Equation 3 · Part 5 · Why the Physical World Is Harder
superscript
superscript
What this part means
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
Its job in the formula
A raised mark can be a power or an index. Its position and the surrounding notation determine which.
Full expression→superscript→Article meaning
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…
Learn the underlying idea
An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.
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Sources cited in the article section
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