»How old is the Matrix? A calculation«

I've heard a lot of people approximate the time between Matrix resets at around 100 years, but I think it's a lot longer than that. Here's a calculation that I've made. . .

I pulled this off of a website discussing human population growth:

Quote:

A rule of thumb for population growth is divide 70 by the rate of population growth, the result is the number of years it will take the population to double in size. The rate of population growth for the world is around 1.7-1.8 at the present time.

Using this rule of thumb (and assuming the growth rate now is the same that Zion would have), it takes 39 years to double the population. To go from 24 (16 females, 7 males, plus the One) to 250,000 (population of Zion as given "One sentinel for every person in Zion"), it would take just over thirteen generations or 500 years give or take.

However, humans are being freed from the matrix as well. So let's be generous and say that they free one human for every one child that is born in Zion (also, one human dies in rescue attempt for every person that dies in Zion of natural causes). So the growth rate is doubled (3.4). This would give a time frame of about 270 years as the life of the 6th Matrix.

We can't really tell how long the other Matrices lasted, but if they were similar (say between 270 and 500 years), than the Matrix is anywhere from 1600 to 3000 years old.

Thoughts? Comments? (Besides that I have too much free time)

Population growth for our world is for people with other activities - how many more babies would there be if TV wasn't around?

Plus you need to add in the escapees from the matrix

Without having any rule to hand for population growth - and uncertain how it would apply, I looked at this from the other angle a while back

The thread is matrix-explained.com...

Which produces (clumsily) a different result, but then I'm not a mathmetician or statistician

Just something to help fill that free time

Thanks for the jump to that thread, they have some good concepts. But, they don't use the law of growth and decay. The "70 rule" is an appoximation based on the natural log and growth and decay would be the way to go in figuring out population growth. The main problem with my assumptions is finding a good growth rate. It could vary from 1.2 (very slow growth because of harsh conditions) to 3.0 (very high growth because of prosperity and nothing else to do, i.e. TV). I also took into account freed people from the matrix by doubling my growth rate.

Anyway, my point was that the time between resetting the Matrices is much greater than 100 years. I'll stand by my numbers that it's between 270 and 500 years (which is a pretty wide margin anyway).

well...there is also a third factor, being the babies that are freed from the harvesting fields...but i can't say how much change that would make.

also, you're assuming that each Zion grew to a quarter-million in population. while it works, it may not be true.

also also (fourth factor), the rate at which they free minds from the Matrix might be a constant, or it might spike whenever the One is found (as it did this time around) or even when a One potential is found.

It's true, there are way too many assumptions to get an accurate calculation of how old the Matrix is. This is just my best possible guess.

The varying factors:
1) Growth rate of Zion born people
2) Rate at which people are freed
3) Death rates (affected by missions)
4) How big Zion gets before the emergence of the One

Explanations:
1) The population growth of the Zion-born is probably the most accurately measured. Almost all population follow the law of growth and deca:

P=P(initial)*ln(rt) where r is growth rate and t is time.

R is the random factor here. It could as low as 1.2 which is human growth at very harsh times or as high as 3.0 which is growth rate at high prosperity. Conditions in Zion seem harsh, but the are also given advanced technology.

2) and 3) I think I am very generous when I say that people are freed at the rate at which children are born in Zion. I'd say it's more likely that more people die on missions than are freed. However, if missions are very successful, than they would grow at a logarithmic rate because more freed people would lead to more missions which would lead to more freed people and so on. So I just double the growth rate (we couldn't just double the population because the freed people could have children too). By the way, when do they free babies? Did i miss that?

4) A population of 250,000 is only true of the last Zion when Neo emerged. It could easily be bigger or smaller in previous Matrices.

Determining the age of a Matrix doesn't depend on how big Zion gets, but how long it takes to find the One (or actually the integral anomaly). Since there's no way to figure out how long it takes to find the Anomaly time after time, I just tried to figure out long it took to find Neo using approximations and what not. Perhaps previous Anomalies were found immediately. Or perhaps it could have taked thousands of years. There's no way to know for sure. However, I think we should definitely throw out that 100 year approximation. I think it's very unlikely. Personally, I'd go with an average of 500 years per Matrix (Zion breeds at current rate of World, and freed people cancels out with people who die on missions). But again, that's almost as pure a guess as 100 years.

bachsoffice wrote:

By the way, when do they free babies? Did i miss that?

read the comics, babeee!

There is another factor

Even if they find The One eventually, in the real world he can still be killed, maybe from an accident of the hovercraft or sentinel atacks, maybe someone accidentally unplugs him , maybe he develops a brain tumora from all that plugging-unplugging ...


So The One doesn't make it to the source, and the Matrix isn't reloaded; and it will probably take some time untill the next One is born and the search starts again....

There were 6 Ones who made it to the source, but what about those that didn't .

Good point about One's not making it, but the Architect says that there counts the number of matrices by counting "the emergence of one integral anomaly to the next" of which Neo is the 6th. This implies that every One that did emerge, made it back to the source. No failures, yet.

Also, the machines seem to have kind of control over/knowledge of the World outside the Matrix. Certain things happen outside the Matrix to fulfill prophetic visions, i.e. a bolt breaks that collapses a bridge that destroys the ship that causes the crew to fail their mission which prompts Trinity to reenter the Matrix which fulfills Neo's vision which the Oracle also saw. There's a thread that discusses how the Oracle knows the future and this is a sticking point. However, the machines know certain things will happen, and perhaps the One returning to the source is one of those things. Regardless of what happens in the real world.

Brings up a good question, though. If the One dies, is that the equivalent of him returning to the matrix? Is there always a Smith-like threat that encourages the One to reset the matrix? Or was the Smith threat unique to Neo's Matrix? Anyway, its a bit off topic, but I've been doing my share of moving other threads off topic, so why not my own? Anyway, i think the Ones 9or anomalies) are guaranteed to return to the source by prophecy or whatever no matter what, and what they do from there is anyone's guess.

How can the rate at which people grow in Zion be the same as the growth rate for the world right now?

Zion = 250,000 people
Earth = 6,000,000,000 people

You can't say the growth rate is the same!

By growth rate, I'm referring to the logarithmic constant, r, in the equation:

P=P(initial)*e^rt (I posted the wrong equation earlier)

anyway, the constant, r, is dependant on the favorability of the environment for growth.

for example, the same formula would be used to calculate how quickly cockroaches would grow in a house. However, r would be higher in a house that's really dirty with food lying all around, and less in a house that is neat and clean.

Anyway, there's no way to say what r would be for Zion, so I used what we have today.

Maybe I should have called it the Growth Rate constant, because Growth rate is technically birth rate minus death rate.