Point + Point => God?

There's a lot more can be said about our two point universe. So far we have recognised:

• Distance
• Time

and made some assumptions: the Points themselves, and the lawfulness of the background universe.

There is as yet no physical substance here. Points, and the properties they reveal, are meta-features. From these we can derive meta-meta-features; e.g. the range of possible motions of our two points in relation to each other; and meta-meta-meta-features, and so on.

The characteristic of a meta-*-feature is that it expresses statically a property of change. For example, a "constant acceleration" is one possible meta-feature of a changing velocity.

Even with just two Points, there is already a potentially infinite range of meta-*-features describing the available changes in the Distance between them.

[Because this is an imaginary universe, and our points have no corporeal substance, it's an arbitrary decision whether we allow the Distance to go zero or not.]

Notice that I've avoided using the word 'number'. In our Universe we represent the features of Points by numbers; but Numbers are themselves meta-*-features. It may mislead us to apply numbers to distance and time in our imaginary universe, as the constancy implied by Number might not be fundamental to it. If that is the case, then there will be available changes in the Distance/Time relationship between our two points that cannot be expressed mathematically. This is highly probable: see Godel's Theorem.

In fact, the implication is that not only mathematical notation, but that any system of static symbolic representation is doomed to be an incomplete expression of reality. Things change, and change changes Things, which changes the range of possible changes, and thus Things. (Feedback, in other words).

In our imaginary two Point universe (which is as simple as a Universe can be) there can be no meta-*-feature that remains eternally constant.

Is the same true of our real Universe?

Yes, because we cannot transmit reality, only information.

One final thought (for now). Our physical Universe is a meta-*-feature of quantum-level properties.

Phew! Time for breakfast :-)

In the beginning ...

"Go back to First Principles" is a common request of pedants and managers.

Okay, let's do it.

Imagine a universe containing a single Point. It has no structure, no mass, no energy, or any property of any sort: it's just a Point. Only there is no point to a single Point. It exists, as we have defined it; but that's all: it only exists. It has no position, as there is no frame of reference for it to have a position in. Without position there can be no motion. It's a very lonely, very boring Point.

*Pop* and a second point exists. Now there is a frame of reference - the other Point. Assuming the universe containing these points is a lawful one, then each point now experiences Distance.

A universe without motion is not only dull, it's improbable. Change is possibly the only 'universal' constant. Thus our Points can move. Thus they also experience Time.

No matter how complex their motion might appear to external observers like ourselves, the Points are only able to notice change in the distance between themselves. Which may vary from infinitesimally small to infinity minus an infinitesimal. There motion may be smooth or rhythmical or complex, or all of these in turn.

If Time and Distance are infinitely smooth, then there are an infinite number of possible variations in the distance between these Points; but if Time has a definite tick and distance a minimum step (which must occur together: there cannot be one without the other) then the number of variations is finite. At some 'point' in time, the sequence of variations would be repeated.

So an imaginary universe of just two imaginary points already exposes one of the key challenges of modern physics.

First Principles have there limits :-)

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Jabber jabber jabber ...

I've just discovered Jabber (XMPP).  Which inspired one thought ...



Sun Inc use the strap line; "The network is the Computer".  True enough.



If Jabber had a strap line, it would be "The Conversation is the Computation".  Which paradigm makes soluble a lot of otherwise intractable problems; e.g. the need for GUI goodness.  GUIs, afterall, are mere frozen conversations.

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