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When my wife, Sharon, died on August 8, 2017, I could not help but wonder if there was an afterlife where I could meet up with her.  She was the best friend I ever had, and I really would not mind spending eternity with her, if that were a possibility. However, I am not a religious person, and could not conceive of what one might do for eternity.  Would you just watch TV reruns forever?  Well, just because I can not conceive of what might transpire in the afterlife, does not imply that it could not exist.  Something similar to this happens in our own life.  E.g., suppose  that when you were a prepubescent child some older kid told you that in just a few years your body is going to change, and as a result you will be able to experience unbelievable intense pleasure.  You might then ask, "more pleasurable than ice cream?" And when the kid says yes, you might say, "that's bullshit, you're just trying to make fun of me because I'm a kid."  But then after you pass through puberty and experience sexual pleasure, you will probably wonder where the Hell did that come from? That kid was right.  So this change in life, that leads us to enjoy sexual pleasure, should serve as a hint that perhaps another change in our existence could occur when we die. After all, if something unimaginable could happen once, why not again?  So just maybe, there is an afterlife, but where does it take place? 

Most Christians believe that there exists a Heaven up above, and a Hell down below.  After the Russians launched their Sputnik in October, 1957, they proudly announced that they could see no sign of Heaven up there.  Similarly our observations of the Universe with various telescopes, has shown nothing resembling Heaven.  The problem here is the meaning of the word  "up."  Suppose that you were two dimensional and lived on the surface of a table. If one of your 2-dimensional friends asked you which way was up, you would point in some direction that laid in the surface of the table.  You would be oblivious of the ambient room in which the table sits.  A similar thing might be going on here with our locations for Heaven and Hell.  Perhaps for us, "up" points in a fourth spatial direction which lies outside of our spatially three dimensional Universe, U. So what is this fourth spatial dimension?  My guess is that it is the "moral dimension."  This is where the soul comes in.  But I am getting ahead of myself. 

If you have a sheet of paper, and you draw a straight line across it, that would divide the paper into two parts.  You could arbitrarily say that one part is above the line, and the other part is below it.  Similarly our Universe, U, could be the 3-dimensional counterpart of that line, sitting inside of a spatially four-dimensional extended universe, which we shall call EU, with U dividing EU into two pieces.  We choose one of these pieces of EU, and call it HV (:=Heaven), and the other piece we call HL (:=Hell).  By the "up" direction for people in U we mean the direction that points from U into HV.  "Down" is the direction that points from U into HL. Of course, no one living in U can point in the HV or HL direction, but we at least have an idea of  where these places could be. One should note that neither HV nor HL contain any points that are in U. In mathematical terms we would say that EU is the union of three disjoint sets, U, HV and HL. (This might have to be "tinkered" with.)

The next topic on our agenda is the soul.   When we are born we continue the physical growth that began when we were in the womb. But we also grow in that fourth spatial direction, and it is that growth that creates our soul. The stuff that exists in the fourth spatial dimension is completely different than the stuff in U.  As we grow in U our soul grows in both the up and down direction in EU.  I believe that what determines growth in these directions  is the morality of our actions. This is where the conventional religions of the world can jump in, but I shall not take that approach. I shall simply say that an act is "good" if it promotes either our life or the lives of others.  An act will be said to be "bad" if it is detrimental to our life or to our species.  (I realize that these definitions could use some "spiffing up," but this is not the place to do that. After all, the subject of morality has been a topic of study and discussion for thousands of years.)  I suspect that our soul grows out of our brain into EU, and contains the record of every act we ever did.  Good acts promote growth in the HV direction, while bad acts promote growth in the HL direction.  I have no idea just how much growth any particular act generates. A religious person might say that God will determine that.  I shall have more to say about God(s) in just a moment. In passing I would like to mention that, due to evolution, all the animals we know of can only act in a salubrious manner, and so their souls always grow in the up direction.

A natural question to ask at this point is: Why doesn't the soul just float off into EU?  Well I believe that while we are alive our soul is firmly attached to our brain by a "life force," that only acts in the 4th (moral) spatial direction.  When we die that life force ceases to exist, and our soul is free to float off into EU.  What determines whether it goes off into HV or HL  depends upon the volume of the two parts of our soul when we die.  Let S+ (S-) denote that part of your soul that lies in HV (HL).  If R is a region in EU we shall let V(R) denote the volume of the region R.  So if V(S+) > V(S-), your soul floats into HV.  On the other hand, if V(S-)>V(S+), your soul "sinks" into HL. I have no idea what awaits souls in HV or HL.  But I doubt there will be fire and brimstone for the souls that end up in HL, only the souls of a lot of "bad" people that your soul  will have to deal with, should that be its destination.  Let theologians argue over this matter, and whether there exists a way to decrease V(S-) while you are alive.  

Do we have to expend any of our own energy to keep the "life force" going?  I think we might.  That would explain why the life force shuts down when we die, since we are not providing it with the energy it needs to perform its task. If this is so, then it provides us with a way of doing an experiment to determine whether the soul, and the moral dimension exist.  For recall that I said that the soul is attached to our brain by the life force. The brain is more complex and use more energy than any other organ in our body. The problem is: can all of the energy that enters the brain be accounted for, or does some seem to disappear?  If some disappears, then we can argue that the loss is attributable to sustaining the life force.  But other people can argue that leakage of energy from U into a higher dimensional space enveloping U is a natural byproduct of some  string theory models.  Then we would try to demonstrate that the leakage only occurs from the brain and no other human organ. Finding that to be true would go a long way towards establishing the existence of a life force.  And if you have a life force acting in a direction away from U (since it is felt by nothing in U, since if it was we would have already found it), it must be acting on something outside of U, and that something, we "believers," would call the soul.

Do we need a God or gods, for a system as I have just described, to exist?  If we do, then the question is, where did these super-beings come from?  Maybe these gods are more like engineers who built EU and U, like we might build a colony of bacteria in a petri dish.  For all intents and purposes, any spatially four-dimensional being residing in EU would be a God to us. This is so because our spatially three-dimensional brain would have zero volume in EU.  Thus in EU, you could stack billions of them together, with the only restriction being the volume of the wiring connecting these brains. If we only need a nanometer of space between brain size computers in EU, then you could probably build a cylindrical shaped computer in EU one meter high, and with a cylindrical cross sections being computers akin to our spatially three-dimensional brains.  This small cylindrical computer in EU would be a computer with the power of a billion brains wired together as a parallel processor.  The brains of some of the entities residing in EU could be computers of this type, but probably would be even more sophisticated. That's why we would view any of the denizens of EU as gods. I shall have more to say about the christian God latter.

For the moment let us review some "recent" theories about our universe, U.  In the 1500's, Copernicus pointed out that the sun, and not the earth, was the center of U, and that all the planets orbited the sun.  (Supposedly Aristarchus of Samos formulated the same idea 18 centuries before Copernicus.)  Later on we realized that the sun was not the center of U, but just a star in the Milky Way, where all of the stars resided.  We then realized that the Milky Way was just one galaxy composed of stars, and that there exists billions of galaxies each containing somewhere between millions and billions of stars.   Some of these galaxies grouped into clusters, and then into superclusters, which were the largest groups of stars in U.  Now some physicists have suggested that maybe our U is not unique, and that there exists infinitely many universes.  They thought that this might be  plausible because there exist so many constants that characterize our U, which, so far, can not be explained.  And for U, these constants take on precisely the right values for us to exist.  So rather than assume that there exist some "super engineers" who choose these constants for  U, these physicists said why not assume that there exist infinitely many  universes, all with different values for the constants. We just happen to be in one universe where the constants are suitable to build intelligent life.  This is the basis of the multiverse theory of the universe. 

With the above remarks in mind, let us return to our U and EU as previously described.  Perhaps EU sits inside of a spatially five-dimensional universe, E(EU).  E(EU) has one additional dimension of time, just like U and EU have, and hence is a six-dimensional space. The souls living in EU, have super-souls that grow into E(EU).  In this way we could construct an infinite chain of universes:

            U contained in EU, contained in E(EU), contained in E(E(EU)), contained in E(E(E(EU))), and so on,

where each E(...(EU)...) divides  the E of it into two separate parts, just like U divides EU into two parts.  If E(...(EU)...) has n E's appearing in its expression, then that space would have spatially n+3 spatial dimensions, and one dimension of time, and hence mathematically would be an n+4 dimensional space.  This series of extended universes would be the metaphysical version of the multiverse.  Although these extended universes may seem kind of goofy, they seem to give direction to what we might be doing in EU  after we die; viz., trying to be "good" in the afterlife so that we can move into E(EU)+, and then into E(E((EU)))+, and so on forever. So perhaps we have quite a future ahead of us. (Aside:  Strictly speaking instead of introducing E(EU)), I should have introduced E(EU+) and E(EU-). This in turn would have led to : E(EU+)+, E(EU+)-, E(EU-)+ and E(EU-)-, and so on.  A notational nightmare! Now you see why I did things as I did, especially when you think of what the correct form of E(...(EU)...) would be.  In addition, this nested series of universes of increasing dimension might remind you of E.A.Abbott's book, "Flatland: A Romance of Many Dimensions."  However, what I am doing here is actually quite different than what Abbott did. )

Now let's consider music.  This might sound like a radical shift in what we have been doing so far, but I plan to tie the two together.  I am not ashamed to admit that I know virtually nothing about music.  You could hit me in the head with a fugue, and I would not know what it was. Back when I was a theoretical physicist (<33 years old), I only listened to rock music.  However, when I began painting full-time in September, 1981, I accidentally turned on the classical music station WRRFM in Dallas, and essentially have never shut it off.  I must listen to classical music when I paint (but some vocal pieces bother me--it is like someone is trying to talk to me, and that interrupts my  painting.)  As I said above, I have no formal music training, and virtually all the music theory I know came from a 1969 pamphlet on how to play the harmonica.  So I am utterly amazed by how moving various musical pieces can be.  They can make you feel spiritual, happy, awestruck, proud, frightened, etc.. But why  can music do this--how does it work? I think that music is actually the language of the soul, and that is why we all understand it without any formal study of music. (Some people refer to music as "food for the soul," but, evidently, that is not my position, since I believe that it is our behavior that "feeds" the soul.)  For me, the existence of music, and our ability to communicate with each other using it through the intermediary of composers and musicians, is virtually proof that the soul does  exist.  Why else would music exist?  Well, the composer Igor Stravinsky has offered another reason for music's existence; viz., as accompaniment to other activity, and that is primarily how I use it.   But I can't believe that music only exists as the sound track for the movie which is each person's life. Often when I am painting, I am completely unaware that music is playing in the background, until all of a sudden "someone" inside my head interrupts my painting and says "Stop! Listen to that! That is unbelievable!" Of course, I stop and listen when I receive that order, and acknowledge that what I just heard is complete genius at work.  I am really lucky to live such a creative and  wonderfully enjoyable life.  It is strange that when I am painting, it almost seems as though the background music is there to entertain some facet of my persona who would only interfere with my work if the music were not there to distract him.

Now as we know, no other mammals sing, except perhaps whales and dolphins, and they are clearly higher forms of the animal kingdom.  And sure, birds sing their songs, but they are not creating new pieces, except as part of Darwinian evolution.  I don't think that we can regard the ululations of animals searching for a mate as singing.  I believe that the music we hear is perceived by our soul through the intermediary of our brain.  A similar remark pertains to  viewing of art.  I know virtually nothing about art theory, and yet I can create paintings that have a visceral appeal to a lot of people.  Sure, not everyone likes my paintings, and similarly, not everyone likes Bruckner.  Different souls march to different drummers.  But, nevertheless, they all march to certain forms of music and art, which seemingly is of no "practical" good.  Although music and art can make us feel that we are part of the thread of  humanity, since such large groups of humans (both living and dead) like certain forms of music or art, and that can be construed as a practical good.  Musicians and artists are always trying to create works that have lasting value to souls yet to be born, and in that way to achieve an "afterlife" through those who happen to be living in the future. Of course, I shall be one of those contemporary artists whose work lives on.  But I am not quite ready to leave this mortal coil, I still have to get more of my work out into the world, and into the "right hands."  Perhaps yours?

Back in 1988 my work appeared in an exhibition of eight Texas artists at the Groninger Museum,  in Groningen, Holland. As part of the show each artist was interviewed by the Dutch version of our PBS.  The reporter asked me if I was the next van Gogh, and without missing a beat, I said yes.  We all got a laugh out of that.  But I like to think that I am beyond van Gogh, since I got to start where he left off, using some of the artistic devices, and ideas, that he developed.  Besides I know much more mathematics and physics than van Gogh did. In fact I shall go so far as to say that if van Gogh did not paint "Starry Night," I would have.  After all, it is simply the depiction of the gravitational equipotential surfaces (the notion of which is probably due to Newton) of a system of gravitating bodies, with light colors used where the fields are strong, and darker colors used where the fields are weak.  After all,  gravity theory is my strong suit, so painting equipotential surfaces would be an obvious thing for me to do, and I do it a lot.

I shall now relate my "Christmas Miracle," which ties into the discussion of whether God(s)  (i.e., supernatural beings with intellectual, and or physical powers beyond ours) exist.  In 1974, while living in Canada, I got my black cat Oscilla.  She adored me, and I took her with me to Dallas when I moved there in 1981.  In late 1982 a homeless adult seal point female cat showed up at my apartment door.  I took her in and named her Stranni.  Oscilla and Stranni hated each other from day one, and had frequent fights, which Oscilla always won since she was a very strong cat.  Now there was one place in the apartment that Stranni was never allowed to go, and that was my bed. Oscilla would always sleep there with me at night.  To accommodate Stranni in the bedroom, I placed a chair with a blanket on it about a foot from the bed, which is where Stranni could sleep with Oscilla's approval.   Then on Christmas morning in 1983 I awoke to find Stranni sleeping on the bed about a foot away from Oscilla--the lamb lying with the lion.  When I started to get out of bed Oscilla awoke and saw Stranni there on the bed, and then, instead of beating her up, Oscilla went back to sleep.  After I washed up and then left the bedroom, both cats followed me into the kitchen for their Christmas breakfast.  Stranni never slept on that bed again--not even after Oscilla died in November, 1991.  Just a coincidence or an AH HA! moment indicating that something very important was being presented to me. I leave it to you to draw your own conclusion.

You often see bumper stickers on cars saying "Don't Believe Everything You Think."  Perhaps much of what I said above falls into this category.  But I see nothing wrong with believing what you think, so long as you do not force others to believe what you think, or your thoughts can be harmful to yourself and others.  E.g., you might think that there exists a spot located two feet away from the guard rail  at the middle of the Golden Gate Bridge where gravity does not work, so you can just stand there and not fall into the bay. I am sure that most of us are skeptical of that idea.  None of the ideas I presented above will lead to your demise.  They simply comfort me while dealing with the loss of my wife.  And who knows, they may even have something to do with reality, since they are mathematically plausible.