For a hundred years we have got used to the idea of space-time as a unifying construct of spatial and temporal dimensions. We have also got quite used to the idea of animated picture-shows, which give the illusion of three-dimensional motion using a succession of two-dimensional images. Put space-time and film together, and we get science-fiction movies. But the fabric of space-time can be studied much more prosaically by considering a few simple objects in a limited number of dimensions.
Take some ordinary handy three-dimensional object - a Pepper, say - and consider it passing through a two-dimensional plane. To do this, imagine cutting the Pepper up into thin slices, and converting the slices into a slideshow. As you run the slideshow, a first pepper-slice appears, and then a succession of slices wriggle around - all slightly different shapes and sizes - and finally disappear.
We can easily recognise the whole Pepper as the sum of all pepper-slices together, simultaneously. In other words, our familiar still-life Pepper, as it passes through a plane, does not change shape as such; it is just an irregular shaped object moving in space.
But now imagine the perspective of the inhabitants of a fictional 'Flatland' - a planar domain inhabited entirely by flat shapes such as squares, circles and assorted sliced grocery products.
The two-dimensional citizen of Flatland would recognise the passage of the Pepper through their plane only as a procession of changing pepper-slice shapes in time. The idea that the pepper-slices could collectively be regarded as a single fixed-shape object in a higher dimension would be completely alien (or at least, counter-intuitive) to the Flatlander.
To perceive the Pepper not as an array of separate 2D slices at different times, but as a whole 3D object at the same time, the Flatlander would have to imagine a sort of time-ordered stacked-up archive of all the stills from the pepper-slice movie - a sort of incorporeal frozen movie-object (conceptually parked partly in a hypothetical third spatial dimension).
So it is possible to conceive of different entities across the dimensions of space-time, though it can sometimes be hard work - even for familiar objects in familiar dimensions.
It is especially challenging where an object in one dimension appears as more than one object in another. For example, imagine a chunk of tree, say a trunk with a single branch off it, passing through the plane of Flatland. First to make an appearance is the roughly circular cross-section of the trunk. As the tree cross-section passes through, it enlarges and sprouts a branch, so that by the time the whole chunk has passed through the plane, there are two roundish cross-sections - that of the trunk and that of the branch. As far as Flatlanders are concerned, where once there was a single object; there are now two separate objects. But from our three-dimensional perspective, there is only the one single three-dimensional object in space: the chunk of trunk-plus-branch.
A similar thing happens when three-dimensional objects connect or diverge over time. For example, when a chicken lays an egg, what was one three-dimensional object becomes two. The post-chicken egg and the post-egg chicken are clearly separate, in our three-dimensional mindset; but they are nevertheless connected through time. In fact, just as our tree trunk and branch - although appearing as separate slices in Flatland - form a single solid object in space, the chicken and its egg can be seen as part of the same diverging object in space-time. In other words, we have a sort of frozen continuum of chickens and eggs stacked up back through time - a four-dimensional object.
Indeed, a family tree is exactly like this: a four-dimensional structure of parents and offspring, a series of separate three-dimensional family members, with different individuals appearing at different positions in time.
Indeed, the whole 'tree of life' - the entire earthly family tree of people, hominids, dinosaurs, eggs, chickens, peppers, sticky rice and unclassifiable creepy-crawly things forms part of a single planetary 'creature', a quivering tentacled four-dimensional entity reaching through space-time.
An alien observer might think of life on Earth as a single grotesque mass of mutant organic tissue, coupling with itself here, spewing out offspring there, consuming and expelling parts of itself, all the while racked by fractured identities, a short-term ancestral memory and a penchant for self-harm. Such a monstrous 4-D Earthling might be just the stuff of the alien's own science-fiction movie.
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