RE: Fundamental Arrogance in Christianity
March 2, 2017 at 7:52 pm
(This post was last modified: March 2, 2017 at 8:16 pm by Aristocatt.)
The bear in cave argument doesn't really work. We have evidence that bears do in fact live in caves.
I can be skeptical that a bear lives in that cave, but the sum of possible dangers that I do know exist within the cave can make entering the cave seem like a bad decision relative to the amount of awesomeness(utility) I expect to gain by entering the cave.
If you showed me a graph with a normal distribution, and a mean and median of 50. Then you said you were going to pick one of the numbers that made up that standard distribution at random, I wouldn't claim "Ohhh I know the number is 50" I would admit that I am completely ignorant of the number. If you pressed me to guess the number, and said that if I were within 1 STD of the number selected, that I would get $10 dollars, I would pick the number 50.
In both cases, I do not assume that the bear is in the cave, nor do I assume that the number is within 1 STD of 50.
However, in both cases, I can use my understanding and knowledge of other concepts to make a decision about what action I should be taking in both instances.
I do know caves house bears, just like I know that the best chance to correctly be within 1 STD of a number plotted on a normal distribution is to select the median(or mean or mode, they are all the same).
You can have absurd null-hypotheses though. If you have an absurd null hypothesis on your hands, sit down and think for a bit, you probably fucked up somewhere.
E.g.
I flip a coin 100 times and hypothesize that it will come up heads at least 10 times.
The null hypothesis is that it will come up 10 or more times.
Clearly this is a bad null hypothesis if my goal were to establish a relationship between coin flipping and probability, but that is because there are millions of experiments of coin flipping that already have shown what that relationship is.
On the other hand, if I suspected that the coin was faulty and biased towards tails, then my experiment is poorly constructed. I have improperly defined my hypothesis and because of it my null hypothesis is backwards.
In this sense, saying P or not-P doesn't really get at the crux of what the null hypothesis should be. It deserves to be qualified.
A good way to think about the null hypothesis, is that if you assert some kind of new-unknown relationship in reality, the null hypothesis is the negative of that.
That is, the new relationship I was looking for with the coin flip was that it was biased towards tails. So my null hypothesis is that it is not biased towards tails.
Basically don't assume you know something until you have evidence for it.
I can be skeptical that a bear lives in that cave, but the sum of possible dangers that I do know exist within the cave can make entering the cave seem like a bad decision relative to the amount of awesomeness(utility) I expect to gain by entering the cave.
If you showed me a graph with a normal distribution, and a mean and median of 50. Then you said you were going to pick one of the numbers that made up that standard distribution at random, I wouldn't claim "Ohhh I know the number is 50" I would admit that I am completely ignorant of the number. If you pressed me to guess the number, and said that if I were within 1 STD of the number selected, that I would get $10 dollars, I would pick the number 50.
In both cases, I do not assume that the bear is in the cave, nor do I assume that the number is within 1 STD of 50.
However, in both cases, I can use my understanding and knowledge of other concepts to make a decision about what action I should be taking in both instances.
I do know caves house bears, just like I know that the best chance to correctly be within 1 STD of a number plotted on a normal distribution is to select the median(or mean or mode, they are all the same).
You can have absurd null-hypotheses though. If you have an absurd null hypothesis on your hands, sit down and think for a bit, you probably fucked up somewhere.
E.g.
I flip a coin 100 times and hypothesize that it will come up heads at least 10 times.
The null hypothesis is that it will come up 10 or more times.
Clearly this is a bad null hypothesis if my goal were to establish a relationship between coin flipping and probability, but that is because there are millions of experiments of coin flipping that already have shown what that relationship is.
On the other hand, if I suspected that the coin was faulty and biased towards tails, then my experiment is poorly constructed. I have improperly defined my hypothesis and because of it my null hypothesis is backwards.
In this sense, saying P or not-P doesn't really get at the crux of what the null hypothesis should be. It deserves to be qualified.
A good way to think about the null hypothesis, is that if you assert some kind of new-unknown relationship in reality, the null hypothesis is the negative of that.
That is, the new relationship I was looking for with the coin flip was that it was biased towards tails. So my null hypothesis is that it is not biased towards tails.
Basically don't assume you know something until you have evidence for it.
