We time-travel a little each time we look at a distant star, as we see an object as it was millions of years ago. In a sense we space-travel a little if we look through a telescope, as we appear to accelerate towards the stars, bringing them closer. In fact, as we look into a telescope - or a microscope - we are embarking on a journey of scale. In our journey of scale, we 'zoom' in or out, but do not move physically in space. Scale appears to be somehow different from the familiar three dimensions of space, yet tied up with them. And for any object or point in space, different scales appear to exist, as it were, simultaneously. But we may sometimes have trouble grasping in our heads an object 'seen' at many different scales at the same time.
Now, imagine an alien species with its brain hardwired to a telescopic-microscopic eye. It might intuitively conceive of a 'zoom dimension' - a kind of independent dimension in which you travel in scale without moving in space. Just as movement in space implies change in location over time, travel in the zoom dimension implies change of scale. Yet change of scale may also affect perception of distance.
A telescopic alien planetary scientist hovering over the Earth might ponder on the total length of its coastline. At a first approximation, the Earth has one landmass. But closer up, more land masses resolve themselves, and each will need to have its coastline measured. Progressively, at closer scales, more land masses and islands appear, and the sum of the lengths of all coastlines will increase correspondingly. By the time the alien is measuring all the little fragments of coral reefs and rockpools, the lengths will be measured more and more intricately, and the cumulative length will get longer and longer still. Human scientists realise this effect: the apparent length will depend on the scale at which it is measured. (Ant science has always claimed that, at the scale of ants, the earth is a bigger place than we would care to admit.) As we zoom in, we find more and more tucks and folds, and more and more 'length' miraculously appears. It seems that by travelling in the zoom dimension, we can unlock more and more length, and gain as much space as we care for. In fact, it seems that there is no end to how much space we can generate, since there seems no limit to scale. We can just go on getting smaller and smaller - or larger and larger. The zoom dimension appears as boundless as any other dimension. (Normal linear dimensions may appear to start or end at zero, but only because we count by addition, not multiplication. Minimalist alien mathematicians who count purely in multiples and fractions have no need for zero or negative numbers, considering these tiresome figments of untidy minds.)
Nevertheless, telescopic alien philosophers wonder if the zoom dimension really extends infinitely, or if instead it curves back on itself. Could there be a bridge between the very big and the very small? Is it possible that if you go far enough east, you come back west? In other words, as things get bigger and bigger, do they pass some kind of international date-line of scale, and come back really small? (If we go far enough into space, will we eventually find giant ants, clumsily peering down at nano-galactic distances?)
But, if we were somehow to zoom all the way outside in, as it were, where exactly would we 'land'? Looking the other way, from which spot would we have emerged, within which to locate our own miniature universe? Or instead of a single spot, perhaps every slice of space has its own subatomic universe (each measured in subatomic units, of course). And if so, does each subatomic universe contain its own subatomic universe (or someone else's) ad infinitum? Then we could have an infinite number of universes within universes, simultaneously at all scales, simultaneously. This surely expands our comprehension of the size of 'the' universe. It must now look considerably bigger (or smaller) than we previously imagined.
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