The three spaces (Physical Space, Conceptual Space, and Computational Space) can be regarded as a reference frame or basic background, while discussing such the topics in below. The most basic question would be how to judge the ownership of a thing, among the spaces.
Firstly, it needs to repeat that, the default context are computer (software) and applications, some main subject (for me) is models and modeling, and in addition, the models and modeling for the app domain, such as the business and enterprise. Then, there are the basic topics on the three spaces including: entities, models, representations and abstractions.
An entity is a thing we would treat or deal with in the context, which is able to be defined, identified, described, operated and, to be regarded as an object. On entities, we can further discuss the operations, relations, events, activities, roles, and process, … and more complicated things.
I prefer use “entities” instead of “objects”, since the term objects with specific meaning in the context: the use in Object-Oriented programming, and this is also somewhat a continuation of the tradition from information/data modeling.
There are three types of entities which are corresponded to the three spaces, can be called as physical entities, conceptual entities and computational entities. In other words, we can say, an entity of (belonged to) the physical space, the conceptual space or the computational space.
From a particular perspective, all types of entities are real-world things, and have some physical presence, such as the mass, shape, color of an object, the state of computer memory, the neurons or certain constructs in brain, and so on.
The basic criteria of the judgment to the ownership for an entity, is the operations (or measurements) on/to the entity. For example:
- As a computational entity (not an entity of a computer), a hard disk is a data storage device when it working in a computer to be stored/accessed of some data. The attributions are such as the format, capacity of data, etc.
- A hard disk is also as a physical entity, its attributions are such as the size, turning speed, input voltage, etc.
- In the conceptual space, a hard disk is some of memory (data) in brain, or in some text/picture on paper that can be read by human being.
There are different operations on the hard disk in different spaces:
- in the physical space, such as the motor rotation and the magnetic head movement;
- in the computational space, such as the data accessing;
- in the conceptual space, such as the thinking activities.
There is a nature of the three spaces: each space has its own operations by its own mechanisms.
Both a model and the object it modeled are some type of entity in certain space(s). Models can also be classified into three group: physical models, computational models and conceptual models, as well as the three types of entities. The ownerships in the three spaces for a model is consistent with the type of the entity of the model. For example, a group of records such as (S/N 093425235, SATA, 500 G, 7200 rps) in a computer memory may be a computational model of a physical hard disk (it depends on if the computer can process with the meaning of the data); in such a piece of paper (or, as in the essay) is a conceptual model (because it can be read and understood by us), of the physical hard disk. A model and its object are often in different spaces, this is one of the reason for emphasizing the three spaces. See the illustration below: it is very clear that the relationships among the disk, the model in the conceptual space and the model in computational space, and we can find that, the relationship between the conceptual model and computational model is different then with the physical disk.
One of my basic concern related to the three spaces are the representations of model (for example, also see the illustration), this involves in the way of the corresponding between a model and its object.
Finally, abstractions is a common and unavoidable topic in the context, it can be discussed on the three spaces more clearly, as will as for models and representations.
 Such the models and modeling of business/enterprise (and the uses) are logically independent of computer and applications, but in fact, from a technical/practical or a using aspect, it is still dependent on computer. it is important that to maintain a clear understanding of both.
 In essence, I think the three spaces can be attributed to some metric space. This is a significant topic which related to the foundations of mathematics.
( Last edited on November 13, 2011)