← All parts of this equation

Equation 3 · Part 2 · Why the Physical World Is Harder

Symbol p^H

Ptask≈pH.P_{\mathrm{task}} \approx p^{H}.
pHp^{H}

What this part means

pHp^H is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

pHp^H is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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 Ptask≈pHP_{\mathrm{task}} \approx p^{H}. 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…

Read this part in the article →

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.

Open the illustrated exponents: repeated multiplication and powers guide →

See this notation across published equations →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.