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Equation 3 · Part 4 · Why the Physical World Is Harder

subscript

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

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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