Querying the future
The progress of science and technology have pushed the boundaries of the unknown, giving us the illusion that we could find answers to everything.
- Will the next card be a Jack?
- How big my goldfish will grow?
- Will a meteor collide with the Earth?
- Will it rain next Monday?
Because the outcome of these events depends on chance, these questions cannot be answered with certainty.
But the nature of their uncertainty is not the same.
The four levels of unpredictability
You want to be acquainted with them because they are often mistaken from one another and some inexact comparisons can lead to misconception and misunderstanding and of course deception.
- Mild randomness
- Borderline mild randomness
- Slow randomness
- Wild randomness
Benoît Mandelbrot distinguished up to seven states of randomness, often by using subtle mathematical distinctions totally out of my league
1 - Mild Randomness
Mild Randomness happens in a closed environment where external factors have no incidence.
Like dice, roulette, card decks or artificially created systems like jars filled with red and black marbles.
An individual outcome cannot be predicted but there is some certainty because some rules are set.
- A classic six-faced die roll can only yield an integer between 1 and 6.
- A normal deck of card has 13 cards of each color and only 4 jacks.
- A roulette can only yield an integer from 0 (zero) to 36.
- A fair coin can only deliver head or tail.
These are convenient to learn about probabilities and get entertained.
This randomness is well understood and surprises are rare.
Uncertainty is contained within the ranges of the possibilities of the dice, the cards or the roulette.
- You are certain that 2 six-faced dice will never add up to more than 12.
- Yet streaks of 12 can and do happen.
- Still, these two dice will add up to 7 more often than to any other possible sum.
So betting on 7 will give you an edge.
This is the randomness that makes casinos rich because regardless of what one person wins, the other will lose it.
Casinos simply create rules so you get only 97% (or less) of what you bet. The casino gives you 35 times your bet if your number comes out but your number has 1 in 37 chance to come out.
Over time the house will win.
Cheating, deception (including self-delusion) is the only way to escape of the laws of this randomness and life is extremely rich in examples of such deceptions.
Will the next card be a Jack? You have 1 in 13 (4 in 52) chances that yes, it will be.
2 - Borderline Mild Randomness
We know the composition of a regular deck of cards in advance.
Any poker book provides tables with the odds relative to each card and card combination.
This is what gives mild randomness its name: There is certainty in its uncertainty.
In borderline mild randomness, the rules are less strict and the range of possibilities is more flexible.
Let say someone shuffled a few hundred decks of cards but had dropped a few dozen cards in the process.
Now the odds of pulling a jack out of that special deck are different than the odds of pulling a jack from a regular 52-card deck.
- Certainty is limited: at best you will not find some Uno cards in the deck.
- The deck is too big to be counted.
- All you can do is look at the cards as they are pulled from the deck.
- All you can do is make statistics about your observations.
Let's consider a giant deck readily available: the human population!
You cannot walk around and measure how tall everyone is.
but you can measure a few hundred people and draw conclusions
It is impossible to guess how tall the next person you meet will be.
All you can guess in what size range he or she may fall into.
Depending on the population (Netherlands or Mexico) the average can be different but basically, the distribution of tall and short people will smoothly follow what we call a normal distribution.
Normal distribution arranges specimens around the average value (drawing a bell curve) and measures how far from the norm specimen are distributed.
For example, looking at the goldfish aquarium in a pet store, you will notice that
- Most goldfish are about the same size
- Some are smaller or bigger.
- A few are a lot smaller or a lot bigger.
That is a normal distribution.
Of course, if you pick 3 goldfish at random they might not follow the same rules, you may end up with one big and two of average size.
Normal distribution needs a lot of specimens to work well.
But one can predict to some degree how many specimens can be found in each size range when the population is normally distributed.
One can also predict that a specimen picked at random will be within a range of size, for example, that an American man will be between 67 and 73 inches (170 - 185cm) tall and be right 68% of the time.
Limitation of Normal Distribution
Although this form of randomness is quite stable (that is over time the events they describe will fall within their boundaries) they can also yield strange results, especially when samples are too small or the terms too short.
In the case of fish or trees or other living organisms, the sizes will obey this law until a giant specimen is discovered.
In such case, the giant specimen is usually not considered because it is not representative of the general population.
Although such approximation is helpful most of the time, it has to be used with caution. It is an error to completely dismiss a possibility only because it is very rare.
Applications of Normal Distribution
Borderline Mild Randomness is studied by insurance companies to offer life policies.
They study populations and adjust to new life expectancy from time to time and stay in business.
Unlike banks, insurance companies rarely go bankrupt.
How big my goldfish will grow? - Well, this depends a lot on the space the fish have, but usual tank conditions will let them grow to 4 inches (10cm). But a foot-long goldfish can happen.
3 - Slow Randomness
Slow Randomness is not much of a concern.
There are events that are predictable on the short term but random on the very long term.
The travels of the Earth through Space is an example.
The Earth spins on its axis in 24h and revolves around the sun in 365.25 of these days (these are actually approximations).
The Earth is also under forces that tilts its axis back and forth in a 41,000 year cycle, its distance to the sun varies on a cycle that itself varies from 19,000 to 26,000 years, depending of other gravitational objects around us, namely the sun and the other planets (those have their own multiple motions as well).
Basically, too many things are at play for us to predict where our planet will be exactly in 10,000 years.
But if we look at it on a smaller scale (a few decades), we can have certainty in extremely fine details as ephemeris can demonstrate.