Consideration of a Fourth Dimension

30 03 2010

Sometimes the most mind-busting line of thought yields the most obvious answer.  It is healthy for us to question our assumptions, and we might enjoy a rather fantasy-driven mental experiment in speculative thought, but sometimes, much to our chagrin, we must consider the likelihood that whatever conclusion we come to will be no different than the one described by a simpleton, only in a far more complicated fashion.  This, I think, is the stumbling block of modern String Theory.  People stretched and wrestled with their minds to arrive at an astounding mathematical explanation of the universe and everything, assuming the universe had a couple dozen dimensions not previously known.  The objective conclusion would have been that String Theory is therefore likely incorrect, but one hates to go to all of that trouble to prove that the formulas on the document for the theory are worth less than the coffee stain caused by the cup that was accidentally placed atop it.  In the end, the spectator claps his hands and leaves the theater feeling entertained.  The performer continues to act his part, hours and days after the curtain falls, in some vain hope that he can convince himself that the whole thing was real.

But it is entertaining to play the game, and so we shall.

The intersection of two line segments is a point.  Each line is a one-dimensional object, and the point is a zero-dimensional object.  The essence is that the intersection resulted in an object with one less dimension than the objects that intersected.

The intersection of two plane segments is a line.  The plane segments are two-dimensional, and the line is one dimensional.  Therefore, the intersection has one less dimension than the objects that intersected.

What, then, would we expect from two intersecting three-dimensional objects, like cubes?

Oh, well, the intersection of cubes forms another cube, if they are arranged just right.  At the very least, they form another three-dimensional object of some sort.  Therefore we conclude that the intersection of two three-dimensional objects is another three-dimensional object.  This breaks with the previous pattern.  If the analogy had held true, then we would have expected a plane segment to be formed by the intersection of two three-dimensional objects.

This might seem strange, at first, until we consider this analogy in reverse.

In this example, the intersection of two plane segments (rectangles) results in another two-dimensional object, just as the intersection of cubes was a cube.  Likewise, we can repeat this scenario with the one-dimensional line segments.

Two line segments, when intersecting end on end, form another one-dimensional line segment between them.  So, in these three examples, the intersection had the same number of dimensions as the objects that intersected.

What is the difference?  The difference is in the dimension of the space around the objects. Two dimensional objects intersect two-dimensionally in a two-dimensional environment.  If that environment has one more dimension than the objects involved, then they intersect with one less dimension than the objects.  Two plane segments yield another plane segment if their universe is two-dimensional, but if the space around them is three-dimensional, then they intersect to form a line, most often.  Two line segments form a line segment between them if their universe is also one-dimensional.  If their universe is at least two-dimensional, then they usually intersect to form a zero-dimensional object.  Add a dimension to the space and you lose a dimension from the intersection.  What we conclude, then, is that we can imagine three-dimensional volumes intersecting to form other three-dimensional volumes only.  This would suggest three-dimensional space.  If space were four-dimensional, then two solid volumes would intersect most often to form a plane.  We cannot even conceive of it.

Space is always the first thing that we take for granted.  We see the objects and miss the space.  We measure the space with objects.  We assume, naturally, that the space around us is three-dimensional because the objects within it are three-dimensional.  We measure an object’s height, depth and width, and we perceive three dimensions.  We do the same for empty space, but we measure that space with a three-dimensional object.  We imagine that empty volume as an invisible cube, but in so doing, we equate filled space with the attributes of empty space.  As in the examples above, a plane can conceivably exist within a three-dimensional volume or a two-dimensional area.

Could empty space be four-dimensional?  In attempting to discover this, we might be tempted to arrange the two blocks side-by-side.

By pressing their flat surfaces together, we have formed a two-dimensional intersection.  Have we thus demonstrated a four-dimensional space?  Well…no.

As it turns out, we can easily form a one-dimensional intersection between two-dimensional objects in two-dimensional space, so long as they both have a flat side and we press them together.  A similar situation exists for the line segment.

If the two segments are pressed end-to-end, they can form a zero-dimensional intersection in one-dimensional space.  Therefore, abutment is the exception that proves the rule.  Simply putting two cubes together side-to-side does not demonstrate four-dimensional space.  It’s a lot like two bubbles stuck together.  Between them is formed a flat circle.  This is a two-dimensional product of three-dimensional intersection, in a way, but it is only abutment, and it does not demonstrate four-dimensional space.

In reality, there is no practical example of 3-D intersection.  Matter is 3-D, but it cannot really intersect.  It occupies space, and no two objects can occupy the same space at the same time.  Their molecules can move about and intermingle, but they cannot really intersect.  Otherwise, we would have nuclear fusion.  Hence, we might be tempted to wonder if our model for the intersection of 3-D objects is limited only by our imagination.

The stinging rebuke that reality sends us in reply is that if empty space really contained a fourth dimension, then all we would have to do is rotate our 3-D object to see the glaring absence of the unused dimension.  This is an inescapable fact.  String Theorists, desperately needing far more than four dimensions, use the argument of scale.  For example, a string is functionally a one-dimensional object, even though it does have all three dimensions.  Paper is functionally a two-dimensional object, even though it, too, has all three dimensions.  Some would have us believe that our whole universe is functionally a 3-D object though it has, say, twenty-four dimensions, give or take a few.  They would have us believe that we are all flat as a pancake in more ways than we might suspect.  But, while this may be a convenient view, it is not a very objective one.  Disproving it would be easy if the claim were made only of occupied space, which we call objects.  But, they make the claim of the empty space also, so that we do not have room to rotate our object and observe it edge-on.  This is not unlike a magician strategically arranging his audience to one side of him so that they cannot see beyond the smoke and mirrors.

Yet, there still remains the fact that we cannot even imagine what 3-D intersection in 4-D space would look like.  We can imagine 3-D intersection in 3-D space, even though it does not really exist in nature, but we cannot fathom the other.  The implication is obvious.

One last thing worth considering is the effect of compression.  Push the ends of a functionally one-dimensional string together and it releases the pressure by increasing along an extra dimension ( it bends).  The same could be said of a functionally two-dimensional piece of paper.  So what happens when you compress a 3-D object from all sides?  It might compress like a gas, or stay rigid, but either way, the matter doesn’t lap over into an extra dimension, substantially.  It is not just functionally three-dimensional.  The Theorists would say that there is no such room for that, anyway.  We cannot very well compress empty space in this way, so we cannot cause this effect upon the whole universe.  With devices such as the hadron collider, people still haven’t managed to invoke this effect.

Three dimensions extend unimaginably far into the depths of space.  Some would have us believe that there are others, which hardly extend beyond the width of an atom.  The length of the available space may be too small for a rotation, that we might see it, and it might be too small to bend matter into it.  However, it cannot be completely filled by matter, or it would be, for all practical purposes nonexistent, having no freedom of movement.  Therefore, at the very least, we should be entitled to insist on some kind of potential for overlap.  That being the case, we should expect to see two tennis balls effortlessly pushed into each other, overlapping on one of the extra dimensions which some people are so fond of.

In the meantime, I choose to invoke Ockham’s razor.

The ability to harness a fourth dimension would yield some pretty incredible power, not the least of which is teleportation, walking through walls and invisibility.  If it could be found, then I would rather a corrupt human race did not find it.  Even so, I suggest that these are attributes of spirits, not physical forms.  That being the case, I do not expect to find more than the standard three dimensions in this world.  This is the most uninteresting conclusion, but it is possibly the most rational.

Perceptual Fog

17 03 2009

We experience in the past.  We act in the future.  By the time it’s reconstructed in our minds, the event is over, and by the time our bodies move to respond, it’s already the future.  Somewhere in between the two lies an infinitely narrow time span known as now.  Now doesn’t exist for any length of time.  It’s not even now by the time we acknowledge it.  It’s never now, because now is like two parentheses with nothing between them.  It’s not a long enough time span to contain any event.  Now is simply the interface between the future and the past.  It’s never now, yet it’s always now.  We exist in the now.  It is now now, yet, it is never now.  Between one second and the next, there are an infinite number of slices of time that at some point could have been called “now,” and each of those slices would be infinitely thin.  It’s another case of infinity divided by infinity.  What does it equal?  Sometimes it equals a second.  Sometimes it equals a year or more.  It’s yet another metaphysical mystery, because to study the laws of physics and their causes is to study the laws of metaphysics.

Sure, if all we did was study the effects of time on the world we know, then we’d only be studying physics, but when we wonder about the forces giving rise to time, then we step outside of the physical universe to examine it circumspectly.  An infinite number of nows could be a second, or it could be a year, so what makes the two any different from each other?  The perception of time arises from the effects that events have on the brain with time.  A year’s worth of events change the workings of the brain in terms of memories.  It works in cycles.  Each thought is experienced over and over, making a thought last for longer than a fleeting fraction of a second.  The more times a cycle runs through the brain, the greater the perception of time.  The key is that the brain, like the world around us, is a product of cause and effect.  Everything that it is now is the result of cumulative effects from the past.  In the next moment, there will have been a few more effects enacted upon it, and the workings of the mind will be slightly different as a result.

The brain can’t know the future, because it hasn’t been affected by the future yet.  The future is just as real as the past, but we just can’t perceive it because cause and effect only work in one direction.  To know the future is to violate this principle, and reverse this order.  This gives us every reason to fear the future, because we cannot see it clearly.  Had cause and effect generally worked in the opposite direction, then what we call the future now, would functionally be the past, and vice versa.  We’d be in the same boat we’re in now, but with the terminology reversed.  If cause and effect worked in both directions…things could get interesting.  Effectively, there would be no such thing as time.  The past would affect the future, which would then turn around and affect the past, and back again.  The time line would not be a line, but a plane.  Each time a cause and effect bounces back and forth on the time line between future and past, the entire line moves up a notch, drawing a zigzagging line depicting causal relationships as they bounce back and forth.

That’s if cause and effect can ever work in reverse order.  If I hit someone, they might fall backward.  However, I’d be shocked if a person fell backward and I responded by involuntarily throwing a punch.  Therefore, if cause and effect could work in reverse order, normal causal relationships would still always work in the same direction as they are seen to do now.  The difference would be in events that do not usually happen, such as foretelling of the future.  Telling the past is easy, because the causes of the past affect the memories of the present.  To tell the future would require an entirely different set of causal relationships, ones that do not normally happen.  The causes would exist after the effects.

Where does prophecy come from?  It comes from God, does it not?  Therefore, though for us time functions one-dimensionally, for God it must exist in two dimensions at the very least.  All we have is a future and a past.  We see a static time line.  It is what it is.  If the effects ever precede the causes, then we’re dealing with two-dimensional time, or a time line that changes with time.  It’s a difficult concept to grasp, but it is necessarily true.  In order to foretell the future, we need the assistance of one for whom time has one dimension more than we do.

The situation was similar in a previous post, Sid, The Defender, where a circle named Sid lived in a two-dimensional world and could only see objects that existed in that plane.  He was unaware of the three-dimensional person that could see him.  He could not understand the entirety of the finger that crossed through his world.  It looked like a circle to him.  If we wanted to, we could have that circle (the finger cross section) walk through one of his walls, a simple line, by lifting our finger out of his plane on one side of his wall, and placing it back into his world on the other side.  With the extra dimension to our advantage, what would be impossible in his world becomes easy for us.  Then, when we see an angel walk through walls or disappear entirely, or when the beings of a supernatural realm observe us without being seen, we marvel at the impossibility of it.  Yet, if they have the advantage of a fourth dimension, then they have the same advantage over us that we had over Sid.  The impossible becomes possible, but within certain limits.  Angels are not omnipotent.  They strive against their own forces of evil, just as we struggle against ours.

Some people see time as the fourth dimension.  I don’t.  Time has a dimension.  It’s the timeline.  For God, that’s a plane, having two dimensions, maybe more.  I don’t even know what it is for the angels and devils.  I can only say that I suspect they’re in the same boat as us on that one.  Otherwise, Satan would have seen his eventual defeat and decided against rebellion, or chosen to undo his rebellion and make it as though it never happened.  Had it never happened, the underlying root of the evil would still have been there.  He’d still be a devil at heart.  The same would be true for us.  Choosing righteousness because we see our own Hell looming before us is no righteousness at all.  Everything we know about Heaven and Hell, God and anything that might make dirty rotten sinners like us act like angels is a matter of faith.  Were it obvious, could people see the Hell before them like the memory of something that has not happened yet, they might not act out the evil that was in their hearts, but the underlying motivation would still be there.  The fog of perception that keeps the future hazy to us makes all the difference between faith that saves and uncontested fact that makes for boring textbooks.  People avoid running into walls, because they are sure that the walls exist.  They can believe what they want about the afterlife.

In the attic of my mind, I asked God if things would work out all right.  He looked up from his writing of history to say that things would turn out just fine for me.  “Then, I won’t end up dead in this story?” I asked.  “No,” he replied, “You’ll die, but it’ll work out all right for you.”  I’ll die, but I’ll be just fine.  Okay….

Be thankful that you’re blind to the future.  If not, then you’d be reliving your life from the very beginning with all of the memories of things that haven’t happened yet, all of the disasters, all of the burden.  You’d know about the September 11 attacks well in advance.  You’d feel like a jerk if you did nothing about it, and you’d be pulling your hair out if you tried to stop it.  You’d hate your enemies before they deserved it, and you would be faulted for your baseless aversion.  You’d love your future spouse while you were nothing but a stranger to that person.  Spontaneity would be utterly dead.  Everything would be scripted.  Your time of death would be known, and life would be a countdown.  Everything would be set so far in advance that life would lose its meaning.  The reason it would lose its meaning is because you’d be the one responsible for giving it that meaning, rather than God, who currently performs that role.  If you knew all events that would result from any action you made, all of life would be scripted by you, not God.  This person only loves you because you knew what it would take to make them love you.  That job you have is only yours because you knew what strings to pull.  All of life is what it is, because you made it that way, if you could see the future the way that you see the past.

Thank God for your ignorance.  Thank him for the perceptual fog that grants him the right to author the meaning of your life.


Sid, the Defender

27 02 2009


This is Sid.

sidSid is a circle.

He doesn’t believe in you.

Sid lives in a two-dimensional world, a flat plane, and you are not in that plane.

Therefore Sid cannot see you.

Therefore you do not exist.

This is your finger, as it passes through Sid’s world.

fingerSid only sees another circle.

Therefore, your finger is just a circle, like Sid,

And you do not exist.

Sid only sees the outside, but you see the inside.

Sid is full of chaff and bits of debris, and you tell him so.

Sid thinks your finger is a liar.

With your other finger, you poke at the debris inside Sid.

Sid is not amused.

He retaliates by stabbing your finger with a mathematical line.


You quickly remove your finger from Sid’s flat world.

Sid has conquered the magical menace.

He is at peace with himself.

He can think that he is only a circle, with no debris inside.

He can’t see debris.

There is no such thing as debris.

Besides, he can’t fix what he can’t reach.

And you don’t exist, so what no one sees doesn’t matter.

What Sid doesn’t see can’t hurt Sid.

Your thumb is hovering directly over Sid.