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The effectively tells us that the middle term — ⌈r · b⌉ - 1 — is always less than the value needed to match r, but the difference is never greater than a single tick of the numerator. We’re as close as we can be; the value of a for the optimal low-side approximation (a / b
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“When people get hurt around our products, we need to take every ounce of education from it that we can,” Jacob Zeiger, a senior air-safety investigator at Boeing, told me, when I visited the Boeing facility this past December. “These technical findings are sacred.” Within hours of any major incident involving a Boeing plane, Zeiger and his team are notified, and they may spend a week to ten days studying the damage and interviewing the crew, piecing together what went wrong. In 2008, for instance, the engines on a 777 stopped responding, and it crash-landed short of a runway in London, shearing off its landing gear. Afterward, a team of investigators re-created the plane’s fuel system in a Boeing lab. A small heat-exchange unit, they found, had accumulated ice during the flight. Every 777 has since been retrofitted with a new version of the unit. Thanks to decades of such refinements, today’s jets may be the world’s most reliable machines. Flying in them is less likely to kill you than walking on staircases.
自动驾驶最核心的目标是安全。但并不意味着安全就可以为所有其他东西让路，没人想要为了安全而要一个慢吞吞、没效率、跑不动的东西。解决这个矛盾，核心是提升基础能力——只有基础能力上去，才能在不牺牲其他维度的前提下，把安全做到更高水平。