Equation 3 · Part 1 · Why the Physical World Is Harder
Symbol P_task
What this part means
the probability.
Its job in the formula
ask is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol P_task→Article meaning
Where the article explains it
If a task requires H decisions and each succeeds independently with probability p , the task succeeds with probability .
The passage around this formula
This compounds badly over long horizons. If a task requires H decisions and each succeeds independently with probability p , the task succeeds with probability . The independence assumption is generous — real failures correlate, because one slip puts the system into a region where subsequent steps are also more likely to fail — but even the generous version is brutal. For a 300-step manipulation sequence to complete nine times in ten, per-step reliability must be about 0.99965. A per-step reliability of 0.99, which would be an excellent number for almost any perception module, yields a task success rate of roughly five percent. This is straightforward arithmetic rather…
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Sources cited in the article section
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