In an earlier witnessing, I professed to believe that I (–we all–) are more than mere body; that I have a soul and a mind, both distinct from my body, and that these two are not a part of our physical universe, that they are in some other spaces, the mind in one and the soul in another.
In particular, I said that I believed that we all actually live in a much higher dimensioned space, a physical x mental x spiritual space, interacting with (at least one) “time”.
(I have used the classical vector cross-product, x, without being convinced that this “higher dimensional space” is actually a classical cross-product; nor even that they are “orthogonal”, as the word us usually used.)
I came to believe all this very early in my life. About ten years ago I ran across a new theory from Physics called String Theory, modified, as I understand it, by the notion of symmetry into SuperString Theory. Since I believe that symmetry is a very strong force, in mind-things and soul-things as well as in physical things, and since I saw a certain natural accuracy in their postulating 10-dimensions, I came to believe that (Super)String Theory may lead the way to a “True Psychology” and a “True Soul-ology” (or whatever you might call a “Science of the Soul”). All this I believed and still believe.
Since I believe, in this multidimensional context, that the soul lives longer than the mind, and the mind lives longer than the body, the idea of “re-births” as well as the (suspicious) notion of “Ghosts” (and other concepts) seem now to make sense. Likewise, since a mind x soul without a body existed in its (their?) 6-dimensional space, when it (they) became re-embodied it (they) might well become a member of some other species than it was (they were) before it/they died.
(There is some question: How fixed is a particular mind to a particular soul? For the entire life of the mind? Or only so long as they, mind and soul, remain compatible?? I see this as an open problem.)
Thus, while clearly there is a different status between a man and a dog, I believe that both are just a body carrying a much more important entity from the mind x soul space-time. (Time? Another open question.) Who is more important? The man or the dog? Surely, by the rules of today’s society, the man is more important. But what if the dog’s mind-soul is vastly more important than the man’s mind-soul. Then which one** should be** more important? This accords, by the way, with Jesus’ comment: “What you do to the least of mine, you do to me” as well as a very different version attributed to Solomon, the Wise.
(As an aside: There are some indications that at one “time”, there were three of these spaces, with no “physical” as we know it. In bibical terms, I call that heaven. It is suggested that upon certain happenings about which we know little, one-third of this 9-dimensional triumvirate was thrust out of heaven and became “hell”. Us. The physical “universe”. 
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There are many implications to these beliefs. One of them is that we, at last, have found a “home” for the Angels: The remaining 6-dimensional space of heaven. (Sorry, I don’t believe that there are any such thing as “devils” or demons. I believe that there is a spirit whose job it is to tempt us into badness and maybe that the foreman of these spirits is called “Satan” but…) This system of beliefs also easily explains such oddities as “child prodigies”,–just a mind x spirit re-born into a new body.
One particularly fascinating aspect of (Super)String Theory’s 10-dimensions is that six of them are curled up into a tiny place smaller than anything we can name. Being other dimensions (–Possibly orthogonal? I don’t know the theory well enough to say.–), they are everywhere in our 3-dimensional space, “the Universe”, at once. And this is exactly as we would like to think of heaven being. An Angel could, for example, complain at a persona on a planet in the Procyon star-system one minute, and then complain at one of us here the next minute! Exactly as we might hope things would be.