THE DENIAL OF COMPLEXITY HIDES OUR FEAR OF UNCERTAINTY

Human beings do not withstand uncertainty very well. Uncertainty induces stress since our minds need to explain everything happening around us. It has been proved that when something occurs, and it is not easily explained by turning to our model of the world, an area in our brain called “left anterior cingulate cortex” (ACC) gets activated. This area would be responsible for conflict detection. On the other hand, another area in the brain gets activated, the so-called “dorsolateral prefrontal cortex” (DLPFC), which would be related to conflict solution. These results were found by monitoring brains of people observing magic tricks. When the magician came up with an impossible trick both areas got activated. Further detail on this can be found in the bibliographic entry (1), at the end of the post.

Actually, it comes quite obvious that uncertainty is something that we do not feel comfortable with. Our mind needs to solve the conflicts and usually, we either adapt slightly our model of the world to embrace a new inexplicable event or the event itself is reinterpreted subjectively to make it fit into our model.

We do not like living into an uncertain world. It keeps triggering conflict states in our brains, what leads us to provide sense by making things fit, often relaxing our objectivity. That is easier for us than accepting that we might need to review our model of the world. Therefore, we rather stick to a simple model of the Reality than accepting that Reality might be more complex than expected.

It does not take a genius to realize that as we get older our models of the world get more and more static. So, this blindness to complexity usually gets worse with age. However not everything is lost, if you are reading this, then you are either a friend of mine or willing to look a bit beyond (or perhaps you fall into both categories…).

 REALITY AND ITS MANIFESTATIONS: THE SAME THING?

When facing the challenge of getting insights into the Reality, we first should wonder whether the manifestations of the Reality that we experiment are the Reality itself or only its footprints in our measurement tools. This section addresses this question.

Plato’s allegory or the cave

Figure 1. The Plato’s allegory

I invite you to see the three-minute video in the link below. Plato, the famous philosopher, pointed out long time ago how different Reality is from the limited perception we can get of it. This video illustrates clearly and shortly the Plato’s allegory.

https://www.youtube.com/watch?v=LTWwY8Ok5I0

Plato came up with a vision on the limited insight that the human observation can get into Reality. In the next sections I proceed to analyse three reasons why Plato’s allegory could be a good vision on how we approach Reality. In the section “Dimensional mismatch between the Universe and the observer” I will be analysing what happens when the observed object and the measurement tool, have a different number of dimensions. In the section “Reality shows multiple manifestations” I will review, through the eyes of the modern Physics, how Reality insists in showing different faces depending on the circumstances. Actually, Reality seems to be a multi-faced object, showing partial features depending on the observation angle. Eventually, in the section “The non-observable Universe” I will explain a third case in which the real object cannot be captured by our observations, but it needs to be deduced from its manifestations. To that end I will illustrate the matter by talking about the Schrödinger’s cat and about the impossibility to measure a terrorist attack risk.

 DIMENSIONAL MISMATCH BETWEEN THE UNIVERSE AND THE OBSERVER

A sphere going through a flat world. Reality in a multi-dimensional Universe

I propose here a thought experiment in which a series of two-dimensional creatures, living in a three-dimensional universe, observe how a sphere (three-dimensional) goes through the flat world in which these creatures live. The figure below depicts the situation in three different phases of the process.

Figure 2. A sphere going through a flat world

In the first phase of the process in the picture, we can see how when the initial contact of the sphere with the plane takes place, the two-dimensional creatures only can see a dot. Even if the evolution of the sphere is ruled by deterministic laws, the appearance of the dot without any prior sign could be interpreted by the two-dimensional creatures as something random or even ruled by a sort type of strange magic.

Once the dot has appeared, the latter will be becoming a growing circle until getting the size corresponding to the diameter of the sphere. Once reached such point, the circle will turn out into a decreasing circle, ending up into a dot again. After that, nothing, the dot vanishes as it appeared to the flat creatures.

This simple thought experiment illustrates how Reality and its manifestations seem to be things completely different. Is that a paradox?.  Not actually, that occurs when we use tools with less dimensions than the real object we are trying to measure, like in the case of our two-dimensional creatures.

A slippery Reality. Dimensional mismatch between the Universe and the observer

Figure 3. A multi-dimensional Universe

The measurement tools (biological or technological) of the two-dimensional creatures in the previous paragraph, are only two-dimensional too. Hence, they cannot observe an additional dimension. The concept of sphere simply does not exist for them.

If the human beings lived in a Universe with over four dimensions (our known universe consists in four dimensions, being the fourth the dimension of time) we would have the same problem as our two-dimensional creatures, when it come to observe five or N-dimensional objects, being N greater than four.

However, Science has not revealed the existence of more than four dimensions so far,… or maybe Science did?. Actually, different physics theories describe a Universe consisting in eleven dimensions (the number of dimensions varies depending on the theory). However, these additional dimensions would be folded into the quantum world. That would be the reason why human beings cannot observe them. Only fiction science has pointed to the existence of additional dimensions at a human scale.

I give up this interesting matter here, since my purpose was only to highlight the effects on Reality observation when existing a dimensional mismatch.

REALITY SHOWS MULTIPLE MANIFESTATIONS

Let’s get serious now. Only short-sighted people could claim that Reality is something simple. That statement would be dismissive with the effort of generations of great philosophers and scientists over the centuries. The fact is that Reality is something that slips through our fingers, no matter our efforts to stick to simple models by trying to make facts fit into them. Let me go through the different physics theories (sorry), and show you when they can be applied and where the boundaries among them are. I will not get very technical, my aim is to introduce a high level vision of how Physics tries to cover the completeness of physical Reality. There is no a unique theory embracing the whole physical Reality so far, hence different theories need to be used, mapping Reality as good as possible and forming boundaries where one theory proceeds to another.

Wave-particle duality

Let’s get started with the wave-particle duality. I am sure you heard of it before. The behaviour of a particle in the subatomic realm is ruled by Quantum mechanics. The first thing that catches our eye is that the particle can behave either as a particle or as a wave depending on the circumstances. Basically the particle is a field of matter (wave) evolving according to Quantum mechanics equations. However, when an experimenter tries to observe this field of matter, it collapses into a small portion of the space becoming a particle. Therefore, the observation of the field of matter provokes the particle to define itself into a portion of the space. This collapse, takes place in a random way, that is to say, the intensity of the matter field in each region of the space is proportional to the probability to collapse in that region. We will not go into the details since we will get back to this matter, at least in two future post. In one of them we will be taking a look at how the experimenter mind seems to interfere the outcome of the experiments in the subatomic world. On the other hand, we will use the analogy of a potential field playing the role of the Reality of a system or quality, collapsing into a specific value when interacting with an observation of the system.  Meanwhile, you can see an illustration of the collapse of the matter field into a particle in the figure below.

Figure 4. A matter wave collapsing into a particle

The boundary of Quantum mechanics

The realm of Quantum mechanics is the world of the tiny things, particles, atoms and molecules. As the size of the system grows forming macroscopic solids, gases and liquids the quantum effects disappear. There is a couple of theories on why the quantum effects disappear in the macroscopic world, but we will not go into them. The fact is that in the macroscopic world Newton mechanics, classical statistics mechanics and other classical theories describe quite well our observations.

The boundaries of Newton mechanics

We have seen in the previous paragraph that the boundary for the Quantum mechanics is the size of the objects we observe. Reaching certain size threshold, Quantum mechanics cannot be applied anymore. We are about to see now that classical (or Newton) mechanics has two different boundaries, one reached when growing in size and the other one when increasing the velocity of the objects. The father of both boundaries is Einstein. His “Special relativity theory” deals with objects moving closely to the speed of light, where Newton equations fail considerably. On the other hand the “General relativity theory” deals with the massive objects like planets and stars. This theory is about the nature of space-time and how the gravity of the massive objects influences the space-time.

Hence, in our daily experience we can apply Newton equations obtaining really accurate results. If we are playing football, Newton equations will describe the trajectory of the ball without any problem. However, if we were strong enough as to kick the ball and speed it up close to the speed of light, then Newton approach would not be useful at all. We should apply then the special relativity equations, since Newton equations would provide results completely wrong. On the other hand, if our ball grew and grew getting as massive as a planet or a moon, then we would have no choice but to apply the general relativity equations.

Therefore, we can say that from a Reality interpretation point of view, Newton was wrong. His physics was only an approximation to the daily Reality we are in contact to. We could say that Newton physics was a failure in some sense. However, Newton provided us with an approach to the physical Universe with enough practical accuracy as to face the daily Reality. We should not forget that Newton built his theory centuries before the mathematical developments allowed the formulation of the relativity theories (special and general). We can say then, that Newton formulation meant a great breakthrough at the time.

In any case (and it is something I am not going to show here), relativity equations become Newton equations when the speed is slowed down or the mass is reduced. So mathematically, Newton equations are a specific case of the relativity ones.

From a practical point of view, we should keep using Newton equations in the daily context, since Einstein equations are far more complex and the differences in terms of accuracy are insignificant when applied to the world we observe on a daily basis. I would like to point out here the difference between the understanding of the Reality and the need for being practical when dealing with it. This blog is about both goals, understanding Reality, from a wish for the pure knowledge, and a wish to find a set of tools to deal with Reality to obtain practical results.

What we have seen so far is that relativity theories (special and general) collapse into the Newton theory under certain circumstances, in the same way like the wave function collapsed into a particle in the context of the Quantum mechanics.

 

Figure 5. Planet Earth distorting the space-time, according to General relativity  theory

The boundary between the Quantum mechanics and the General relativity theory

So far, we have been talking about why Newton mechanics is not a good theory for explaining the completeness of the physical Universe, but a specific limit for the relativity theories, which are really considered to be the exact explanation ( except when we go into the subatomic world).

Let’s summarize, we have the world of the high speed, and the world of the massive objects, ruled by the relativity theories. Slowing down the speed and decreasing the size we have Newton theory, that is considered to be a limit for the previous ones. If we keep decreasing the size, we get into the Quantum mechanics world. It is probably the theory providing more accurate results in its context. So far, Quantum mechanics is considered as a real view of the subatomic Reality rather than a practical model to get good results. On the other hand, the relativity theory is considered nowadays as a real description of the nature of the space-time. So, if the world of the massive and the world of the subatomic are ruled by theories, regarded as exact descriptions of the Reality, logically both theories should converge in the limit of the small and big world. I am sorry to say that it does not happen. This point has been a nightmare for the theoretical physicists over the latest decades. Quantum mechanics and relativity theory are irreconcilable.

What we owe Stephen Hawking and the search for the theory of everything

Stephen Hawking has become famous for the general public due to a series of books about popular science. We all know that he is a famous researcher in his field, but perhaps it is less known why exactly he became famous among the physics community. He was the first person to combine the General relativity theory and the Quantum mechanics successfully. He applied that combination in his study of the black holes in the Universe. It was the first time, and the last as far as I know, that both theories have been combined with good results.

Physicists keep trying to find a theory about everything, capable of embracing the Relativity and Quantum theories, in the same way in which the Relativity theory embraces the Newton mechanics. We are still waiting for that new theory.

Figure 6. Stephen Hawking combined the General relativity theory and Quantum mechanics in the understanding of what happens in the boundaries of a black hole.

I stop here since this first post is getting too long and I would not like you to get bored. I will get back soon with the remaining material to complete this subject of “Reality is a complex object”. I hope see you back in this blog.

References

1. Sleights of Mind, by S.L. Macknik and S. Martínez-Conde http://www.sleightsofmind.com/about-the-authors/
2. http://es.wikipedia.org/wiki/Atractor_de_Lorenz