# Describing the difference between things that are 'atomic' or 'self-contained' and those that are 'indeterminate' or 'boundless'

Sorry for the poor title, I'm asking this question because I can't think of a good way to phrase this...

When we describe the stress required to extend a spring to a given length, we describe this stress in Newtons - a single, specific quantity of force.

When we describe the stress required to extend a material to a given length, we describe this stress in Pascals (pressure) - an amount of force per area.

This is because a material is an abstract concept without dimensions, unlike a self-contained device with specific dimensions and boundaries. A material can have physical properties, but a device can be represented by a CAD model while a material cannot (only a piece of a material, which is itself like a device).

How can this distinction - these two categories of things - be described?

If that didn't make sense, here's another example.

A molecule can be thought of as a molecule if it has determined limits - it has a set number of atoms of each type. (Please don't get hung up on the specifics of why this definition is right or wrong, as that's not relevant to the full question).

A lattice cannot be thought of as a molecule because it is of indeterminate size - it does not have the same limits. It can stretch on indefinitely and when its behaviour is described it is thought of as doing so.

Again the same distinction is seen between the self-contained and the indeterminate. How do I describe this?

• Constrained vs unconstrained? Dec 18, 2016 at 21:09
• @KatherineLockwood that's close, but I don't feel it quite hits the nail on the head. Constrained implies (to me) that something external limits the bounds of a system, which is not the case - instead it's constraints are it's own if that's a sensible distinction to make. Dec 18, 2016 at 21:12
• Bounded vs unbounded? But unbounded often has a connotation of expression of emotion, and bounded has mathematical connotations as well. I think maybe I'm not understanding why the words self-contained and indeterminate won't work. They seem like better words than any that I can think of that is in a neat (adjective) vs. un(adjective) package. I'm not really trying to answer; just tto get a better sense of what you're looking for. Dec 18, 2016 at 21:30
• @KatherineLockwood that was the best I could do, but again it doesn't feel like it conveys the concept adequately. It implies to me that the two concepts are different only due to one small tweaked parameter - whether or not there is a bound on their dimensions, while in actuality they are completely different and should be treated as such. Dec 18, 2016 at 21:33
• @KatherineLockwood self-contained doesn't feel right to me, it doesn't give the sense of... modularity, or atomicity, that I think should be conveyed. Neither of those words quite work either - atomic in the original sense of 'indivisible' fits well but has connotations to atoms, which is unhelpful, and modular implies that an entity only completes part of a task, which is not necessarily the case. Indeterminate is somewhat better IMO, but it gives the sense of '[dimensions] cannot be determined at this time' rather than Dec 18, 2016 at 21:38

Caution is needed. In science Stress is defined, as force over area, and is always measured in Pascals. Thus your initial example is incorrect. The Force is the force, not the stress. If it's measured in Newtons, it's a force. I make this point because information for a material is specific, which is defined as per unit (whatever) of the material. Thus stress is the force PER UNIT area (i.e. 1 m^2) of the material. You will be more familiar with this term from, say, specific latent heat, which is Energy PER UNIT mass (i.e. 1 kg). I have always used the term particular to refer to a piece of a material, such as the particular spring in your first example, and specific to refer to the material properties. Anything else is likely (and in my experience always does) cause confusion in students. So, whilst a material is a concept, the properties of that material DO have dimensions - unit dimensions, by definition. The underlying problem is that scientific terms are bandied about by non-scientists as if they are all synonyms (sports commentators are the worst), and they aren't. I don't think that there is a good single comparison for all the examples you have given. I would use unbounded or infinite for space, like a lattice. I would use unlimited for something like mass or particle numbers General can also work. One of the big issues is not creating (too much)confusion in the students' minds between the use of terms in everyday language,and the defined uses in science. In early lessons, I'll often use stuff for something indeterminate, like copper - "we've got some of this stuff here".

I think you are trying to get at the notion of an individual (sometimes called an identifiable object). Distinguishing an individual is the process of individuation (WordWeb Online). The verb is individuate. I'm guessing that's behind what you are asking about as "describing the difference" between an individual and stuff that is not seen as such.

How and whether this is done depends on the field and the level of study in a given field. What distinguishes a biological individual (whether organelle, organism, community,...) is different from what distinguishes a physical individual (particle, planet,...).

I think, having thought over this, that the best choice of words is determinate and indeterminate. These are commonly used in grammar and linguistics to distinguish between countable and uncountable entities, and in my view encapsulate the concept I was originally trying to express.

A molecule is of finite size.

A single crystal is of finite size. A crystal lattice is notionally (or theoretically or mathematically) infinite, notionally because no piece of matter can actually be infinite in size.

A liquid droplet is of finite size. The statistically disordered structure of a liquid is notionally infinite.

Crystal lattices and liquids have translational symmetries that are discrete and continuous, respectively. Molecules, single crystals, and liquid droplets do not. Only matter that extends infinitely in one or more directions can have translational symmetries.

Bounded and unbounded (limited or unlimited in spatial extent) also work as surrogates for finite and infinite.