## Friday, 23 November 2012

### Order From Chaos

One of the things which seems to baffle people is how order can come from a chaotic system without help. After all, if the system is truly chaotic, what could give it direction, assuming of course that order implies some sort of direction?

This confusion is often seized on by people who push religions for a living, to sell the idea that there must be some sort of directing intelligence doing it, with the implication that this directing intelligence must be the locally popular god in which ever culture they are marking their snake oil. This predominates in Creationism where it's the single most used argument by Creation 'scientists' to keep their normally scientifically illiterate market buying their books and voting they way they are told to vote. But it can also be found in other areas of science where professional religious apologists tend to go to find confusion, ignorance and misinformation to exploit.

I'll take a few simple scientific principle to illustrate how order can and does emerge spontaneously from chaos in ways which we often take for granted.

### 1. The Gas Laws

Most people will have heard of the Gas Laws. These Laws are regarded as some of the most basic fundamental laws of physics, explaining how volume, pressure and temperature of gasses are related.

There are two such laws complimenting each other: Boyle's Law and Charles's Law. They explain much of how internal combustion engines and steam engines work. Don't worry about the technical stuff too much. That's not the point of this blog. There isn't going to be an exam at the end of it.

#### Boyle's Law.

 Boyle's law (sometimes referred to as the Boyle–Mariotte law) states that the absolute pressure and volume of a given mass of confined gas are inversely proportional, if the temperature remains unchanged within a closed system.[1][2] Thus, it states that the product of pressure and volume is a constant for a given mass of confined gas as long as the temperature is constant. The law was named after chemist and physicist Robert Boyle, who published the original law in 1662.[3]

#### Charles's Law

 Charles' law (also known as the law of volumes) is an experimental gas law which describes how gases tend to expand when heated. A modern statement of Charles' law is: At constant pressure, the volume of a given mass of an ideal gas increases or decreases by the same factor as its temperature on the absolute temperature scale (i.e. the gas expands as the temperature increases).[1] It was first published by French natural philosopher Joseph Louis Gay-Lussac in 1802,[2] although he credited the discovery to unpublished work from the 1780s by Jacques Charles.

To understand what's going on with these gasses in closed systems, we need to understand what pressure is. Pressure is the total force exerted by all the molecules of the gas as they hit to wall of the container. Some of their kinetic energy, depending on their velocity and the angle at which they strike the wall, is transferred to the walls of the container which would be pushed outwards if it could move - which is why balloons get bigger as you put more gas into them.

The total force exerted on the wall of the container will depend on the average energy transferred multiplied by the total number of molecules striking the walls of the container per unit of area at any one moment, which is proportional to the density of the molecules in the container. If we reduce the volume of the same mass of gas (by making the container smaller) we increase the density of the molecules in that mass so there are more of them to strike the walls of the container per unit area of wall. (Boyle's Law)

But, molecules of gas are moving randomly and chaotically within the body of the mass of gas in the container. When they strike the wall of the container, nothing is directing them to; they simply happen to be randomly moving in a trajectory which hits the wall (of course, if they didn't strike other gas molecules on the way, they would eventually strike a wall because they are in an enclosed system. As it is, they are zig-zagging about chaotically because they are also striking one another. The probability of any one molecule striking a wall at any one moment is randomly distributed somewhere between certainty and impossibility.

So, individual molecules are randomly striking the walls of the container in a truly random and chaotic, therefore unpredictable, manner.

How much energy they have will depend on the temperature, which is why pressure rises when the temperature rises (Charles's Law). However, not all molecules will have the same energy; the distribution of energy amongst all the molecules will fit a bell curve, with some having more than the average and some less. When the temperature increases, it's the shape of the bell curve which changes as the average energy increases. For any individual molecule, however, it's energy will still be random. The angle at which they strike the wall is also randomly distributed between 0 and 180 degrees to the surface of the wall.

So, the amount of energy individual molecules transfer to the walls of the container which they randomly and chaotically strike is also random and chaotic, therefore also unpredictable.

And yet, from a chaotic system, we get emergent order, which is so dependable we even call it a Law - which in science means we can be certain it will happen under normal circumstances such as the universe continuing to exist.

There is no magic or direction, nor intelligence required to produce the Gas Laws, merely the chaos of randomly moving gas molecules with randomly distributed kinetic energy. What we have there is an example of a 'law of mass action' where we can only predict what the average outcome will be from properties which fit bell curves, like the kinetic energy of gas molecules and their direction of travel.

So, the Gas Laws, upon which steam power and motor car engines depend, are emergent properties of chaos.

### 2. Clouds

The thing about clouds is that they look different depending on how far away from you they are.

Normally, when you look at them from the ground and they're up in the sky, they look like distinct things. We talk about them as though they are distinct objects. They can even look like solid objects, at least solid enough for ancient superstitious folk to imagine gods and angels standing on them.

When we fly into them in a plane, we realise they have no real outline; no edge as such.

When they are at ground level, or we are up a mountain at cloud level, we realise they are just microscopic droplets of water suspended in the air. Inside this fog we don't see the cloud as a thing at all; it's just different air which is difficult to see through.

And yet, in these pictures on the right we can see shape and form; we can see structures, even patterns. Surely there is order in clouds, isn't there? And this is not the usual humans looking for patterns and seeing faces and castles in the air, Jesus in toast and virgins in dropped ice-cream, sort of structure. (It's a pity for Muslims that there aren't more pictures of Mohammed otherwise they could see him in their toast as well.)

And yet the individual droplets of water or particles of ice which make up clouds are randomly distributed and randomly moving about and were formed from a chaotic weather system.

So clouds have no definable outline and are composed of chaotically moving particles formed in a chaotic system. And yet they look like discrete objects and have structure.

Again, structure is an emergent property from chaos. Not quite such predictable order as the Gas laws, but we can be fairly sure that, given certain meteorological conditions like wind direction and speed, temperature gradients as we go up through the atmosphere and humidity, we will get particular 'types' of clouds (in other words, clouds with different structures). We can also make a fairly good guess about what the weather is going to be from this emergent order from chaos, which took no direction and no intelligence to emerge.

There are other structures which flow from the emergent nature of clouds from chaos, of course.

Under the right conditions, the microscopic water droplets start to join together into larger droplets which become too large to stay in suspension in the air, and fall out as rain. They may also form the incredibly ordered snow flakes, the precise form of which is also random and emergent from chaos.

The next section deals with this.

### 3. Flowing Water

Falling rain eventually reaches the ground where it erodes the land into river valleys, chalk hills into caves and gorges, wears jagged rocky mountains into rounded hills and rough stones into smooth pebbles. Flowing rivers carrying eroded silt form sand bars, oxbow lakes, river beds and mud flats. All emergent structures out of chaos.

In Southern England we have a wonderful structure called Chesil Beach (from Old English ceosel or cisel, meaning "gravel" or "shingle") made entirely from pebbles. This entire 18 mile long structure was an emergent structure formed by the chaotic action of water molecules. As you go from one end to the other, the pebbles change in size. They have been graded into order by the same chaotic actions of water molecules.

Rivers, seas and oceans are composed of countless billions of water molecules all moving chaotically. It would be impossible to take any single water molecule and accurately predict its movements even for a few seconds because that depends on what the water molecules around it are doing, whilst what they do in turn depends on other water molecules. And yet, give something directional like gravity, order will begin to emerge and structures will appear in the water, some brief and transitory, some longer-lasting, but all being unpredictable. An order of sorts emerges from chaos.

Look at this video of a gentle stream. It's worth watching anyway. You will see little eddies forming, ripples on the surface of the water, peaks and waves and splashes. All of these are emergent structures, emerging from the chaos of mass action responding to gravity alone.

No intelligence and no direction save the natural force of gravity is required.

All of these examples of order emerging from chaos, and especially the latter of order emerging under a natural force giving a direction such as gravity, illustrate a basic principle of evolutionary biology.

They illustrate how order can emerge from randomly imperfect replication of genes under the directing influence of natural selection to give structures and forms best able to replicate genes in that selecting environment. Evolution by natural selection is an iterative process, complete with directing feedback system which requires no more direction nor intelligence than does water flowing down a stream.

And it is as mindless and majestic as flood water washing away bridges, cars, buildings and people.

1. You have a significant problem with your argument: particles are not moving randomly and chaotically. They are subject to other laws (for example, Coulomb’s Law) which dictate their motion. They are “unpredictable” in the sense that we cannot predict their motion with our modern technology because they are so small and numerous, but if we were to somehow be able to measure every single particle’s speed and mass and charge then we would be able to accurately predict their movement.

1. >but if we were to somehow be able to measure every single particle’s speed<

1. Heisenberg's Uncertainty Principle.

2. That part of the blog wasn't about particles, so charge doesn't come into it, but molecules.

2. 1. Yes, with our current technology we can’t measure particles without disturbing them, but if we could measure the particles’ speed, mass and charge without affecting them, then we would be able to accurately predict their movements. The point is that their motion is governed by laws and therefore they are not moving chaotically.

2. Molecules are particles.

3. 1. Heisenberg Uncertainty is not a technological limitation; it is a fundamental characteristic of matter. Wikipedia -Uncertainty principle

2. Molecules are composed of atoms which are composed of elementary particles. Even the position of particles within those atoms is indeterminate due to chaos and quantum uncertainty.

4. 1. I was confusing Heisenberg’s Uncertainty Principle with the Observer Effect, my bad.

2. I never said molecules are “elementary particles,” I said they are particles. Regardless, molecules are subject to intermolecular forces such as London Dispersion or Dipole-Dipole that affect their motion. Just think about it logically, if molecules didn't have any forces acting on them then they wouldn’t be moving at all.

5. Indeed. Brownian Movement is random because it is caused by random collisions of randomly moving molecules with suspended (macro) particles. It can be observed in smoke.

I think we are trying hard to disagree here, don't you? My original point was that the Gas Laws are emergent order from the chaotic movement of individual molecules within the mass of gas. In other words they are statistical laws of mass action which emerge from chaos and yet they are entirely predictable, with no intelligent design or direction.

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