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[SEQ RERUN] The Sin of Underconfidence

2Rukifellth

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This question doesn't seem worthy of it's own Discussion post, and seems to fit reasonably well here.

Whenever I try to learn math, I try to know *why* such a thing is a certain way, making sure I'm not just carrying a feeling of being correct, or even a vague feeling for what the answer *is* without there being an explicit sequence of ideas that convey that answer. But if I do get such a sequence of ideas, I never know if I'm finished, so I try to assume that I'm not finished.

For example, I was watching some of Salman Khan's introductory videos on probability theory two days ago. The first few videos were very basic, using coin flips to explain where the fractions representing probability came from.

It occurred to me that I wasn't really thinking about the video. I just *knew* that a probability of 1/4 means that there's a 25% chance of something happening, and was more waiting for the video to end so I could go on to something new. I asked myself "Wait, can I take that fractional representation of probability and connect it directly to what probability actually *is*, or am I just playing Chinese room with numbers?"

I thought about it for a minute, and decided that the denominator represented the quantity of "runs" needed for the desired "results", the quantity of which was represented by the numerator. A probability of 5/9 means that if the situation is run 9 times, the result which is assigned a probability of 5/9 will occur 5 times.

Which is all well and good, but I still felt confused. How do I know when I'm finished thinking about this? My only arbiter is a subjective feeling of comprehension, and comprehension can occur after knowing *how* to use a method, *as well as* knowing *why* a method works.

Today's post, The Sin of Underconfidence was originally published on 20 April 2009. A summary (taken from the LW wiki):

Discuss the post here (rather than in the comments to the original post).

This post is part of the Rerunning the Sequences series, where we'll be going through Eliezer Yudkowsky's old posts in order so that people who are interested can (re-)read and discuss them. The previous post was My Way, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.

Sequence reruns are a community-driven effort. You can participate by re-reading the sequence post, discussing it here, posting the next day's sequence reruns post, or summarizing forthcoming articles on the wiki. Go here for more details, or to have meta discussions about the Rerunning the Sequences series.