what integrals are.

A derivative of a function gives you its rate of change. So, say you have a graph that shows the velocity of an object over time. Its derivative function gives you a graph of its acceleration over time. A derivative of that will give you the rate of change in its acceleration, and so on.

An integral simply does the reverse, taking what is assumed to be a derivative function and turning it back into the original. However, since some information is lost when derivation is done (namely, any constant values), you can't get back the true original function. In any case, you can do partial derivatives and partial integrations, but I'm not sure those are what you are talking about, unless you are thinking of differential geometry.

I'm still not clear what it is you want to know about them. If you want to learn how to do them, there is plenty of info out there, and advanced tutorials.

 

[linkerjpatrick]

I think this is a very fascinating topic. I'm glad you brought it up and it seems to explain a lot in terms of gut feelings, ESP, some UFO's, deja vu, etc.

How can we dig deep and extroplocate further down this rabbit hole?

sometimes I can look at a person a as Dave Bowman in 2001/2010 as the Star Child was able to be the star child I can often look at others and see other aspects of their life.

 

[think]

I'm thinking you don't understand what integrals are.

A derivative of a function gives you its rate of change. So, say you have a graph that shows the velocity of an object over time. Its derivative function gives you a graph of its acceleration over time. A derivative of that will give you the rate of change in its acceleration, and so on.

An integral simply does the reverse, taking what is assumed to be a derivative function and turning it back into the original. However, since some information is lost when derivation is done (namely, any constant values), you can't get back the true original function. In any case, you can do partial derivatives and partial integrations, but I'm not sure those are what you are talking about, unless you are thinking of differential geometry.

I'm still not clear what it is you want to know about them. If you want to learn how to do them, there is plenty of info out there, and advanced tutorials.

for the function F to have the derivative function E and the integrated function G where we can say very loosely that E=F@-1 and G= F@1 and of course F@0=F with that if we say the second order derivative is E@-1 or F@-2 or D and then the volume under the function F would be F@2 and so on - does this make sense?

and then say F@X where x is a real number rather then a whole or integer number we find the value of this function F as it approaches the limit x...

this seems really like recursive meta derivatives but I am sure I am not allowed to say meta-derivatives LOL

I think this is a very fascinating topic. I'm glad you brought it up and it seems to explain a lot in terms of gut feelings, ESP, some UFO's, deja vu, etc.

How can we dig deep and extroplocate further down this rabbit hole?

sometimes I can look at a person a as Dave Bowman in 2001/2010 as the Star Child was able to be the star child I can often look at others and see other aspects of their life.

I know what your saying like the cosmic egg hatching the cosmic conscientiousness is known as eternity and then the year 3000 book leaving us wondering if the nexus is just an epiphany dunescapes in an endless cycle of lint gathering ceremonies

 

[YellowSubmarine]

I bet that you can define some kind of integral over a fractal dimension, say by putting a function inside the formula for the Hausdorf content. When you're summing the content of the balls multiply it by a value of the function inside the balls. Now I'm not sure if such a definition would be valid (a direct addition obviously wouldn't work if the function can have negative values) or whether you can calculate it, but it's definitely doable.

But the number of variables will be an integer, and higher than the dimension. Even if you try to define an indefinite integral, the number of variables will still be an integer (remember the original function is more-dimensional). I don't think it's possible to imagine describing the positional information with one and a half variables – I've never seen any construct that could make it imaginable.

 

[think]

I bet that you can define some kind of integral over a fractal dimension, say by putting a function inside the formula for the Hausdorf content. When you're summing the content of the balls multiply it by a value of the function inside the balls. Now I'm not sure if such a definition would be valid (a direct addition obviously wouldn't work if the function can have negative values) or whether you can calculate it, but it's definitely doable.

But the number of variables will be an integer, and higher than the dimension. Even if you try to define an indefinite integral, the number of variables will still be an integer (remember the original function is more-dimensional). I don't think it's possible to imagine describing the positional information with one and a half variables – I've never seen any construct that could make it imaginable.

thinking theoretically what about the imaginary numbers and such or the surreal number theory.. (*grasping at straws*) that should be able to solve part of the transparency of partially covered whole number values? the whole number theory like originally it was a*a plus b*b equals c*c as a Pythagorean these were originally whole integers but now with computers we just blend between. thinking along those lines and limits between the actual integers we can maybe solve integrating but not completely and just getting close somewhere between the integers ... ? I mean by any standard this should not be possible. but then we can make this happen if we want to,,? (have to get back to the job)

 

[YellowSubmarine]

I can't give you much details about it (since I'll get into trouble with my temporal agency if I do), but I can assert that the universe has N spatial and M time dimensions, where N and M are complex surreal numbers and their sum is a negative integer. One and a half of the spatial dimensions are time-like.

 

[think]

I can't give you much details about it (since I'll get into trouble with my temporal agency if I do), but I can assert that the universe has N spatial and M time dimensions, where N and M are complex surreal numbers and their sum is a negative integer. One and a half of the spatial dimensions are time-like.

I hear that counter-temporal agencies are everywhen and inside the outside when the cosmic egg men are one and one and one for each raindrop of acid rain that we walk on when water is too scarce to be fair. meaning one rain drop plus one rain drop plus one rain drop is a storm of some kind?

back on track I think the train ran off the universe's edge beyond the First Realty that they think is the source of all things real and under the event horizon of meanings meaninglessness.

yes I have gone beyond audience understanding and need a break at work to come to this post again, in this temporal cycle of time's concrete stickiness,,,

Ahhhhh can anyone save this thread from complete matrixide oxymorphic lint?

But serious people are reading what we type here,..

jellybeansoup it is all jellybeansoup.

dying in a temporal flux of constant phone's ringing everywhere. OK what is our job description right now? answer the phone.?

 

[Robert Maxwell]

think, I am going to close this thread unless you try to discuss this in a way other people can understand. You were talking about fractals and calculus. And? What about them? I think you've been given pointers on learning more about those things, if you feel so inclined. What is it you actually want to discuss here? Can anyone even tell?

 

[YellowSubmarine]

I just remembered my first math classes. Whatever think means here, I feel it's almost certainly impossible.

Any set satisfying the axioms for a vector space would correspond to a vector space of n dimensions where n is always an integer, with the only exception being a vector space with infinite dimensions. So anything that has fractal dimensions can never be represented as a vector space.

The least that this means that you can never describe relationships between the points of a fractal set with the basic set of mathematical operation (addition and multiplication). On a line you can use a real number, on a plane you can use a 2-dimensional vector supporting addition and scaling, but on a fractal sets those things can't be done. Any representation where addition and multiplication (or an analogue of theirs) are applicable would either include points not in the set or it would not include all set points.

Also, I have a suspicion that any mathematically sound representation would require a set of numbers between reals and integers, which is impossible to be proved to exist let alone constructed. Any set represented by n reals and a single integer would be equivalent to a set representable by n reals, so you need something between them to talk about half a dimension.

In short, regardless of what this means, it can't be done.

 

[think]

I just remembered my first math classes. Whatever think means here, I feel it's almost certainly impossible.

Any set satisfying the axioms for a vector space would correspond to a vector space of n dimensions where n is always an integer, with the only exception being a vector space with infinite dimensions. So anything that has fractal dimensions can never be represented as a vector space.

The least that this means that you can never describe relationships between the points of a fractal set with the basic set of mathematical operation (addition and multiplication). On a line you can use a real number, on a plane you can use a 2-dimensional vector supporting addition and scaling, but on a fractal sets those things can't be done. Any representation where addition and multiplication (or an analogue of theirs) are applicable would either include points not in the set or it would not include all set points.

Also, I have a suspicion that any mathematically sound representation would require a set of numbers between reals and integers, which is impossible to be proved to exist let alone constructed. Any set represented by n reals and a single integer would be equivalent to a set representable by n reals, so you need something between them to talk about half a dimension.

In short, regardless of what this means, it can't be done.

that really does leave my theory at a dead end so yes you are correct i was thinking along the lines of blending levels between the dimensions... at work again I will bid good by ..