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Author Topic: To what extent should space be described to be three dimensional?  (Read 4813 times)

Offline Greg_Kaye

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I have recently uploaded a website relating to a proposed philosophy on the topic of the origin of existence and went off on a debatably necessary tangent so as to attempt to tackle the topic of the nature of the dimensions of volumetric.  I would greatly appreciate some feedback regarding the views that I have presefgonted as, in essence, I have suggested that the view of volumetric space being structured with three dimensions might not be correct.  I have extracted the following lengthy piece of writing from a larger context that relates to relatively philosophical understandings of our "Interactions with Existence" so a couple of references to philosophical themes should be expected.  I should also mention that I have written the text in a way in which I hope may be read by the lay person and from the position of a non-mathematician.  I have tried to remove repetition but still have in mind to bring the text into a more concise form in future reviews.  The following text extract follows on from comments that were made regarding a baseline philosophy of perception.  I hope that this may help explain the use of the very basic view of the dimensions that is presented within in the text.
This extracted text can be found in its original context at:
newbielink:http://www.divinism.net/en/inx.htm [nonactive]
Despite its repetition here the usual claims to copyright still remain.
The quoted text ends with a request for feedback and with hyperlinks that are directed to the Physicsbanter.com page that hosts the original copy of this feedback required.  These links can be removed if required but all feedback will be appreciated.

"Out of the box"
Space, in the way in which it is commonly experienced, is quantified according to its volume. The manifestation of space that we experience is clearly volumetric. But here's a question that has been troubling me. To what extent should space be described to be three dimensional?
There is no doubt about it. Space is quite sensationally spacious and yet, if the theorists have got it right, there may be a great deal more to it than just that. The idea that space might have a large number of non-temporal dimensions would seem to have been around for hundreds of years but it was only in relatively recent times the theory of supergravity went as far as to suggest that there are ten non-temporal dimensions. Never-the-less, many members of the scientific community held the conception that there were a mere nine non temporal dimensions but this all changed when the mysteriously named M theory proved to be able to tie up many of the loose ends of the previously proposed string theories and to bring the common conception of the non-temporal dimensions into double figures.
I don't claim to have any great level of skill with regard to statistical analysis and yet one thing is immediately apparent. The numbers three and ten don't match.
What possible justification might there be for the existence of all the extra dimensions? I don't really have the ability to personally comment on the maths and, this being the case, I think that I had better restrict my comments to other aspects of cosmology.
In the language of Ancient Greece the cosmos was an ordered system, a fairly worldly ordered system but one that definitely worked. In modern times the word cosmos has been taken as being synonymous with the word universe and, in many respects, this is quite fair. The astounding qualities displayed by our universe are truly worthy of the description "cosmic". There are qualities within the cosmos that allow for: the stability of atomic nuclei, the potential for suitably proportioned quantities of matter to be grouped together, the existence of large quantities of hydrogen, the potential for the development of a significant abundance of larger atomic forms, stars that are hot enough to process the larger atomic forms but not so hot that they get burned out overly quickly, a sufficient generation of neutrons so as to allow for the production of large atoms but to an extent that results in an over production of neutron stars, a stability level within the working of stars that will occasionally allows for the dispersion of heavy elements but that will not produce any over abundance of supernova type explosions, an ability for protons and electrons to associate together within social situations that allow atoms both to bind together and to split apart again that is tuned in a way in which this can occur across a wide range of temperatures and the production of a sufficient abundance of carbon to provide a basis for carbon-based forms of life and the production of a proportionately suitable abundance of oxygen to amongst other extremely notable things allow them to then be eaten with a significant level of efficiency.
There is no doubt about it. There is a wonderful order at work within the universal system. How, we might ask, did it get to be so good?
One idea an idea that particularly appeals to me is that there may be a large number of universes. In my opinion, for what it's worth, it's a marvellously elegant idea. It's an idea that can be interpreted to fit in with the grand scheme of things and I'd like to illustrate the point through the use of one of the fundamental questions of existence.
What is life?
As far as the biological sciences are concerned, life appears to be a dizzyingly complex subject. Even if we were to conceive of the most simple possible form of biological life and by that I mean the most simple possible form of biological life that would have the ability to have substance added to itself and have the ability to organise this substance within itself and to have the ability to then get everything moved around into some form of duplicated arrangement and to have the ability to divide or to be divided and to, thus, have the ability to reproduce and (in this kind of way) to, in effect, get onto any conceivable rung of any conceivable evolutionary ladder even this form of simple life would be, by necessity, complicated. It would be phenomenally complicated. Life is quite simply, quite incredibly and quite phenomenally improbable. However, this is not a fact that should be considered in isolation. Life is a phenomenon that appears to exist within a universal context and the universe, we might do well to note, is quite simply, quite incredibly and quite phenomenally big. It might be interpreted that there may be a connection between these two facts.
But what is the universe? The universe is a place that is governed by a wide variety of physical laws within the context of a wide variety of physical "constants". The situation of the universe is quite cosmologically improbable. In response to this astounding situation it has been quite logically been proposed that there may be a great multitude of universes.
So there you have it. Life is incredibly improbable and yet the universe is quite, inconceivably large. The universe works according to cosmological rules that are of benefit to forms of life that have a high level of energy consumption in a phenomenally improbable way and yet a phenomenal multitude of universes may potentially be conceived. If there is a god an if this god had wanted high energy forms of life to come into existence then it may well be considered that, perhaps, this is how God would have done it.
{at this point I should point out that I don't consider that the page is particularly pushing for or against the idea of God in my page and this would be apparent if you read this extract in context newbielink:http://www.divinism.net/en/inx.htm [nonactive] or took a read of the page on Judeo-Christian-Islamic Divinism, newbielink:http://www.divinism.net/en/jcid.htm [nonactive] }
It may be conceived that there are a multitude of universes but if this might be considered to be the case then a very basic question might be asked. Where are they?
There are plenty of ideas that may be considered. One idea has it that, during a period of inflation following a "Big Bang" event, a great number of separate universes will random characteristics may have been generated. Another idea has it that any number of universes may exist in a chronological sequence along the line of time. Each universe will have its own individual beginning and yet it may, potentially, be considered that the expansion of each universe may coincide with a fresh expansion of volumetric space. I mention this detail on the simple reason that I'd like to demonstrate the extent to which agreement can be found between this interpretation of universal origin and the claims of the Biblical text of creation.
The Hebrew and Aramaic texts of Genesis state that: In [a] beginning, He created, "Gods", the skies and the land. The first word of the original language texts is bereysheet which directly translates as: in [a] beginning. It is not written bahreysheet and does not directly translate as: in the beginning. The fact is that the definite nature of the mentioned beginning is not articulated. The wording of the text is clear and yet, even if the definite article had been used, it would not preclude the existence of other beginnings. In everyday life we can talk of things like the phone, the toilet, the house, the door, the garden, the pub, the bike, the bus, the boat, the sea, the sunset and the moon and still acknowledge that there may be other phones, toilets, houses, doors, gardens, pubs, bikes, busses, boats, seas, sunsets and moons. In a similar way we may also talk of the universe, the cosmos or even the skies and the land and still consider the possible existence of other universes, other cosmoses, other duplications of the skies and other lands. In this light it can be considered that the Biblical text begins in a radical way. It does not speak of the beginning. It just speaks of beginning. So what of our Biblically believing friends? They have no immediate reason to object to the idea of multiple beginnings. If anything the reverse can be interpreted to be true.
Having cleared that up, perhaps we can get back to the topic of multiple universes. So far we have considered that various universes may be conceived to exist in parallel with our universe and that they can also be conceived in a different time frames to our universe. It may additionally be conceived that universes may even exist both in parallel with our universe and within a different time frame. Within this idea it is possible to envisage that there may be situations that cause a number of universes to start simultaneously and it may also be possible to interpret that universes may even be created on a more flexible timescale.
As mentioned, it is widely interpreted that the existence of additional universes will require the existence of extra dimensions. M theory suggests there to be ten non-temporal dimensions. That's a lot of dimensions and yet it is commonly asserted or at least suggested that experienced (volumetric) space is constructed with just three of them. Why is it thought that space has three dimensions? There may be a number of reasons for it - there may even be some good mathematical reasons - but I have a hunch that one of the causative factors behind this way of thinking is simply that this is the view that we grew up to believe. Its almost as if we were conditioned towards to believe it.
To prove the point let's take things back a bit. You probably don't remember your birth and yet it may be interpreted that there may be good reasons to believe that the event actually happened. You entered a world and what did you find? The world contained people who were, amongst other things, tall. The tall people reached down and looked after us and, as luck would have it, you would most probably have lived with them in their typically secure and squared off homes. Within the context of buildings like this you would get moved from place to place by the tall people and, in the earliest of times, you would stay where you were put. It wasn't a situation that was likely to last forever. For sure there were early difficulties in pushing upwards. It wasn't even that easy to move around but, again, you were up to the challenge. You took your chances. The thing beneath you was typically big and flat. Don't you love a level playing field. This floor gave you a chance of free movement and you took it.
In the early days everything used to come to you and yet you progressively gained the ability to go out into the world. Your progress was good - no - more than that - it was remarkable. You mastered space and time and conquered gravity. How did you get to be so good so fast? It was as if you were a natural. Yes - that might help explain it. Your genes may be interpreted to have packed themselves with as many performance enhancing bits of coding as they were able. Genetics had its game plan and, if everything worked as it should, gravity had no chance.
You found that the world was filled with amazing things of all sorts of shapes and sizes. All the things existed within the context of the floor and of other impressively proportioned things. There were tables and chairs and beds and TVs and a floor and walls and doors and windows and a ceiling. It was obvious that some things were either tall or long but there were other things that were just big. You learned that these things had width and, at some point, the concept of depth would also have been acquired. Then you went to school and all these ideas were placed into the ingenious language of maths. It all made so much sense. Widths were measured along an x axis, heights were measured along a y axis and depths into the distance were measured along a z axis. Everything was neatly squared away. As far as the system was concerned, there were three axes of measurement and these axes could be used for the measurement of the dimensions of any object or space.
This axes based method of the measurement of space has proved to be so useful within the mathematical sciences and is so instinctively intuitive that it would seem to have become the basis of a widely accepted understanding of space itself. Space exists within a context of three perpendicularly aligned dimensions. It might be considered that this was an idea to which we were born to gravitate.
But what if there had been no such thing as gravity? What if humanity had been born into a situation of weightlessness and what if we were genetically adapted in ways in which we were suited for a weightless existence? What if the physical structures within society had been based on shapes other than squares? What if, for instance, physical structures had tended to be based on that extremely stable shape - the triangle? What if spheres had predominated?
Here is a truth that may be worth bearing in mind. At the universal scale we don't actually know which way is up. We don't even know if there is a universal up.
Our concept of up, in effect, relates to the effects of gravity and, as such, it is a concept that only has relevance in our local environment. We take our stand on a gravitationally active and relatively spherical planet. We stand up and, in effect, we stand out. This is the way that things work with gravity but it can be noted that the phenomena of up is not solely dependent on gravitation. In any situation in which momentum becomes the dominant factor things tend to get reversed. In becomes the new out, standing out becomes standing in, hanging in becomes hanging out and, in effect, down and up exchange positions.
Basically, even if we had been born into a situation in which gravity had been less dominant we may still have had a concept of up. However, it may be argued that, if it we had lived in a society within which gravity had been less of a dominant factor and if it had not required such a consistent effort to stand upright, we may have felt less attachment to the concept of the right angle. The right angle would always have been a tool for measurement and geometry. It's just practical.
It will always be clear that space can be measured according to the three dimensions. However, it may be less clear whether space has any form of three dimensional structure. This being the case, perhaps we can give some attention to a subject that may perhaps be understood with greater clarity crystal.
Salt crystal have a clearly cubic crystal structure. Water, however, has a noted property in which it typically freezes with a clearly hexagonal crystal structure. Picture a snowflake. Even when you look at a flat image of a snowflake it is clear that it already presents a lattice structure in which the lattice lines run in three directions. A fourth lattice line in indicated within the depth of the crystal structure. Moving beyond snowflakes we can note that hexagonal crystal structures are exhibited in the common solid forms of 36 elements (Americium, Berkelium, Beryllium, Cadmium, Californium, Carbon, Cobalt, Curium, Dysprosium, Erbium, Gadolinium, Hafnium, Helium, Holmium, Hydrogen, Lanthanum, Lutetium, Magnesium, Neodymium, Nitrogen, Osmium, Praseodymium, Promethium, Rhenium, Ruthenium, Scandium, Selenium, Technetium, Tellurium, Terbium, Thallium, Thulium, Titanium, Yttrium, Zinc, Zirconium). Another 42 elements have solid forms that are commonly based on cubic crystal structures while another 19 elements have solid forms that are typically based on other crystal structures that may have three lattice lines but depart, in various ways, from a purely cubic form (Antimony, Arsenic, Bismuth, Boron, Bromine, Chlorine, Gallium, Indium, Iodine, Mercury, Neptunium, Phosphorus, Plutonium, Polonium, Protactinium, Samarium, Sulphur, Tin and Uranium).
Crystals indicate that it is possible for something to fill volumetric space and yet have something other than a cubic structure. The physical dimensions of these crystals can still be measured to have lengths, widths and breadths and yet, on a structural level, this changes nothing. When the building blocks of matter come together in close formation they can do so according to organisational formats that do not necessarily progress in a systematically cubic way.
With all this in mind perhaps we can finally return to the topic of the "dimensions". The concept of three dimensions is all very likable. What's not to like?
Its only when we take the concept of three dimensions and then start to pile on other dimensions that things get complicated. What are they? Where are they? People sometimes talk of higher dimensions so as to typically describe dimensions that may link the form of space that we experience to other contexts of space. These higher dimensions may even be considered to various parameters of hyperspace. But the question may be asked, just how hyper can space really be? How many dimensions can be piled onto the volumetric space of experience?
With all the talk of higher dimensions there could potentially be a worry of things getting top heavy. However, there is an alternative route by which the apparent dimension glut may be dealt with. It is now commonly thought that certain dimensions may exhibit themselves, at an extremely small scale, through the phenomenon of repeating structures that are considered to be evenly spaced across space. It is an intriguing idea and we may be forced to wonder about the consequences that these structures might potentially have on the rest of space and upon the ways in which the other dimensions might be structured.
All the same, even with the inclusion of ideas like lower dimensions, it becomes clear that the dimensions are not fully understood. Will their ever be a full understanding of the dimensions? It is beyond doubt that some measure of exocubic thinking will be required for this to be achieved.


 

Offline Greg_Kaye

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Still hoping for thoughts regarding the potential validity of the dimensions issue
 

Offline LeeE

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Try to get it all down to short abstract and then people might make the effort to read it.  What you've posted above is too much to read for casual readers and is too much like hard work for people who might specifically be interested.
 

Offline Soul Surfer

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I have waded through this and had a look at the websites but see little but garbage complex language and confusion so as I could find little positive to say about the ideas I have held my peace until requested to give my opinion.

Here is what I wrote a few days ago but decided not to publish.

This is a great many words for someone to use to say very little except to prove that the writer should learn a good deal more about basic geometry and mathematics.

Greg you seem to be in awe of the concept of a dimension when it is purely a mathematical convenience.  A dimension is one of an array of properties of an object that is measurable and can change independantly of other measurable properties of that object. There are many occasions say for example in the basic interactions of molecules in a gas where the overall number of dimensions of the system can be virtually infinite that is each individual particle has six dimensions three of position and three of momentum and thre motion of each of the particles is independent of each other until they interact.

An electron for example is a fundamental particle that can move in space but it also has properties of charge mass and spin and it is therefore reasoably obvious that more dimensions are needed to describe it fully.

Our familiar dimensions of space and time are useful approximations but relativity also clearly shows that more are needed.

 

Offline Greg_Kaye

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My question, as presented on this site, asked: To what extent should space be described to be three dimensional?  It was a genuine question and I am grateful that you have presented an authoritative view of a dimension being a "purely a mathematical convenience". 

In response to this information it seems to me that I should perhaps present my question in other forms. 

What is it that makes space spacious?  If a dimension is a "mathematical convenience" what is it, if anything, that extends the boundaries of volumetric space and is it three dimensional?  People often talk of space as 'being' three dimensional - but is this right?

I also appreciate the succinct description that "A dimension is one of an array of properties of an object" but, if possible, I would appreciate further clarification on this matter.  Forgive me if I am using the incorrect terminologies but it has occurred to me that, in very general terms, a block of ice may be ascribed to have properties that indicate that it can be measured along the Cartesian coordinates x, y and z while its genuine properties would seem to indicate that it actually has a hexagonally based structure. 

Space can be measured according to three perpendicularly aligned axes of dimension but I am still left to wonder: what are the properties that cause space to manifest a volume and to what extent these properties might be described to be three dimensional?

I have now expanded on my question and am still hopeful to receive an answer.

In my post I freely admitted that "I don't really have the ability to personally comment on the maths" and I quite agree that I need to "learn a good deal more".  That is why I am here. 

I do not believe that I am in awe of the concept of the dimension.  It is however a concept that relates to a widely perceived structure or format within space that I would like to question. 
 

Offline Greg_Kaye

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I guess that my question, what remains of it, may merely address an issue of somantics and yet I'm not sure.

Should the manifestation of space that we experience be defined to be:

'three dimensional space'

or

'volumentric space'
in the context of Cartesian geometry being considered to be:
'a method by which volumetric space can be measured along three axes of dimension'.

My main reason for mentioning the issue is that it always seemed to me that the three dimensions were the property of space rather than a property of geometry.  This view was compounded when scientific reports began to present the idea that there might be tiny looped manifestations of dimensions embedded into the fabric of space and placed on the intersection of dimensions.

I still hope to gain a better understanding of the issue.
 

Offline Gasparri

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My question, as presented on this site, asked: To what extent should space be described to be three dimensional?

  To what extent... I suppose your intention is to describe space as
  3 dimensional and you want to know how far you should go with it.

  Well, not very would be my advice. You see, dimensions are ambiguous
  things so you have to define what a dimension is before you can do
  anything useful with it. In space no one can measure the same frame twice. Odd as it is it defines the essence of motion as being that which gives rise to motion. So we reference a thing with reference to another thing and if what we are measuring is motion we call it time.
Space and time are one in the same thing really, sort of dimensionless non entities that in of themselves define no definition.

 When you look and 'see' therein you 'become' and know that you
 are theta to a sphere of your perceived surroundings. You become an element of the universe and your consciousness a point of demarcation.
 By observing you become part of the observed. No phenomena is a phenomena unless it is an observed phenomena.

  When you limit yourself to x,z,y as directional distribution indicators the nuance of x',z',y' may be overlooked leaving you
open to unintended blunders like not shooting craps with God.

  I would advise thinking of dimensions as perceptions indicators.
 Most normal ones are square law by design. Nature has a thing with numeric dimensionality and really digs Fibonacci. Mozart too had a
thing for dimensions found in harmonic geometry.
 
 

Offline Greg_Kaye

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Thanks Gasparri for that.  You've provided some great perspectives and directions for further study.
If anyone is interested or willing to take a look I have placed some streamlined information regarding the dimensions of volumetric space on newbielink:http://www.divinism.net/en/3d.htm [nonactive]
I am open to all further clarification.
 

Offline Mr. Scientist

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I guess that my question, what remains of it, may merely address an issue of somantics and yet I'm not sure.

Should the manifestation of space that we experience be defined to be:

'three dimensional space'

or

'volumentric space'
in the context of Cartesian geometry being considered to be:
'a method by which volumetric space can be measured along three axes of dimension'.

My main reason for mentioning the issue is that it always seemed to me that the three dimensions were the property of space rather than a property of geometry.  This view was compounded when scientific reports began to present the idea that there might be tiny looped manifestations of dimensions embedded into the fabric of space and placed on the intersection of dimensions.

I still hope to gain a better understanding of the issue.

Three dimensions, of course.

The word ''dimension'' just means 'realm of freedom'. We have three realms of freedom - height, width and bredth.
 

Offline yor_on

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It's a good question to me too. One I'm wondering about.
Dimensions is very much a mathematical subject. Difficult to prove experimentally. In China a long/some time ago they used a length called 'Li' if I remember right. From A to B was 5 LI but from B to A there was 6 LI (downhill / uphill) To me that was a closer approximation of distance than our Newtonian unvarying one.

If we by relativity can say that no distance is 'given' but only express itself as a relation then what is 'dimensions'? If I draw it to its utmost conclusion then 'Dimensions' is something 'unfolding' from a zero origin. And then all discussions about several more 'dimensions' glued to ours become debatable.

---

By that I mean that our 'SpaceTime' is a 'whole' object 'materializing'.
Not 'bits and ends' that fits together.
« Last Edit: 17/10/2009 02:58:21 by yor_on »
 

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