Order contains disorder

[HydrogenBond]

Much of physics toys with the idea of uncertainty and chaos. But if we look at macro-reality the internal chaos is usually contained by a principle of order. For example, if we start with a cloud of interstellar hydrogen, the amount of disorder is at a maximum. As gravity takes over to form a galaxy, the amount of possible disorder or chaos decreases. It is still there but is reduced by the orderring principle of gravity.

 

Another example, a single cell, within a nutrient solution, is surrounded by disorder with the liquid and gas that surround itself. It faithfully, reduces the level of disorder by fixing the randon into the stuff it is made of. If all goes well, it produces a daughter cell that now doubles the rate at which disorder is organized.

 

Even if you look at a forest, the trees may appear to have a random distribution. But even this is orderred. Trees will grow best in those places where sun peaks through the canopy at that point in time. Thousands of viable seeds will be spread, but the existing canopy will order which of these will reach the canopy in 50 years.

 

An electron in an orbital may still follow the uncertainy principle but the level of uncertainty has decreased relative to a free electron due to the EM force and the formation of the orderred container called the orbital.

 

For some reason, the existence of disorder and chaos has led to the theory that the formation of life is a relatively unique event. It is assumed that through upteen disorderly random trials and errors something clicked. But another way to look at it, more consitent with macro-reality, is that order is predefined by the laws of nature and that random click, wasn't random at all, but was a natural and logical result of order putting chaos in one of its containers.

[Tormod]

I am not sure I follow. Chaos theory does indeed indentify an order in things. The branches of a tree and the seeds of sunflowers (and many other objects, like the spiral arms of our galaxy) tend to follow a very orderly end predictable (statistically speaking) distribution which tends towards phi, or the golden ratio (although not *exactly* the golden ration, I am not trying to mystify this, it is perhaps a statistical necessity for all I know).

 

Mario Livio wrote very well about this in his book about phi.

 

Golden ratio - Wikipedia, the free encyclopedia

[Tormod]

Hm...I must have misread your post entirely. M u s t g o t o b e d.

 

Yes, I agree with you. I do not think life was a one-off event that was completely unlikely to happen. If it were, it was NOT likely to happen. It could equally well be that life is very likely to happen due to the way order imposes itself upon complex things.

 

The problem is we have only one statistical sample of planets with life, and we know nothing about how life arose here in the first place, so until we find life elsewhere it is bound to be pure speculation. :doh:

[InfiniteNow]

Entropy increases, HB. That "order" came from increased disorder somewhere else. How is this social science?

[PsyCho]

There is order within chaos, it appears more or less ordered depending on the scale with which you view it. All your examples of order are also highly disordered (to varying degrees, again relative to observer and scale)... Reality is an illusion oscillating between the two, a bit like a necker cube or paradoxibox.

 

A related link to this which may interest...

 

User:Lakinekaki/Bios theory - Wikipedia, the free encyclopedia

[InfiniteNow]

How is this social science?

Unless maybe this order to which you refer is only a perceptual quaility, and does not relate to the system itself... :doh:

[HydrogenBond]

This weird, I was posting this in physics but it ended up in social science. I guess I needed to eat something. Physics has trained our minds to look at nature in terms of chaos and random. This does indeed exist. But ordering principles reduce disorder instead of disorder reducing order, which is what is often taught.

 

If we look at a crystal there are always some random inclusions making the order less than perfect. But if one considers where the crystal came from, either gas, molten or dissolved, the original disorder was much higher until crystal order took over. When order was done, choas was only a tiny fraction of its original self. Physics blows up that tiny fraction of chaoas and treats it like it is the prime directive. This has biased the way we look at the origins of life. If one assumes order plays second fiddle, you end up with what we have in the way of evolution, which is a rare universal event that nevertheless increases order to the earth.

 

The trees take random photons, CO2, H20, etc. and fix them into biomass. Humans take the forest of random sized treess and make 2X4's that are assembled together as houses. This allows physicists to sit and ponder why the chaos is so important. That is the product of a choatic instead of an orderred mind.

[PsyCho]

Your ordered mind is built on chaotic processess; regularity producing disease.

 

Viewed over a long enough time peroid, your mind is certainly not ordered; but tells itself it is to maintain the illusion of control

[Tormod]

Moved to physics.

[BibleBeliever]

Chaos, is this different from Randomness, or a factor of it?

Randomness, is this not more complicated order?

 

These are genuine questions, there is much to think about if Random is only an illusion due to the fact our limited understanding cannot see the order in it.

[PsyCho]

Random is what we don't understand

[HydrogenBond]

Random is what we don't understand

 

One of the practical uses of chaos and disorder is to help make correlations work, easier. If one set the constraint of order, theories that don't quite add up, woud have to go back to the old drawing board. If add the philosophy of chaos or disorder, all theories have a nice fat fudge factor.

 

A good analogy is drawing a bunch of disconnected lines on a piece of paper. Next, lets add a blur filter. Now all of a sudden the lines all appear to be connected. Blur helps theories to appear integrated. I realize random blur that is the easy way to do science. But if one looks around reality, disorder is always losing ground as orderred principles of nature combine matter into orderred forms. Some disorder always remains but once disorder finlaly reaches a blackhole, there is not that much disorder left in the universe.

[BibleBeliever]

A good analogy is drawing a bunch of disconnected lines on a piece of paper. Next, lets add a blur filter. Now all of a sudden the lines all appear to be connected. Blur helps theories to appear integrated. I realize random blur that is the easy way to do science. But if one looks around reality, disorder is always losing ground as orderred principles of nature combine matter into orderred forms. Some disorder always remains but once disorder finlaly reaches a blackhole, there is not that much disorder left in the universe.

 

So how does that affect entropy and the Second Law, I thought order was tending towards disorder.:doh:

[Erasmus00]

Hydrogen bond, you seem confused about the second law, where it comes from, and the general ideas of entropy.

 

Lets look at your system of ice/water (why the ice forms a crystal), and do some math.

 

Lets divide our world into two parts, our "system" (the water) and our "heat bath" (everything else). We have a temperature for our heat bath of T.

 

Now, lets look at the entropy S. Our entropy is a function of energy, and we note that Temperature is defined as [math] \frac{1}{T}=\frac{\partial S}{\partial E} [/math] in units where Boltzman's constant is 1.

 

Now, lets look at the condition for our entropy to be maximized. Noting that total energy E is constant. Noting that the total entropy is the system plus the bath entropy.

 

[math]\frac{\partial S}{\partial E_{bath}} =0=\frac{\partial S_{system}}{\partial E_{bath}}+\frac{\partial S_{bath}}{\partial E_{bath}} [/math]

 

Now, use that [math] \Delta E_{bath} = \Delta E_{system} [/math], and the deffinition of temperature we see our entropy maximized condition becomes [math]T_{bath}=T_{system} [/math] Hence, we see that if our system goes the same temperature, our entropy has its maximum possible entropy.

 

Hence, your ice, even though its a crystal, must be at the same temperature as the environment (or else it changes temperature), hence, that ice crystal has maximized its entropy. "But" you say "its ordered! How can we understand that?"

 

I'm glad you asked. Because the temperature is the same everywhere we can put E as a function of entropy at constant temperature. What we find (in a process similar to Legendre transformation) is that maximizing entropy is the same thing as minimizing energy (at constant temperature). Hence, energy is a minimum.

 

This is nice and all (total energy being minimized at constant temperature) but leaves us with a bad description: we can't know the energy of the bath. We want something in terms of just the energy of the system. So:

[math]\frac{\partial E}{\partial S} = 0 = \frac{\partial E_{bath}}{\partial S}+\frac{\partial E_{system}}{\partial S}[/math]

 

Now, use that the same delta E relations from above, and the deffinition of temperature (as well as the fact that its constant)

[math]0= \frac{\partial}{\partial S} (E_{system}-TS_{system})[/math]

 

This is the result we want, E-TS is minimized for our system. Note: what we have shown is that when E-TS is minimized, the total entropy of the bath and the system is MAXIMIZED. E-TS is called the free energy, F.

 

How does this apply to the ice? Notice that when T is small, we can make F smaller by minimizing E, and the entropy is not as important because of the T prefactor. Hence, our ice freezes into a crystal, which minimizes the energy. But we have shown that decreasing the entropy of the ice in this manner ACTUALLY RAISES the entropy of the bath to compensate: i.e. the entropy of the "universe" increases.

 

At high temperatures, instead of minimizing the energy of our system, we are better off maximizing the entropy, hence at high temperatures the water is a gas (max entropy). BUT, this is still the condition of maximum entropy of the "universe."

 

A problem left for the interested reader: show that the fact that entropy is MAXIMIZED and the energy MINIMIZED (i.e., take the second derivative and require it to be positive or negative depending on max/min) leads to other insights. (i.e., specific heats must be positive).

 

Edit: Latex glitches. I may have been hasty with my math, but the results are standard (see for instance, Reif's Statistical Physics)

-Will