How can Abraham Wald's approach lead you to ignore crucial features of a problem?
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Kindly see the red sentence below. What exactly does "that approach" mean? I don't know the term for "he peered right through to the mathematical struts and nails holding the story together"?
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How exactly does Wald's approach $\color{red}{\text{"lead you to ignore features of the problem that really matter"}}$? Examples please? The author provided no examples.
Wald’s other advantage was his tendency toward abstraction. Wolfowitz, who had studied under Wald at Columbia, wrote that the problems he favored were “all of the most abstract sort,” and that he was “always ready to talk about mathematics, but uninterested in popularization and special applications.”
Wald’s personality made it hard for him to focus his attention on applied problems, it’s true. The details of planes and guns were, to his eye, so much upholstery—he peered right through to the mathematical struts and nails holding the story together [Emphasis mine]. $\color{red}{\text{Sometimes that approach can lead you to ignore features of the problem that really matter.}}$ But it also lets you see the common skeleton shared by problems that look very different on the surface. Thus you have meaningful experience even in areas where you appear to have none.
To a mathematician, the structure underlying the bullet hole problem is a phenomenon called survivorship bias. It arises again and again, in all kinds of contexts. And once you’re familiar with it, as Wald was, you’re primed to notice it wherever it’s hiding.
Ellenberg, How Not to Be Wrong (2014), p 8.
1 answer
If we add 1000 g of ethanol to 18 g of ethanol, the result has a weight of 1018 g.
If we add 1000 mL of water to 18 mL of water, the result has a volume of 1018 mL.
A person who focuses on the abstract (and not the concrete) would only look at 1000+18=1018 (the "struts and nails"); the other details (the unit of measurement, the chemical composition of the object) (the "upholstery" or the stuffing) do not matter.
If you ask such a person what happens if 1000 mL of ethanol were added to 18 mL of water, they would say that the result has a volume of 1018 mL. But someone who is familiar with partial molar properties would know that the result has a volume of 1014 mL (at 25 degrees celsius).
In this case, abstraction (Wald's approach) would lead to ignoring the chemical composition of the objects, which in this case really matters.
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