Entry 21: in which We kick around a hypersphere

"Pater" says the boy.

"Hmmm?"

"This pink string disc thing ... hey I like it, it's got a ring! Pink string disc thing! Or we could ping pink string, or ... "

"Yes, yes, what about pink string?"

"Well you know how there's this 2D chap that we plop onto a 3D world and then first he's outside his pink string disc thing and then suddenly he's inside it and it all seems very magical ..."

"Yesss ..."

"Well you said to extend that by another dimension and Bob would be my uncle, who is Bob by the way?"

"Never mind Bob!"

"Yes, well anyway I've given it a lot of thought and can you explain it to me please?"

Good grief, what is the point of planting seeds of wisdom when they wither on the vine if I may mix my metaphors a bit. I sigh but continue:

"Right, so essentially we have our magical ball of pink string, the one that won't run out, and this time we plonk Mr 3D on a small 4D hypersphere. Well just as Mr 2D on the north pole of a 3D planet looked around him and thought he was on a familiar 2D plane, so Mr 3D looks around him and concludes he's on a familiar 3D sphere.

"His job is just to walk around and around the (initially small) sphere, playing out the pink string as he goes. As he does so, the sphere gets covered with pink string and starts to get bigger and bigger, just like one of those 'biggest ball of string in the world' things.

"He keeps going and the sphere gets bigger and bigger, huge in fact, so that the horizon is a very distant thing. But he just keeps going.

"After a very long time he gets a very big surprise; one that is possibly in 'nasty shock' category. He was on the outside of a very large pink sphere, but suddely he finds himself on the inside of a pink hollow, and what's more, a hollow that gets smaller and smaller the longer he continues.

"Just as Mr 2D could not understand how he went from being on the outside of a disc to being on the inside of the same disc (which to us, from a 3D persepective, was perfectly obvious), so Mr 3D simply cannot understand how he went from being on the outside of a sphere to its inside".

A long pause.

"Which to us, from a 4D perspective is perfectly obvious".

Another long pause.

Finally he pipes up "I'd give a lot to see one of those 'biggest ball of string in the world' things."

Wouldn't we all? Mercifully I am almost certain I hear Mrs G's dulcet tones requesting my presence and exit stage left.

Entry 20: in which We visit alternative worlds

I have been by turns irritable and frustrated by this whole dimensional conundrum. I think an explanation is in order.

The first thing to realise is that for an n-dimensional entity, higher dimensions do not exist, or if divined, make no real sense. However, all lower dimensions can be apprehended or comprehended. If an n-dimensional entity is able to interact with lower dimensions, that interaction will appear magical to entities in those lower dimensions, as we shall see shortly.

So let's explore some dimensions to see how this thing works.

A zero dimensional world is a point of infinite smallness. Let us call that world Zut; it is populated by Zuties. Zuties too are points of infinitely small size. They cannot move in any direction. The universe, before a big bang, is a bit like Zut.



Now consider a one-dimensional world. This world is a line of infinite length, but no thickness. We will call it Wun. It is populated by Wunies. Wunies resemble arrows, and a Wunie is born as a Left Arrow or a Right Arrow. Wunies can move along the line that is Wun, but they obviously cannot turn around; that would require a plane. Thus you are left or a right arrow for life.

Note that if Wun intersects Zut, and arrows move through it, Zuties have the strange experience of having points come into existence apparently from nowhere, and then going out of existence again. We however would simply see that as an arrow in transit through Zut.

OK, up a step to the two-dimensional world that is Too, populated by Tooties. It is an infinitely thin plane, that extends to infinity in both X and Y. Tooties are circle creatures of fixed size.

If arrow creatures lived here they would suddenly be freed from the constraints of living in a line; they could turn by rotating in the plane. Thus Lefties and Righties could "transform" into each other, which would be considered miraculous on Wun, but is commonplace on Too.

Tooties can move in any direction on the plane, but they cannot change size.

Now consider a three dimensional world called Threa. It has X, Y and Z dimensions and is populated by bubble creatures called Threaties. As Threaties float up and down, they might pass through the invisible plane that is Too. When a sphere intersects a plane, it is represented in that plane by a circle; the size will depend on just where the plane intersects the bubble. Thus the Tooties of Too witness a miracle. A tiny spot becomes a circle, becomes a bigger circle, becomes a small circle, then a spot, then disappears.



On Too this is impossible, because Tooties are of fixed size. But this is commonplace on Threa.

By much the same token when I interact with the three dimensional universe the effects are often paradoxical and baffling to any three dimensional creature who happens to witness such. The same is true for other four dimensional elements.

For example, in this realm we have strings, which intersect the third dimension in the form of particles. Here we have tachyons, which in the third dimension show as photons and so on.

In the third dimension I am present everywhere simultaneously, which sounds like a big deal, but is simply a dimensional artifact. I mean it's handy, don't get me wrong, because you don't actually have to go anywhere since you're already there. But in reality you tend to focus on one place or another, not everything at once. This is what I was trying to explain to Mrs G. In our realm, I'm in one place at a time, same as anyone else.

As for actually doing anything with the universe (or bits of it), well that's another matter entirely. For a start, these cross-dimensional interactions are extremely weak. If it wasn't for deions I'm not even sure they would be possible.

Second, there's no such thing as a free lunch. If you really want to stop two planets colliding, or some tectonic plates from slipping, you have to lay in outrageous amounts of energy. We're dealing with a physical universe here. It's not playdough. Plus the books need to be balanced, which means offsetting energy use in one place with anti-energy in another and all the deion shuffling that implies.

It's not just a matter, as those tedious little cherubs think, of saying to a volcanic chain "Look chaps, could you keep it down a bit, what?" It just doesn't, er, work like that.

Dear oh dear. Sometimes I find the expectations that various lobbies have of me are quite exhausting. Perhaps the boy has a point after all. Retirement is starting to look like an attractive option.

Entry 19: on omnipotence

Those wretched cherubim. What they, and the rest of the free-loaders that inhabit My realm have no idea about, is how difficult this omnipotence thing is. (Where do the little buggers come from? - sorry that's rhetorical, no one actually seems to know).

Sought solace by having a good gripe about cosmic responsibilities to Mrs God. She's a good soul, if a trifle inattentive. This latter tendency masked by a ready stream of platitudes, served up by autopilot. Mind you, when I'm in one of my moods, like now, platitudes are better than nothing.

"Well, you know I'm omnipotent ..." I said as a lead-in.

She sniffed. Or possibly snorted. "Really dear?"

"And omnipresent".

"Except when I'm looking for you" came her tart reply.

Well, you can see the kind of thing I'm up against. For goodness sake! I never said I was omnipresent in this dimension. If I was the sodding cherubim wouldn't have to come looking for Me, would they? Doesn't anyone but Me take the time and trouble to understand dimensional topology?

Entry 18: in which Cherubim are sent packing

Good grief. Just when I think that eternity is dull, it suddenly gets duller.

That's right, another delegation. This time a bunch of soppy cherubim who seem to have adopted a planet with cute (their description) silicon-based life forms. Alas, said planet is tearing itself apart with a hefty bout of vulcanism, silicon life forms are reverting back to sand (well, glass actually) and will I please do something about it.

Well there are just two wee problems (a) I'm philosophically opposed to interventionism as anyone who pays me the slightest heed should know and (b) doing anything in a dimension other than your own is a tad tricky. Now I don't like to overplay the latter because I have a reputation to uphold, so I said I would give it some thought and it would help me a lot if they would go away and produce some drawings of said life forms.

This seemed to divert them a bit and off they went chattering happily like a bunch of happy chattering things. With any luck, they'll forget all about it; cherubim have remarkably short attention spans.

Entry 17: In which One is made to feel One's age

Sitting around with not much to do when the lad mooches in with Lucy trailing behind. Now I've seen this sort of thing before and it is invariably the case that while Lucy may not be in the vanguard, the visitation will have been prompted by him.

After the usual rather drawn out pleasantries they get to the point, or at least the lad does.

"Well I've been thinking ....."

(Chance would be a fine thing). "Hmmmm?"

"Well it's like this. I mean, you know, time passes, none of us is getting any younger, I've learnt all I'm going to and stuff."

Not quite sure where this is going, but see Lucy shifting his feet and gazing off into the distance. Not a good sign. "Hmmm?"

"Well, I mean, perhaps we should talk, you know, just maybe start thinking about succession planning".

"Succession planning?"

"Yes, you know, for when you retire and when I eventually take over."

There was a pregnant pause. "Son, you haven't quite got the hang of this immortality thing have you?"

And they wandered off.

Entry 16: in which We explore other dimensions

Finally found the words it would take to explain "it" to the boy. Tracked him down staring into space, actually rather than figuratively.

It's all a matter of spatial dimensions I explained. Stick to the spatial; don't bet bogged down with time, curvature or flaxotomy. In essence, the universe we're tracking has three spatial dimensions, while we deities exist in four. That means that they exist in our space, but we don't exist in theirs.

Blank.

We can see them, but they can't see us.

More blank.

It means that that which is commonplace in our space would be baffling in their space. Actually I could see it was baffling in his space too, so I led with the following simplified illustration, contrasting two and three dimensions along these lines:

"Imagine a two dimensional creature dropped at the north pole of a three-dimensional planet. At first glance, this would feel like his old familiar two-dimensional world - looking around him he would see a flat plane extending (apparently) to infinity in all directions. So far, so good.

"Now we put a peg in the ground and give him a ball of pink string (magically, this will not run out). We ask him to walk around the peg and to play out the string as he goes. He is to stay on the outside of the string, and just to keep going. Well as he does this, the string forms an ever-bigger pink disc, and he is on the outside, walking along the perimeter. As time passes, the pink disc becomes very big, and he loses sight of the peg, but he keeps going.

"From our three-dimensional perspective we see him covering the northern hemisphere with pink string. He is still walking round and round it, playing out the pink string, and in this fashion works his way slowly down the planet. He reaches the equator, and then he is past it. Mr 2-D thinks, reasonably enough, that he is still on the outside of very large flat disc of pink string.

"Imagine his astonishment when, as he nears the south pole, he discovers that, far from being on the outside of the disc of string, as he was when he started, he is now inside it.

"To him, thinking in 2-D, this seems crazy or miraculous. To us, thinking in 3-D, it is obvious and inevitable. Now extend that thinking by another dimension and Bob's your uncle".

There was a long silence. "Pink, eh?" he said as he wandered off to find more milk and cookies.

Entry 15: in which Mrs God is unhelpful

I had been wrestling with the boy's question; the one that , in effect, asks what we are "in". Asked Mrs God her views on what we are in - "The Mire" was her unhelpful reply, but it seemed to amuse her enormously and she spent most of the next millenium cackling at her own wit.

Now I like a joke as much as the next entity, or perhaps marginally less; OK, quite a lot less, but that's not the point. To be witty you have to be more than, oh I don't know, infantile.

And I've been distracted. Oh well, another time.