For a conceptual discussion on a general-interest website, yeah, it’s tough. As a physicist do you agree that Consciousness/ the Subjective is a “dimension of reality” that Humans feel exists that is distinct from the Physical, even if, when the layers are peeled back, it (may) turn out that Consciousness is illusory? It may be, but we don’t live our everyday lives as if I is illusory, yes?
It could be fundamental to the whole question. it’s really not at all clear what you mean by ‘dimension’ - and thus the subdivisions of the physical world could be argued to be ‘dimensions’ in their own right.
MrDibble,
Please give me an example of an object that exists independent of the information about the object and outside of informational relationships with the rest of the universe.
How about a photon?
IMHO the discussion of which is more primary and emerges from the other gets into goofy chicken egg territory but it must be noted that some very seriously see information as the most primary stuff of reality with objects emerging as a result: the information interpretation of quantum mechanics. Wheeler’s “it from bit” articulation of the concept is most well-known.
I would argue though that objects and information both exist at all times and are both reality. No Mangetout, information cannot exist without physical medium … and a physical medium does not exist without information. Not sure that I would label information and physical objects as different “dimensions” of reality though.
Further I see no need or utility in conceptualizing Platonic ideals as on that same level of primacy. Platonic ideals are abstract concepts that are a subset of thought/information, the relationships between more primary information, and can only be considered at that level of analysis. IMHO.
Yeah, what he said 
Defining “dimension” - I am very open to hearing that it can’t be done, or if it can, at least it can’t be done by me. I am trying here!
It is my understanding that it is commonly accepted that the Physical and the Subjective / Consciousness exist, at least somewhat, distinctly. What we experience as we think may emerge from our physical existence, and our thoughts may reflect what we are experiencing in the physical world, but are not limited to them.
If that isn’t sufficient, I may need to keep reading and come back when I have more to attempt to share and ask about.
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Further I see no need or utility in conceptualizing Platonic ideals as on that same level of primacy. Platonic ideals are abstract concepts that are a subset of thought/information, the relationships between more primary information, and can only be considered at that level of analysis. IMHO.
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Okay, cool. I need to ponder that.
When you say Information, are you talking about the properties of a real object? (i.e. the energy of a photon, the colour of an apple, etc?)
I think I’d agree that all objects have properties. I can’t think how there would be an exception to that, but I don’t think objects are existentially dependent on their properties - the properties are attributes that depend on the object - the properties arise from the object - the object does not arise from its properties, I think.
ETA: and I think my proof for that is that we can add properties to an object - we can bite an apple, or spin it, or bake it in an oven and it becomes something that needs more terms to describe it, but we can’t take properties and add more objects to them.
In that case, I’ll stick with my original “two” - the Ideal is just a subset of the Subjective IMO. I don’t agree that there’s a substantive difference between the two categories.
All of them? Information *about *a physical property isn’t the property itself, anything else is confusing map for territory. The thing must exist before there can be any *about *to speak of - you can’t have a predicate *before *a subject exists. And I’m of the view that existence *itself *isn’t predicative.
Objects in fact are their properties. You change the properties and you change the object; you change the object you change the properties.
So in your example “apple” is an independent “object” only as defined by information in relation to other information. Only BY the properties that we define as “apple” does it have such an identity. Identity is a function that occurs at the information level.
“I disagree.” 
Seriously.
Let’s get most basic: the wavefunction in quantum mechanics. Until information is observed (by interaction) from the wavefunction an object does not exist. The observation of the specific information creates the object to (at least) the same degree as the object’s becoming one thing out of all the possible states that could have been creates information.
If I had to take a side in choosing information or object as more primary to me the easier side is information if for no other reason than that objects can be destroyed but, according to current thinking in physics, information in the universe is preserved (albeit not always accessible).
Okay - back to this: so, what about the seemingly-independent concept of Twoness? I believe MrDibble is saying that they are Thought and become shared due to culturalization. So there is no “truly shared” quality that differentiates a Form from Subjective thought. Is that what you are saying, too?
I certainly cannot state what the best definition actually is but to me “dimension” is thought of as different axes and how an object or concept can be the same as another object or concept along one of the axes (dimension) yet vary among any number of others and thus be very different things: two chairs identical in size shape and mass but different in along color, time, and location dimensions for example are descriptions of different things. Or alternatively how an n minus 1 slice of a thing that exists in n-dimensions is different that a different n minus 1 slice of the same n-dimensional thing, or an n minus 2 slice.
I see “information” and “the physical” not as that but as concurrent equally valid descriptors of the same exact complete things with equally valid and meaningful real existences.
And to you last question - yes, I think … that twoness is a concept of information and as such exists observable in the information/thought level of analysis, not independent of it.
Specific to this is this I am sure bastardization of the Stephen Wright joke:
I have a map of the world. Actual sized. You’re standing on it.
Actually a bit profound.
I think you are confused about what maps are. Maps are objects that have filtered, eliminated, and reduced (by way of transformation and translation of properties) information/objects to representations of them that are symbolic representations, useful because of what is left out. If you had a map that shared all the properties of the object what you have is the object.
The information level sounds like an unnecessary and artificial distinction, rather than something that exists in its own right. Identity is a function of the object itself. Information is an artifact of our perception when we interact with the object.
I’ve held this view for more than fifty years; now I have a name for it!
Is there room for some of each? Some numbers are experienced by us in a physical context – two, three, a dozen, a hundred, thousands, even millions – and other numbers are abstract symbols that don’t have any physical representation – pi, 10^450, infinity, the square root of negative one, and so on.
I sure don’t see why not. My basic point is that the question of whether Numbers/Ideals exist in a Platonic way has been around since, you know, and is still a viable concept today. I respect the POV’s of other folks on this thread saying that Numbers are just a specific form of information, but, to my knowledge, this is opinion, not settled Science.
[QUOTE=DSeid]
I certainly cannot state what the best definition actually is but to me “dimension” is thought of as different axes and how an object or concept can be the same as another object or concept along one of the axes (dimension) yet vary among any number of others and thus be very different things: two chairs identical in size shape and mass but different in along color, time, and location dimensions for example are descriptions of different things.
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Cool. That works for me. It gets to what has been sticking for me with regards to Ideals. When I think of defining an object or concept, I am noodling about how I think about it, and I think that I consider
- What can be stated about it Physically = “It”-based language
- What can be stated about it Subjectively = “I”-based language
- What can be staged about it Collectively = “We”-based language
Back to Half Man Half Wit’s reference to Roger Penrose - at least someone out there holds the idea of 3 dimensions out as viable! 
So, Penrose is incorrect and is commonly thought to be? I will dig around and see what I can find out.
By the way, yay for this thread. It started off slowly, but I am appreciating what folks have to say and enjoying the discussion that has arisen. Hope others are, too.
I belive that possibly several demensions may exhist that the human mind has yet to recognise the concept of. Nothingness might somehow be a place where energy and matter coeixst with a third force of some kind that keeps them stable as nothing. Possibly absolute density.
If nothingness is a thing, then it’s not in fact nothingness, surely?
Penrose is one of the best mathematicians, and best mathematical physicists, ever. True genius.
But he lost a lot of fans when he tried to prove that artificial intelligence is impossible, using quantum physics. He got to flirting with vitalism, which, these days, is kinda cray-cray.
Grin! There is an empty set. The set of all empty sets has a cardinality of one.
So, yeah, there is “nothingness.” And you can observe it, right now, by taking a close examination of all of the zebras in your living room right now.
(Unless, y’know, you’re one of the very lucky few who actually have zebras in your living room!)
Not going to go the whole Von Neumann route here? That is you then have two, that set of all empty sets that contains the empty set and the empty set itself … hence the Von Neumann Hierarchy continues literally ad infinitum creating all natural numbers out of nothing.