Fundamental Relationships

[throng]

I'm back for more speculation.

 

I would like to construct an origin point A, but this can't be done unless there is prior space to place it in, so I'll call the space SP.

 

Alternatively, I would like to construct a space, but this requires a focal point as reference. This means an empty space and a focal point are reliant and no construct can be made without dual elements.

 

It can't be said that a space is prior to the origin or vice versa since these are simultaneously required.

 

Having no prior or causal property there is no duration, hence an empty space is not actually requisite of time, or it could be said that there is one event so duration is exactly 'one moment'.

 

Hence, by having no prior, one moment and no duration are equal quantities. I'll call the moment 0T

 

Now the construct is established as a relationship between A, SP and 0T. Thus a minimum of three related componants are required for a minimal fundamental primary event.

 

[ajb]

I would like to construct an origin point A, but this can't be done unless there is prior space to place it in, so I'll call the space SP.

 

Ok, so we have a (topological) space and you single out a point. In topology, this is known as a pointed space.

 

Alternatively, I would like to construct a space, but this requires a focal point as reference. This means an empty space and a focal point are reliant and no construct can be made without dual elements.

 

I don't understand what you are trying to do here.

 

It can't be said that a space is prior to the origin or vice versa since these are simultaneously required.

 

The point and the space need to be specified if we have a pointed space (we have the category of pointed spaces where the maps are base point preserving continuous maps). That I agree on.

 

 

Having no prior or causal property there is no duration, hence an empty space is not actually requisite of time, or it could be said that there is one event so duration is exactly 'one moment'.

 

Hence, by having no prior, one moment and no duration are equal quantities. I'll call the moment 0T

 

The causal structure on a space-time comes from the Lorentzian metric. You have not said anything about metrics, thus I would not expect a causal structure.

 

 

 

Now the construct is established as a relationship between A, SP and 0T. Thus a minimum of three related componants are required for a minimal fundamental primary event.

 

You need to sort out my previous comments before one can continue.

[throng]

Ok, so we have a (topological) space and you single out a point. In topology, this is known as a pointed space.

 

 

 

I don't understand what you are trying to do here.

 

 

 

The point and the space need to be specified if we have a pointed space (we have the category of pointed spaces where the maps are base point preserving continuous maps). That I agree on.

 

 

 

 

The causal structure on a space-time comes from the Lorentzian metric. You have not said anything about metrics, thus I would not expect a causal structure.

 

 

 

 

 

You need to sort out my previous comments before one can continue.

 

If there is a space how is it defined if there is no point to refer to?

[ajb]

A topological space is a set of point and a topology. So, (classically at least) a space is a set of points. (We also have ringed spaces and schemes, both of which do not have the notion of a point in their definition. However, one can get back to a set theory description using the functor of points.)

 

Space-time consists of points = "events" and a topology, for example the Alexandrov topology which is tied to the metric.

 

I think what you are doing is singling out a particular point. Your "focal point" or "origin". When you do this you are now is the category of pointed spaces.

Edited September 25, 2009 by ajb

[throng]

I fail to see how there can be any kind of thing, real or imagined, unless there is an interaction between at least two elements eg space/point.

 

Just thinking of a 1 dimensional space, Still it has two ends.

 

Why is an empty set different to nothing? It seems something empty is always in relation to a set containing things.

 

I'm just theorizing about the minimum number of componants required to create any object or emptyness. Any minimal formation or concept at all.

Edited September 25, 2009 by throng