Complexity Science: Emergence and our Perception

Figure 1: Physical and perceptual (neurological) emergence

Almost everything we see and interact with around us is emergent.

That is, things we think of as objects are actually made up of many small particles.

These objects are also actually a story we tell ourselves, icons in our mind, which, from the point of view of the constituent particles, do not exist.

To give an example, imagine a rigid blue cube:

That cube is made up of many molecules which stick together, and when stuck together have certain rigid properties and a cubic shape. Light hitting the cube is absorbed, except for a particular range of wavelengths we call 'blue'.

We can then call these 'blue' and 'cube' characteristics - macroscopic observables of the thing we call a blue cube. (From Greek, makros 'μακρός' means large and skopein 'σκοπεῖν' means look at or observe, as in 'telescope'.)

But that's not all there is to it! That was the physics side, the construction of the physical entity.

However, it would not be a cube if we had never observed it. That is, imagine a planet in a far-off galaxy, with a rigid blue object, or imagine humans had never existed. Until humans exist and observe that object, it does not even become an object, much less a 'blue cube'. In fact, until we observe this particular collection of molecules, what's really to separate it from the rest of the planet, or to separate the 'planet' from the space around it. All of this objectifying is human choices.

Now we enter the picture. We reach out our hand, we grab this collection of molecules, and we look at it. Our visual and neurological system responds to our sensory input (vision, touch) and these signals travel up our neurons into our brains, vast networks of neurons.

Our neuronal networks fire in patterns, aggregating the visual information from individual neurons in our retinas and hands, and compare it to past input patterns we have observed, as well as written or verbal inputs we have associated with those patterns.

Our neuronal network, through this process of aggregation, also reaches a macrostate of firing patterns, and does what we call 'decides' (represents) that the current input patterns closely match those past patterns, and yields the associated verbal and written patterns, which are 'blue cube'.

So isn't that interesting?! In order to create a representation of a 'blue cube', we had two emergent processes [Fig. 1].

First, physically, the molecules had to come together into a macroscopic object, then our neuronal system had to aggregate many individual neuronal inputs to internally create a macroscopic representation in the brain.

We can do some thought experiments to understand this better. Let's suppose we reading this are like the audience in a movie. We can observe the physical situation, but also the brain of a human astronaut who lands on the planet of the 'cube':

Let's look at each thought experiment from the physical and neuronal point of view:

Imagine our astronaut lands on the planet and just sees a patch of blue smeared on the surface.

Physical: This isn't even an object, much less some separate macroscopic entity resembling a cube.
Neuronal: This pattern of inputs doesn't match what we typically call a 'blue cube'.

How about some holographic image projected onto a cloud of gas which we moviegoers can see looks like a blue cube?

Physical: Hmm, ok, this is again emergence of a collection of light rays that create some kind of macroscopic object. However we moviegoers can clearly say that this is not a physical cube.
Neuronal: Our astronaut's visual system aggregates the information and decides it's a blue cube. However, then the astronaut reaches out to grab it, and his or her glove passes through it. When this new touch sensory information is aggregated with the visual, the astronaut's neuronal system maps this to a different internal representation ('an optical illusion of a blue cube').

What about this?: A hyper-intelligent organism which can project wavelengths of light in different directions, and change its form from rigid to soft, etc. Or what if it can do this so quickly, much more quickly than a neuron can fire, so that it is changing form and emitted light so quickly that the astronaut doesn't observe it. What if 99% of the time, it emits the red wavelength of light and is actually as soft as jello, but not when the astronaut's nerves sense it.

Physical: We moviegoers can see that these are very different collections of atoms or molecules. From our point of view, we might not call these collections blue cubes at all.
Neuronal: Our astronaut's neuronal input continues to match 'blue cube'. When the astronaut's neurons receive visual input, they happen to always be the blue of the blue cube. The astronaut's neurons receiving touch input, when it is aggregated in the brain, matches patterns of rigidity and cubic shape.

We could go on like this for some time, coming up with creative examples that we moviegoers would not call blue cubes, but which fool the astronaut.

We could probably come up with examples which physically are blue cubes, but our astronaut's brain thinks are not. For example, case number 3 where the cube is blue and rigid 99.999% of the time, but not when the astronaut's neurons sense it! Or if the sun gives off a strong red light, making the cube appear black, etc. etc.

So, what exactly is emergence? Let's do some more thought experiments...

Let's go back to the physical blue cube.

How many different materials can we make a blue cube from? There are many materials that are rigid.

Let's make some simplifying assumptions (it will occur to us why these are simplifying, but they don't matter much for our experiments).

Suppose there are 20 different molecules (substances) that are rigid and do not absorb the blue wavelength of light, so they appear blue. So then for each molecule of the 'cube', we have 20 choices.

Now, just for a moment, let's suppose our cube is made only of 2 molecules (a very tiny cube). So, for the 1st molecule we have 20 choices, and for the second molecule, we have 20 choices. So we have 20 * 20 or 20^2 = 400 ways to make a blue cube!

Now let's make a larger blue cube. Let's suppose it has approximately 4.27 x 10^27 molecules, physically a more realistic number. With that many molecules, there are 20^(4.27 x 10^27) ways to make a blue cube.

This is a HUGE number, so big that it has 1.30103×10^27 decimal digits just to write it down!!!

When we zoom out, all of these versions of the cube appear the same, so an observer would call all of these ways to put together these molecules the same blue cube!!

In physics, each of those ways of making the blue cube are called 'microstates'. They are particular instances of choices of each particle or element that make up a system. Usually, the number of microstates is huge, since most objects around us are made of a very large number of molecules.

We can call the blue cube itself --which looks the same to us moviegoers no matter how we choose the molecules-- the macrostate, which always has the same macroscopic observables (large-scale appearance).

Now, let's go back to our Astronaut's neurons and brain.

The astronaut sees this collection, this clump of rigid blue molecules -- many individual neurons in the retina respond to a collection of blue light input in a cubic pattern.

This information travels up into the brain to be aggregated, where other neurons are stimulated when neighboring retinal neurons give similar input, until it is encoded (represented) in a pattern corresponding to 'blue cube' in semantic and linguistic neuronal representations.

Notice that, in the brain, we could argue that until the semantic or linguistic representation of 'blue cube' is activated, there is no blue cube. (However it is represented doesn't matter here.)

Let's again make some very simplifying assumptions:

Suppose the light from the blue cube stimulates only 2 neurons in the retina, and each of these neurons can be in state blue, green, or red (3 states). There are then 3 x 3 = 3^2 = 9 ways these neurons can be activated. Notice that each of these ways are again microstates.

Notice that we only call one of these ways --when both neurons are in state 'blue'-- the 'blue cube'. This is again the macrostate, the large-scale description of the system.

Suppose instead that the light from the blue cube stimulates 1000 neurons in the retina, and that each of these neurons can again have 3 states. This is now 3^1000 or 1.32 x 10^477, another extremely large number! (This is probably a very small estimate since the retina has approximately 100 million neurons!)

So again, out of those different ways of stimulating 1000 neurons, we probably have a few choices. If there were a small number of green or red tiny dots, we might not notice them, and the astronaut might still call the cube 'blue'. But that number of ways of having dots on the blue cube is probably small compared to 10^477.

Even if there are 10^100 ways to have a few green or red dots, these slightly dotted ways of having blue cubes are only

(10^100)/(10^477) = 1/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

of the ways to have a solid clump of neurons stimulated by only blue light!

This is so small, let's disregard these dotted ways! We could say something similar about rotating the cube. Yes, there are many ways to rotate, but these are again very small compared to ways of seeing a solid block of blue.

So out of all of the 1000-neuron images the astronaut could see, roughly only 1 of them looks like a blue cube, the solid geometric clump of blue. This is again the macrostate.

This macrostate emerges from the number of ways of obtaining it, the microstates.

In fact, when we reflect on it, the macrostate is forced upon us, stepping unstoppably out of the vast space of possible collections of molecules.

Now, let's take a look around us. Everything we see, everything we think of as an object, has both of these types of emergence going on, the physical and the perception through our neurological system.

That is, although 'clumps' of molecules or other objects exist, physical macrostates, until we perceive them, they do not exist for us. So both the physical and perceptual emergence must occur for these objects to exist for us.

We can use a similar way of thinking to see that the number of ways of obtaining almost any 'macroscopic' (large scale) object around us is extremely large, but it is very small compared to all the arrangements of molecules.

For example, there are many ways to arrange carbon, calcium, hydrogen, oxygen etc. atoms to have a 'hand', but there are vastly many more ways to arrange those atoms which we would not call a 'hand' from a physical perspective (for example, a block of carbon, a block of calcium, and a puddle of water).

On the neurological side, there are many patterns of light which, falling on the retina, would stimulate the neurons and brain in a way resulting in a semantic representation 'hand'. However, there are again vastly vastly more ways of stimulating those same neurons which would not activate semantic representations of 'hand', and instead would be represented by some other macrostate (e.g., blocks of white stuff, black stuff, and a puddle).

Perhaps it is interesting to carry out similar thought experiments for yourself, and think about other examples in physical or perceptual emergence, or a combination of the two:

How many ways physically can we have an object that looks like a cube only on the outside?
Why do we choose to say that a blue cube is an object?

Why not interpret part of the corner of the cube and a triangular chunk of the table (etc.) as one object?
Do the micro- and macro- states in our brain correspond to the physical micro- and macro-states?

How to improve the estimates above?
Why do we need a sense of touch?
Can we measure the effectiveness of our senses by their reduction of possible microstates of the world around us?
How this relates to misunderstandings in communication?
How this relates to optical illusions?