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Ramblings On Relativity

April 22, 2007

I was just reading Sartre the other night, and he was speaking of time.  First he stated the problem dealt with by Descartes, dealing with the problem of change and instants.

It’s an interesting philosophical dilemma.  Whenever a person experiences change, such as an object moving, the experience is unique yet there is something consistent that stays the same.  Leibniz stated this problem as: “Change implies permanance”

I remember as I was taking my walk I was wondering how the mind accomplishes this feat.  I saw an old stump off in the distance and made my way toward it.  As I approached the stump each subsequent image I perceived with my eyes changed.  At first it was just a small brown little spec, but as I got closer and closer it soon took the entire image perceived by my eyes.  I then saw the bark, the exact shape of the stump, the rings in the wood, etc.

What is interesting about this happening is that for whatever reason my mind “knows” that the brown spec I perceived earlier off in the distance is the same stump as the thing I’m seeing right in front of me when I get near it.  How in the world do I do this?

You may not think a thing of it, but I have a passion for writing an artifical intelligence algorithm which does this very thing.  Think if you had to write a software program that took images from a camera (such as a live feed from a webcam) and actually “perceive” the objects that are in view.

You know how awesome that would be!  You could come sit down in front of your computer, and your computer could say, “Hey Jason.  Welcome back”.  I could be wearing different clothes, have on a hat, and give it a thumbs up, and it would still know it’s me.

I’d like to walk down the street I walk down all the time, with a camera, and it make a 3D blueprint of the entire street based on the images seen through the camera.  The entire goal of the project is for the algorithm to take 2D images (such as that from a camera) and it perceive objects, and spatially arrange the objects how our mind does… That’s my biggest passion in life.

That’s how our own mind does things.  Our mind “parses” information from our senses and stores “objects”.  These objects are related into a conception of “space”.  Space is a relationship between the objects.  Time is a change of the relationship between these objects.  Time is “it was here relative to this other object… Now it’s farther away relative to that same object”.  This is where we get the concepts “before”, and “after”.  The object was once here, but now it’s there (relative to some base frame of reference).  You can’t have time without space.  They imply each other.

Now I wonder myself sometimes whether I can have space without time.  You can’t have time without space, but can you have space without time?  I feel pretty confident that answer is no as well.  There has to be a change in the state of the observer from “there is no objects” to “there is objects arranged in this spatial arrangement”.  If there is change, there is a before/after relationship, which is time.  If the spatial arrangement was there from the beginning, and there is no change, I think you’re simply left with a unity.  How can you have a negation unless you start off as a unity first, then you negate?  We’ll get back to this here in just one second.

I used to wonder a lot about what Kant said when he mentioned that we do not know how matter “really exists”.  There is how we perceive the matter, but how it exists truly we can never know.  That sounds like nonsense, but let’s think about playing a video game.  Say I’m playing World of Warcraft with several of my friends online.  I see my friend over on a hill waving to me to come kill some orcs.  So I see my friend on my computer screen.  Let me ask you a question:  Is there any “space” between us?

If you think so, you’ll certainly have to get rid of your “common sense” perspective on what space is.  Most of us when explaining space to one another take our hands and move them about in a motion from our chest outward.  If that is the case, then what is space in this video game we’re playing with one another?  Whatever it is, it’s not captured in that motion of your hands.

So what is space?  We can look at the computer screen, watch the change in the images displayed to us, and we can perceive objects.  We see hills, other characters running around, we see trees, we see clouds, etc.  These objects then that we see with our eyes get stored in our minds (however that happens) and then they get related to one another.  This is what space is.  It is a fancy doing by your mind which takes a series of 2D images and parses various objects out from it.  It then forms these relationships between them, and you perceive both space and time, even in a world of a video game.

What Kant is really saying is that when you’re playing a video game (or immersed in a particular reality) you cannot know how the “programmers”
of that reality made the source code as to how that reality “really works”.  You look around and see walls, ceilings, some guy standing there in a suit, or a waterfall on your computer screen… But how things appear on the screen and the actual logic that produces those images in the computer are two completley different things.

There’s a man named John Carmack who is a founder of a company named id Software.  I used to look up to him as a sort of idol when I was young, as he was the writer of the best 3D graphics engines to date (and he still is).  What I always found amazing, learning how to write 3D games is that by using fancy matrix mathematics, some physics, and a C++ compiler I could make an entire world.  I just sit down and I could do literally anything I wanted to.  I had a blank canvas.. the computer monitor, and I could make it display anything I wanted to, and in any fashion.

He made the Doom engine a long while back.  I think it was 1994? 92? 93?  I don’t know.  I found it fascinating that what you saw on the actual computer monitor was in no way how the game actually produced the images you were seeing.  Doom, though the game LOOKS 3D is actually represented internally to the game as 2D.  Take for instance when you see an imp in front of you, you point your shotgun at it and shoot it.  The environment is basically stored as a bunch of 2D polygons.  Imps are basically squares, and your character is a square.  You shoot your gun, and a 2D line is projected from where you are aiming and the game engine calculates when that bullet hits a “wall”.  If any bad guys are found along that line they are “shot”… Their animation states change, their health variables are taken down as to how close to center you hit them, etc.  Fascinating stuff.  It looks 3D, but it’s not.  It’s just drawn 3D with a 2D back-end engine running the entire thing.

Back to our initial question: What is space?  Well what is it in these video games?  It’s a logical relationship between these “objects” of the source code.  It’s pure mathematics.

I remember when I first started writing 3D engines I always wondered about time…When you’re writing your own video game, source code logic has no sense of “time”.  There is no “time”.  There is no “space”.  You’re literally dealing with numbers, variables, and assinging these variables number values according to the logic you write.  That’s IT.  That is all you’re doing.  “Sound” is an array built via a mathematical sine wave.  “Images” that you paint to the computer screen are 2D X by Y variable matrices where you assign a value of 0-65536, where each different integer value represents the color that will be displayed on the monitor of a particular pixel.
Whether the user is pressing a keyboard command is represented by a numeric 0-1, and these values are stored in a big array labeled ‘keyboard’.  It was all mathematics.  That’s why I love mathematics.  It’s the key to all perception.

Think if you wrote a 3D game engine on an infinitely fast computer, and the game engine did not require any user input for the camera to fly about the game world.  The basics of the computer program was just to fly a camera around the game world, show you everything, and then it would be done.

Well if this computer was infinitely fast, all the images would be instantly displayed on the computer monitor at once.  Whenever you started the program you’d be at the same time ending it as well.  It would have executed all the logic, done every calculation to build every image, displayed every image, and be done with the entire routine instantly.  WoW.  What’s interesting about that concept is that logic itself is seperate from time or space.  Logic seems to be timeless.  If, then, else, while loops, etc, are all outside of time.

Did “time” pass in our example?  Actually it did, just not relative to YOU the observer.  You experienced no change, and therefore time was different relative to you.  Objects within the computer changed relationships, but no mental objects within your mind changed relationships.  If your mind was moving as fast as the infinite speed computer, you would have experienced time just as this computer had.

But can the speed actually be ‘infinite’?  Think about it.  Infinite speed computer.  Wouldn’t infinite speed relative to an observer mean no speed at all?  If the infinite speed computer can execute all that logic instantly, then isn’t that simply a unity?  Everything happened at once. Time requires change, but since this does all the changes instantly, then how do we have change?  You have multiple “instant changes” in one single instant.  Those concepts can’t go together.

That’s why you cannot have an infinite speed anything.  Infinite speeds throw everything off balance.  Time cannot exist when infinite speed is allowed.  Therefore time has to have a ‘speed limit’ imposed upon the change in the objects.  That is how time and space are related.  Einstein found that our maximum speed limit is the speed of light.  It has to work this way, and when you furthur reflect on this notion, weird things start to happen that are strangely neccessary, such as time stopping as you approach the speed of light (maximum speed limit).

Really when you formulate a definition of ‘time’ or ‘space’, you’re not REALLY labeling something that really exists.  If scientists started playing World of Warcraft and began doing experiments and did Einstein’s time and space formulations based on changes in the images of that video game… They wouldn’t be capturing what ‘space’ and ‘time’ really are, they would be creating a useful fiction.  It may help them predict what is going to happen in that video game world, but their formulas as to how they represent time and space will not neccessarily reflect how the programmers of that game engine represent time and space.

When you’re playing Doom, you find Carmack, in order to optimize his game engine, uses an ultra crazy algorithm called ‘Binary Space Partitioning”.  He subdivides all the walls, floors, ceilings, etc, into a bunch of different polygons, and he mathematically optimized it to where based on an angle the observer (the game player) is looking, he could grab only those polygons the user is actually looking at.  This way the computer could save computational cycles by not having to deal with walls, floors, ceilings, bad guys, etc, that you’re not looking at.

When you look at the mangled mess Carmack’s optimization algorithms leave behind, it’s hard to say if that’s even a “wall”, or a “ceiling”, etc.  It’s just abstract mathematics at that point.  You still get the same end-result image, but this fancy mathematics made the computer have to do far less work to build that image.

Phew, all of that background information to finally get at my thoughts during my walk.

Time, Instants, and Unification of Instants

I’ve been thinking that everything that goes on in the mind is Negation.  Everything.  You can view time as a whole, or as an instant, or as all kinds of different chunks by negating it in different ways.  No change can happen without negation.  If space and time are relationships between objects, then we first need objects to form relationships between.  You have to negate out objects from the big mass they call “reality”.

Normally my thought has only dwelled upon taking a big mass, and working my way down to being more and more specific, but I’ve also noticed that the mind can unify as well as divide.  That’s what got me thinking about the “Unification of Instants”.

I kept thinking over various objects flying around in a 3D engine, and the camera man flying through this game world at different velocities and accelerations.  I keep thinking about uniform vs accelerating reference frames.

The objects move relative to one another and the the camera man moves relative to them all, but no problems arise.  Computer graphics engines don’t have a concept of ‘light’.  If you think you’re seeing lighting in a video game, it’s not really ‘light’.  In the game engine, there is no light waves moving at 186,000 miles/second, all eminating from a light source.  Lighting in most senses, in the game, is a trick.  Really the game engine is just doing fancy math, and then it finally chucks out an image on your computer screen.

Objects in a video game aren’t rendered (drawn to the screen) according to Light logic.  3D game engines have the good ol’ Z-buffer, and objects are translated via a translation matrix into a frame of reference.  Every object that comes within the viewing frustum is rendered and each pixel rendered is given a Z-value.  Then the next object is drawn to the screen, but if its Z-value in the Z-buffer is greater than that of the previous object drawn, those particular pixels of that object are not displayed.  This way objects which are in front of other objects are displayed on the screen correctly.  It’s important to draw the objects to the screen in the right order.  If an object (such as a game character) who is wayyyyyy off in the distance is drawn in front of an object which is right in front of you… you lose your sense of depth perception (space).

Einstein’s relavitity problems do not even come into play in this game engine.  They can’t.  Objects just are not handled in that manner.  There is no time dilation because there is no speed of light.  All observers, regardless of reference frame,  see the same thing, because there is no light traveling to the observers at a finite speed.  Therefore there is no problems.  No weird space and time linkages.

I’ve always used my 3D game engine thinking methods to help me understand philosophy and physics, but at this time, with Einstein’s relativity it fails me.  My analogies in programming just have to go away.  Now I have to think, “God, why would you make our reality in this fashion?  Why are space, time, and the speed of light linked together?”

Well… First reflections.  Do you allow infinite speed objects?  I reflected on that, and found that with infinite speed objects you have one of two things happen:

1.  If the two objects are moving in the exact same direction (at infinite speed), then they can travel together side by side, but there will be no change in relationship between these two objects.

Fair enough.  Now we get to the problem of absolute reference frames… You’re looking at these two objects from above, moving at an infinite speed along with them.  Since you perceive no change, how do you know if you’re moving at an infinite speed, a finite speed, or not moving at all?  Without a reference point, there’s no way for an observer to perceive any change.

2. If two infinitely fast objects are moving even the slightest different direction, then they can literally NEVER be perceived together within a single reference frame.  If you as the camera man are not moving at the same infinite speed and in the same exact direction as the object it will be an infinite distance from you in literally an instant.

Ok, so if we allow infinite velocities, we can either perceive no change, or not perceive the objects at all… Infinite speeds and observers just can’t go together.

Moving onward, so we set a speed limit.  If objects are going to be perceived alongside other objects, we cannot allow infinite speeds.  If two people ever want to interact, they will have to interact at finite speeds.

So God makes this speed limit the same speed of conscious thought (neurons and electricity in our brains move at the speed of light).  The speed of light is introduced.

Light… Light.. such a core basis.  It is THE basis.

I can understand why a finite speed is introduced.  So a speed limiter is set in place.  Fine.  Why make the very perception of objects based on “light”.  Why does this “light” concept exist.  Why is it linked with time?

If I’m looking at the Earth, from some distance away, why can’t I just see Earth.  Why isn’t that drawn to my conscious mind?  Why do you have these little radiation particles fly from some light source, bounce off the Earth, then fly back toward me, hit my eyes, and me see the Earth?

I can say one thing that’s nice about it.  Stupid concepts like Mip-mapping, texture compression, etc, all go away.  Hmmm, with 3D engines, telescopes wouldn’t work.  Unless the telescope was programmed as a game object to render objects that are a certain distance away, you could never do anything related to “optics”.  There is no light for the telescope to take in, bend via optics, and see a more focused image.

Hmmm.  I can remember a strange paradox in the old Duke Nukem 3D game engine, one of the first games to introduce “mirrors”.  In a game engine, if you had one mirror looking into another mirror…. Bad news… That just didn’t work.  Your computer would hang.  Mirrors were basically game “cameras” placed at a reference point and a… oh what did they call that… They’d set up a mask on the wall texture.  What the game would do, if you’re looking in a mirror is it would take the game camera, render the scene as if you were standing at that point of the mirror (a distance behind the wall), then the game would switch back to the player’s perspective, apply a mask to the screen around where the mirror is, then it would draw what you would normally see out of your eyes, but leave the contents of the mirror alone.

So with video game mirrors you always rendered the scene twice, from two different perspectives.  once from the mirror, then from the player’s viewpoint and the two images are merged together via the mask.   Hmmm, light seems to take care of that issue nicely.

Hmm, another fascinating point to dwell on.  In video games, one of the core concepts of the game engine is to not deal with objects that are not in view.  I hear of programmers using concepts like Octrees, or Binary Space Partioning, etc.   With a universe as large as ours, it would be a crazy amount of objects in view.  If the universe was truly INFINITELY BIG, then there would be no black space at all when looking into the sky.  It’d be a big smoosh’d and swirly smash of colors of every sort.  You’d see planets, stars, and everything else all smoosh’d together.  It definitely wouldn’t look very nice.

If that’s the case, then it would be ASTRONOMICALLY more efficient to deal with only the few light particles hitting your eyes to build the image you are seeing.  They’d have to move at a finite speed, as mentioned before (if stuff is to interact)….

As always, when I start to think things over, God knew what he was doing.  I like God.  I can’t wait to meet him.  I’m sure there’s countless reasons my petty mind cannot even comprehend.  I like knowing reasons though.  I like to envision other ways it could work and always find the amazing discovery that things are ALWAYS done the BEST WAY POSSIBLE.  You cannot EVER and I mean EVER out do God.

I look at the world as a giant video game engine.  God is the most amazing programmer EVER.  EVER.  EEVVEEERRRR.  There is never a bad basis.  Never something that isn’t thought out.  No bugs.  No quirks.  It’s exactly, and I mean EXACTLY how you’d want it to work.  EVERY TIME.

Every force, to every particle, to every thing possible to see with your eyes is perfection.  I look at video games out today, and I see realities man tries to make.  They create a giant online role playing game.  As good as it is, I must say it’s pathetic if you were to compare it to things God has made.  There’s more complexities to my finger nail in real life than there is in the entire game World of Warcraft.
Atoms, electrons, light, blood, molecules, DNA… all this ochestrated whole, not to mention great functionality.  This body is great machine.  I can do all kinds of things in my human body.  I’m definitely not complaining.

Now I learn realtivity and see time dilation… There’s probably some ultra thought out reason why it works that way and when I find it out (and I will find it out) I’m going to sit back and say, as I always do, “God, you always do things right.”

This doesn’t sound like very convincing reasoning, but they’re just my thoughts for the moment on relativity.  I think they’re better than what this physics book I was reading presented.

The Physics textbook I was reading gave an example of how if a speed-limit is not introduced, objects are not recorded correctly by observers.  He had a spaceship flying at 2 times the speed of light moving toward the moon, and since the observers could only see based on the light that hit their eyes… It was kind of messed up.  I can understand why infinite speeds are not allowed, and why a finite speed limit is introduced that cannot be broken.  But… why moving faster than the speed of light sends you backward in time… *blows right over my head*… Back to thinking.  I’ll figure it out.

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