You probably shouldn’t read this

If I have a standard dice, I know that:

  • It has 6 sides, all outcomes are known;
  • It’s fair, allowing me to infer each side has 1/6 probability/frequency;

What if you didn’t know what are all the possible outcomes?

Let’s suppose someone is passing me colored balls, one at the time and I want to know what is the color of the next ball, given that:

  • I received 10 balls;
  • All were Red;
  • I don’t know how many more balls are coming, It could be:
    • a few more;
    • infinite;
    • none;

So, what is the color of the next ball?

Now consider another example.

I worked every day in the last 30 days. Will I go tomorrow? Again, I can’t say yes because my ability to travel to the future isn’t currently working and even if it were, how can I know every little detail will happen as expected? I can’t.

Well, we could go with “probably”. Let’s take a look in the dictionary:

Probably: “almost certainly; as far as one knows or can tell.” Oxford

The problem is, as far as I know this word is used when you actually know the size of the set of possible outcomes to say if, in fact such sequence of events that allow me to work tomorrow is actually significant enough to, at least do better than a coin flip.

But how many possible combination of tiny events can happen from the moment the question was posed to the moment I used to be at work?

Remember, tiny events can start chain reactions and the moment the question was posed, you may assume that very, very little will change. What if the assumption that everything will go as expected turn out to be wrong? well, that’s when chaos theory start the havoc.

In the example of the red balls, all I knew is that I received 10 red balls, but:

  • I have no idea which is the color distribution of the balls to use the word “probably/likely”;
  • Everything I received is based on sample, which is similar to:
    • picking a glass of water, filling with sea water and inferring that the sea has no sharks since you detect none in your sample;
    • saying “probably” going to work tomorrow when all I know is that I worked most of the previous days (samples). Each day is different, and I never lived the “tomorrow” yet, it’s outside of my samples and even an small event could start a chain reaction and could take me in a completely different direction. Same principle as Monty Hall, variable changes, change everything. I simply don’t have control over the sequence of events that could allow me to work tomorrow.

You see, the assumption that a given sequence such “I’ll go to working tomorrow” relies is very fragile and unlikely, so why the word “probably” and “likely” keeps showing up in conversations about future events? Well, samples and frequencies.

Yet, it would be naive to think this will remains always as expected, nature isn’t built to meet our expectations. Change is the default, not the exception.

Statements with assumptions relying on the future are, by nature, fragile.

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