Amedeo Blog: Order in Nature

It’s spring! Not that this winter on the East Coast was bad, but I am always happy to leave those cold months behind. I like being able to roll out of bed, put on some flip flops and walk to the bagel store at 8am on Saturday without being cold. In fact, I like walking anywhere without being cold. I’m not a big fan of cold. Or wind. Or the word “blustery.”

The upturn in temperatures means more greenery, more life outside and more flowers. One of my most (er, only) favorite parts of living in Boston was the Public Garden in springtime. The flowers and trees were always so gorgeous. Now I have cherry blossoms to look at and petals flying all over Rittenhouse Square in Philadelphia. I still love it.

Here are some beautiful photographs of flowers that I found on NationalGeographic.

So pretty. So ordered. Life is very ordered, is not? These flowers have very specific patterns. The body of a human being is a well-engineered machine. People build homes, cities, and roadways to create order out of the world. Our computers have files that are logically organized and our homes have places for just about everything.

But then… things aren’t ordered, are they? I’ve neglected my apartment for the past two months due to illness (damn kidneys!) and it swiftly became a war zone. Bring one baby into a home and blankets, toys, bottles, and diapers are quickly strewn about. It takes a lot of energy to keep things organized and almost none to mess it up.

In science, we talk about entropy (also referred to as S) and often times equate it to the degree of disorder in a system. Higher entropy means more disorder and lower entropy means less disorder. Just as a ball will roll down a hill or heat will flow from a warm place to a cold place, systems tend towards states of more disorder. By sheer probability, this has to be the case. Think about a deck of cards. There is only one way that deck of 52 cards is ordered (in a stack on the table), but there are literally millions of other ways the cards could be thrown around the room. The probability of your deck of cards being a mess is nearly 100%.

The second law of thermodynamics states that the entropy of the universe is always increasing. This means that the universe is always moving towards more and more disorder. If that is true, how do we explain those beautifully, ordered flowers? Or living organisms with organized bodies? Or any kind of order in our world?

Let’s use the example of the deck of cards.

We are going to call the deck of cards our system and everything else the surroundings.

System:

Imagine that all 52 cards are randomly spread across the floor. That deck of cards has a large amount of entropy.

Now, you pick up the cards, organize them and stack them neatly on the table. The deck of cards now has a small amount of entropy.

Scientists like to talk about the change in the system. A natural question for a scientist to ask about our system now is “What was the change in entropy?”

Change in entropy can also be written as ΔS and means this:

(Entropy of the final state of our cards) minus (the entropy of the initial state of our cards)

For our purposes, the actual number is not important. We are more interested to know if that number is positive or negative.

What was the entropy of our final state of cards? A small number.

What was the entropy of our initial state of cards? A large number.

A small number minus a large number equals a negative number.

If you told a scientist that the ΔS of your system was negative, he would know immediately that your system went from more disorder to less disorder.

Surroundings:

Systems don’t live in vaccuums. Depending on what the system does, the system will absolutely affect its surroundings. If the system heats up, that heat will dissipate into the surroundings. If the system cools down, it might draw heat from the surroundings into it. These two parts are intertwined.

So, by picking up the deck and organizing the cards, what have we done to the surroundings?

A person came in, moved around haphazardly scattering air molecules all over the place. The deck was placed together and probably tapped around a lot to make cards match in height, which probably increased the heat and movement of the air molecules. Before that person came in, the air was calm.

Think about what the ΔS of the surroundings would be.

What was the entropy of our initial state? Low. Lots of order.

What was the entropy of our final state? Higher. More disorder.

A large number minus a smaller number equals a positive number.

If you told a scientist that the ΔS of your surroundings was positive, he would know immediately that your surroundings went from less disorder to more disorder.

Second Law of Thermodynamics

This law says that the entropy of the universe is always increasing. It is always going from less disorder to more disorder. ΔS universe is always positive.

So, why did we spend so much time talking about a system and surroundings?

Because this is how the three are related:

ΔS universe = ΔS system + ΔS surroundings

The second law states that ΔS universe must be a positive number.

ΔS system + ΔS surroundings must equal a positive number.

For our case:

ΔS universe = negative number + positive number

As long as the surroundings become very disordered (a large positive number), then the ΔS universe will be a positive number.

If you look at any system and surrounding situation in nature, carefully measure its entropy changes and add them together, you’ll always get a positive number. If they don’t add up to a positive number, then it does not occur in nature.

So, the flowers and people and organized life exist in this world. If you think of them as systems, then their entropy is definitely decreasing. However, they must disorder their surroundings quite greatly to compensate. This is also true. People are constantly moving, breathing and changing their surroundings. Plants are no different. Living organisms are constantly uptaking some nutrients and giving off others. Their surroundings are always changing. As the organism gets more ordered, the surroundings become more disordered and so the universe becomes more disordered and we’re all here.

Okay - if I've totally confused you, then here are more pretty flower pictures to relax your brain.