Jun 29, 2008

Empty Spaces

Today's posting is on a topic that has been perplexing us for quite some time, and it is something we take for granted more often than not in our world.

When modeling an entire Universe, it cannot be overlooked that in the process there is bound to be quite a deal of raw data involved. Space, as we know, is a very large place. In our universe, we are bound to come across a mind boggling amount of celestial bodies, of which are part of the countless galaxies and solar systems throughout this place we call home.

When we think of a Solar System, we like to think of our own little corner of the universe. A single star in its perceived center with a handful of celestial planets revolving around it. Around those planets, sometimes, we also find smaller bodies revolving around them as well. In these orbits, these nearly predictable orbits, we see what appears to be some manner of order involved.

Sure our galaxy, what we call the Milky Way system, is roughly 750,000 light years across in size. And when we look at these astronomical numbers we often fail to realize the magnitude of what we are looking at.

A light year is the distance that light could travel in one year as measured by the rotations of this planet we call home, Earth. Since we know that light can travel at 186,000 miles per second (approximately), how far can we surmise light may travel in a year? If we extrapolate the distance travelled into a light minute, that is 186,000 miles times 60, we get an answer of approximately 11,160,000 miles per minute. 11.16 million miles in a single minute, that is an exceedingly large number to deal with, let alone attempt to model in a virtual environment.

But that is simply a single light minute, and we know that the very least that our own Milky Way galaxy should encompass is roughly 150,000 light years across but I've decided to go as far as 250 light years so we can get an idea of scale (and mostly because the calculator is fighting me on that level).

So we figure out a single light hour, and are greeted with yet a previously unthinkable complexity for distance. 669,600,000 miles per hour. Light apparently travels very, very fast indeed. Nearly 670 million miles per hour is the approximation for this figure, and yet we are nowhere near the edge of our own galaxy, and in fact we've barely left home by these figures.

So we extrapolate again in order to figure out what a Light Day would cover in distance. There are 24 hours in our Earth day, and we know that there is 669.6 million miles per hour. So we do some math again to get a single Light Day.

In the course of 24 of our Earth hours, light will travel approximately 16,070,400,000 miles. At this point we're reaching into the early billions of miles. In just a single day light will cover approximately 16 billion miles. But now we must figure out how many days make up an entire year and multiply again. For the sake of argument, let us simply take a standardized 365 days in a single year.

I understand we can calculate that with much better complexity and maybe even to the minute or second, but for this exercise we'll try to keep it simple.

5,865,696,000,000 miles in 365 Earth days. Close to 6 trillion miles in a single Earth year. That is how far light will travel over that given span of time. And yet we are not done yet, because the Milky Way galaxy that we call home is approximately 100,000 Light Years across if we go by only the lowest estimates.

This number is going to be exceedingly large, and we know it. We're talking mind bogglingly large at this point.

1,470,632,759,080,745.869156905 miles in 250 years. That is the approximate distance of light over that period of time. It is a fantastically large number in itself, and if we don't ignore that the Milky Way is 100,000 light years across and not a measly 250, it makes the mind boggle.

What comes after a trillion? It is at this point that I had to actually look it up, and found that there is indeed a name for a number with 15 zeros after it. Quadrillion, and after that is Quintillion (which immediately brought a geek reference to my mind of Quintilla from Hitchhikers Guide), so we're going to say that since the Milky Way Galaxy is about 150,000 Light Years across -

Let us round up to make this easier to digest. Let us say that ridiculous number is not
882,379,655,448,447,521 but instead a more manageable 882 Quadrillion miles. Again, we're not looking for dead accuracy, but just a general idea of these distances involved. We'll leave the accuracy for astrometrics assuming anyone in their right mind would ever want to start a space program in Andromeda Universe.

The reason for this little exercise is to give people a sense of proportion when asking us how soon the universe will be ready to populate. I will not say that the entire virtual universe will be populated by planets and celestial bodies like our own universe is today for real, but I will say that a number of questions have been raised during this research which lead me redefine the requirements of this project daily.

For instance, do we really need an entire universe? If so, then how do you suppose to handle 882 quadrillion miles of space in a galactic spiral arm?

It turns out, the answer isn't as hard as we thought. In space, we think of these ridiculous numbers and distances as though some database needs to keep track of every inch. In reality, the database merely needs to keep track of non-empty space and your relation to it.

All else is just empty spaces.

On paper,
882,379,655,448,447,521 quadrillion miles seems terribly impressive, but in a database, simply keeping track of the locations and layouts of 800,000 celestial bodies is a matter of about than 80 Gb of space for the coordinates. I'm sure there is more than 800,000 celestial bodies in the Milky Way galaxy, but after doing some math (based again on rough estimates) figuring about 10 bytes of info in the database per coordinate (which would be about 10 numbers per coordinate and way more than we actually need to plot a single celestial body in our universe), and taking into account that there is roughly 1000 bytes per kb and 1000 kb in a megabyte (1024 actually, but we're approximating), we arrive at roughly 1,000 celestial coordinates per Megabyte of storage.

So the trick isn't to try and think of the empty space as part of the whole, but instead your relation to the non-empty coordinates in the system. Space, it seems, it a very vast and empty area. Sure there are elementary particles filling it up, but we're not very concerned about things on that scale for the moment. We are also interested to see if we would ever need to dedicate and entire 80 Gb of space to handle the coordinates for 800,000 celestial bodies.

For people used to other means of virtual environments such as Active Worlds, think of this as 800,000 world servers. And yet, in the grand scheme of things, it may be very possible indeed to see that many and more. How many web sites are there on the Internet today? What if they were all virtual worlds in this digital universe?

As for these astronomical numbers, and talk concerning the universe, galaxy and a solar system, I must point out that when put back into perspective, a Galaxy in the classical sense is a force to be reckoned with. 1.5 Quadrillion miles across, and what has to be ten times as many or more celestial entities than even I can suppose today. 1 million just seems like a very tiny fraction of how many planets would exist in a single Galaxy.

So the next time you see the Active Worlds server pricing, and you see their listings for Sol, Galaxy and Universe, put it into perspective.
882 Quadrillion miles is awfully large on its own, let alone a universe, and with a few hundred and maybe even a few thousand world servers in their universe configurations, it just doesn't seem appropriate to call it a Universe anymore... let alone a Galaxy.

With that in mind, we have been working on the framework that will allow us to structure the Solar Systems, Galaxies, and even the Universe itself digitally. While we feel that it may in fact be impossible to statistically fill the entire virtual universe with virtual worlds, the real world is welcome to try. As it stands, the framework for the Solar Systems and Galaxies are mostly intact and running, and as it is we would just scale up for the Universe should we ever need to place anything outside the galaxy.

For those of you who are curious as to how many miles are in the full Milky Way galaxy, and not just the 250 Light Years, I present to you this number, step by step:

If you ask Google it gives you scientific notation, and while that is technically accurate, it doesn't really give you a sense of scale when looking at the number. When written out in its entirety, 882 Quadrillion miles seems ridiculously huge - which I think is a good thing because the Milky Way Galaxy itself is ridiculously large as well. The problem with even this number is that it's not as accurate as it could have been when doing the calculation leading up to 150,000 Light Years, so I'll do the stages of calculations using more accurate numbers -

Follow along:

Light Travels approximately

186,282.397 miles per second

There are 60 seconds in a minute, and 60 minutes in an hour. So take the speed of light per second and multiply it by 60 to get a minute, then multiply that number by 60 to get distance per hour.

670,616,629.4 miles per hour.

Times that number by
24.01643836 to get miles per day. (yes that's the exact number of hours per day)

16,105,822,943.2 miles per light day. (more accurately 16,105,822,943.176063784)

Multiply that number by 365.2425 days in a year (yep, this is the more accurate number) and we get this number for a single light year -

5,882,531,036,322.98347662762 miles in a Light Year.

Continuing on, we run into a bit of an issue. We don't actually have an exact number for the size of the Milky Way galaxy. The numbers range between 100,000 Light Years across and 200,000 light years across. So what to do?

We'll take the average of the two and say the Milky Way Galaxy is only 150,000 Light Years across.

5,882,531,036,322.98347662762 multiplied by 150,000 is -

882,379,655,448,447,521.494143 miles. Which is the closest and most accurate number I can figure for the diameter of the Milky Way galaxy at the moment.

The Milky Way Galaxy is 882 Quadrillion, 379 Trillion, 655 Billion, 448 Million, 447 Thousand, 521 Point 494143 miles across. Or if we want to round up we can say the Milky Way galaxy is roughly 1 Quintillion miles across.

Hopefully I've followed the maths correctly with this and found a fairly accurate number. The first few times I tried to calculate this high up, I seemed to have botched the number.

In the end, it's just a coordinate and a lot of empty spaces.

- The Management


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