Shades of Darker

We'll develop this line of thought later on with more examples but for now let's make a pause to realize what we just analysed. We described the act of performing an experiment as the interaction of one item with the many, as a mechanical interplay of a bigger, blunter agent with a more susceptible one. The study of this simple model with dramatically unorthodox outcomes proved that the idea is more than just a philosophical concept but one of real world significance and, as such, it showed us the importance of understanding the implications of being ourselves a natural phenomenon. Too often do we study the stuff we're made of as a dead substance, subject only to the simple rules we make of its behaviour, without realising it also turns us into mere happenings, general tendencies in the motions of atoms, cultural trends in the behaviour of molecules. Our thoughts, our emotions, everything we trust to set us apart from all that oblivious stuff are like moving shades in the wheat on a windy day, pressed between opposing forces.
As scientists, we know that perception, measurement and decision must be natural phenomena and therefore we can only to a limited extent approximate them by an external agent, independent of the whole system. While that simpler view can help us understand simple things, it can also blind us to the greater implications of our true nature.
To bear this in mind is a crucial ingredient if we are to study the mind of other phenomena. It's an essential sanity aid if we are to accept and explore a world filled with rich subjective experiences, of conscious perception at every corner of existence. In the next section we will describe how concepts, learning, pleasure and suffering come about naturally in many systems.

The curse of the attractive observer

Imagine you have a magnet and you want to measure its orientation. You design an apparatus with two polarizations along a solid rod. At any instant it can be in state + with a probability p and in state - with a probability 1-p. Picture yourself tossing a weighted coin labeled + and - on each side every second. A probability p means after an hour or so, having tossed the coin N times, you will have obtained close to p*N times + and (1-p)*N times  - .
When left alone, the detector relaxes to p = 0.5, i.e., it's positively and negatively polarized an equal number of times during any large enough interval of time. If the polarization is something like a electric tension and we read it from a voltmeter (which measures the average voltage over some short time), we'll view on its screen the value V = (+1)*p + (-1)*(1-p) = 2 * 0.5 -1 = 0.
Let's now say the detector is placed in such a way that it makes an angle x with the direction along which the magnet is pointing. Then p will tend to p = 1 (V = 1) if the detector is aligned with the magnet and to p = 0 (V = -1) if they are anti-aligned, and to p = (cos x +1) / 2 in general, so that

  V = (cos x +1) / 2 - [1 - (cos x +1) / 2] = cos x

which is the component of the magnet along the rod. Thanks to this, our detector allows us to fully measure the spatial orientation of the magnet: you first measure V along one direction, then V along its perpendicular and you combine the results. This figure sums it up:

We have plotted the evolution of V and p over time, so you can track what's going on in the detector as it performs a measurement at an angle of 45º. As you can see, V tends to cos 45º = 0.71 :

Now consider that you're not measuring a big magnet but a tiny one. So tiny, that actually the influence of your detector on the magnet is no longer negligible. Whenever you turn on your detector and it polarizes positively or negatively, the magnet will try to point in the same direction. Then what can we expect from this complicated interaction? Well, if you measure the direction of the magnet long enough so that you can tell its value with certainty (that is, V has reached a stable value) then so will the magnet have aligned itself with your detector. That means only two well defined outcomes are possible: V =1 and V = -1.

We ran a simulation with a very simple set of equations satisfying the properties described above. For each angle we ran the experiment a 1000 times and plotted the percentage of times the detector converged to a positive polarization. Here's our result:

The plotted curve is (cos x +1) / 2 . The result may appear at first as being the same as before but after close examination it is profoundly different. An observer trying to determine the orientation of a large magnet will indeed measure at the end of each experiment a value V that follows the curve above. However, an observer trying to measure a very small magnet will always measure a polarization V = 1 or -1 at the end of each experiment, even though an average of V over many experiments performed in the same conditions will result in the drawn curve. A very important consequence is that if you try to determine the spatial direction of your magnet by doing two measurements along two perpendicular directions you won't come to any conclusion at all, since the first measurement will ruin it for the second one.

A subject using such a tool to perceive the world around him will come to the puzzling conclusion that microscopic magnets have an inherent randomness to them, and that they can only be in two possible states. It is a curious fact that the peculiar properties described above happen to be exactly the ones found when you try to measure the spin of an electron. In this case, the weird quantum mechanical behaviour of particles can be fully understood using this classic analog we just studied. One might even wonder if the microscopic behaviour we see in electrons has something to do with the limits of how very delicate things can create discernible structures in very bulky ones.

The limits of reality

Everyone loves to tweet that one sentence that's going to be retweeted hundreds of times. That's why facebook keeps track of likes and why we stare at that little like counter whenever we post something valuable, and wait for it to boil. But unless you're some kind of celebrity, or a hot girl, chances are your stuff won't cause much stir. And the humility this experience teaches us should make us wonder about the limits of our own perception.

Electrons interact with each other and with protons through little tweets we call photons. Light, turns out, is simply a large number of tweets between a large number of electrons. They can be seen with a photomultiplier. When one free electron tweets with a specific energy another electron in the photomultiplier, the latter will retweet the tweet to his neighbours and so on, creating a cascade of interactions and a movement in the trillionfold electron population strong enough to generate a macroscopic current. If you think of it, this little electron's tweet is a tweet only akin to Snowden publishing his data on internet surveillance, only akin to Russell Brand tweeting his latest outrageous say or to a syrian journalist posting pictures of a chemical massacre. It is the tweet that starts a revolution.

Knowing just how difficult and rare it is to tweet anything popular, one might sympathize, feel proud and even awe at this electron's achievement. It could also lead us to question our own experience. Can anything in the microscopic world create macroscopic structures, signals in our detectors and memories in our brains? Next comes a thought experiment which draws stringent limits on reality at the large scale and exhibit behaviour that reminds of quantum mechanics.

The word of a century

    His body shook with an excitement he perceived as revolt. The little facts that had brought him to his present situation no longer fiddled with each other and were now blatantly yelling in his mind. A clashing of thoughts at the root of his pain that was starting to show the dynamic enthusiasm of troops lining up for battle. Soon they would agree. Soon they would drive his body to action and soon the crowds would cascade under the knowledge still known to them as silence, and justice would flow in a rage of turmoil. Then he paused. And said:

Big thermometers (clarification)

Here is a mathematical description of the temperature measurement experiment described in the previous post:

On the distinction of subject and object

We stated in the last post how artificial it is to consider the observer and the observed object as two separate entities, but so far it sounds more like a philosophical statement tailored for an LSD trip than an interesting fact to be explored. We will now present a few examples to show just how important it can be to consider it. Some parts of this post might be a bit mathematical, but we will try to juice out the most important features and leave the details aside.

Consider a very simple measurement: the temperature of a body. The simplest tool for it is a mercury-in-glass thermometer. When the tip of the thermometer is put in contact with a hot body, heat from the body is transfered to the mercury which expands inside the bulb of glass. Once thermal equilibrium is reached the column of mercury will have a stable length. The Celsius perscription to calibrate a thermometer is to dip the tip in ice and make a mark on it indicating 0ºC and then dip it in boiling water and mark 100ºC where the mercury column stabilizes. In between draw a hundred marks which correspond to a Celsius degree each. Then you just have to place the tip on the body whose temperature you wish to measure, wait for the end of the mercury column to stop moving and write down the temperature of the corresponding mark.
This procedure works because the volume of mercury is very small and therefore the heat released by a large body will generate a large change in the length of the column, whereas the heat poured into the body by the thermometer will be irrelevant.
Let's however imagine we are studying the temperature of a collection of delicate objects, of very small volume themselves. Their temperatures are uniformly distributed between 0ºC and 100ºC. That means there are just as many bodies between 1ºC and 2ºC as between 78ºC and 79ºC; in fact, between any two temperatures separated by the same amount.

If these bodies were heavy, performing 10 000 measurements of the temperature of these bodies would yield a histogram corresponding exactly to that distribution. But as the mass of the bodies gets smaller and smaller, the distribution of the measured temperatures shrinks (because the temperature of the body and of the thermometer will try to reach some middle ground), until it reaches a single value when the thermometer is much heavier than the bodies, which is the temperature of the thermometer. For this extreme case, picture yourself measuring the temperature of a small drop of water with a big thermometer: the drop of water heats up to the temperature of the thermometer, not the opposite.

This means a macroscopic observer who uses this thermometer to describe the microscopic world around him will see a very different world from another microscopic observer with a better (i.e., smaller) thermometer. The macroscopic observer cannot measure the temperature of small things without changing it and therefore will come to the conclusion that all these bodies are at temperatures which lie in a small range, which is true, but only because he looked. His knowledge is constrained by physical limits which have nothing to do with the precision of his apparatus, which in theory may be infinitely precise. The constraint lies in the fact that his perception is an interaction with the object, a logical loop which he's forced to step into: if he doesn't look he can't perceive the object, if he does he can only perceive the object in a limited range of states.
Of course, such small objects are short lived in our world for you to test this conclusion at home. Since we're all immersed in an atmospheric thermal bath, any small object reaches thermal equilibrium with the air long before you get any chance to measure its temperature with your oversized thermometer.
Which is why in the next post we will present a much more interesting system where the effects of a measurement are much less artificial and far more intriguing.

The correspondence principle

It has been pointed out to us that the concepts of "experience" and "consciousness" previously mentioned were a bit hazy. Let's elaborate a bit on them so that the underlying structure may become more apparent. For that we must first clear up what the present mainstream picture is and what its problems are.

So far, we have streered away from the term 'subjective experience' for reasons which will become obvious later, but that is what we refer to when we write 'experience'. The commonly accepted view is that there is a conscious subject which perceives objects and has thereby an experience of them. The subject can be a person or an organism who owns a nervous system. Additionally, neuroscientists have uncovered physical processes happening in the brain which are in a one-to-one correspondence with our subjective experience. Nevertheless, conceptually, there is a difference between the subjective perception and the underlying physiological phenomenon. Take, for example, a given cell in a monkey's cortex and show the monkey various objects. You notice that whenever the monkey is shown a banana, that neuron fires at a high rate. Sometimes it also fires less rapidly when he is shown a yellow elongated shape but clearly the brain cell responds to the perception of a banana. The monkey is subjectively experiencing a banana, but the corresponding physical process is the firing of specific brain cells.

Unfortunately, this is where the present day clear picture ends. From here on now we have a confusing and often conflictuous wilderness of philosophical definitions. Because of this equivalence between two seemingly so different things -- one the stimulation of a gooey cell, the other one the delicious and colorful perception of a banana --  people have introduced the definition of qualia. A qualia is the subjective experience of a physical object, the mental rendering or illustration if you will of an otherwise blunt thing. Things which can perform this rendering are said to be conscious whereas the rest of the stuff has no experience of the world, of any kind. 

Within it is deeply rooted the idea of a subject and an object separate from each other. And because of that, one may very well wonder if two people render the same object in the same way. When you and I look at a leaf, do we both render the color green in the same way? This leads us inevitably to picture the universe as a redundant fan of many paralel universes, as many as there are observers, each one coloring the world in its own randomly chosen way. In our view this picture is wrong in two ways.

First, it states there is a one-to-one correspondence between subjective experiences and physical phenomena, but only for stuff that is similar to us. It artificially imposes that the only possible subjective experiences are the ones we humans experience, such as thoughts, emotions and so on. As Pocahontas would put it: "You think the only people who are people are the people who look and think like you." This human-centered distinction between what is conscious and what isn't then allows people to draw the line wherever pleases them, according to whichever criterium of similarity appeals to them the best, like the presence of a well developed nervous system or the deliciousness of its meat. Some will include all mammals, others all the animals all the way to the oysters, and others will even accept that artificial intelligence may one day become conscious. Confronted with this chaos the most sensible will generally take an agnostic stance, dismissing the question as unanswerable. Yet to them, in their own personal case, that question, of whether they are themselves conscious, is obviously answerable.

In our view the origin of this immense confusion is the distinction between conscious things and unconscious ones. If you remove it everything works again. It means everything has some kind of experience, but that experience varies from system to system. The only constraint is that it be in a one-to-one correspondence with the underlying physical phenomena.

Of course, you might now protest by saying: "What about when I'm asleep? In a deep sleep I'm clearly not conscious." Sure. It kind of is the very definition of being unconscious, lying down still with your eyes closed, asleep or dead. However, is it accurate to say you were unconscious? All you can say is that you have no recollection of anything, that you are unaware of what may or may not have happened during the night, the same way an amnesiac is unaware of what he did previously, even though no one in their right mind would claim he was previously unconscious. This doesn't mean you were thinking about work or humming your favorite song in your head while you were asleep; what went on during the night might have been extremely different from what you experience during the day and it definitely didn't leave any trace you can access. But all you can say is that you awake and you asleep are not mutually conscious.

Which brings us to the second problem we see in the mainstream picture. It assumes there is an observer who perceives and an object which is perceived. This picture is a purely theoretical one and a very wrong one when you look at the system in detail (that's why we didn't want to use the term subjective experience). Yes, the monkey is looking at a banana and experiencing it, but what's really going on is that the atoms on the surface of the banana are interacting with the cone cells on the monkey's retina through light, which then interact with the braincells of the visual cortex through chemical reactions, and so on, and so on. Is there really a distinction between the banana and the monkey? Not in this view. There are changes in the type of interaction that mediates the event of perception but no fundamental change. What you can say is that the cortex of the monkey is aware of the banana, but not that the monkey is aware in general. There is no absolute consciousness, no things that are conscious and things that aren't, there is only relative consciousness, things that are aware of each other and things that aren't. Interaction is consciousness. This doesn't however mean it goes both ways. The visual and motor parts of the brain of the monkey are aware of the banana but the banana isn't aware of the monkey nor is the liver of the monkey aware of the banana, though the ecosystem of bacteria in the fruit might be aware of the ape through the chemicals that emanate from it.

These two principles, formulated by getting rid of any human-centered artificiality, by not thinking in terms of what is conscious and what isn't, have allowed us to ponder about the consciousness of different phenomena without running into self contradictions or infinite loops and at the same time have openened a vast new area of scientific exploration: the study of the mind of physical systems. We will soon address some specific examples and techniques on how to go about doing this.