Tyranny of the mediocre

A) Galton’s bean machine

“No matter how defiant you might be, you will finally follow the mean.”

1. It may seem surprising, but throughout the ages human history has been written neither by a group of exceptionally intelligent people nor by some extremely powerful nation. Instead, what seems to finally determine our actions is the call of mere everyday need, while the common view is what eventually determines and defines science.

2. An illustrative example of the previous principle (which in fact is called principle of mediocrity) is Galton’s bean machine (previous image):

The bean machine is a device invented by Sir Francis Galton to demonstrate the central limit theorem. The Galton Board consists of a vertical board with interleaved rows of pegs. Beads are dropped from the top, and when the device is level, bounce either left or right as they hit the pegs. Eventually, they are collected into bins at the bottom, where the height of bead columns accumulated in the bins will eventually approximate a bell curve. Galton was fascinated with the order of the bell curve that emerges from the apparent chaos of beads bouncing off of pegs in the Galton Board. He eloquently described this relationship in his book Natural Inheritance (1889). [1]

3. Instead of beans, one might use beads, balls, particles, human heights, attitudes, or whatever variable. We say that the variable is normally distributed, in the sense that it follows the previous rule (the law of large numbers, according to the central limit theorem): If you let a sufficient amount of beans fall into the machine, or if you measure heights of a lot of people, or if you consider your behavior in many different occasions, finally you realize that either the beans, or the heights, or your behavior follow the same pattern- they tend to gather close to the average.

B) Young’s double slit experiment

4. A relative example is that of Young’s double slit experiment in physics, exhibiting the way interference patterns form:

The double-slit experiment in quantum mechanics is an experiment devised by physicist Thomas Young. It shows that light has both a wave and a particle nature, and that these natures are inseparable. The same is true of electrons and other quantum particles.

This experiment requires only a double slit device, and a good laser to ‘draw’ straight lines. The laser is supported so it can only be moved on purpose. It is aimed at the central point between the two slits about half a meter away. Something like a movie screen or a smooth white wall is put up on the other side of the double slit device several meters away. When everything is fixed, a pattern of light and dark bands will show up.

The double-slit experiment has been of great interest to philosophers, because the quantum mechanical behavior it shows has forced them to rethink their ideas about classical concepts such as ‘particles’, ‘waves,’ ‘location,’ ‘movement from one place to another’ and ‘observation.’ [2]

5. Incidentally, the deepest mystery of the double slit experiment is not the interference pattern, but that the particle behaves either as a particle or as a wave, according to the conditions set by the experimenter. For example, if we put some devise on one of the two slits in order to observe the passing particle, then, because the particle is disturbed by the observation, the interference pattern disappears, and the particle appears on the screen as a ‘dot.’ Therefore, as a consequence, we have to conclude that a particle is neither a ‘particle’ nor a ‘wave’ before we observe it. (In fact, before we observe it the particle doesn’t even exist- as we are not aware of it at all.)

C) What is ‘probability?’

6. Let’s make an effort to delve a little deeper into the field of statistics, which is indeed a very strange science. In fact, nobody knows what probability really is. In the case of a weather forecast, for example, if there is 40% probability that it will rain, this means that it usually rains 40 out of 100 days with similar weather conditions. In the case of physics, the probability of finding a photon at some place is related to the intensity of the light. This is its expectation value (the average position). We can also consider that the average value is determined not only by statistical expectation but also by the expectation of the observer.

7. Another aspect is that statistical sets may by nature inhomogeneous. By this I mean that when tossing a coin, for example, the true probabilities are never 50-50. The reason for inhomogeneity could be the influence of the subject who tosses the coin, or simply the impossibility of having an objective flipping of an absolutely fair coin. As a matter of fact, the ultimate determining factor of any sort of anomaly could be the fabric of space-time itself (if spacetime is inhomogeneous on its own).

8. But the weirdest thing about probabilities is the aspect of simultaneity. In the case of tossing a coin, for a fair coin the probability of taking either heads or tails is 50%. In other words the events (the tosses) are independent from each other. However, the fundamental law of statistics- that of large numbers- says that the result will be 50% for either heads or tails if we toss the coin a sufficient number of times. Therefore, if we initially take a lot of ‘heads,’ the result will have to ‘normalize’ to ‘tales’ at the end. But how does the set knows that it has to normalize (that most of the following tosses should be ‘tales’) if it has no memory of the past tosses? It is this aspect of simultaneity, or wholeness- that the distribution somehow has the knowledge of its overall form- what normalizes the final outcome. So even if the separate results do not interact with each other, they are all instantaneously connected to each other as a sum. By the way, this is similar to falling objects- although there’s no interaction between them as they fall, they all fall to the ground at the same time (assuming that they are dropped from the same height), because they are all connected to a common force (gravity in this case).

9. Although modern physics seems to have been separated from astrology or alchemy, its basis can still be traced in the realm of fantastic entities which compose the world. Particles are described as probabilistic wave-functions, which themselves may be considered real entities according to some interpretations of quantum mechanics. While probabilities are not treated as a physical field, particles seem to know beforehand the paths they have to follow. Thus the distribution of physical entities becomes a whole entity, whose parts may be independently operating, but which are also instantaneously connected at a distance. The result is that the distribution or entity cannot be localized at a particular point in space and time without losing its identity as an entity. Furthermore, all processes which constitute physical phenomena cannot come about without the participation of the observer who considers the phenomena. Therefore, the observer is part of the phenomenon he observes, either this is the weather or a probability distribution. The extent to which the observer can influence the weather or the toss of a coin, is another question...

D) The normal distribution

10. Imagine that the universe is like an ocean. But in this case, we can’t see the ocean- we may also call such an ocean ‘spacetime’. Every moving object in the universe follows a trajectory in the waves of this ocean of spacetime. Such waves interfere with each other, and they are also influenced by moving objects, so that their paths can change. Now imagine that instead of a ship there is an electron moving in this medium, and that the wrinkles it produces in the waves are not made of water but of photons. Such wave-like wrinkles can appear on a screen or on any obstacle in the form of an interference pattern. Thus, what appears on the screen is not an ‘electron’ which was cut into many little pieces, but the disturbance the moving object (the electron in this case) caused to the waves of the medium (i.e. spacetime). Whether we call such a medium ‘ocean,’ ‘spacetime,’ ‘quantum potential’ as David Bohm used to call it, or ‘field of probabilities,’ is secondary. What matters is that it pre-exists, and that it pre-determines the interference pattern caused by any moving object. If the object cuts straight through the waves, it will appear on the obstacle as a solid object instead of having an interference pattern. The point is that the distribution or field of probabilities has a true existence in one form or another.

11. The mathematical description of probabilistic distributions, such as interference patterns, is given by the Gaussian function. Formally, the Gaussian distribution, for any variable x, as a function f(x) of that variable, has the following form:

In that form, the function f(x) is normalized (so that its value for all x is equal to 1). The quantity μ is the mean (average or expected) value, while σ is the standard deviation (distance from the mean). The quantity σ² is called variance. [3]

12. In any case, the shape of the normal distribution is that of a bell (you can also take that shape if you draw a line joining the beans at the top of each row in Galton’s bean machine). Although randomly chosen specimens for a given property may not exactly fit a normal distribution, the more specimens we include, the more these specimens will tend to be normally distributed. This is called the central limit theorem:

In probability theory, the central limit theorem (CLT) establishes that, in most situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (informally a ‘bell curve’) even if the original variables themselves are not normally distributed. [4]

13. An important aspect of the normal distribution is that if a population is normally distributed for a given property, then there will be certain percentages of that population for the given property across the distribution:

In the normal distribution, approximately:

• 68% of the data will fall within one standard deviation of the mean.

• 95% of the data will fall within two standard deviations of the mean.

• 99.7% will fall within three standard deviations of the mean.

50% of the distribution lies within 0.6745 standard deviations of the mean (that is, ‘centered about the mean,’ or ‘in the middle’). [5]

14. A consequence of the normal distribution is that the presence of one member of the population at some extreme of the distribution, presupposes the existence of more members closer to the mean. For example, if there is a very advanced extraterrestrial civilization in the Milky Way, whose technological level is, let’s say, 2 standard deviations of the mean, then, since that civilization will belong to an exceptional 5% (1 out of 20) of all civilizations, there will be another 19 less advanced civilizations (including us) in the Milky Way. Although the problem is that we will first have to detect such an advanced civilization, our own presence infers the probability of their existence.

15. Thus the cliché:

“The bigger the better,”

should be replaced by:

“The closer to the average size the better.”

E) The tyranny of the mediocre

16. A principle closely related to the notion of the normal distribution is the mediocrity principle. In a mathematical sense, the mediocrity principle is based on the law of large numbers (that the bigger a sample is, the more the values of a property of the sample will tend to the average value). This is a simple definition of that principle:

The mediocrity principle is the philosophical notion (which may also be expressed as a probabilistic argument) that if an item is drawn at random from one of several sets or categories, it’s likelier to come from the most numerous category than from any one of the less numerous categories. The principle has been taken to suggest that there is nothing very unusual about the evolution of the Solar System, Earth’s history, the evolution of biological complexity, human evolution, or any one nation. The idea is to assume mediocrity, rather than starting with the assumption that a phenomenon is special, privileged, exceptional, or even superior.

Also, the mediocrity principle suggests, given the existence of life on Earth, that life typically exists on Earth-like planets throughout the universe. [6]

17. The principle of mediocrity does not necessarily imply that we are average, but that most alien civilizations will be gathered close to the average value (as in a normal distribution). If we were an average civilization, there would be many other civilizations like our own out there, and the probability would be high of having detected some of them. Therefore, either we are too primitive to be able to detect another civilization, or most of them are too primitive to leave detectable signals.

18. But even if we finally trace or be contacted by another civilization, the mediocrity principle suggests that we would treat them in the same way we treat ‘aliens’ on our home planet. If, on one hand, we meet somebody whose intelligence is superior to ours, in most cases we deny the fact and pretend we are better. If, on the other hand, we meet somebody poor or ‘dummy,’ we find the opportunity to take advantage of him. In fact, this attitude also reveals are true nature: we are not intelligent enough as a species to acknowledge and promote intelligence. This may be the privilege of a few human beings and, by analogy, of a few civilizations in the history of the Milky Way.

F) “Where are they?”

19. Here are, conclusively, some questions:

“Where are they?”

“Where are you?”

“Do they care?”

“Who cares?”

“Do you remember Diotima?

She was stoned to death by the mob…”

“How can I explain to them that the Earth is neither flat nor round?”

“Blessed are the poor in spirit...”

But are they blessed or should they be cursed?

“Should stupid people vote?”

“Is democracy the perfect constitution?”

“Does the 2% of the normal distribution stand any chance that someday they might be understood by the rest 98%?

Or is the true meaning that they are not meant to be understood?”

“Will the ghosts wondering about the darkest corners of our own misconceptions ever find vindication?”

“How can one protect oneself from the curse of the mob?”

20. The answer to such questions is that the normal distribution is predictable. Thus, an above average person may always be prepared for the outcome.

[1]: [https://en.wikipedia.org/wiki/Bean_machine]
[2]: [https://simple.wikipedia.org/wiki/Young%27s_double-slit_experiment]
[3]: [https://en.wikipedia.org/wiki/Normal_distribution]
[4]: [https://en.wikipedia.org/wiki/Central_limit_theorem]
[5]: [https://mathbitsnotebook.com/Algebra2/Statistics/STstandardNormalDistribution.html]
[6]: [https://en.wikipedia.org/wiki/Mediocrity_principle]

10/7/2018

Image: Bean machine

[https://en.wikipedia.org/wiki/Bean_machine]