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Explaining Bayesianism Without Using Math Formulas

26 Dec

This post will be an attempt to explain Bayesianism without using any complicated math formulas. Granted, this won’t be all encompassing, but will be a post meant to explain the Bayesian concept of falsifiability. As such, maybe this post could even be called an intuitive explanation of falsifiability. Thought experiment time!

Say you’re sitting in the back of a tutoring session of two 2nd graders. The teacher is going over the end of a lesson by asking the two students a battery of questions about the math that they’ve just learned. The teacher asks to the two kids “So which one of you knows why 4 + 4 = 8?”. Little Johnny raises his hand enthusiastically. The teacher doesn’t actually ask him to explain why 4 + 4 = 8, but just takes a mental note. She then asks “Which one of you knows why 5 + 5 = 10?”. Again, little Johnny raises his hand enthusiastically. She then asks “Ok. Which one of you knows why 1 + 1 = 2?”. This time, both little Suzie and little Johnny raise their hands. Again she takes note and then asks another question “Why does 6 + 6 = 12?”, and again only Johnny raises his hand. “Why does 2 + 2 = 4”? Both Suzie and Johnny raise their hands.

At this point the teacher starts throwing in random nonsense questions as a test. “Why does 11 + 10 = 99?” Johnny raises his hand. “Why does 10 + 10 = 20?” Both Suzie and Johnny raise their hands. “Why does 7 + 8 = 53?” Johnny raises his hand. On and on it goes, with Johnny raising his hand for the vast majority of the teacher’s questions, with Suzie raising her hand for very few.

If you were the teacher, what would you think about Johnny compared to Suzie? Johnny can answer many more questions than Suzie can, but at the same time Johnny supposedly knows why 11 + 10 = 99. Would you conclude that, just because Johnny says he can answer more questions than Suzie can that he is actually right? That he actually knows the answers? If the teacher had asked the students to explain how they know what they know, would you think that Johnny actually knew what he was talking about? Would you think Suzie knew what she was talking about?

Hopefully, the you will arrive at the correct answer intuitively. That one being that Johnny probably doesn’t know what he’s talking about, and probably isn’t going to be the one to give you the correct answer. This is what it means when it is stated that, as far as building correct models of the world, if you can equally explain any outcome then you have zero knowledge. It isn’t so much what you can explain that determines whether to trust your explanations, but what you can’t explain. That’s the main problem behind unfalsifiable hypotheses like an omnipotent god, Sophisticated TheologyTM, most conspiracy theories like 9/11 trutherism, or psi. They are all analogous to Johnny in this thought experiment, able to explain the equivalent of why 2 + 2 = 4 and why 10 + 11 = 99; they don’t restrict the types of things that they can explain, and that restriction is what makes a hypothesis more likely to be correct.

Of course, if you want the math for why this is so, the math behind it is in my Bayes’ Theorem and Falsifiability post.

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Posted by on December 26, 2012 in Bayes

 

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