Why UNLIMITED Exponential Growth of Pigeons would DESTROY the Universe!

[ProtoJeb21]

It all began with a word problem about exponential growth in Algebra class today. The scenario was simple enough: someone is feeding pigeons. 10 come at first, but each minute the number of rat birds triples. It sounds like a simple problem, but when you do the math, something horrifying is revealed: This can wipe us all out of the Universe.

First let's get to the topic of exponential growth. It is a function of change where the y-values are always being changed by multiplication - either of fractions or whole numbers. The result is a non-linear trend that becomes quicker and quicker as time goes on. It is a good way of graphing incomes and population of organisms. But if left unchecked, certain things undergoing a rapid exponential growth over a certain amount of time can result in disastrous consequences. Humans are just a weak example of this. If a population keeps growing at an exponential rate that's large enough, it can cause quite an issue with mass.

Let's get back to the pigeons. One of the goals of this problem was to find out how many pigeons would appear after just 4 minutes. Now, keep in mind that the starting number of pigeons (10) keeps tripling every minute. Also keeping in mind this handy equation: y=a*b^x, where a is the starting number, b is the factor of change, and ^x is the x-value you choose. The latter can be a unit of time, or amount of tries, or something along those lines. For our problem the equation we would use is y=10*3⁴. Plug it in a handy-dandy calculator and you get a whopping 810 pigeons begging for food. That's going to suck for the person feeding them - so many wings smacking you in the face (I can relate to that). However, we're just getting warmed up. Prepare to hate pigeons!

Remember that the amount of pigeons increases by THREE TIMES every MINUTE. That is a very quick exponential growth, much faster than that of humanity. This means that over a short period of time you would get so many pigeons. Let's just imagine that this example of exponential growth is solely dependent on the bird food. The amount of pigeons on our planet - in our UNIVERSE - does not matter in the context of the problem. They just keep coming! Just one minute after the 810 pigeons, you now have a whopping 2,430 of them. But it gets a whole lot worse from here. By 10 minutes you have 590,490 pigeons fluttering around you. That's enough to crowd an entire park. But what about an HOUR later? Believe it or not, there will be an astronomical amount of pigeons - 423,911,582,752,200,000,000,000,000,000 in total. That is 423.9 OCTILLION pigeons! Madness! But having 4.239e+29 birds in that area would essentially destroy the entire planet. Taking into account that the average pigeon has a mass of approximately 0.907 kilograms, we can calculate that the total mass of these pigeons would be 64,388.4 times the mass of Earth. That's over 202 times the mass of JUPITER, or 19.3% the mass of the SUN! This collection of pigeons would be so massive it could collapse into a thermonuclear ball of superheated plasma and begin NUCLEAR FUSION. This would form a red dwarf star, swallowing up Earth and destroying all life on it! That's 7.5 billion humans gone in the drop of a hat - all because of some pigeons.

But how, do you say, will all these pigeons destroy reality as we know it? Well, in this scenario, they would still be coming despite any other cataclysms. After 3 hours they would reach a mass of 6.91e+86 kilograms. If that sounds like a lot that's because it is - approximately 3.022e+44 times the mass of OUR ENTIRE FLEEPING GALAXY!!! If our universe consists of 100 billion galaxies, and if they're all about the mass of our galaxy (unlikely), then our entire UNIVERSE is quadrillions of times less massive than this pigeon mass! It would become its OWN PLANE OF EXISTENCE, then quickly start to rip apart the fabric of reality. This is the new Big Rip model, where dark matter rips a hole in space-time, sucking all the universe somewhere into oblivion - maybe into an alternate dimension. If this is the same case with the Pigeon Mass, then it would create a giant rip in our universe, sucking everything into a superheated maw of oblivion. The Pigeon Mass would quickly self-destruct, destroying all of what's left of our universe and whatever reality the spacetime hole leads to. Essentially, this would kill trillions upon trillions of lives and completely destroy two whole dimensions, including our own.

Starting to fear pigeons now? If so, you're having the right reaction! Have a nice day!

Spoiler

Honestly, I'm not too sure which is worse - slowly burning away an entire galaxy through Hawking Radiation from a subatomic black hole created by the runaway collapse of an Imperial Interdictor cruiser, or a universe-mass growing mass of pigeons wiping out everything we know about in the blink of an eye before destroying two entire dimensions. It's a close tie.

DISCLAIMER:

Spoiler

The calculations shown above are strictly staying to the context of the problem. Because the problem had no mention of limiting factors or population carrying capacity, it essentially means that the amount of pigeons would keep on increasing exponentially until there is no more universe to put them in. With real population dynamics involved, the only way to get this many pigeons is to have an infinite amount of bird food and wormholes leading to other parallel Earth dimensions to suck out all their pigeons. That's going to be quite hard to accomplish.

 

Edited May 4, 2017 by ProtoJeb21

[cubinator]

Aaaand that's why the universe has this handy failsafe mechanism called a logistic function. See, as you get a larger population, the growth looks exponential at first, but the environment can only sustain a certain number of pigeons so the growth tapers off at some point and approaches a horizontal asymptote, preventing the destruction of the universe.

Edited May 4, 2017 by cubinator

[FleshJeb]

What am I going to do with all these cats I just ordered?

My introduction to exponential growth was the grains of rice on a chessboard problem.

And if you really want to have trouble sleeping, look up Von Neumann probes.

[Ultimate Steve]

This reminds me of this.

[Urses]

This reminds me of the chess legend.

As chess was presented to landlord he was so empressed by the idea that he granted a wish to the inventor.

And he said. I don't wish for to much, give me some Corn.

He was asked how much.

The answer was.

Give me as much as it are fields on chess but double it per field please. For the first one, for second 2, for 3rd 4 and so on...

The landlord was not able to fullfill this wish

Funny Kabooms 

Urses 

PS: this legend is common for the land where i was born

 

[p1t1o]

5 hours ago, FleshJeb said:

And if you really want to have trouble sleeping, look up Von Neumann probes.

We ARE Von Neumann probes.

Think about THAT.

[magnemoe]

59 minutes ago, p1t1o said:

We ARE Von Neumann probes.

Think about THAT.

All life is self replicating and will expand, it has logistic issues as described. 
But no its no fundamental difference between an space living civilization with interstellar capabilities and an von neuman probe.
Space living is the big thing here as being restricted to planets would be limiting. 

[Green Baron]

But it is also a nice example of information sharing these days. I am trying to dissect the thought and mean no offence, ProtoJeb !

 

Use of a lurid title to gain attention

Post a basic principle out of context, applied to a subject it was not made for

Ignore natural principles, side effects and controlling factors

Draw premature conclusions while neglecting the scientific background

 

The lurid title claim goes without proof. The basic principle of exponential growth is a mathematical model. It can be used (and often is so in party talk) to describe the multiplication of living organisms but it was not made for that subject.

In a certain stage, when adaptation of an organism meets the requirements of the environment it will multiply but only until it reaches the limits, provided by the resources in the environment. This is where it will stop, spoiling the environment with it's excretions and thus narrowing its own niche. And/or, if it meets competition, will try to displace or be displaced.

In any case, the natural processes meet limiting factors. A phase of exponential growth, if it exists at all, can only last for a very limited time.

That is the easy version :-)

Whatever mechanism is at work, it is never the only determinant in describing a complex system. There are always interdependencies, like food chains, resource availability, cycles of matter, metabolisms. Some are obvious, others need deeper investigation. And that is where science comes back into the game. It is meant to explore these complexities !

 

Have a nice day everyone, and again, no offence, beat me up as a party spoiler :-)

 

Edited May 4, 2017 by Green Baron

[p1t1o]

14 minutes ago, Green Baron said:

But it is also a nice example of information sharing these days. I am trying to dissect the thought and mean no offence, ProtoJeb !

 

Use of a lurid title to gain attention

Post a basic principle out of context, applied to a subject it was not made for

Ignore natural principles, side effects and controlling factors

Draw premature conclusions while neglecting the scientific background

 

The lurid title claim goes without proof. The basic principle of exponential growth is a mathematical model. It can be used (and often is so in party talk) to describe the multiplication of living organisms but it was not made for that subject.

In a certain stage, when adaptation of an organism meets the requirements of the environment it will multiply but only until it reaches the limits, provided by the resources in the environment. This is where it will stop, spoiling the environment with it's excretions and thus narrowing its own niche. And/or, if it meets competition, will try to displace or be displaced.

In any case, the natural processes meet limiting factors. A phase of exponential growth, if it exists at all, can only last for a very limited time.

That is the easy version :-)

Whatever mechanism is at work, it is never the only determinant in describing a complex system. There are always interdependencies, like food chains, resource availability, cycles of matter, metabolisms. Some are obvious, others need deeper investigation. And that is where science comes back into the game. It is meant to explore these complexities !

 

Have a nice day everyone, and again, no offence, beat me up as a party spoiler :-)

 

 

The OP was clearly writing in a somewhat satirical manner, but the OP, and your description of it, matches some scientific "journalism" quite closely.

[Green Baron]

Well, in principle i got that :-) Sorry if i didn't hit the right tone ...

My intention was only to grab the opportunity and strengthen science. A bit.

 

[ProtoJeb21]

@Green Baron Remeber, the problem does not state any variables that would limit pigeon growth. The results I calculated are going with what the problem said. Sure, it's unlikely (unless you create wormholes to suck all the pigeons from parallel Earth dimensions) but I'm just going with what the problem said: pigeons keep appearing.

But if we were to add in limit factors to the context, then the pigeons would probably stop appearing after 10-20 minutes. By then you basically have most of the United States' population of those rat birds. Eventually competition would wipe a good chunk of them out.

[Green Baron]

Sorry, please attribute this question to my not being a native english speaker: "to science the crud out of everything", does it mean that in the post you simply didn't care about science and just put forward something, as silly as it might be ?

 

Edited May 4, 2017 by Green Baron

[ProtoJeb21]

4 minutes ago, Green Baron said:

Sorry, please attribute this question to my not being a native english speaker: "to science the crud out of everything", does it mean that in the post you simply didn't care about science and just put forward something, as silly as it might be ?

 

It's essentially going full-on Mark Whattney or ShoddyCast - calculating and sciencing about a subject with no remorse!

In my case it's calculating quite a LOT just for the heck of it. Usually it's planetary parameters but occasionally it's something like Hawking Radiation or the Schwartzchild Radius. This is the case with the pigeon problem - I could've left it alone but I was bored and wanted to see how far UNLIMITED exponential growth can go.

[p1t1o]

17 minutes ago, ProtoJeb21 said:

It's essentially going full-on Mark Whattney or ShoddyCast - calculating and sciencing about a subject with no remorse!

In my case it's calculating quite a LOT just for the heck of it. Usually it's planetary parameters but occasionally it's something like Hawking Radiation or the Schwartzchild Radius. This is the case with the pigeon problem - I could've left it alone but I was bored and wanted to see how far UNLIMITED exponential growth can go.

Well with these parameters, you dont need to do any science at all, you dont even need a calculator. Once you have said the words "unlimited" and "exponential", of course the universe will be destroyed!

[Green Baron]

Well, unlimited exponential growth is countable infinite.

But (besides the evolutionary things above) it has no connection to science because pigeons don't appear magically. You can of course calculate the expansion rate of your pigeon ball, it'll probably be faster than light after minutes, violate evolution, relativity, thermodynamics and disney productions, but what for ?

I can think of stranger things :-)

Edit: mathematics is not a natural science in itself. It is a tool like a language, used by natural science as well as by philosophy. Just sayin' ...

Edited May 4, 2017 by Green Baron

[Green Baron]

@ProtoJeb21:

I have another one that involves many more pigeons than the just infinite ones of the exponential growth (handwave):

Start with two pigeons. Put one in between. Ignore space. Now put two pigeons between the three pigeons. Carry on putting a pigeon between any two pigeons. Ignore complaints about narrow space.

See ? :-))

Edited May 4, 2017 by Green Baron

[ProtoJeb21]

1 hour ago, Green Baron said:

@ProtoJeb21:

I have another one that involves many more pigeons than the just infinite ones of the exponential growth (handwave):

Start with two pigeons. Put one in between. Ignore space. Now put two pigeons between the three pigeons. Carry on putting a pigeon between any two pigeons. Ignore complaints about narrow space.

See ? :-))

.....

I don't get it  

[magnemoe]

1 hour ago, Green Baron said:

Well, unlimited exponential growth is countable infinite.

But (besides the evolutionary things above) it has no connection to science because pigeons don't appear magically. You can of course calculate the expansion rate of your pigeon ball, it'll probably be faster than light after minutes, violate evolution, relativity, thermodynamics and disney productions, but what for ?

I can think of stranger things :-)

Edit: mathematics is not a natural science in itself. It is a tool like a language, used by natural science as well as by philosophy. Just sayin' ...

This, its theoretical, as you feed pigeons the birds come from the surrounding area where its limited number of them even if number can be far to high.
Now in computer games you don't have this limit. One stupid idea is to mod Skyrim and giving summonable creatures the ability to summon more of themselves.
Even if they can only summon one and killing one of them will break the chain removing all below its also very likely to crash the game 

[Spaceception]

Did you get extra credit for destroying the Universe?

[Green Baron]

Sorry, my bad. You probably didn't have that in algebra yet.

 

You can count the natural numbers in infinite time, but not for example the rational real numbers (not sure about the rational numbers !). Every gap between two rational numbers, as small as it may be, opens up a gap for an infinite number. Rational real numbers, in contrast to the natural ones, are uncountable infinite.

If you like to find out more: cardinal numbers is the search expression, here infinite cardinals. If that's not enough then carry on with the aleph numbers. But they go over my head.

 

Edit: though i need many more  pigeons than you in your example (edit: at least infinite as well ...), they all fit into a small interval (e.g. all rational pigeons between 0 and 1). The universe gets a second chance ;-)

2 edit: rational number are countable, real numbers not. Phew.

Edited May 4, 2017 by Green Baron

[KAL 9000]

50 minutes ago, Green Baron said:

-snippety snip-

Your first sentence is kinda patronizing... 

And yes, there are an uncountably infinite number of real numbers, but that's not actually the point. 

Pigeons are physical objects, and as such, there cannot be an infinite number of pigeons in a finite volume. Thus, your pigeon version of the Zeno paradox is fundamentally flawed, 

The OP is obeying all known scientific laws, only ignoring the problem of where the pigeons get the food to grow from. 

You, however, are breaking the most basic of physical laws with your assertion! 

@ProtoJeb21 clearly knows more about the subject than you. 

Sorry, guys, I had to get that off my chest.

[Green Baron]

 

Oops, did i step on someone's foot ?

 

23 minutes ago, KAL 9000 said:

Your first sentence is kinda patronizing... 

It wasn't meant to be. It was what i thought when i re-read that they talked about exponential rows in algebra in school.

23 minutes ago, KAL 9000 said:

Pigeons are physical objects, and as such, there cannot be an infinite number of pigeons in a finite volume. Thus, your pigeon version of the Zeno paradox is fundamentally flawed, 

No paradox here, op said to ignore physics an science. I tried that in my first two posts but was requested to forget about physics and science.

23 minutes ago, KAL 9000 said:

The OP is obeying all known scientific laws, only ignoring the problem of where the pigeons get the food to grow from. 

Oh, come on :-) Pigeons emerge magically, don't need resources, multiply in space, fuse like hydrogen, destroy dimensions and are sucked through wormholes ? Physic's laws must have changed fundamentally since i last watched ...

23 minutes ago, KAL 9000 said:

You, however, are breaking the most basic of physical laws with your assertion! 

 My excuse: i was explicitly invited to do so ! And i offered a solution to get rid of the pigeon plague without destroying the universe. Isn't that an admirable step ? :-)

 

23 minutes ago, KAL 9000 said:

Sorry, guys, I had to get that off my chest.

Feel better now ?

:-)

[ProtoJeb21]

Just to clarify: I am following all laws of physics with the exception of bird food and how the pigeons keep appearing. It's following the limited variables of the problem and letting quantum mechanics and other physics determine the fate of the pigeon ball.

Now can we have a nice discussion about what would lead to this exponential growth without getting the mods involved?

[Green Baron]

But then are wherever we were before with this type of discussion: what happens to physics if i ignore physics or switch it on and off as i like it ?

If pigeons appear endlessly out of nothing then everything can happen. You can have an endless ball of space cats or hawks chasing around the pigeons. Or anti pigeons.

Irl pigeons do not fuse, form red stars or break dimensions. They don't destroy reality or planes of existence (what's that anyway ?), do not rip the space-time for whatever that means. A mass doesn't self destruct and destroy the universe. It may collapse into a singularity but it is still there.

I can discuss the principles i know of (see above), but it is hard to discuss an infinite mass destroying the universe.

Edited May 4, 2017 by Green Baron

[kerbiloid]

I believe we still can stay not pessimistic.

The growing and gravitationally collapsing ball of pigluon plasma would cause a local Big Rip, entirely eradicating the pigeon part of the Universe from any kind of interaction with its another part.

So, they will infinitely collapse in their pocket universe.

Edited May 4, 2017 by kerbiloid