21 replies to this topic

[zanzibarjones]

Do you believe in the notion that there is a part of the universe that is not controlled, by.... something? Chaos, utter and complete chaos?

I believe Chaos does not exist. I can throw you some examples or why I believe that.

1) If chaos truly existed, would planets have formed into spheres? I mean a sphere has got to be the least favorite shape of chaos, because it is the easiest one to make. It's the path of least resistance.

2) Could chaos also create symmetry? I don't think so. Look at yourself in the mirror. Do you really think chaos made you, by mistake or by accident? Nope.

3) Could chaos have invented math? Probably the most ordered thing in our universe...

4) How about laws of nature that exist just not here but on other planets or in space....

What do you think?

[rvalkass]

Maths can be chaotic too. Take a look at the logistic difference equation:

x_n+1 = R * x_n * ( 1 - x_n )

Looks like a perfectly logical, simple equation. Watch what happens when the value of R is changed by small amounts:

 logistic-equation.png   166.17K   15 downloads

Is this true chaos? Given the equation and the starting parameters, there are cases where you have little chance predicting what the outcome will be. It's like stepping out your front door, walking a few steps, then suddenly being on Mars, then in the supermarket, then on the sun, then on your sofa.

Chaotic shapes also exist. Take a look at fractals - shapes with finite volume but infinite surface area. As simple to create as a sphere, but infinitely more complex and intricate.

[zanzibarjones]

rvalkass, on 25 August 2010 - 11:10 AM, said:

Chaotic shapes also exist. Take a look at fractals - shapes with finite volume but infinite surface area. As simple to create as a sphere, but infinitely more complex and intricate.

I don't know about that. I mean you can predict where the nest surface area is going to be right? I mean I have seen programs zoom in on fractals, and they all have symmetry to them. Is that really chaos?

[rvalkass]

You know where the surface area (or volume for a 3D shape) is. But any two points on the edge of the shape are separated by an infinite distance along the shape's edge. From a distance the points appear right next to each other. As you look closer, as you correctly say, you see more and more detail. That detail continues forever, adding more and more complexity to the perimeter of the shape. So, if the edge is getting more complex, and therefore longer, with no limit then it follows that the distance between any two points on the perimeter of the fractal must be separated by an infinite distance along the perimeter.

[Bikerman]

Thats exactly the same explanation I normally start with - the good old difference/logistics equation.
Just to add - the equation is of a type used by biologists for simple models of populations. The R corresponds to the 'fecundity' or 'randiness' of the animals and 1 is full population, 0 is extinction. The 1-X represents environmental constraints - food, competition etc.

In fact they were using the thing for years and just disregarding the results when it seemed to go bad. Not unlike the way that mathematicians are first taught to solve polynomials and ignore the ones that have no real solutions - just junk - when in fact they are probably the most interesting :-)

---

Here is something that should astonish readers (it blew my mind when one of my lecturers asked me to code it on an old BBC microcomputer back in 1982)...

Draw a triangle - any size and shape (as long as it IS a triangle of course).

1. Choose a point completely at random somewhere in the triangle and put your pencil down to make a point.
2. Repeat the following 2 steps
3. Choose one of the vertices (corners) of the triangle at random
4. Move your pencil halfway from where it is to that vertex (corner), put it down and draw a point.
5. as many times as you can

Rvalkass might know this (in fact I bet he does), but I bet nobody else can tell me what you get after repeating this a few thousand times. I was gobsmacked when I came back to the computer after an hour and saw what was on the screen - in fact I thought it must be an error in the graphics chip...

If you want to try it, or try to work it out, then don't scroll down. If you can't be bothered then scroll down to see what results - and it works everytime..

Edited by truefusion, 25 August 2010 - 07:15 PM.

[rvalkass]

Bikerman, on 25 August 2010 - 06:15 PM, said:

Rvalkass might know this (in fact I bet he does)

Sierpinski's triangle - already had one in my gallery of fractals, flames and other weird images:

http://rvalkass.co.u...is-050717-2.jpg

[Bikerman]

rvalkass, on 25 August 2010 - 06:57 PM, said:

Sierpinski's triangle - already had one in my gallery of fractals, flames and other weird images:

http://rvalkass.co.u...is-050717-2.jpg

Thought you might :-) I like this way of generating it. You can use the normal method of just connecting the sides but this way brings it to life by showing how order emerges from apparent random choices. The lecturer who gave me it knew it would be right up my street, and it got me interested enough to do some more reading and learn a bit about the whole interesting story. Since then, of course, everyone now has seen the Mandlebrot set - seems to crop up regularly. My other favourite is of course the Koch - which bangs home the bounded infinity (and is also pretty) :-)
http://math.rice.edu.../frac/koch.html

Edited by Bikerman, 26 August 2010 - 12:57 PM.

[zanzibarjones]

Hmmm... not that I am a genius or anything, but I still ask this, if chaos supposedly reigns, how do you explain the simple sphere? It's nature's, or the universe's simplest shape and it's, for lack of a better word, perfect.

[Bikerman]

zanzibarjones, on 30 August 2010 - 01:49 PM, said:

Hmmm... not that I am a genius or anything, but I still ask this, if chaos supposedly reigns, how do you explain the simple sphere? It's nature's, or the universe's simplest shape and it's, for lack of a better word, perfect.

Chaos doesn't 'reign' but it is relatively easy to create a sphere, even in a chaotic system. Water, for example, has surface tension - ie the molecules attract each other. The optimum way to arrange water (or for it to arrange itself) is in a way where the minimum number of molecules are not surrounded by others (they all pull on each other).
That arrangement is what we call a sphere. Put some water in space and wait- you will soon have a sphere.
http://stevespeeves....re-experiments/

Edited by Bikerman, 30 August 2010 - 06:24 PM.

[Rael IAK]

I don't consider the logistic equation chaotic at all. Like any other deterministic model of anything, you plug in some values (like for N(0) and R) and it spits out a result. You always get the same result when you plug in the same starting values. Stochastic models allow for some unpredictability in the output when you have a given input.

Whether chaos exists depends a lot on what you mean by "chaos", I think. I'm not sure what the point of using the existence of math as an example of chaos is all about. Math is entirely a construct of the human mind. It was not created "out there somewhere". I suspect I'm on a different page somehow.

[Okara KAmi]

By chaos, I'll assume he means anything nail bitingly close to "too entropic" for logistic liking. But then again, if any seemingly chaotic event x takes place on time t0, I can watch it happen. Rewind back to t0. And x would take place again. If under the same parameters and circumstances, one "chaotic" event is reborn, can we really call it the creation of chaos? Which might then suggest that in the physical universe, where everything is determined my space/time and mass/energy, we can't ever get "true" chaos. An occurrence might "seem" to have no clear cut explanation, but that just makes it inexplicable in our visor of understanding, not chaotic.

But the points you bring up are also a bit moot Zanzibarjones. The spherical shape, as someone above said, is the most diffusion-friendly shape for any liquid matter under 0 outside force. On top of that, spheres can occur through a variety of other factors. Celestial bodies in our universe, functioning under the theory that the Big bang really happened and that God almighty didn't put us together from clay, were constantly spinning and constantly being affected by the tremendous pull of the "core" of the bang. Take a random shape, put your finger on it, and rotate it in every possible angle (not 360 degrees, I mean in the spherical sense), and after a thousand years, you'll have a sphere because of the equilibrium that the input force arrives at. We're also going to assume that when this "big bang" happened, the celestial bodies that we know them as now weren't congealed, sizable chunks of mass as they are now. They were vastly large rocks loosely held together from a series of clashes over a preposterous amount of time. It would then be logical to assume that the large entity's own gravity would encourage the outlying pieces (which originally gave the shape a non-spherical form) to move closer to the center until finally (give or take a few infinities) you'd have the large masses becoming spheres.

Symmetry isn't actually in the same category as the celestial bodies... in my opinion. Symmetry in life forms comes from the biological progression of life on our planet. We're not "really" symmetric, we're just vaguely put together that way. The human cell isn't symmetric, no organ is, to my knowledge, and even the human body isn't perfectly symmetric. Heck, your heart is on the left side. Your muscles are probably larger on your right/left side if you're a righty/lefty respectively.

Also in line with Math. Math isn't an object to be invented. It's a principal. 2 + 2 = 4, regardless of where/when/what you are (unless you're in 1984) because basic Math is logic-oriented (fundamental math in this case), and usually has little to do with the practicality of where it's being applied.

[Bikerman]

Rael IAK, on 02 September 2010 - 08:51 PM, said:

I don't consider the logistic equation chaotic at all. Like any other deterministic model of anything, you plug in some values (like for N(0) and R) and it spits out a result. You always get the same result when you plug in the same starting values. Stochastic models allow for some unpredictability in the output when you have a given input.

Chaotic systems are deterministic by definition, and the logistic equation is a simple but valid example. It displays the characteristic bifurcations of chaotic systems when the driving term gets above 3.5 - ie there is neither convergence or oscillation of result.

Stochastic systems are random - not chaotic.

Quote

Whether chaos exists depends a lot on what you mean by "chaos", I think. I'm not sure what the point of using the existence of math as an example of chaos is all about. Math is entirely a construct of the human mind. It was not created "out there somewhere". I suspect I'm on a different page somehow.

If you want a more formal definition of a chaotic system then it is one which:
1. is sensitive to initial conditions;
2. is topologically mixing; and
3. has dense periodic orbits.

Edited by Bikerman, 15 September 2010 - 05:36 AM.

[Harlot]

Chaos is simply what we do not know. The sense of order that humanity has was a creation. The creation of math & science, is the creation of order. We never knew what a sphere was until we came up with the name "sphere" and noted its natural characteristics. We ourselves determined that a sphere was orderly opposed to something shapeless. For a dog, the world outside of his dog house may be completely disorderly. For a human, the world outside of this solar system may be completely disorderly.

Even when you look at math, it was a creation to explain the unknown in scientific terms, which was also a creation. 1+2=3...was non-existent before humans. What is 1? What is 2? What is 3? Our only explanation is that it was a numeral system. Numeral systems are a creation of humans, and are naturally non existent. Science is even a creation, and we use the numeral system in which we created in order to shape scientific theories and turn them into scientific law.

If our existence is orderly, why are we here? Where do we go when we leave? Where were we before we got here?

If we can not answer those questions, how can the world through our eyes possibility be orderly. How can the world be orderly for a species that their explain their own existence and non-existence. Where we created by a God or did we evolve from a monkey? If we were created by a God why is the God? Who created God, and who created the thing that created God? If God always existed, was there never a beginning? If God was created, was there a point where nothing existed? If nothing existed, what created God? On the other hand, if we evolved from a monkey, where did the monkey come from? If the monkey evolved from bacteria, where did the bacteria come from? Did the bacteria have no beginning? Did germs simply always exist and had no beginning whatsoever? Bacteria is life right, doesn't all life have a beginning and an end?

The end result is that no one knows. Just as a dog has no idea that he or she lives on a planet, and is surrounded by space. A dog has no idea why he exist, he simply lives by nature and doesn't even have the capacity to question his existence. Many humans are the same, they just live and have no capacity to question their existence. They are just focused on jobs and material, just as a dog is focused on a bone and a bowl of water.

On the other hand, there may be complete order....I simply don't have the brain capacity to know.

Edited by Harlot, 20 September 2010 - 03:23 AM.

[Bikerman]

Harlot, on 20 September 2010 - 03:22 AM, said:

Chaos is simply what we do not know. The sense of order that humanity has was a creation. The creation of math & science, is the creation of order. We never knew what a sphere was until we came up with the name "sphere" and noted its natural characteristics. We ourselves determined that a sphere was orderly opposed to something shapeless. For a dog, the world outside of his dog house may be completely disorderly. For a human, the world outside of this solar system may be completely disorderly.

Well, the earth existed before we came along and although it is not a perfect sphere it is pretty damn close. You think the logic of mathematics is entirely a human invention? So when the ancient Greeks looked at a circle and realised there was a relationship between the circumference and the radius (pi) were they inventing or discovering, do you think? Wasn't that relationship there before? If an alien had come along and looked at Earth, do you not think the Alien would have discovered Pi ? It bears some thinking about... :-)

Quote

Even when you look at math, it was a creation to explain the unknown in scientific terms, which was also a creation. 1+2=3...was non-existent before humans. What is 1? What is 2? What is 3? Our only explanation is that it was a numeral system. Numeral systems are a creation of humans, and are naturally non existent. Science is even a creation, and we use the numeral system in which we created in order to shape scientific theories and turn them into scientific law.

Actually maths was a creation to keep track of things. Our early ancestors probably didn't need to count beyond 1,2,many because they had no particular need to. Then once people began to congregate together (probably around the time agriculture was discovered) then suddenly you needed to be able to count. The history of numbers is a fascinating subject but it would take pages to even make a proper start on it....

Quote

If our existence is orderly, why are we here? Where do we go when we leave? Where were we before we got here?

Who says there is a reason? Who says we had to be anywhere before and anywhere after? I suppose the simple answer is that before you were born you existed as a set of cells in your parents. Before that a set of cells in their parents.....and so on back.....Ultimately we are all the stuff of stars - which is nice, I think. The early universe only had hydrogen and helium so it wasn't until the first stars got going that the heavier stuff (that makes us) was made in the solar furnaces. In fact some of the elements that make us are only formed when stars die (supernovas) so there had to be several generations of stars to make us...I like that thought....

Where do we go after we die? Same thing...ultimately back to the stars :-) That's not too scarey a prospect for me, though some don't like the thought. The way I think about it is that the universe got on quite well for 13.7 billion years without me, and I didn't know anything about it. Once I'm gone it will continue to go along without me, and I won't know anything about it - just as I didn't for the last many billion years....not so scary really...

Quote

If we can not answer those questions, how can the world through our eyes possibility be orderly. How can the world be orderly for a species that their explain their own existence and non-existence. Where we created by a God or did we evolve from a monkey?

We certainly evolved from a common ape ancestor - there is no doubt about that (not a monkey - that is a different part of the family tree :-)

Quote

If we were created by a God why is the God? Who created God, and who created the thing that created God? If God always existed, was there never a beginning? If God was created, was there a point where nothing existed? If nothing existed, what created God? On the other hand, if we evolved from a monkey, where did the monkey come from? If the monkey evolved from bacteria, where did the bacteria come from? Did the bacteria have no beginning? Did germs simply always exist and had no beginning whatsoever? Bacteria is life right, doesn't all life have a beginning and an end?

This is commonly called the question of 'first cause' or to give it the posh latin name 'Primum movens'. If everything is caused, then there must be a first causer which is itself not caused. That is the argument in a nutshell. As you correctly summise God does not actually answer that apparent problem (we are just supposed to accept that God didn't need a causer, which is a bit of a cop out I think :-) ).

There are some possible answers but they are a bit mind boggling. The main problem is that when we ask questions like this, we expect to get answers that we can understand. We think that if the answer is not 'common sense' then it must be wrong. That is a very peculiar attitude when you think about it. Our common sense is based on an ape brain evolved to yell at other apes about food and enemies. Why do we expect that same brain to be able to understand questions which we have no experience of?

Still, since you asked the question I will try to give at least a possible answer (well actually 2).

1st answer: The Big Bang is where our universe starts. Now, of course, you will ask what came before, but in this answer that is not a valid question. Space and time are linked together into what Einstein called 'spacetime'. They were both created at the instant of the Big Bang. Now if there was no time before the Big Bang then the question 'what came before' doesn't make any sense because there was no before...

Most people don't like that answer because it feels like a cop out - but it really isn't....Still, that is only one possible answer.Modern physicists have a few other possibilities (though it is important to realise that this first answer is still the one with the most evidence to support it).

Another reason people do not like this answer is because it apparently means you have to create something from nothing - which any scientist will tell you is a big no-no.

Imagine....there is nothing - no space, no time.
Then suddenly a tiny piece of something starts to expand rapidly, like a huge balloon being blown up by a team of champion balloon blowers - doubling in size, doubling again, and again, and again....and so on. So where did the first bit of the balloon come from? - that is the question.

Literally nowhere is one possible answer. When you look into space you imagine there is nothing there - no air, no matter of any sort. It turns out that this is wrong - very wrong. The most empty space imaginable is full of particles popping in and out of existence in pairs of opposites (we call them particle-antiparticle pairs). This is the famous anti-matter from Star-Trek, and it is quite real. The thing that makes anti-matter so valuable is that when it comes into contact with matter it completely annihilates itself and the matter to give just pure energy (photons). It is the best source of energy possible in our universe....

One way to think of it is the simple sum:- 1-1=0. If you rewrite that, you get 0 = -1 +1 Now the +1 is matter and the -1 is anti-matter. Put them together and they vanish. So it follows that we can start with nothing and split it into a plus 1 and a minus 1 (a particle and an antiparticle). All we need is some energy (the same energy that is given off when they annihilate each other).

But wait, you say. You still need energy, so it still isn't something from nothing. Well, here is where common sense has to go for a walk. It turns out that if you make the particles and annihilate them really really quickly, then you can 'borrow' the energy and nature doesn't notice, as long as it is paid back quickly enough. So in 'empty' space we have gazillions of particle pairs winking into existence for a teeny fraction of a second.

This happens because of something called Heinsenberg's Uncertainty Principle (HUP). Basically the HUP says that you can know one thing, but the better you know that one thing, the worse you know another. So you can know pretty accurately where a particle is, but the more accurately you know where it is, the less accurately you know how fast it is going (well, actually the momentum, but let's keep it simple). It doesn't matter whether you get the best equipment imaginable - there will always be a fuzzy area between the two things. This fuzzy area allows enough time for nothing to become something and then nothing again - and it is going on all around you all the time.

I probably haven't explained that very well, but it is pretty tricky without using maths, so it is about as good as I can do. The important thing to realise is that this is not just a guess - it is quite real. So that is answer number 1 - there was nothing, no time, no space. Then that very nothingness split into two opposite quantities (the plus and minus 1).
So the only question left is - if we (mass and energy) are the plus 1, then where is the minus 1? One answer to that is that gravity is the minus 1, and that all the matter in the universe (and energy - they are different ways of looking at the same thing - e=mc^2) is exactly balanced by the gravity it creates. it would take another few pages to explain that, so you'll have to take my word for it :-)

And very quickly - a 2nd answer
It could be that our universe is part of a greater whole - call it the 'multiverse'. There are many (possibly an infinite number) of other universes, but we can never see or visit them because we are trapped in our own spacetime within this universe. When our universe came into existence it just 'shoved the others out of the way'. We can never see or visit these other universes because they either are so far distant that even light (the fastest thing possible) could not get from us to them, or them to us. Our universe is expanding too fast, so light will never be able to pass between them. Or possibly they exist in other dimensions. We are used to 4 dimensions - length breadth width and time. To specify where something can be found in our universe you give 3 numbers for it's location in space and one number for its location in time - we call that a spacetime coordinate. There are some good reasons to think that there may actually be more dimensions than just those 4 - there could be 10 space dimensions and 1 time dimension, with 6 of the extra dimensions curled-up at the tiniest scale imaginable (gazillions of times smaller than atoms)so all around us are another 6 dimensions but we cannot see, feel or interact with them because they exist at such a small scale that even our atoms are too big to notice.
This is what physicists call superstring theory and that is definitely where I must leave it.

Hope I haven't confused you even more :-)

Chris.

Edited by Bikerman, 20 September 2010 - 08:45 AM.

[inea]

The first thing to make things clear is to define chaos. Maybe in this topic by chaos is meant not order. And if order exists it is thinkable that non-order exists too. So in this sense chaos can be thought of like it exists.

Another approach is to look at chaos. And it might be thought that chaos can never create anything. This means that out of chaos can never proceed order. So that means that chaos doesnt exist very long because it will proceed into order.

These are not meant to be revelations of the truths of the universe. These are some ways of exploring thoughts that wander around.

[Bikerman]

inea, on 23 September 2010 - 12:49 PM, said:

The first thing to make things clear is to define chaos. Maybe in this topic by chaos is meant not order. And if order exists it is thinkable that non-order exists too. So in this sense chaos can be thought of like it exists.

Mathematically/physically a chaotic system is one which is dynamic (constantly changing) and very sensitive to differences in one or more of the factors (variables) in the system. That makes such systems inherently unpredictable, even if you have all the maths describing the individual factors.
So mathematically speaking chaos is certainly disorder, but it is disorder from order - non-pattern where there was pattern. Examples of real-life chaotic systems would include the weather, stock market behaviour, population growth....

Chaos theory establishes patterns within the disorder. It means that although we cannot predict the outcome of a chaotic system like weather, beyond a certain period, what we can do is give a good estimate of what that period is. So you can get some weather forecasts that are good for a week or more and others which are only good for a few hours - depends on how chaotically the system is behaving at that time.

Edited by Bikerman, 23 September 2010 - 10:21 PM.

[Saint_Michael]

To step away from the math of chaos, if you to look at planets again they are neither perfect spheres nor are their poles straight up and down. Earth is angled at a 23 degrees, but the problem is you really can't tell regardless of how far away you are from the planet because of perception of that sphere says otherwise. Chaos does exist but there are many forms of it, chaos in the human genome, chaos in animal species, chaos in the universe they exist because not everything is predetermined. Yes there is beginning and and end, however, logic dictates that are known and unknown various that determine both the beginning and the end and thus you have your chaos.

[Bikerman]

But you are still mixing up chaos with indeterminacy. Chaotic systems are determinate - there are no random factors in a properly chaotic system.

Edited by Bikerman, 02 October 2010 - 10:49 PM.

[Saint_Michael]

Then could they be considered chaotic then? If your thinking in terms of mathematics then that maybe true, but outside the box then chaos is nothing but randomness. Granted there maybe a few exceptions such as comets and asteriods, however, throw in gravity and of course getting knocked off course by another object and that objects "destiny" is no longer determined. I will agree choas as a structure but trying to bring order ouy of chaos will no longer make it chaotic, it will just fall into one of many categories we will determine that person, place or thing it should be in.

[Bikerman]

This is why it is important to define what is meant by the word.
In the everyday use of the word then, yes, it implies unpredictability. Chaotic systems ARE unpredictable.
In the scientific/mathematical sense a chaotic system is one which has several elements, all of which are, or can be, known and modelled exactly, but it is still unpredictable. Note that it is NOT random.
The simplest example I can give is the logistic/difference equation which I have already mentioned.

p_n+1 = r*p_n(1-p_n)

This is an equation used by biologists (amongst others) to predict populations. When they use it r is the fecundity (the breeding ability of the species) and p varies from 0 (extinct) to 1 (maximum possible population).

In simple terms : p_n+1 (the population next year) - is equal to p_n (this year's population) multiplied by r (the fecundity) multiplied by (1 minus this year's population).
(The last bit (1-p_n) is a way of modelling the fact that there are natural limits on a population - food, competition for space and resources etc).

Now, if you know the last value of p, and you know the value of r, there is nothing random and you can work out an exact answer for p at any time.
Biologists keep feeding the value of p back into the equation hoping that it will settle on a single value eventually. This would be a stable population.

Let's run it and see: assume the starting population is 1/2 max (0.5) and the fecundity ® is 1.5. (I'll work to 2 decimal places for this bit to keep it quick and simple)

p₁ = 1.5*0.5*(1-0.5) = 0.38
That now becomes the value of p for the next run
p₂ = 1.5*0.38*(1-0.38) = 0.35
p₃ = 1.5*0.35*(1-0.35) = 0.34
p₄ = 1.5*0.34*(1-0.34) = 0.34

So you see the population settles down, after 3 years, to 34% of maximum possible.

Let's run it one more time so you really get the idea. This time we will start with the same population (0.5) but increase the fecundity to 1.75 (ie the creatures breed more rapidly).

p₁ = 1.75*0.50*(1-0.50) = 0.44
p₂ = 1.75*0.44*(1-0.44) = 0.43
p₃ = 1.75*0.43*(1-0.43) = 0.43

So this time the population settles down after 2 years to 43% of the maximum possible.
Get it?
OK, you will agree that there is nothing random here I hope?

OK, so what happens if they breed really fast - set r to 2.9
(For speed I'll run the calculations on a spreadsheet)
Fecundity®= 2.9
p(1)=0.73, p(2)=0.58, p(3)=0.71, p(4)=0.60, p(5)=0.70, p(6)=0.61, p(7)=0.69, p(8)=0.62, p(9)=0.68, p(10)=0.63, p(11)=0.68, p(12)=0.64, p(13)=0.67, p(14)=0.64, p(15)=0.67, p(16)=0.64, p(17)=0.67, p(18)=0.64, p(19)=0.66, p(20)=0.65, p(21)=0.66, p(22)=0.65.......

So now the population jumps around and doesn't finish on one stable value - it alternates between 65% one year and 66% the next. So it is still, eventually, giving a stable predictable output - just 2 instead of 1.
(Actually this is a result of limiting the number of decimal places - if we ran it for long enough with more decimal places then it would settle on one value).

With r at 3 or more, our population settles to 2 values alternating - like above.

But now ramp r up to 3.5 (I'll leave that as an exercise for you to do)..
What you should find is that the population becomes chaotic (ie it doesn't settle down to any fixed values). So for one value of r the population is stable and predictable. For a different value we get a chaotic population.

We can draw a graph of the results of this equation as follows:


Notice that when r hits 3 you get 2 stable values and then when r goes higher you get 4 alternating values, then 8, then 16 and very quickly the system becomes chaotic with no stable values at all.

That is what chaos means in the scientific/mathematical sense. This doubling up of values is characteristic of a stable system about to become chaotic (it is called bifurcation - lit. splitting in two).

I hope this helps....

Edited by Bikerman, 03 October 2010 - 05:44 AM.

[Harlot]

Bikerman, on 20 September 2010 - 08:38 AM, said:

Well, the earth existed before we came along and although it is not a perfect sphere it is pretty damn close. You think the logic of mathematics is entirely a human invention? So when the ancient Greeks looked at a circle and realised there was a relationship between the circumference and the radius (pi) were they inventing or discovering, do you think? Wasn't that relationship there before? If an alien had come along and looked at Earth, do you not think the Alien would have discovered Pi ? It bears some thinking about... :-)
Actually maths was a creation to keep track of things. Our early ancestors probably didn't need to count beyond 1,2,many because they had no particular need to. Then once people began to congregate together (probably around the time agriculture was discovered) then suddenly you needed to be able to count. The history of numbers is a fascinating subject but it would take pages to even make a proper start on it....

If math was a creation to keep track of things, it was a creation of men. Therefore, math in a natural sense does not exist. It would be irrelevant if men did exist, because why would there be a need to keep track of anything? Why would there be a need to know the radius of a circle? Math is very interesting, but it is in fact a creation. At one point it didn't exist. Math was not discovered, but created. A human didn't wake up one day and say...I discovered math. Numbers were created to keep track of one thing, and it was discovered that counting and numbers could be used to keep track of different things such as architecture and physical science. Math does not exist in the sense that an atom exist. It can not be seen as a physical object, it is simply an instrument of thought. Math could in fact be replaced with another form of keeping track of things, we have simply yet to create a better way. As for aliens, they are biological beings also, and therefore it is the same as the creation of math by humans. It would be like arguing what race of humans created math, it is irrelevant outside of a social context. Aliens are nothing more than another biological form, or another race of beings in a sense. If a monkey created math, it would still be a creation of a biological being. If a dog created it, the same applies.

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Who says there is a reason? Who says we had to be anywhere before and anywhere after? I suppose the simple answer is that before you were born you existed as a set of cells in your parents. Before that a set of cells in their parents.....and so on back.....Ultimately we are all the stuff of stars - which is nice, I think. The early universe only had hydrogen and helium so it wasn't until the first stars got going that the heavier stuff (that makes us) was made in the solar furnaces. In fact some of the elements that make us are only formed when stars die (supernovas) so there had to be several generations of stars to make us...I like that thought....

Where do we go after we die? Same thing...ultimately back to the stars :-) That's not too scarey a prospect for me, though some don't like the thought. The way I think about it is that the universe got on quite well for 13.7 billion years without me, and I didn't know anything about it. Once I'm gone it will continue to go along without me, and I won't know anything about it - just as I didn't for the last many billion years....not so scary really...

If there is no reason, then there is no order. There is only a random cycle of chaos that is being contained by mankind. How can there be order with no purpose, and no logical reasoning behind the existence of man or the universe. In fact, that may be why religion exist. Men lived in chaos and disorder, and therefore created a reason for their existence. The man looked to the stars and asked himself where the hell was he, and in fact, what was he. We still don't know where we are or what we are, and our only form of order is the illusion that society creates. Our only order is false purpose created by our societies. We strive to survive, when we know that survival isn't possible. Then when we ask ourselves what was our purpose for living to die, we conclude that it is for the good for humanity. Therefore, our existence is to perpetuate the limited existence of others, and a pointless life and death cycle.

As for going back to the stars, what exactly goes back to the stars? Our physical body or our soul? Or...do we in fact have a soul? If an individuals thought is maintained by their brain, once the brain has physically deteriorated, do we exist as ourselves any longer? Is what we consider our soul, really nothing more than our brain. Is our brain the primary source of consciousness? So what exactly goes to the stars? The body that we bury under the ground, the soul, or the brain? Or, do we in fact not go anywhere at all except for back into the Earth after a existence that can not be understood? Then again I guess life and death is after all beyond our understanding at the moment. Maybe the current discussion is pointless and meaningless. Maybe it is nothing more then humans rambling about what we don't know, attempting to display the a kind of intellectuality that we truly lack.

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We certainly evolved from a common ape ancestor - there is no doubt about that (not a monkey - that is a different part of the family tree :-)

Fine by me

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This is commonly called the question of 'first cause' or to give it the posh latin name 'Primum movens'. If everything is caused, then there must be a first causer which is itself not caused. That is the argument in a nutshell. As you correctly summise God does not actually answer that apparent problem (we are just supposed to accept that God didn't need a causer, which is a bit of a cop out I think :-) ).

There are some possible answers but they are a bit mind boggling. The main problem is that when we ask questions like this, we expect to get answers that we can understand. We think that if the answer is not 'common sense' then it must be wrong. That is a very peculiar attitude when you think about it. Our common sense is based on an ape brain evolved to yell at other apes about food and enemies. Why do we expect that same brain to be able to understand questions which we have no experience of?

Still, since you asked the question I will try to give at least a possible answer (well actually 2).

1st answer: The Big Bang is where our universe starts. Now, of course, you will ask what came before, but in this answer that is not a valid question. Space and time are linked together into what Einstein called 'spacetime'. They were both created at the instant of the Big Bang. Now if there was no time before the Big Bang then the question 'what came before' doesn't make any sense because there was no before...

Most people don't like that answer because it feels like a cop out - but it really isn't....Still, that is only one possible answer.Modern physicists have a few other possibilities (though it is important to realise that this first answer is still the one with the most evidence to support it).

Another reason people do not like this answer is because it apparently means you have to create something from nothing - which any scientist will tell you is a big no-no.

Imagine....there is nothing - no space, no time.
Then suddenly a tiny piece of something starts to expand rapidly, like a huge balloon being blown up by a team of champion balloon blowers - doubling in size, doubling again, and again, and again....and so on. So where did the first bit of the balloon come from? - that is the question.

Literally nowhere is one possible answer. When you look into space you imagine there is nothing there - no air, no matter of any sort. It turns out that this is wrong - very wrong. The most empty space imaginable is full of particles popping in and out of existence in pairs of opposites (we call them particle-antiparticle pairs). This is the famous anti-matter from Star-Trek, and it is quite real. The thing that makes anti-matter so valuable is that when it comes into contact with matter it completely annihilates itself and the matter to give just pure energy (photons). It is the best source of energy possible in our universe....

One way to think of it is the simple sum:- 1-1=0. If you rewrite that, you get 0 = -1 +1 Now the +1 is matter and the -1 is anti-matter. Put them together and they vanish. So it follows that we can start with nothing and split it into a plus 1 and a minus 1 (a particle and an antiparticle). All we need is some energy (the same energy that is given off when they annihilate each other).

But wait, you say. You still need energy, so it still isn't something from nothing. Well, here is where common sense has to go for a walk. It turns out that if you make the particles and annihilate them really really quickly, then you can 'borrow' the energy and nature doesn't notice, as long as it is paid back quickly enough. So in 'empty' space we have gazillions of particle pairs winking into existence for a teeny fraction of a second.

This happens because of something called Heinsenberg's Uncertainty Principle (HUP). Basically the HUP says that you can know one thing, but the better you know that one thing, the worse you know another. So you can know pretty accurately where a particle is, but the more accurately you know where it is, the less accurately you know how fast it is going (well, actually the momentum, but let's keep it simple). It doesn't matter whether you get the best equipment imaginable - there will always be a fuzzy area between the two things. This fuzzy area allows enough time for nothing to become something and then nothing again - and it is going on all around you all the time.

I probably haven't explained that very well, but it is pretty tricky without using maths, so it is about as good as I can do. The important thing to realise is that this is not just a guess - it is quite real. So that is answer number 1 - there was nothing, no time, no space. Then that very nothingness split into two opposite quantities (the plus and minus 1).
So the only question left is - if we (mass and energy) are the plus 1, then where is the minus 1? One answer to that is that gravity is the minus 1, and that all the matter in the universe (and energy - they are different ways of looking at the same thing - e=mc^2) is exactly balanced by the gravity it creates. it would take another few pages to explain that, so you'll have to take my word for it :-)

And very quickly - a 2nd answer
It could be that our universe is part of a greater whole - call it the 'multiverse'. There are many (possibly an infinite number) of other universes, but we can never see or visit them because we are trapped in our own spacetime within this universe. When our universe came into existence it just 'shoved the others out of the way'. We can never see or visit these other universes because they either are so far distant that even light (the fastest thing possible) could not get from us to them, or them to us. Our universe is expanding too fast, so light will never be able to pass between them. Or possibly they exist in other dimensions. We are used to 4 dimensions - length breadth width and time. To specify where something can be found in our universe you give 3 numbers for it's location in space and one number for its location in time - we call that a spacetime coordinate. There are some good reasons to think that there may actually be more dimensions than just those 4 - there could be 10 space dimensions and 1 time dimension, with 6 of the extra dimensions curled-up at the tiniest scale imaginable (gazillions of times smaller than atoms)so all around us are another 6 dimensions but we cannot see, feel or interact with them because they exist at such a small scale that even our atoms are too big to notice.
This is what physicists call superstring theory and that is definitely where I must leave it.

Hope I haven't confused you even more :-)

Chris.

Maybe our world is just a piece of dirt in the corner of someone's butt crack.

[Bikerman]

Harlot, on 27 October 2010 - 03:55 AM, said:

If math was a creation to keep track of things, it was a creation of men. Therefore, math in a natural sense does not exist. It would be irrelevant if men did exist, because why would there be a need to keep track of anything? Why would there be a need to know the radius of a circle? Math is very interesting, but it is in fact a creation. At one point it didn't exist. Math was not discovered, but created. A human didn't wake up one day and say...I discovered math. Numbers were created to keep track of one thing, and it was discovered that counting and numbers could be used to keep track of different things such as architecture and physical science. Math does not exist in the sense that an atom exist. It can not be seen as a physical object, it is simply an instrument of thought. Math could in fact be replaced with another form of keeping track of things, we have simply yet to create a better way. As for aliens, they are biological beings also, and therefore it is the same as the creation of math by humans. It would be like arguing what race of humans created math, it is irrelevant outside of a social context. Aliens are nothing more than another biological form, or another race of beings in a sense. If a monkey created math, it would still be a creation of a biological being. If a dog created it, the same applies.

In what sense do you think man is not natural? If man creates something then why is that not natural? We create all sorts of things - including things which CAN be seen as physical objects.
The real question is whether maths encompases truths about the universe - and it appears to do just that. Yes, it is a human creation, but that creation seems to have correspondence with reality and it is therefore reasonable to suppose that there is something universal about maths as regards any intelligent beings.

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If there is no reason, then there is no order. There is only a random cycle of chaos that is being contained by mankind. How can there be order with no purpose, and no logical reasoning behind the existence of man or the universe. In fact, that may be why religion exist. Men lived in chaos and disorder, and therefore created a reason for their existence. The man looked to the stars and asked himself where the hell was he, and in fact, what was he. We still don't know where we are or what we are, and our only form of order is the illusion that society creates. Our only order is false purpose created by our societies. We strive to survive, when we know that survival isn't possible. Then when we ask ourselves what was our purpose for living to die, we conclude that it is for the good for humanity. Therefore, our existence is to perpetuate the limited existence of others, and a pointless life and death cycle.

No this is wrong. Order emerges quite naturally with no 'reason'. Look at a snowflake. Evolution is a cracking example of emergent order with no purposse but it is not the only one.
There is nothing pointless about life. Just because there is no transcendent meaning that does not mean one's life is pointless. One sets one's own point. Mine is to learn as much as I can, be relatively happy and try not to cause injury to others on the trip...

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As for going back to the stars, what exactly goes back to the stars? Our physical body or our soul? Or...do we in fact have a soul? If an individuals thought is maintained by their brain, once the brain has physically deteriorated, do we exist as ourselves any longer? Is what we consider our soul, really nothing more than our brain. Is our brain the primary source of consciousness? So what exactly goes to the stars? The body that we bury under the ground, the soul, or the brain? Or, do we in fact not go anywhere at all except for back into the Earth after a existence that can not be understood? Then again I guess life and death is after all beyond our understanding at the moment. Maybe the current discussion is pointless and meaningless. Maybe it is nothing more then humans rambling about what we don't know, attempting to display the a kind of intellectuality that we truly lack.

Our physical bodies go back to the stars. They decompose into the chemicals they are made up from and eventually those chemicals, along with the rest of earth, will be converted into gas and rubble which will then form the basis for another star in the distant future.