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BlueSun comments on Another way our brains betray us - Less Wrong
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My take away from this is that you need to "shut up and multiply" every single time. Looking at the math skills study, the thought was that people glance at the raw numbers (instead of looking at the ratios) and stop there if they fit their ideological beliefs. If it conflicts with your beliefs though you spend a little longer and figure out you need to look a the ratio. So if we train ourselves to always "shut up and multiply" hopefully some of this effect will go away. Maybe a follow-up study to see if people who actually do the math still get it wrong?
If preconceived notions make it impossible to do math, then how can we possibly get a result that contradicts with our preconceived notions?
I don't think the article suggests it's literally impossible (some of the respondents passed the test), just terribly hard.