Order From Chaos: The Reason We Are So Big
Seven octillion wrongs make a right.
Everywhere I go, I carry around atoms that were once in the body of Albert Einstein. I keep them alongside atoms from Socrates’ last drink and atoms that splashed Julius Caesar’s feet as he crossed the Rubicon. So do you! This is because, for every cup of water in the world, there are about a million atoms in your body. This means that if you pick any cup of water in the history of the world, it is almost certain that some atoms from that cup have made their way, through the unceasing motion and shuffling of atoms, to your body.
The ultimate reason for this unintuitive fact is that the number of atoms in your body is incredibly large – about seven octillion (7,000,000,000,000,000,000,000,000,000). This naturally inspires us to ask: why? Why do we need so many atoms? A simple answer is that atoms are incredibly small, so it takes an enormous number of them to make something as big as us. Yet this begs the question – why are we so big?
If you could see the atomic world, you would understand why. It is ruled by chaos. Atoms bounce around randomly, crashing into each other at the speed of jet planes, haphazardly pairing up and breaking up with one another without rhyme or reason. We could never survive such pandemonium. Yet, at a large enough scale, order emerges from this tumult. Paradoxically, the combined effect of the chaos of enough atoms is predictability. We can understand how this is by studying the process we take for granted more than any other – breathing.
How We Breathe
Imagine your next breath simply doesn’t work. You are surrounded by air, and your lungs still function perfectly, but air just doesn’t come into your body. This is a physical possibility! To see why, and why it is incredibly unlikely, we need to understand how breathing works. We inhale by lowering a muscle below our lungs, called the diaphragm, to increase the size of our chest cavity. This results in lower air pressure inside your chest than outside; that is to say, there is less air in your chest than in a volume of the same size outside your body. Air rushes into your chest since it naturally moves from places of higher pressure to those of lower pressure.
This movement of air in this way is as reliable as any other scientific phenomenon, and we depend on it happening without fail every minute of our lives. Yet, there is no fundamental physical force drawing air molecules towards low-pressure regions or pushing them out of high-pressure regions; each individual molecule is actually no more likely to enter your lungs than leave them. Instead, the predictable motion emerges out of the randomness as an overwhelming statistical tendency.
In fact, it is the same tendency that you use when playing cards. When you shuffle an ordered pack of cards, there is no law that requires that each suit will end up spread roughly evenly across the pack. Yet, almost without fail this is what happens. The reason is that there are far more possible arrangements of the cards in the pack for which this is true than arrangements where the suits are ordered. For example, there are one hundred trillion times as many arrangements where there are equal numbers of red cards in the top and bottom half of the pack as the number where all red cards are in the top half.1 This means that if we randomise the order of the cards by shuffling, it is a hundred trillion times more likely that the red cards will distribute evenly than that they will all remain at the top.
The number of possible configurations consistent with a condition is measured by entropy. Statistically, high entropy states are more likely than low entropy states because there are more possible ways they can arise. This means that systems tend to move from lower entropy states to higher entropy states. The larger the entropy difference, the more reliably this will occur. In physics, this is called The Second Law of Thermodynamics. Shuffling a pack of cards works because a disordered arrangement of cards has much higher entropy than an ordered arrangement, so the pack tends to become more disordered when it is randomised.
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Breathing works on the same principle. Just as spreading red cards evenly across a pack of cards has higher entropy than having them all in one half, spreading air molecules evenly across two regions has far higher entropy than accumulating them all in one place. So, when you open up your chest cavity, the random movements of air molecules naturally result in the air moving into your lungs to balance the pressure. Just as there is a chance that a shuffled pack of cards comes out perfectly ordered, there is a chance that the air will not enter your lungs. It is just very unlikely.
The Emergence of Predictability
It is not only breathing that depends on entropy and the second law of thermodynamics. The same is true of energy. Physical objects tend to lose energy because there are far more ways for the energy in them to be spread out across the whole universe than concentrated within them. This is why hot objects cool down and cold objects heat up towards room temperature. It is why things pushed along the ground tend to slow down rather than speed up. This is ultimately the effect that determines the outcomes of all chemical reactions. The basic phenomena that we take for granted as facts of life are all in truth only statistical tendencies. Life is only possible when these effects can be depended on. Just as we could not live if we could not depend on air rushing into our lungs when we inhale, no organism can live without depending on the predictable outcomes of myriad chemical processes that run our cells and our bodies.
Importantly, entropy differences are exponentially bigger for larger systems than for smaller ones. If we shuffle only the four kings in a pack of cards, there is a very real possibility (one in four) that the red kings will both end up on top. By contrast, if we combine two full packs of cards and shuffle them all together then it is incomparably more likely that there will be equally many red cards in each half as that all will be in the top half.2 This is why order emerges out of chaos when a system becomes big enough; what is just a likelihood when there are only a few cards (or atoms) becomes so overwhelmingly likely as to be essentially inevitable when there is a much larger number. This is ultimately why life is not possible at the atomic scale. We need the dependability that only emerges when enough atoms are present to balance out statistical variation and make the world predictable.
The Size of Life
However, it is still reasonable to wonder whether we really need to be this big. Are all seven octillion atoms really necessary for life? The short answer is no. The statistical variations that make the microscopic world unpredictable diminish on the scale of tens or hundreds of atoms, and become negligible on the scale of thousands. We should therefore expect that life could thrive at even this scale.
Indeed, this is the case! The smallest living things are ultramicrobacteria which can be as little as 200 nm long. Since atoms are about 0.1 nm long, this means that ultramicrobacteria are only about two thousand atoms long. This is as small as we should expect life to get, and it seems that it is; all smaller entities that have been studied have ultimately been found to be non-living.
So what about us? Why are we so much bigger than the scale at which order emerges? It is because our bodies have a complex structure made up of smaller parts that also depend on predictability to function. Our cells contain many discrete parts — called organelles — that are comparable in size to bacteria. These organelles could not be smaller, since they perform essential processes that depend on predictability. Because our cells contain many of these organelles, they are somewhat larger than bacteria — perhaps a hundred thousand atoms long.
Our bodies also contain differentiated organs and structures made of different types of cells. This means that they must be large enough to fit many such cells. For this reason, even small animals like ants must be hundreds of cell lengths, or tens of millions of atoms, long. Since being larger than other animals opens up new biological advantages and opportunities, it is natural that there is a spectrum of animal sizes. We are on the upper end of this spectrum, and so are about a thousand times longer than an ant. This means a human is tens of billions of atoms long. Because we are three-dimensional, the total number of atoms in the volume of our body is the cube of this number, which is about seven octillion!
At first glance, the enormous number of atoms in the human body seems arbitrary and perhaps even absurd. However, we can now see that there is an ultimate reason for it; the chaos of the atomic world places a lower limit on the size of life. Large as we are, the smallest scales of biological functioning in our body push on this limit and can go no smaller. The behaviour of individual atoms is wrong for biology — it is too unpredictable and unreliable. Fortunately, when it comes to atoms it turns out that seven octillion wrongs make a right.
For every configuration in which all red cards are in the top half, you can create a unique configuration with thirteen red cards in each half by choosing thirteen red cards to move to the bottom half and thirteen black cards with which to swap them. Therefore, for every such configuration there are (26C13)²=1.08x10^14.
Similar to the previous calculation, the ratio of configurations is (52C26)²=2.46x10^29.
So how or why is it the neg-entropy (order) emerges from massive combinations of entropy?