Infinite Inside The Finite

[VossistArts]

Im a stone carver. Yesterday I was driving and considering carving. I found a perspective on it that I hadnt seen before. Say I start out with a cube of quartz, the size isnt important, and when Im done I have, just for instance, a little bell, or it could be anything, a star with points going 6 directions. Whatever the finished form is, it is the only part of the orginal cube, that has had nothing done to it, the only remain material left from the original cube that remain intact. Carving is purely subtractive. I considered polishing it and for a moment it seemed as though that is doing something to the finished form, but in reality it isnt. Polishing after all is just removing larger scratches to make them smaller to the point where they cant be seen by the eye anymore.

It lead me to a question. Say I have a cube of quartz to begin with, to leave a carving from. the dimentions of the cube are finite. Are there infinite forms I can possible create from withing the boundaries of the finite cube, in theory? Im not talking about infinitly sized forms, just forms, because form isnt dependant on size that Im aware of. I suspect, without knowing much about math or physics that there are infinite possibilities,which is sort of counter intuitive so the notion of there being infinite possibilities within a finite space seems pretty strange to me.

If that is the case though, what if what we call our universe is actually a set shape, like a cube with set dimentions. there is an absolute center so at the boundaries of all the sides of the cube in six directions it is o and counts to the center, call it 20. if you go from zero at one side, to 20 in the center and continue on in that line the next number is 19 until you get to zero on the opposite side. if you were to follow that line beyond the boundary, the next number after zero would be -1 and so on until -20 in the center etc.
maybe the bigger picture isnt that our one and only universe goes on and on perhaps there are defined limits and byond that is a mirrored space, on all sides, and within each space are infinite possibilities. heh, sort of like how some crystals form.. i imagine. I dont know, somehow something like that seems more tangible to my mind than one universe that goes on forever and ever. But still, my idea of it would still be an infinite number or finite mirrored spaces. and there would still be the question of the center and the boundaries and why. one of you math guys should know right? :P

a lot of the thoughts i have with their weird logic and possibities, musings I know but still, probably nothing but fantasy, but somehow, i often find them leading to my wondering if the phenomena of crystaline formations and even the elements that theyre composed of arent mirrors and building blocks of the fundamental reason, rhyme and fabric of all of phenomenal reality. i wonder if if there does come a time when we can follow our origins back to some primordial infancy if our ancestors might themselves be crystaline in nature. shrug

ps. nice to see you mr quack :)

[scameter]

hmm. interesting. crystaline structures are actually very interesting in and of themselves in nature, and the manner of their formation is almost unknown to us, but they still are very interesting just to even think about, and their possible place in the greater area of existence is even more interesting. :)

[zewc]

This is very interesting and worth a thought.

To begin with I dont know if there is an infinte form that can be placed upon a finite sized bit of matter....(just for clarity, i am using form as per the modern desc and not the ancient greek idea of form and ideas)

As a physicist the first thing that sprang to mind when I read this was the idea of fractal surfaces...have you come across them before? Do a google search if not.

Its intersting to note though, that something finite can also be infinite...take a straight line for instance. Lets make it 10 cm long. Now, i want you to divide that line in half and then repeat indefinately...im sure you can see where im going with this. Even though the line has one, stated dimension, it can be divided into smaller and smaller parts until you get down to the very atoms themselves...to the ancient greeks, who created the idea of atoms, they could in theory keep dividing the line ad infitium. We know that we cannot divide forever because eventually you would reach sub atomic particles, which can only be divided a few times more...so its not completely infinte, but approaching a number so large that to our puny minds might as well be!

as for the idea of the universe having a set shape...the verdict is still out on that one, but for me the universe has no shape, or if it does its so weird and not descript, that it makes no difference to us what shape it is. I do hope that its flat, or near enough...but thats another discussion!

And, on another thought, what if you created a mobius strip with the marble, or a simple curve. Both of these shapes are infinte in the sense that there is no start or end point.

One more thing, i liked the idea of infinite possibilities in a finite universe. Just one question: does 2 + 2 =5?

Of course not, therefore there are not infinite (not completely!) possibilities.

I know, its kinda spurious, but what can you do?

:hahaha:

[Thomas Knierim]

vossist: the dimentions of the cube are finite. Are there infinite forms I can possible create from withing the boundaries of the finite cube, in theory?

Certainly. For example, you could carve the Mandelbrot set. The Mandelbrot set is a fractal form that exists inside a finite rectangular area on the complex plane. The rectangle is roughly defined by Re -1.5 ... 0.5 and C -1 ... 1. A very handy size indeed. The length of the Mandelbrot set boundaries inside that area is infinite.

Though, I doubt that you will find an infinitely small carving tool... :lol:

Cheers, Thomas

scameter: and the manner of their formation is almost unknown to us...

Not so. Crystal structure, their symmetry properties, and atom alignment are well understood.

[MidnightSun]

Yes but where are new things about crystals, for example that they are alive. (can control themselves growing, regenarate, and even breed)

[zewc]

how do they breed?

[MidnightSun]

not like humans though, but anyway i cant explain it in english, i hope someone smarter will appear here and explain it soon :)

[MidnightSun]

We depends on natures kindness. It will give us answers or it may not.

[Smurf]

no nature does not give, it waits for one to find/create answers to our problems. nature does not question, it just exists. we create the questions so we must create/find the answers

[MidnightSun]

Of course it gives....us meal :P

[Smurf]

:rolleyes: :D you know that's not what i meant :lol:

[MidnightSun]

Kidding ;)

[deepakgang]

but if we make something out of cube - say a cone. Isnt the cube lost. Now the possibilities arise from the cone :think:

[Smurf]

yeah i just don't get this thread at all :think:

[locomotive]

If there is a cube of 100x100 and you want to get the most forms out of it down to the smallest forms? It will be finite. A huge number of possibilities but still finite.

[deepakgang]

Infinite can be made out of finite using Fractal approach.
In fractals we can make infinite length in a finite area.
Search for Fractals for more.

[sahyo]

what is there to get and who/what is there to get it...

here...you can have it...no one will mind as there is no one and no mind...



then maybe don't post?

;)

[locomotive]

that is infinite in theory, in reality the smallest is the smallest.

[scameter]

Right locomotive. We can estimate how the infinite would be in a finite situation using conceptuality, but that does not definitely prove it's reality.

[the_aphid]

I was online today looking for an "infinite" number of images of fractals, I find they inspire creativity. I came across this neat gif image in the wikipedia entry on Fractals (http://en.wikipedia.org/wiki/Fractal):
http://upload.wikimedia.org/wikipedia/commons/e/ed/Phoenix%28Julia%29.gif
This lead me to search thebigview for past discussions on fractals and the concept of infinity. Of course such a concept would have already been discussed here.


It lead me to a question. Say I have a cube of quartz to begin with, to leave a carving from. the dimentions of the cube are finite. Are there infinite forms I can possible create from withing the boundaries of the finite cube, in theory?Indeed this is an interesting thought, but I think I would have to disagree with Thomas here.
Certainly. For example, you could carve the Mandelbrot set. The Mandelbrot set is a fractal form that exists inside a finite rectangular area on the complex plane. The rectangle is roughly defined by Re -1.5 ... 0.5 and C -1 ... 1. A very handy size indeed. The length of the Mandelbrot set boundaries inside that area is infinite.

Though, I doubt that you will find an infinitely small carving tool... :lol:

Cheers, ThomasSee, the problem is not finding an infinitely small carving tool, but the problem of limitations of quantum material. In a BBC interview titled God, the Universe, and Everything Else with Stephen Hawking, Carl Sagan, and Arthur C. Clarke, Clarke was discussing the similarities between the form of galaxies and areas of the Mandelbrot set, showing what he believed to be visual (and of course mathematical) representations of black holes and the like. He then posed a question to Hawking as to whether there is an infinite scope into the quantum realm. Somewhat to my surprise Hawking said that it was unlikely, he mentioned that there is a theoretical limit which he referred to as the Planck length (http://en.wikipedia.org/wiki/Planck_length).

Thus, from this it would lead me to believe that if the material making up the sculpture in the thought experiment above is limited or quantized, that the number of possible structures that could be formed with a given amount of material could certainly be large, but by no means infinite.

[j000han]

The a_fid:
Thus, from this it would lead me to believe that if the material making up the sculpture in the thought experiment above is limited or quantized, that the number of possible structures that could be formed with a given amount of material could certainly be large, but by no means infinite.[/quote]
Me thinks a calculation based on the permutation of pixelcombinations that can be generated on a computerscreen multiplied with say 4.10^9 would allready be quite
impressive.
So what if it is not infinitive?
Perhaps the number of mandelbrot fractals after a certain point will be proven to be
cyclic something like the great cycle of pi:lol:

[j000han]

Provcided that one could adopt a mindset that allows for a ‘believe’in existence of a more advanced technology then we currently have.
to the degree that some sort of ‘timetraveling’
is not considered to be entirely impossible.
True such a mindset will likely not be strongly inclined to call this kind of technology magic,
Nevertheless I hold it that a mere nucleair explosion is quite a magical event if one
can abandon the current scientific explanation and thus reject an entire paradigma
that is based on a somewhat retarded understanding of matter.
One also has to be willing to let go of the judgement of such a fenomen as something ‘évil’,’wrong’ and/or even ‘sad’.
Can one embrace all this ‘suffering’ as being (as yet) perhaps unavoidable sideeffect
of the way we journey through this galaxy?
Are we a quasar in reverse?
or are we in progress?
I remember a saying:
”the first shall be the last and the last shall be the first’
Be it as it may ‘what comes around goes around’;):wallbash:

he Planck length equals [1] (http://en.wikipedia.org/wiki/Planck_length#_note-0)[2] (http://en.wikipedia.org/wiki/Planck_length#_note-1):
file:///C:/DOCUME%7E1/johan/LOCALS%7E1/Temp/msohtml1/01/clip_image001.gifmeter (http://en.wikipedia.org/wiki/Meter),
as the first number of this product precedes the multiplier
the formulae can be “re-encoded’ as L=1^-8.

Thus
c√c=L√hG/3= 1^-8.*√hG/3
so…
what does that mean?
Basicly 2me it means the Planc-wave- mistery somewhat less conventional
formulated however perhaps not nessescairily inaccurate.



I mean, one to the power of minus eight…..
that is in my book infinitely small.
It would read one divided,
by one to the power of eight.
In SI units (http://en.wikipedia.org/wiki/SI_units), the Planck length is approximately 1.6 × 10−35 meters. (4.4 × 1026 m (http://en.wikipedia.org/wiki/Metre) or 46 billion light-years) is 2.7 × 1061 Planck lengths.
So..
The estimated radius of the observable universe (http://en.wikipedia.org/wiki/Observable_universe) = 9*10^6=9* 1^6 light years.
Now if I consider this as the space in which we move,
Then the most simple model would be that we are in a blackbox of any shape
Provided that the size of that box is limited over a length of 9 lightyears in all directions, it can have any shape tubular/cubic/sferical.aso

The estimated radius of the observable universe (http://en.wikipedia.org/wiki/Observable_universe) is the radius of the ‘observable’
universe.
So…
because beyond that
it is not observable.
A scientist only believes what he can observe (observation comes from measuring).hence by the logic of his/her mind
he/she imagines a limited universe.
The medium (the c-o-m-p-u-t-e-r) as it is today,
is the message and the messenger.
The message is clear but the observer is amputated/allienated
from her/him- self.
J. Krishnamurti (K) pointed out that
the observer is the observed.
So…
What has technology (be it alien or not alien) resulted in?
A universe where there is plenty of space and time where eventually
(Schrodingers projection is 1000 years) we may try to blow up the black box and see what happens.
Perhaps we will not do it because we do not want to be here but we’ll do it just because we are insatiable curious about what lies beyond the known/imaginable bounderie(s).
If ever we do it( or have done allready perhaps)
the theory of fractals is entirely in allignment with this possiblity.
It is all a matter of relative density of conciousness.

Ii makes sense that we then(if we do it) make sure that we have our administration
well organized and have assigned any task that needs to be done the the right woman/man in must be in the right place.
And most importanly we must have designed a good plan for recombination,
As the chance that we’ll arrive in one piece is least to speak dubious if that would be our first try, maybe others(aliens) have done it and they know from experience the ramifaction(s) that such an action has or can have..
Perhaps this might all sound somewhat confusing,
But to avoid longwinded discussions on wheter eternity is 4 ever or not,
It suffices to me to say that, it is a hell of long time for sure.
Now…
regarding this process of recombination process, this is a ‘job’
that one has to do by choice as a single mind,
hence the bodhisatva’s of today are the budhissatva’s
of the past manifested in the future.
So…
what about alien technology?
What could it be a-l-i-e-n-
technology?
Where does it come from?
What are aliens?
We?
Is what a-l-i-e-n to Us is n-o-r-m-a-l to Them?
So….
what’s the diffrence between them and us?
Do they love/hate eachother like we do?
How far more advanced is their technology compared to ours?:blink:

[Tom]

The original poster proposed using a block of quartz to carve a figure. I think what he wanted to know is the count of the number of different forms that can be made from that block. If the end result is a quartz figure, then the number of different forms is finite. The number is also easy to write down.

Silica dioxide has known density in quartz crystals. This will give a count of the number of silica dioxide molecules. (HUGE) Any carving of the quartz block is the result of removing some number of molecules. How many different ways are there to choose molecules to remove? Let n be the number of silica dioxide molecules in the block. The number of different ways to select molecules for removal is n! (Read: n factorial) If n is HUGE, n! will be ridiculously huge. But it will still be finite.

The real number will be a lot smaller. It is not possible for a chisel to remove a molecule from *inside* the block. The math above allows for that possibility. Still a number so large as to be meaninglessly large. Although finite.

Carving something that has infinite length isn't possible given that there is a smallest unit: the silica dioxide molecule.

I hope I maintained the spirit of the original poster.

[schrodinger]

The original poster proposed using a block of quartz to carve a figure. I think what he wanted to know is the count of the number of different forms that can be made from that block. If the end result is a quartz figure, then the number of different forms is finite. The number is also easy to write down.

Silica dioxide has known density in quartz crystals. This will give a count of the number of silica dioxide molecules. (HUGE) Any carving of the quartz block is the result of removing some number of molecules. How many different ways are there to choose molecules to remove? Let n be the number of silica dioxide molecules in the block. The number of different ways to select molecules for removal is n! (Read: n factorial) If n is HUGE, n! will be ridiculously huge. But it will still be finite.

The real number will be a lot smaller. It is not possible for a chisel to remove a molecule from *inside* the block. The math above allows for that possibility. Still a number so large as to be meaninglessly large. Although finite.

Carving something that has infinite length isn't possible given that there is a smallest unit: the silica dioxide molecule.

I hope I maintained the spirit of the original poster.

Your reasoning is technically correct if we only consider the maximum possible number of permutations and combinations allowed by a finite number of discrete non-elastic molecules which can be arranged by carving or chiseling. However, I believe you are not accounting for morphing attributed to twisting as well as electroactive morphing in piezoelectric materials, such as quartz crystal. When these additional types of transformations are taken into account, I believe that the number of possible forms in any given block of crystal should theoretically approach infinity. Anytime we speak of infinity it must be on theoretical grounds, and theoretically we can twist an infinite amount of sub-degrees in any direction. There is an entirely new technology evolving at present in the field of electroactive morphing, which you may find interesting. One of the primary interests is to be able to change the topology of aircraft wings, allowing for previously impossible flight configurations. I don’t know if anyone has yet adapted any of this research to the field of art or sculpture, but I am sure it would result in some novel art forms!

[Malinson]

When you create a 10X10 cube of space, understand that this space CANNOT exist apart from the space surrounding it. The boundaries dividing the 10X10 area have to exist dimensionally in order to constitute the division, much like the number zero divides the negative and the positive.

In contrast to actual space, volumes can never arrive at measurements in terms of quantifications. In other words, we can never actually HAVE a 10x10 area due to the infinite regressive refinement of the boarders. There simply are no areas of space with a smallest division, in order to truly separate one area from the other.

To account for this we simply declare a hypothetical scale, drawing measurements within the theoretical volume. Saying that there is an infinite number of smaller points within a measured amount of space is a common mistake. It's easy to overstep our established scale of measurment without refining the other end. Measurements only exist within a hypothetical construct.

Thus the ballence is restored. We have an infinite number of smaller points, within an unquantifiable volume of space!

-Malinson