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Monthly Archives: August 2014
Absence of evidence is evidence of absence
The W’s article about Evidence of Absence is confusing. They have an anecdote: A simple example of evidence of absence: A baker never fails to put finished pies on her windowsill, so if there is no pie on the windowsill, then … Continue reading
Beliefs and aliefs
What does it mean to believe? This is not supposed to be some Deeply Wise prod to make someone write philosophical accounts of the mystical uniqueness of human consciousness or some such. It’s an actual question about the actual meaning of … Continue reading
Learning Bayes [part 1]
I have a confession to make. I don’t actually know Bayesian statistics. Or, any statistics at all, really. Shocking, I know. But hear me out. What I know is… Bayesian theory. I can derive Bayes’ Theorem, and I also can probably … Continue reading
Bayesian falsification and the strength of a hypothesis
At the end of my post about other ways of looking at probability, I showed you a graph of evidence against probability. This is the relevant graph: Looking at this graph was one of the most useful things I’ve ever … Continue reading
Posted in Mathematics, Probability Theory, Rationality
Tagged mathema, mathematics, maths, probability theory, rationality, tagging maths for a friend
4 Comments
How and when to respect authority
When I discussed the usefulness (or lack thereof) of Aumann’s Agreement Theorem, I mentioned that the next best thing to sharing the actual knowledge you gathered (or mind melding) was sharing likelihood ratios. But sometimes… you can’t. Well, most of … Continue reading
Posted in Basic Rationality, Rationality
Tagged Eliezer Yudkowsky, less wrong, lesswrong, rationality, scott alexander, squid314
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How to prove stuff
A while ago, I wrote up a post that explained what a mathematical proof is. In short, a mathematical proof is a bunch of sentences that follow from other sentences. And when mathematicians have been trying to prove stuff for hundreds … Continue reading
Posted in Intuitive Mathematics, Logic, Mathematics
Tagged logic, mathema, mathematical logic, mathematics
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Agreements, disagreements, and likelihood ratios
The LessWrong community has, as a sort of deeply ingrained instinct/rule, that we should never “agree to disagree” about factual matters. The map is not the territory, and if we disagree about the territory, that means at least one of … Continue reading
Posted in Basic Rationality, Mathematics, Probability Theory, Rationality
Tagged lesswrong, mathema, probability theory, rationality
1 Comment
Bayes’ Theorem
Bayes’ Theorem has many, many introductions online already. Those show the intuition behind using the theorem. This is going to be a stepbystep mathematical derivation of the theorem, as Jaynes explained it in his book Probability Theory: The Logic of Science. However, … Continue reading
MIRI paper on logical uncertainty
Talking to raginrayguns again and he mentioned that a month and a half ago, Paul Christiano wrote a paper exactly on the subject of logical uncertainty. While I haven’t finished reading it yet, I’ll publish it here because it’s relevant. … Continue reading
Posted in Logic, Mathematics, Probability Theory, Rationality
Tagged ai, logic, mathema, mathematics, maths, miri, probability theory, rationality
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Logical Uncertainty: an addendum
And I forgot to mention one thing in the last post which is relevant. Gaifman, in his paper, states that if in we have that then . I’ll quickly show that that’s a theorem of my approach, and, indeed, any similar … Continue reading
Posted in Logic, Mathematics, Probability Theory, Rationality
Tagged Bayes’ Theorem, logic, mathema, mathematical logic, maths, probability theory, tagging maths for a friend
2 Comments