Hypothesis Testing the Dark Forest Theory (It's more like a hypothesis really)

I have a really great professor that often swears in class. He's an Englishman so he often takes to saying words like ass and cock. Its not a problem, in fact it is his many quirks that make his teaching enjoyable.

Plus it would make for a really good drinking game. Take a shot for every 'ass' or 'cock'.

He teaches Computational Mathematics and Statistics. His name Robin Hankin and he's a pretty smart cookie. He went to the same school as Sir Isaac Newton.

Full Power Robin. He's about to undergo apotheosis into a being of absolute statistics. Which if you know anything about Statistics means Unity.

He recently went full circle and completed a course section on Hypothesis Testing introducing the concepts of Type I error and Type II error. He introduced the concept of the 'alternative Hypothesis' where we would compare the Null Hypothesis against the Alternative Hypothesis.

Type 1 error: Rejecting the Null given that the Null is true
Type 2 error: Failing to Reject the Null given that the Null is false

He used this example in the case of sentencing a man to jail the case is 'statistically' broken down as follows:

Ho = The Accused man is innocent (By default Innocent until proven guilty)

Ha = The man is guilty (In the weight of the Evidence(p-value))

So he used this example to Explain that if a Type I error occurs that's a case of sentencing innocent man going to jail, and that a Type II error occurs, that's a case of letting a guilty man go Free.

Both are undesirable outcomes. Both are unfortunate occurrences with respect to the justice system.

Here's how we illustrate the Regions that the Errors would Exist in:

Concepts:
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a = the probability of getting a type 1 error
b = probability of getting a type 2 error

power = 1 - b

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So while in class I got to thinking about Alien Civilizations within the context of  Hypothesis testing while also examining the Dark Forest Theory as a solution to Fermi's Paradox. Made popular by Ciu Lixin's novel  'The Dark Forest'. The Dark Forest talks about an emerging interstellar conflict between humans and extraterrestrials called the Trisolarans.

10/10 Amazeballs and would blow your mind

There was a paragraph from the book that had chilled me to the bone the moment I encountered it.

"The universe is a dark forest. Every civilization is an armed hunter stalking through the trees like a ghost, gently pushing aside branches that block the path and trying to tread without sound. Even breathing is done with care. The hunter has to be careful, because everywhere in the forest are stealthy hunters like him. If he finds another life—another hunter, angel, or a demon, a delicate infant to tottering old man, a fairy or demigod—there's only one thing he can do: open fire and eliminate them."

The Dark Forest Theory implies the Universe is filled with hostile civilizations and that communicating our presents in the cosmos would mean suicide.

Now let the Dark Forest be our null Hypothesis:

Ho = The Alien Civilizations are inherently Hostile. Contacting them would be suicide. (Grimdark Universe)

what would an alternative (Ha) to Dark Forest be?

Ha = Alien Civilizations are not Hostile and that there is a vibrant galactic community of civilizations working towards Survival. (Federation of Planets)

so in Hype testing we have something called a p value defined as:

p = The probability given that the null is true of finding and observation or an observation more extreme.

if the the p value falls inside or our of a critical region of significance value (a) that determines whether we reject our null hypothesis or fail to reject our null hype. 

so if the p value were inside the critical region of significance value (a = 0.05) of the Dark Forest Null Hypothesis this would mean we reject an inherently hostile Universe for one that is friendly to communication between civilizations. Referring to our above definition of the Type 1 Error:

Type 1 Error: Rejecting the idea that the Universe is hostile. Basically the probability of encountering a friendly civilization, a culture eager to break bread with us. (more Federation of Planets, less Imperium of Man) in a Universe that is actually hostile.

our Type 2 Error: (failure to reject the Null in a situation it is false) would imply; Encountering a hostile civilization in a Universe that is actually Friendly.

That would be unfortunate wouldn't it. In all that vastness, in all that obscurity. In a universe that is actually friendly towards intelligent life, we discover a civilization that would wipe us out in an instant. In statistics we can do something to reduce the number of type 2 Errors we make. We can collect more data. I guess SETI searches may have a function beyond wasting tax payer money after all.

We come in peace to liberate you from your hubris.

Sincerely
Afiq Abdul Hamid