It is important to distinguish the apeiron, or wu, from the space which emerges from it. They are not the same thing – or if they are, I need to be careful.

Just because the Dynamic and the Static define Points and then 1D Rotations etc., that does not mean that every Point *is* the Dynamic or whatever. Instead it means there is a Point wherever a zero-dimensional Reflection occurs. Wu is the *substance*, and the Point is the *space* which emerges from it. Transformations are the *substance* of Reality, at least I maintain. But transformations do not ‘occupy’ space, they *define* it.

This is the slipperiness of the notions we’re working with. Wu (apeiron) is not the null set, no matter how tempting it is to define it that way. Yes, the null set *has no members*, and Wu is the uniform unchanging substance of Everything and consequently *has no relations*, but it is not a set precisely because it has no boundaries, and so *cannot* be delimited by the concept of a set (remembering that null is “The *set* containing no members”). Wu cannot be contained but is the container. So the first ‘element’ of Wu is the null set, i.e. a delimited portion of Everything, which is not Wu. The null set is defined by the zero-dimensional Reflection ‘not.’

Maybe Wu can be defined by x ∉ ∅, without {}, thereby making it *not-a-set*, i.e. an element – but an element that cannot be an element of any set!

Even the ‘finesse’ available in set-theory which is the *proper subset*, where every element of a subset is identical to the set (from which it is ‘subbed’) yet this is *not the same set*, doesn’t fit the bill. This is why the null set is its own subset but not its own *proper* subset. Apeiron still doesn’t fit, because you still can’t say it is a proper subset of the null set, since it’s not a set!

There is another tack available to my reasoning though – because I said initially that Wu is transformations, it doesn’t mean that *all transformations are identical*. Yes, they are all inter-dependent (transformations transforming other transformations), but the first Static is sufficient for the emergence of Space, and the first Dynamic is sufficient for the emergence of Time, but is that to say that all of space is an infiny of points? I don’t think so. Yes, we use Points to refer to the position of something, so yes, this creates the possibility of *reference*.

Unfortunately I know far too little of Topology to begin to understand the various configurations available for a collection of Points. Yes, they certainly could be spherically arranged. They can also be flat (Euclidean). But an infinite expanse of an infinity of Points renders the ‘curvature’ of space a moot point, since an infinity of points allows for any shape imaginable – the concept of curvature ceases to hold any meaning.

Bah! I’m losing steam here. Running out of ways to move forward. Could my reasoning have gone down a dead-end path? Could I have thought myself into a corner? It looks like it, but I’m not giving up. I may have to start from Nothing again.

If wu is the container, and null set contains no numbers, and wu contains no numbers, wouldn’t the null set also be a container? Wouldn’t the null set possibly be wu then? Would the first container contain the container? Yes it would. So wu would contain itself because it is itself. The concept of the null set contains the concept of the parentheses, only because we are talking about its concept.

Hi Jeff,

Thanks for commenting! It’s important you know that you are commenting on a post I put up a fairly long time ago and so I will tell you now that my ideas have evolved a bit since that post. That being said I will try to answer your points from my current understanding.

First it’s important to know that a container is itself a thing, where wu is not a thing (it is that from which things are ‘made’ so-to-speak), so to see wu as a container is the wrong idea – that’s one of the things I have to amend to the post above. A Thing is extant and thus bounded – so then the null set is a ‘Thing’ because a set (just the brackets) is a boundary. So the null set bounds a ‘piece of wu’ but not wu ‘as a whole’ because there is no ‘whole’ (what is a ‘whole’ if there are no boundaries? A ‘whole’ is necessarily a Thing and is thus bounded). And it’s important to remember that the brackets of a set are ‘made of wu’ also. It’s only tricky because wu is the ‘undelimited all’ where essentially there are no boundaries anywhere. But in that light, then yes one can ‘kind of’ think of wu as containing itself (with the caveat that ‘containing’, when speaking of wu, is meaningless).

I took issue with the popular concept of null set because it is highly problematic and yet so few people see it. If ‘null’ is to be equated to ‘wu’ then the null set should not be a ‘set’.

I realize that sounds so convoluted as to resemble utter nonsense. It isn’t an easy concept to grapple with, certainly! Continue reading more recent posts – like the one on adjacency theory, and my ‘set theory 2.0’ first attempt – a humble beginning, but a beginning nevertheless. I’m far from finished though, there’s a lot of work to be done to refine these ideas!

All the best to you,

Tom